Student Solutions Manual to accompany Principles of General Chemistry

Citation preview

Student Solutions Manual

to accompany

Prepared by Patricia Amateis and Martin Silberberg

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Student Solutions Manual to accompany

Principles of General Chemistry Martin S. Silberberg

Prepared by

Patricia Amateis Virginia Tech and

Martin S. Silberberg

_ Higher Education Boston

Burr Ridge, IL

Bangkok Milan

Bogota

Montreal

Dubuque, IA

Caracas New Delhi

Madison, WI

Kuala Lumpur Santiago

Seoul

New York

Lisbon

San Francisco

London

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The McGraw-Hili Companies

•

Student Solutions Manual to accompany PRINCIPLES

OF GENERAL CHEMISTRY

PATRICIA AMATEIS AND MARTIN S. SILBERBERG Published by McGraw-Hili Higher Education, an imprint of The McGraw-Hili Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright

© 2007 by The McGraw-Hili Companies, Inc. All rights reserved.

No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hili Companies, Inc., including, but not limited to, network or other electronic storage or transmission, or broadcast for distance learning.

Recycled/acid free paper This book is printed on recycled, acid-free paper containing 10% postconsumer waste. 34

5 6 7 8 9 0 QPD/QPD 0 9 8 7

ISBN-13: 978-0-07-310721-9 ISBN-I 0: 0-07-310721-2

www.mhhe.com

Contents 1

1

Keys to the Study of Chemistry

2

The Components of Matter

4

The Major Classes of Chemical Reactions

3

11

5

Gases and the Kinetic-Molecular Theory

7

Quantum Theory and Atomic Structure

9

Models of Chemical Bonding

11

Theories of Covalent Bonding

6

8

10

12

26 52

Stoichiometry of Formulas and Equations

66

Thermochemistry: Energy Flow and Chemical Change

93

Electron Configuration and Chemical Periodicity The Shapes of Molecules

119

111

83

102

142

The Properties of Solutions

15

Organic Compounds and the Atomic Properties of Carbon

14 16

17

152

Intermolecular Forces: Liquids, Solids, and Phase Changes

13

161

Periodic Patterns in the Main-Group Elements: Bonding, Structure, and Reactivity Kinetics: Rates and Mechanisms of Chemical Reactions Equilibrium: The Extent of Chemical Reactions

221

184

207

18

Acid-Base Equilibria

20

Thermodynamics: Entropy, Free Energy, and the Direction of Chemical Reactions

19 21

22

23

239

Ionic Equilibria in Aqueous Systems

261

Electrochemistry: Chemical Change and Electrical Work

301

The Transition Elements and Their Coordination Compounds Nuclear Reactions and Their Applications

335

176

325

289

PREFACE Welcome To Your Student Solutions Manual

Your Student Solutions Manual (SSM ) includes detailed solutions for the Follow-up Problems and highlighted End­ of-Chapter Problems in Martin Silberberg's Principles of General Chemistry. You should use the SSM in your study of chemi stry as a study tool to: • better understand the reasoning behind problem solutions. The • •

plan-solution-check format illustrates the problem-solving thought process for the Follow-up problems and for selected End-of-Chapter problems. better understand the concepts through their applications in problems. Explanations and hints for problems are in response to questions from students in general chemistry courses. check your problem solutions. Solutions provide comments on the solution process as well as the answer.

To succeed in general chemistry you must develop skills in problem solving. Not only does this mean being able to fol low a solution path and reproduce it on your own, but also to analyze problems you have never seen before and develop a solution strategy. Chemistry problems are story problems that bring together chemistry concepts and mathematical reasoning. The analysis of new problems is the most challenging step for general chemistry students. You may face this in the initial few chapters or not until later in the year when the material is less familiar. When you find that you are having difficulty starting problems, do not be discouraged. This is an opportunity to learn new skills that will benefit you in future courses and your future career. The following two strategies, tested and found successful by many students, may help you develop the skills you need. The first strategy is to become aware of your own thought processes as you solve problems. As you solve a problem, make notes in the margin concerning your thoughts. Why are you doing each step and what questions do you ask yourself during the solution? After you complete the problem, review your notes and make an outline of the process you used in the solution whi le reviewing the reasoning behind the solution. It may be useful to write a paragraph describing the solution process you used. The second strategy helps you develop the ability to transfer a solution process to a new problem. After solving a problem, rewrite the problem to ask a different question. One way to rewrite the question is to ask the question backwards-find what has been given in the problem from the answer to the problem. Another approach is to change the conditions-for instance, ask yourself what if the temperature is higher or there is twice as much carbon dioxide present? A third method is to change the reaction or process taking place-what if the substance is melting instead of boiling? At times, you may find slight differences between your answer and the one in the SSM. Two reasons may account for the differences. First, SSM calculations do not round answers until the final step so this may impact the exact numerical answer. Note that in preliminary calculations extra significant figures are retained and shown in the intermediate answers. The second reason for discrepancies may be that your solution route was different from the one given in the SSM. Valid alternate paths exist for many problems, but the SSM does not have space to show all alternate solutions. So, trust your solution as long as the discrepancy with the SSM answer is small, and use the different sol ution route to understand the concepts used in the problem. Some problems have more than one correct answer. For example, if you are asked to name a metal, there are over 80 correct answers. You may also find slight differences between the answer in the textbook appendix and the one i.n the S S M . These differences occur when questions are open-ended, such as, "Give an example of an acid." The example given in the SSM may differ from the one in the Appendix, but both answers are correct. Patricia Amateis

Chapter 1 Keys to the Study of Chemistry Most numerical problems wil l have two answers, a "calculator" answer and a "true" answer. The calculator answer, as seen on a calculator, will have one or more additional significant figures. These extra digits are retained in all subsequent calculations to avoid intermediate rounding error. Rounding of a calculator answer to the correct number of significant figures gives the true ( final) answer. FOLLOW-UP PROBLEMS

1.1

Plan: The real question is "Does the substance change composition or just change form?" Solution: a) Both the solid and the vapor are iodine, so this must be a physical change. b) The burning of the gasoline fumes produces energy and products that are different gases. This is a chemical change. c) The scab forms due to a chemical change.

1 .2

Plan: We need to know the total area supplied by the bolts of fabric, and the area required for each chair. These two areas need to be in the same units. The area units can be either ft2 or m2 . The conversion of one to the other will use the conversion given in the problem : 1 m 3 .28 1 ft. Solution : 200 m 2 (3 .28 1 ft) 2 I chair 205 .047 205 chairs (3 bOltS) I bolt 3 1 .5 ft 2 (l m) 2 Check: 200 chairs require about 200 x 32 / 1 0 640 m2 of fabric. (Round 3 1 .5 to 32, and 1 / (3.28 1 ) 2 to 1 / 1 0) Three bolts contain 3 x 200. = 600. m2 .

1 .3

(J

J(

(

=

=

]=

=

P lan: The volume of the ribosome must be determined using the equation given in the problem. This volume may then be converted to the other units requested in the problem. Solution : 3 V i 1tf 3 i ( 3 . 1 4 1 59 ) 2 1 .4 nm 5 1 3 1 .45 nm3 3 3 2 ( 1 0- 9 m) 3 ( 1 dm) 3 (5 1 3 1 .45 nm 3 ) 5. 1 3 1 45 X 1 0-2 1 = 5.13 X 1 0-2 1 dm3 3 3 ( I nm) (0. 1 m) =

=

]= ( )( ) = ( )( 6 ] =

(

l ,l1L 1L 5 . 1 3 1 45 X 1 0- 15 5.13 X ( I dm) 3 1 0 L Check: The magnitudes of the answers are reasonable. The units also agree.

(5 . 1 3 1 45 x 1 0- 21 dm 3 )

-

1 .4

=

10-15 ilL

Plan: The time is given in hours and the rate of delivery is in drops per second. A conversion(s) relating seconds to hours is needed. This will give the total number of drops, which may be combi ned with their mass to get the total mass. The mg of drops will then be changed to kilograms. The other conversions are given in the inside back cover of the book. Solution : 60 � I .5 droPS 65 mg I O-3 g 1 kg 60 min 2.808 2.8 kg 8.0 h 1h 1 mm 1s 1 drop 1 mg 1 0 3 g Check: Estimating the answer - (8 h) (3600 s / h) (2 drops / s) (0.070 kg/ I 0 3 drop) 4 kg. The final units in the calculation are the desired units.

(

J( J(

J( J[ )[ ) = =

=

1 .5

Plan: The volume unit may be factored away by multiplying by the density. Then it is simply a matter of changing grams to kilograms. Solution: 7.5 g 4.6 cm 3 � 0.0345 0.034 kg cm 3 1 000 g Check: 5 x 7 1 1 000 0.035, and the calculated units are correct.

( J(

=

1 .6

J

=

=

Plan: Using the relationship between the Kelvin and Celsius scales, change the Kelvin temperature to the Celsius temperature. Then convert the Celsius temperature to the Fahrenheit value using the relationship between these two scales. T (in°C) T (in K) - 273 . 1 5 =

Solution: T (in°C) =234 K - 273 . 1 5 -39. 1 5 =

=

-39°C

T (in O F) � (-39. 1 5°C) + 32 -38 .47 -38°F 5 Check: S ince the Kelvin temperature is below 273, the Celsius temperature must be negative. The low Celsius value gives a negative Fahrenheit value. =

=

=

1 .7

P lan: Determine the significant figures by determining the digits present, and accounting for the zeros. Only zeros between non-zero digits and zeros on the right, if there is a decimal point, are significant. The units make no difference. Solution: a) 3 1 .Q7Q mg; five significant figures b) 0.06Q6Q g; four significant figures c) 85Q.oC; three significant figures - note the decimal point that makes the zero significant. d) 2.000 x 1 02 mL; four significant figures e) 3 .9 x 1 0-{i m; two significant figures - note that none of the zeros are significant. f) 4.Q l x 1 0-4 L; three significant figures Check: All significant zeros must come after a significant digit.

1 .8

P lan: Use the rules presented in the text. Add the two values in the numerator before dividing. The time conversion is an exact conversion, and, therefore, does not affect the significant figures in the answer. The addition of 25 .65 and 37.4 gives an answer where the last significant figure is the one after the decimal point (giving three significant figures total). When a four significant figure number divides a three significant figure number, the answer must round to three significant figures. An exact number ( l min 1 60 s) wil l have no bearing on the number of significant figures. Solution: 25.65 mL + 37.4 mL 5 1 .434 5 1.4 mL/min 1 min 73.55 s 60 s Check: (25 + 35) 1 (5 1 4) (60)4/5 48. The approximated value checks well.

(

=

J

=

=

END-OF-CHAPTER PROBLEMS

1 .2

Plan: Apply the definitions of the states of matter to a container. Next, apply these definitions to the examples. Solution: Gas molecules fill the entire container; the volume of a gas is the volume of the container. Solids and liquids have a definite volume. The volume of the container does not affect the volume of a solid or liquid. a) The helium fills the volume of the entire balloon. The addition or removal of helium will change the volume of a balloon. Helium is a gas. b) At room temperature, the mercury does not completely fill the thermometer. The surface of the liquid mercury indicates the temperature.

2

c) The soup completely fills the bottom of the bowl, and it has a definite surface. The soup is a liquid, though it is possible that solid particles of food will be present. 1 .3

Plan: Define the terms and apply these definitions to the examples. Solution: Physical property A characteristic shown by a substance itself, without interacting with or changing into other substances. Chemical property A characteristic of a substance that appears as it interacts with, or transforms into, other substances. a) The change in color (yellow-green and silvery to white), and the change in physical state (gas and metal to crystals) are examples of physical properties. The change in the physical properties indicates that a chemical change occurred. Thus, the interaction between chlorine gas and sodium metal producing sodium chloride is an example of a chemical property. b) The sand and the iron are still present. Neither sand nor iron became something else. Colors along with magnetism are physical properties. No chemical changes took place, so there are no chemical properties to observe.

1 .5

Plan: Apply the definitions of chemical and physical changes to the examples. Solution: a) Not a chemical change, but a physical change simply cooling returns the soup to its original form. b) There is a chemical change cooling the toast will not "un-toast" the bread. c) Even though the wood is now in smaller pieces, it is still wood. There has been no change in composition, thus this is a physical change, and not a chemical change. d) This is a chemical change converting the wood (and air) into different substances with different compositions. The wood cannot be "unburned."

-

-

-

1 .7

Plan: A system has a higher potential energy before the energy is released (used). Solution: a) The exhaust is lower in energy than the fuel by an amount of energy equal to that released as the fuel bums. The fuel has a higher potential energy. b) Wood, like the fuel, is higher in energy by the amount released as the wood bums.

1.11

P lan: Re-read the section in the Chapter on experimental design (Experiment step of the scientific method). Solution: A well-designed experiment must have the following essential features. I) There must be two variables that are expected to be related. 2) There must be a way to control all the variables, so that only one at a time may be changed while keeping all others constant. 3) The results must be reproducible.

1 . 14

P lan: Review the table of conversions in the Chapter or inside the back cover of the book. Solution: a) To convert from .In 2 to cm 2 , use

(2.54 cm) 2 (lin) 2

.

(1000 m) 2

b) To convert from km2 to m2 , use. -'----'--2 (1 km)

c) This problem requires two conversion factors: one for distance and one for time. It does not matter which conversion is done first. Alternate methods may be used. To convert distance, mi to m, use: 1 .609 1 000 m 1.609 X 103 mimi l km 1 m)

( �)(

)

=

3

(

)( )

To convert time, h to s, use: 1h 1 min __ _ 60 min 60 s

=

1 h / 3600 s

(

. f: . 1 .609 X l O m Therefore, the complete conversion actor IS 1 ml when you start with a measurement of mi/h? .

1000 g 2.20 51b

d) To convert from pounds (lb) to grams (g), use use

(

(1 ft) 3 ( 1 2 in) 3

)(

( 1 in) 3 (2.54 cm) 3

)

=

)( ) Ih 3600 s

--

=

0.4469 m h ' . Do the UnIts cance I mi s

; to convert volume from ft3 to cm3

3.531 x 10-5 fe/cm3

1.16

Plan: Review the definitions of extensive and intensive properties. Solution: An extensive property depends on the amount of material present. An intensive property i s the same regardless of how much material is present. a) Mass is an extensive property. Changing the amount of material will change the mass. b) Density is an intensive property. Changing the amount of material changes both the mass and the volume, but the ratio (density) remains fixed. c) Volume is an extensive property. Changing the amount of material will change the size (volume). d) The melting point is an intensive property. The melting point depends on the identity of the substance, not on the amount of substance.

1.18

Plan: Anything that increases the mass or decreases the volume will increase the density ( density

=

mass ) volume

Solution: a) Density increases. The mass of the chlorine gas is not changed, but its volume is smaller. b) Density remains the same. Neither the mass nor the volume of the solid has changed. c) Density decreases. Water is one of the few substances that expands on freezing. The mass is constant, but the volume increases. d) Density increases. Iron, like most materials, contracts on cooling, thus the volume decreases whi le the mass does not change. e) Density remains the same. The water does not alter either the mass or the volume of the diamond. 1 .2 1

Plan : Use conversion factors from the inside back cover: 1 0-12 m Solution: 2 1 O- 1 m I : 1.43 nm Radius 1 430 pm 1 pm 10 m

[

=

1 .23

)( )

=

1 pm; 1 0-9 m

=

a) Plan: Use conversion factors: (0.0 1 m? ( 1 cm) 2 ; ( I km) 2 ( 1 000 m)2 Solution: (I km) 2 (0.0 I m) 2 1.77 X 10-9 km2 1 7 .7 cm 2 ( l cm) 2 (J000 m) 2 b) Plan: Use conversion factor: ( l inch)2 (2.54 cm) 2 Solution: $3.2 5 (J in) 2 = 8.9 1 639 =$8.92 1 7.7 cm 2 (2.54 cm) 2 l in 2 =

(

=

)

)(

=

=

[

)( )

4

=

1 nm

1.25

Plan: Use the relationships from the inside back cover of the book. The conversions may be performed in any order. Solution: 5.52 g (l cm)3 a) = 5.52 X 103 kg/m3 cm3 (0.0] m) ' 1 000 g

( )(

b) l .27

( )( 5.52 g cm3

)(� )

(2.54 Cm)3 (l in)3

)(

)( J(

J

(1 2 in)3 � 2.205 Ib = 344.66 1 = 3451b/ft3 I kg ( 1 ft)3 1 000 g

Plan: The conversions may be done in any order. Use the definitions of the various SI prefixes. Solution: (l mm)3 1 . 72f.1Jl13 ( I X l O-6m)3 9 a) Volume = , = 1.72 X 10- mm3 /eell ' cell (l f.1Jl1)3 (I X 1 0 3 m) l .72f.1Jl13 ( 1 x 1 0 -6m)3 1L = l .72 X 1 0-10 = 10-10 L b) Volume = (l Os cell i \ cell ( I X 1 0 -3 m (l f.1Jl1)3

(

l .29

,

)(

)(

)(

)

)(

)

Plan: The mass of the contents is the mass of the full container minus the mass of the empty container. The volume comes from the mass density relationship. Reversing this process gives the answer to part b. Solution: a) Mass of mercury = 1 85 . 5 6 g - 5 5 .32 g = 1 30.24 g

( )

Volume of mercury = volume of vial = (1 30.24 g ) � = 9.6260]6 = 9.626 em3 1 3 .53 g

(

)

0.997 g = 9.597 1 4 g water l cm3 Mass of vial filled with water 5 5 .32 g + 9.597 1 4 g 64.9 1 7 1 4

b) Mass of water = (9.6260 1 6 cm3 ) =

1 .3 1

=

=

64.92 g

Plan: Volume of a cube = (length of side) 3 Solution: The value 1 5.6 means this is a three significant figure problem. The final answer, and no other, is rounded to the correct number of significant figures. 1 m 1 O -3 m 1 5.6 mm � = 1 .56 cm (convert to cm to match density unit) I mm 1 0 2 m Al cube volume = ( 1 .56 cm) 3 = 3 .7964 cm3 1 0.25 g mass = 2.69993 = 2.70 g/em3 density volume 3 .7964 cm3

[ )( )

=

l .33

=

Plan: Use the equations given in the text for converting between the three temperature scales. Solution: a) T (in 0c) = [T (in O F ) - 32] � = (72°F - 32) � = 22.222 = 22°C 9 9 T (in K) = T (in 0c) + 273. 1 5 = 22.222°C + 273 . 1 5 = 295 .372 = 295 K b) T (in K) = T (in 0c) + 273 . 1 5 = - I 64°C + 273 . 1 5 = 1 09. 1 5 = 109 K T (in O F) = 2. T (in 0c) + 32 = 2. (- 1 64°C) + 32 = -263 .2 =-263°F 5 5 c) T (in 0c) = T (in K) -273 . 1 5 = 0 K 273 . 1 5 = -273 . 1 5 = -273°C -

T (in O F)

=

2. T (in 0c) + 32 = 2. (-273 . 1 5°C) + 32 = - 459.67 = 5

5

5

-

460.oF

1 .36

2 Plan: Use 1 0-9 m = I nm to convert wavelength. Use 0.0 1 A = 1 pm, 1 0- 1 m = 1 pm, and 1 0-9 m = 1 nm Solution: 7 1 0-9 m a) 255 nm = 2.55 x 10- m I nm 0.0 1 A 1 pm I O-9 m = 6830 A b) 683 nm 1 pm 1 nm 1. 0- 12 m

[ ) [ )[ --

)( )

1 .4 1

Plan: Review the rules for significant figures. Solution: Initial or leading zeros are never significant; internal zeros (occurring between non-zero digits) are always significant; terminal zeros to the right of a decimal point are significant; terminal zeros to the left of a decimal point are significant only if they were measured.

1 .42

Plan: Review the rules for significant zeros. Solution: a) No significant zeros (leading zeros are not significant) b) No significant zeros (leading zeros are not significant) c) 0.039Q (terminal zeros to the right of the decimal point are significant) d) 3 .Q900 x 1 04 (zeros between nonzero digits are significant; terminal zeros to the right of the decimal point are significant)

1 .44

Plan: Use a calculator to obtain an initial value. Use the rules for significant figures and rounding to get the final answer. Solution: ( 2.795 m )( 3 . 1 0 m ) = 1 .337 1 = 1.34 m (maximum of 3 significant figures allowed) a) 6.48 m b) V = c)

(�)

1t

( 9.282 cm )3 = 3.34976 x 1 0 3 = 3.350

X

103 em3

(maximum of 4 significant figures allowed)

1 . 1 1 0 cm + 1 7.3 cm + 1 08.2 cm + 3 1 6 cm = 442.61 = 443 em (no digits allowed to the right of the decimal since 3 1 6 has no digits to the right of the decimal point)

1 .46

Plan: Review the procedure for changing a number to scientific notation. Solution: a) 1.310000 x 105 (Note that all zeros are significant.) b) 4.7 x 10-4 (No zeros are significant.) c) 2.10006 x 105 d) 2.1605 X 103

1 .48

Plan: Review the examples for changing a number from scientific notation to standard notation. Solution: a) 5550 (Do not use terminal decimal point since the zero is not significant.) b) 10070. (Use terminal decimal point since final zero is significant.) c) 0.000000885 d) 0.003004

1 .5 0

Plan: Calculate a temporary by simply entering the numbers into a calculator. Then you will need to round the value to the appropriate number of significant figures. Cancel units as you would cancel numbers, and place the remaining units after your numerical answer.

6

Solution : ( 6.626 x 1 0-34 JS) ( 2 .9979 x 1 08 mls) 4.062 1 8 x 1 0-19 a) 9 X 489 1 0- m 9 4.06 x 10-19 J (489 X 1 0- m limits the answer to 3 significant figures; units of m and s cancel)

( 6.022

2 2 1 0 3 molecules/mol ) ( 1 . 1 9 x 1 0 g) = 1 .5555 X 1 024 b) 46.07 g/mol 24 2 1.56 x 10 molecules ( 1 . 1 9 x 1 0 g limits answer to 3 significant figures; units of mol and g cancel) 2 1 1 c) ( 6.022 x 1 0 3 atoms/mol)( 2. 1 8 x 1 0- 1 8 J/atom ) 2 2 = 1 . 82333 x 1 0 5 2 3 1.82 x lOs J/mol (2. 1 8 x 1 0-18 J/atom limits answer to 3 significant figures; unit of atoms cancels) X

( - )

1 .52

Plan: Exact numbers are those that have no uncertainty. Unit definitions and number counts of items in a group are examples of exact numbers. Solution : a) The height of Angel Fal ls is a measured quantity. This is not an exact number. b) The number of planets in the solar system is a number count. This � an exact number. c) The number of grams in a pound is not a unit definition. This is not an exact number. d) The number of millimeters in a meter is a definition of the prefix "milli-." This � an exact number.

1 .54

P lan: Observe the figure, and estimate a reading the best you can. Solution : The scale markings are 0.2 cm apart. The end of the metal strip falls between the mark for 7.4 cm and 7.6 cm. If we assume that one can divide the space between markings into fourths, the uncertainty is one-fourth the separation between the marks. Thus, since the end of the metal strip fal ls between 7.45 and 7.55 we can report its length as 7.50 ± 0.05 em. (Note: If the assumption is that one can divide the space between markings into halves only, then the result is 7.5 ± 0. 1 cm.)

1 .56

P lan: Calculate the average of each data set. Remember that accuracy refers to how close a measurement is to the actual or true value while precision refers to how close multiple measurements are to each other. Solution : 8.72 g + 8 . 7 4 g + 8.70 g = 8.7200 = 8.72 g Iavg = a) 3 8 .56 g + 8 .77 g + 8.83 g = 8.7200 = 8.72 g Ilavg = 3 8.50 g + 8.48 g + 8.5 1 g lIIavg = = 8.4967 = 8.50 g 3 8.4 1 g + 8.72 g + 8.55 g = 8.5600 = 8.56 g I Vavg = 3 Sets I and II are most accurate since their average value, 8.72 g, is closest to the true value, 8.72 g. b) To get an idea of precision, calculate the range of each set of values: largest value - smallest value. A small range is an indication of good precision since the values are close to each other. lrange = 8.74 g - 8.70 g = 0.040 g IIrange = 8.83 g - 8.56 g = 0.27 g IIIrange = 8.5 1 g - 8.48 g = 0.030 g IVrange= 8.72 g - 8.4 1 g = 0.3 1 g Set III is the most precise (smallest range), but is the least accurate (the average is the farthest from the actual value). c) Set I has the best combination of high accuracy (average value = actual value) and high precision (relatively small range).

7

d) largest range). has both low accuracy (average value differs from actual value) and low precision (has the 1. 5 9 SolPlan:utiIfon:it is necessary to force something to happen, the potential energy wil be higher. b) a) Set

IV

>

Q>

(J)

as

c l.lJ

___________ _

o

o

+= c

+= c

�

�

+

a) Theng have balls aonhitghhere relpotaxedentisprial energy, ng havebecause a lowertpothe balentlisalwienergy andonceare tmore stnagblies. released. The ballsThion sthconfigurat e compressed spri l move h e spri ion ib)s lTheess sttwoable. charges apart from each other have a lower potential energy and are more stable. The two charges near each other have a higher potential energy, because they repel one another. This arrangement is less stable. 1.62 PlSolan:utiUseon: the conversions presented in the problem. a) (33.436 g ) ( 100.90.00%% ) ( 31.1tr. ogZ'J( $20.tr. oz.00 J = 19. 3 520 = before price increase. t31.1r. ogZ'J ( --$35.tr. oz.00 J = 33 . 8660 = . a er prIce Increase. (33 . 436 g ) ( 100.90.00%% )(--Coi n 0 100. % J )( ( b) ( 50.0 tr. oz.) ( � tr. oz. 90.0% 33.436 g J = 51. 674=51.7Coins c) (2.00in3)((2. 5li4nC',m)3 )( 19.lcm33 g )(100.90.00%% )( 33.Coi436gn) J = 21.0 199 = 21.0COinS 1. 64 SolPlan:utiIonn:each case, calculate the overall density of the sphere and contents. a) DenSI.ty of evacuated ball: d volmassume 5600.12cmg3 2.1429 x 10'4g/cm'' Convert density to units of giL: 2.1429cm3x 10-4g ( 1 cmmL3)( 10-mL3 L ) 0.2 1429 0.2 1 giL evacuattehde baldensil wityl offloCO2at because b)TheBecause is greatietsr tdensi han tthyatisofleaissrt,haanbalthlatfilofledaiwir. th CO2 wil sink. c) 560 cm3 [I cmm�)[ 10-3mLL ) = 0.560 = 0.56 Mass of hydrogen: (0. 5 6 L)(0.0899L g ) 0.0503 g The 0.17 H2 figl ed ball wil have a total mass of 0.0503 0.12 g = 0.17 g, and a resulting density of d 0.56L 0.30 giL The ball wil because density of the ball filled with hydrogen is less than density of air. 8 +

+

I

$ 1 9.4

I

I

$33 9 ft

I

.

.

I

I

I

=

=

=

I

I

L

I

=

I

=

=

+

float

I

=

=

Note: The densities are additive because the volume of the ball and the volume of the H2 gas are the same: 0.0899 + 0.2 1 glLb = 0.30 giL. d) Because the density of O 2 is greater than that of air, a ball filled with O2 will sink. e) Density of ball filled with nitrogen: 0.2 1 giL + 1 . 1 65 giL = 1 .3 8 giL. Ball will sink because density of ball fi lled with nitrogen is greater than density of air. g .0560 L 0.665 84 g For ball filled with f) To sink, the total mass of the ball and gas must weigh

· �� )(

)

C

=

hydrogen: 0.665 84 - 0. 1 7 g = 0.4958 = 0.50 g. More than 0.50 g would have to be added to make the ball sink. 1 .67

P lan: Use the surface area and the depth to determine the volume. The volume may then be converted to liters, and finally to the mass using the giL. Once the mass of the gold is known, other conversions stem from it. Solution: 1 000 IL 5 . 8 X I O - 9g a) (3800 m)(3.63 x 1 08 km 2 ) = 8.00052 X 1 0 12 = 8 .0 x 1 0 1 2 g 3 3 (l km) 1 0- m b) Use the density of gold to convert mass of gold to volume: 0.0 1 m) 3 1 cm 3 (8.00052 x 1 01 2 g) = 4. 1 4535 x 1 0 5 = 4.1 X 1 0 5 m 3 1 9.3 g ( l cm) 3

(

c) ( 8.00052 1 .69

x

m( )(

( )( ) )( )( )

2 1 01 g

1 tr. O Z . 31.1 g

)( L )

$3 70.00 = 9.5 1 830 x 1 0 13 = $9.5 X I tr. oz.

10

13

Plan: Use the equations for temperature conversion given in the chapter. The mass and density wil l then give the volume. Solution : a) T (in 0c) = T (in K) - 273 . 1 5 = 77.36 K - 273 . 1 5 = -1 95.79°C

b) T (in OF ) = � T (i n 0c) + 32 = � (- I 95.79 °C) + 32 = -320.422 = -320.42°F 5 5 c) The mass of nitrogen is conserved, meaning that the mass of the nitrogen gas equals the mass of the liquid nitrogen. We first find the mass of liquid nitrogen and then convert that quantity to volume using the density of the liquid. g 4. M ass of liquid nitrogen = mass of gaseous nitrogen = (895 .0 L = 4086.57 g N 2

{ �� )

( )

Volume of liquid N 2 = (4086.57 g) � = 5 .05 1 4 = 5.05 L 809 g 1 .72

Plan: Determine the volume of a particle, and then convert the volume to a convenient unit (cm 3 in this case). Use the density and volume of the particles to determine the mass. In a separate set of calculations, determine the mass of all the particles in the room or in one breath. Use the total mass of particles and the individual mass of the particles to determine the number of particles. Solution: 3 4 4 2.5/lm V (�m 3 ) = 31rr 3 = 3 1t -- = 8. 1 8 1 2 = 8.2 /lm 3 2 ( l cm) 3 V (cm3 ) = 8 . 1 8 1 2 �m 3 = 8. 1 8 1 2 X 1O-12 cm 3 ( 1 0 4 ,lJ111) 3

()

() ( ) ( ) ( )

Mass (g) = 8. 1 8 1 2 X 1 0- 1 2 cm 3

2.5 g = 2.045 cm 3

Calculate the volume of the room in m3 : Volumeroom = 1 0.0 ft x 8.25 ft x 1 2.5 ft = 1 .03 1 9

x

x

1 0-11 = 2.0 x 1 0- 1 1 g each microparticle 1 0 3 fe

0-2 m)3)=2. 9 1 95 x 101 m3 3 )( 0 (1 .031X 103 ft3)( (112in)ft)33)( 2. 5 4cm) in)3 cm)3 (2. 9 195 x 101 m3)( 50.1 m3Jig )( 10I --{)Jigg)= 1.460 x 10-3= 1. 5 x 10-3 g for all the micropartic1es in the room icle ) Number of microparticles In room = 1.460 x 10- g [2.I mi045cropart x 10- g =7.1394X 107= -6 ( 50 10 m ( 3 ( ) ) Mass 0. 5 00 I L m --Il gg) = 2. 5 x 10-8 g in one O. 5 00- L breath c 1 e Number of micropartic1es I.n one breath = 2. 5 x 10-8 g ( 12.mi045croparti x 10- g J = 1.222X 103= 1.73 andPlan:densiDetteyrmialonnge thwie tthotconversi al mass ofonsthfrom e Eartthhe'sincrustsideinbackmetcover. ric tonsThe(t) bymasscombiof each ningitnhdie vdeptidualh, elsurface area e ment comes from t h e concent r at i o n of t h at element mul t i p l i e d by t h e mass of t h e crust. Solution: 2. 8 g )(� J( It J=4. 998X 1019t Ooo m)J 3)( (0.(t0cm)Im)33)( Icm3 (35 km)(5.10x 108 m )( ( (lkm) 1000g 1000 kg (4.(4.(4.999998988 xxx 101101101999t)t)t) (2.(4.x752510-Xx 4105105g Rutheni gg Oxygen Siliconum t)t)=t)==12..4.32595974198 Xx 1025101025=== 1. 7 5 SolPlan:utiIonn:visualizing the problem, the two scales can be set next to each other. There are 50 divisions between the freezing point and boiling point of benzene on the ox scale and 74.6 divisions (80.1°e - 5SC) on the °e scale. So ox= ( --74.5060°eX J °e This does not account for the offset of5. 5 divisions in the °e scale from the zero point on the ox scale. So ox= ( 74.5060°eX J cae - 5. 5°C) eheck: Plug in 80.1 °e and see if result agrees with expected value of 50oX. So oX= ( 74.50°6°eX J (80.1 °e - 5. 5 °C)=500X Use this formula to find the freezing and boiling points of water on the oX scale. = ( 74.5060°eX J (o.oooe - 5. 5°C)= oX = ( 500X ) (lOo.ooe 5. 5 °C) = 74.6°e (l

(I

3

.

7. 1

=

1

L

0 -3

X

107

II

microparticIes in the room

� 3

11

1 .2

k

1 0 3 microparticIes in a breath

l

2

/

(I

FPwater OX

BPwate r

X

/

X

/

-3.7°X

-

63.3°X

10

IS

2.3 X 1 025 g Oxygen 1 .4 X 1 025 g Silicon 1 5 X 1 0 5 g Ruthenium (and Rhodium)

Chapter 2 The Components of Matter FOLLOW-UP PROBLEMS

2. 1

Plan: The mass fraction of uranium in pitchblende was determined in the problem as (71.4/84.2 = 0.84798). The remainder of the sample must be oxygen (1.00000 - 0.84798 = 0.15202). The mass fraction of the uranium will be used to determine the total mass of pitchblende. The total mass of pitchblende and the mass fraction of oxygen may then be used to determine the mass of oxygen. Solution: . Mass 0 f PltC · hblende = 2 . 3 t Uramum

(

1.00 t Pitchblende

0.84798 t uranium

(

)

. hblende = 2 . 7 1 23 = 2.7 t PltC

)

. 0. 1 5202 t oxygen = 0.4 1 23 = 0.41 t oxygen Mass of oxygen = 2.7123 t PItchblende 1 .00 t pitchblende Check: Adding the amount of oxygen calculated to the mass of uranium gives the calculated 2.7 t of pitchblende. 2.2

Plan: The subscript (Atomic Number = Z) gives the number of protons, and for an atom, the number of electrons. The Atomic Number identifies the element. The superscript gives the mass number (A) which is the total of the protons plus neutrons. The number of neutrons is simply the Mass Number minus the Atomic Number (A - Z). Solution: a) Z= 5 and A = II, there are 5 p+ and 5 e- and II - 5 = 6 nO Atomic number = 5 = B. b) Z= 20 and A = 41, there are 20 p+ and 20 e- and 41 - 20 = 2 1 nO Atomic number = 20 = Ca. c) Z= 53 and A = 131, there are 53 p+ and 53 e- and 1 3 1 - 53 = 78 nO Atomic number = 53 = I.

2.3

Plan: To find the percent abundance of each B isotope, let x equal the fractional abundance of lOB and (1 - x) equal the fractional abundance of liB. Remember that atomic mass = isotopic mass of lOB x fractional abundance) + (isotopic mass of 11B x fractional abundance). Solution: 1 Atomic Mass = (loB mass) (fractional abundance of lOB) + ( 18 mass) (fractional abundance of liB) Amount of lOB + Amount liB = I (setting lOB = x gives liB = I - x) 1 0. 8 1 amu = ( 1 0.0129 amu)(x) + ( 1 1 .0093 amu) (1 - x) 10. 8 1 amu = 11.0093 - 11.0093x + 10.0 1 29 x 10.8 1 amu = 1 1 .0093 - 0.9964 x -0.1993 = - 0.9964x x = 0.20; 1 - x = 0.80 ( 1 0.8 1 - 1 1 .0093 limits the answer to 2 significant figures) Fraction x 1 00% = percent abundance. 1 l % abundance of OB = 20. %; % abundance of 1B = 80. % 11 Check: The atomic mass of B is 1 0.81 (close to the mass of B, thus the sample must be mostly this isotope.)

2.4

Plan: Locate these elements on the periodic table and predict what ions they will form. For A-group cations (metals), ion charge = group number; for anions (nonmetals), ion charge = group number minus 8. Or, relate the element's position t o the nearest noble gas. Elements after a noble gas lose electrons t o become positive ions, while those before a noble gas gain electrons to become negative ions. Solution: a) 16S2- [Group 6A(l6); 6 - 8 = -2]; sulfur needs to gain 2 electrons to match the number of electrons in 18Ar. b) 37Rb+ [Group IA(I)]; rubidium needs to lose I electron to match the number of electrons in 36Kr. c) 56Ba2+ ]Group 2A(2)]; barium needs to lose 2 electrons to match the number of electrons in 54Xe.

11

2.5

e second namewhile the l anditshunchanged, thtoe tfihrestperinameodibelc taoblngse. Theto thmete metal aname ing with Iifonithcerebinisaryanycompounds, Plaon:ngsWhento thdeale nonmetal. refer , doubt belnonmet to the nonmetal root. Sola) ution:ails hasin an -ide suffix added andand fromfromoxibromi de, is dine, is in b)c) is iins in and and fromfromchlsulorifidde,e, iissiinn d) is in PlSolan:utiUseon: the charges to predict the lowest ratio leading to a neutral compound. a) Zinc shouldsoform Zns an2+ accept and oxygen shoulda.form 02-, these wil combine to give The charges cancel t h i s i a bl e formul b) Silversoshoulthisdisforman accept Ag+ andablebromi ne should form Br-, these wil combine to give AgBr. The charges cancel formula. c) Lithiumso should formacceptLi+aandble chlformula. orine should form cr, these will combine to give The charges cancel t h i s i s an d)ThiAluminum should form A13+ and sulfur should formsoSt2h-,istoisproduce al combia. nation the formula is s way the charges wil cancel an accepta neut ablerformul Plnamean: Detor formula. ermine thThee names ororsymbol seofionseachalwofaysthegospecifirste.sRevi presentew .thThen combi ne the piaetcesuretcovered o producein athe met a l posi t i v e rul e s for nomencl For metofalsthliekmete manyal iotnransiis intdiiocnatmeted abyls,athRoman at can form eachimwimedi th a aditefferent tchapt hmete iaoleni'r.scname. charge numeralmorewitthhanin oneparentionheses ly follocharge, wing the SolTheution:Roman numerals mean that the lead is Pb4+ and oxygen produces the usual 02-. The neutral a)combi a istwo copper ions, each of which must be I. This is one of the b)twoSulcommon finatde,ionikicharges es oxide, foris copper Thissoiisons.spltheTheitformul betwIeencharge on thcuprous e coppersulisfiide).ndicated with a Roman numeral. Thic) Bromide, s gives thleikname ( c ommon name eofothertoelements in thout.e sameThus,coltuhmne irofonthmuste peribeodic (tianbldiec, atforms ath-Ia Roman ion. Twonumeral of these). Thiionss requi r es a t o t a l cancel them e d wi is onedofe).the two common charges on iron ions. This gives the name (or ferrous bromi d) The mercuric ion is Hg2+, and two ions (Cn are needed to cancel the charge. This gives the formula n: DetermiThenemettheanames ortisymbol salofweach offithrste .species present. Then combine the pieces to produce a name orSolPlaformula. l or posi v e i o ns ays go utiocupri n: c ion, Cu2+, requires two nitrate ions, N0 -, to cancel the charges. Trihydrate means three water The 3 mol e cul e s. These combi n e t o gi v e: The zinconlion,y forms Zn2+, requi res+ itown,osohydroxi denumeral ions, s aretounnecessary. cancel the charges. Thesede icombi ne thaso gitvhe:e appropriate c)b)charge. Lithium t h e Li Roman The cyani o n, These combine to give n: DetermiThene mettheanames ortisymbol salofweach offithrst.e speci escorrect presentio. nsThenaccordi combinglney.the pieces to produce a name orSolPlaformula. l or posi v e i o ns ays go Make n: ion is NH/ and the phosphate ion is P0 3-. To give a neutral compound they should combine a) Theutioammonium 4 t o gi v e t h e correct formul a b) Aluminum givtoesgiA1ve3+thande correct the hydroxi dea ion is Parent To gihvesese a neutare rrequi al compound theytheshoul d ocombi nn.e formul r ed around pol y at mi c i o c)numeral Manganese is Mn, and Mg,Theinotthhere formul a, is magnesium. Magnesi uhydrogen m only formscarbonat the Mge (or2+ ibion,carbonat so Romane) ion. s are unnecessary. i o n i s HC0 -, whi c h i s cal l e d t h e 3 or The correct name is Zinc Group 2B(1 2) oxygen, Silver Group lB(ll) bromine, Lithium Group IA(I) chlorine, Aluminum Group 3A(13) sulfur,

2.6

Group 6A(16). Group 7A(17). Group 7A(17). Group 6A(16).

ZnO.

(+2 -2 = 0),

(+1

-1 = 0),

LiCl.

-I

(+1

= 0),

AhS3 '

[2(+3) + 3(-2) = 0],

2.7

I

[+4 + 2(-2) = 0], -2.

Pb02.

+

+

copper(I) sulfide

=

+2

+2

iron(II) bromide

-1

2.8

HgCh.

a)

CU(N03)2·3H20.

OH-,

Zn(OHh

CN",

lithium cyanide.

2.9

[3(+1) + (-3) = 0]

(NH4 )3 P04 .

OH-.

[+3 + 3(-1) =0]

AI(OHh

magnesium hydrogen carbonate

12

magnesium bicarbonate.

d) Either use the "-ic" suffix or the "(1Il)" but not both. Nitride is N 3-, and nitrate is N0 3 -. This gives the correct name: chromium(III) nitrate (the common name is chromic nitrate). e) Cadmium is Cd, and Ca, in the formula, is calcium. Nitrate is N0 3 -, and nitrite is N02-. The correct name is

calcium nitrite. 2.10

Plan: Determine the names or symbols of each of the species present. The number of hydrogen atoms equals the charge on the anion. Then combine the pieces to produce a name or formula. The hydrogen always goes first. For the oxoanions, the -ate suffix changes to -ic acid and the -ite suffix changes to -ous acid. Solution: a) Chloric acid is derived from the chlorate ion, CI0 3-. The -I charge on the ion requires one hydrogen. These combine to give the formula: HC103. b) As a binary acid, HF requires a "hydro-" prefix and an "ic" suffix on the "fluor" root. These combine to give the name: hydrofluoric acid. c) Acetic acid is derived from the acetate ion, which may be written as CH 3 COO- or as C2H 3 02-. The - I charge means that one H is needed. These combine to give the formula: CH3 COOH or H C 2 H 3 0 2• d) Sulfurous acid is derived from the sulfite ion, SO/-. The -2 charge on the ion requires two hydrogen atoms. These combine to give the formula: H 2 S0 3• e) H BrO is an oxoacid containing the BrO- ion (hypobromite ion). To name the acid, the "-ite" must be replaced with "-ous." This gives the name: hypobromous acid.

2. 11

Plan: Determine the names or symbols of each of the species present. The number of atoms leads to prefixes, and the prefixes lead to the number of that type of atom. Solution: a) Sulfur trioxide one sulfur and three (tri) oxygens, as oxide, are present. b) Silicon dioxide one silicon and two (di) oxygens, as oxide, are present. c) N 2 0 Nitrogen has the prefix "di" 2, and oxygen has the prefix "mono" 1 (understood in the formula). d) SeF6 Selenium has no prefix (understood as 1), and the fluoride has the prefix "hexa" 6. -

-

=

=

=

=

2.12

Plan: Determine the names or symbols of each of the species present. For compounds between nonmetals, the number of atoms of each type is indicated by a prefix. Solution : a) Suffixes are not used in the common names of the nonmetal listed first in the formula. Sulfur does not qualify for the use of a suffix. Chlorine correctly has an "ide" suffix. There are two of each nonmetal atom, so both names require a "di" prefix. This gives the name : disulfur dichloride. b) Both elements are nonmetals, and there is more than one nitrogen. Two nitrogens require a "di" prefix; the one oxygen could use an optional "mono" prefix. These combine to give the name dinitrogen monoxide or dinitrogen oxide.

c) The heavier Br should be named first. The three chlorides are correctly named. The correct name is bromine trichloride. 2.13

Plan: First, write a formula to match the name. Next, multiply the number of each type of atom by the atomic mass of that atom. Sum all the masses to get an overall mass. Solution : 2 a) The peroxide ion is 02 -, which requires two hydrogen atoms to cancel the charge: H 2 0 2. Molecular mass (2 x 1. 008 amu) + (2 x 16.00 amu) 34. 016 34.02 amu. formula mass 132.9 amu +35.45 amu 168. 35 1 68.4 amu. b) A Cs + 1 ion requires one C I- 1 , ion to give: CsCI; 2 c) Sulfuric acid contains the sulfate ion, S04 -, which requires two hydrogen atoms to cancel the charge: H 2 S04; molecular mass (2 x 1.008 amu) + 32 . 07 amu + (4 x 16.00 amu) 98.086 98.09 amu. d) The sulfate ion, SO/-, requires two + I potassi urn ions, K+, to give K 2 S04; formula mass (2 x 39.10 amu) + 32 . 07 amu + (4 x 16.00 amu) 1 74.27 amu. =

=

=

=

=

=

=

=

=

=

=

13

2. 1 4

Plan: Since the compounds only contain two elements, finding the formulas involve simply counting each type of atom and developing a ratio. Solution: a)There are two brown atoms (sodium) for every red (oxygen). The compound contains a metal with a nonmetal. Thus, the compound is sodium oxide, with the formula Na20. The formula mass is twice the mass of sodium plus the mass of oxygen: 2 (22.99 amu) + ( 1 6.00 amu) 61 .98 amu. b) There is one blue (nitrogen) and two reds (oxygen) in each molecule. The compound only contains nonmetals. Thus, the compound is nitrogen dioxide, with the formula N02. The molecular mass is the mass of nitrogen plus twice the mass of oxygen: ( 1 4.0 I amu) + 2 ( 1 6.00 amu) 46.01 amu. =

=

END-OF-CHAPTER PROBLEMS

2. 1

Plan: Refer to the definitions of an element and a compound. Solution: Unlike compounds, elements cannot be broken down by chemical changes into simpler materials. Compounds contain different types of atoms; there is only one type of atom in an element.

2.4

Plan: Review the definitions of elements, compounds, and mixtures. Solution: a) The presence of more than one element (calcium and chlorine) makes this pure substance a compound. b) There are only atoms from one element, sulfur, so this pure substance is an element. c) The presence of more than one compound makes this a mixture. d) The presence of more than one type of atom means it cannot be an element. The specific, not variable, arrangement means it is a compound.

2.6

Plan: Restate the three laws in your own words. Solution: a) The law of mass conservation applies to all substances - elements, compounds, and mixtures. Matter can neither be created nor destroyed, whether it is an element, compound, or mixture. b) The law of definite composition applies to compounds only, because it refers to a constant, or definite, composition of elements within a compound. c) The law of multiple proportions applies to compounds only, because it refers to the combination of elements to form compounds.

2.7

Plan: Review the three laws: Law of Mass Conservation, Law of Definite Composition, and Law of Multiple Proportions. Solution: a) Law of Definite Composition - The compound potassium chloride, KCl, is composed of the same elements and same fraction by mass, regardless of its source (Chile or Poland). b) Law of Mass Conservation - The mass of the substance inside the flashbulb did not change during the chemical reaction (formation of magnesium oxide from magnesium and oxygen). c) Law of Multiple Proportions - Two elements, 0 and As, can combine to form two different compounds that have different proportions of As present.

2.8

Plan: Review the definition of percent by mass. Solution: a) No, the mass percent of each element in a compound is fixed. The percentage of Na in the compound NaCI is 39.34% (22.99 amu / 5 8 .44 amu), whether the sample is 0.5000 g or 50.00 g. b) Yes, the mass of each element in a compound depends on the mass of the compound. A 0.5000 g sample of NaCI contains 0. 1 967 g ofNa (39.34% of 0.5000 g), whereas a 50.00 g sample of NaCI contains 1 9.67 g of Na (39.34% of 50.00 g). c) No, the composition of a compound is determined by the elements used, not their amounts. ]f too much of one element is used, the excess will remain as unreacted element when the reaction is over.

14

2.9

•

2. 1 1

Plan: Review the mass laws: Law of Mass Conservation, Law of Definite Composition, and Law of Multiple Proportions. Solution: Experiments 1 and 2 together demonstrate the Law of Definite Composition. When 3 .25 times the amount of blue compound in experiment I is used in experiment 2, then 3 .25 times the amount of products were made and the relative amounts of each product are the same in both experiments. In experiment I , the ratio of white compound to colorless gas is 0.64:0.36 or 1 . 78: I and in experiment 2, the ratio is 2.08: 1 . 1 7 or 1 .78: 1 . The two experiments also demonstrate the Law of Conservation of Mass since the total mass before reaction equals the total mass after reaction. Plan: The difference between the mass of fluorite and the mass of calcium gives the mass of fluorine. The masses of calcium, fluorine, and fl uorite combine to give the other values. Solution: Fluorite is a mineral containing only calcium and fluorine. a) Mass of fluorine = mass of fluorite - mass of calcium = 2.76 g 1 .42 g = 1.34 g F b) To find the mass fraction of each element, divide the mass of each element by the mass of fluorite: 1 .42 g Ca = 0.5 1 449 = 0.5 1 4 Mass fraction of Ca = 2.76 g fluorite 1 .34 g F Mass fraction of F = 0.4855 1 = 0.486 2.76 g fluorite c) To find the mass percent of each element, multiply the mass fraction by 1 00: Mass % Ca = (0.5 1 4) ( l 00) = 5 1 .449 = 5 1 .4% M ass % F = (0.486) ( l 00) = 48 .55 1 = 48.6% -

2. 1 3

Plan: Since copper is a metal and sulfur is a nonmetal, the sample contains 88.39 g Cu and 44.61 g S. Calculate the mass fraction of each element in the sample. Solution : Mass of compound = 88.39 g copper + 44.6 1 g sulfur = 1 33 .00 g compound 1 0 3 g compound 88.39 g copper = 3 . 4983 8 x 1 0 6 M ass 0 f copper = (5264 k g compoun d) . 1 kg compound 1 3 3 .00 g compound

(

Mass of sulfur = (5264 kg comp O Und)

(

I 0 3 g compound 1 kg compound

)( )(

44.6 1 g sulfur l 33 .00 g compound

)

)

=

=

=

2. 1 5

3.498 x 1 0 6 g copper

1 .76562 X 1 0 6 6 1. 766 X 1 0 g sulfur

Plan: The law of multiple proportions states that if two elements form two different compounds, the relative amounts of the elements in the two compounds form a whole number ratio. To illustrate the law we must calculate the mass of one element to one gram of the other element for each compound and then compare this mass for the two compounds. The law states that the ratio of the two masses should be a small whole number ratio such as 1 :2, 3 :2, 4:3, etc. Solution: 47.5 mass % S = 0.90476 = 0.904 Compound 1 : 52.5 mass % CI 3 1. 1 mass % S = 0.45 1 379 = 0.45 1 Compound 2 : 68.9 mass % CI 0.904 = 2 .0044 = 2.00 / 1 .00 Ratio: 0.45 1 Thus, the ratio of the mass of sulfur per gram of chlorine in the two compounds is a small whole number ratio of 2 to 1 , which agrees with the law of multiple proportions. -----

15

2. 1 8

Plan: Determine the mass percent of sulfur in each sample by dividing the grams of sulfur i n the sample by the total mass of the sample. The coal type with the smallest mass percent of sulfur has the smallest environmental impact. Solution: 1 1 .3 g sulfur Mass % In Coal A (1 00 %) 2.9894 2.99% S (by mass) 378 g sample ·

=

Mass % In Coal 8 ·

=

( ( (

J J )

=

1 9.0 g sulfur ( 1 00 %) 3 . 8384 3 . 84% S (by mass) 495 g sample =

20.6 g sUlfur (1 00 %) 675 g sample Coal A has the smallest environmental impact. M ass % In Coal C ·

=

=

=

=

3.05 1 9 3 .05% S (by mass) =

2. 1 9

Plan: This question is based on the Law of Definite Composition. If the compound contains the same types of atoms, they should combine in the same way to give the same mass percentages of each of the elements. Solution: Potassium nitrate is a compound composed of three elements - potassium, nitrogen, and oxygen - in a specific ratio. If the ratio of elements changed, then the compound would be different, for example to potassium nitrite, with different physical and chemical properties. Dalton postulated that atoms of an element are identical, regardless of whether that element is found in India or Italy. Dalton also postulated that compounds result from the chemical combination of specific ratios of different elements. Thus, Dalton ' s theory explains why potassium nitrate, a compound comprised of three different elements in a specific ratio, has the same chemical composition regardless of where it is mined or how it is synthesized.

2.20

Plan: Review the discussion of the experiments in this chapter. Solution : a) Millikan determined the minimum charge on an oil drop and that the minimum charge was equal to the charge on one electron. Using Thomson 's value for the mass-ta-charge ratio of the electron and the detennined value for the charge on one electron, Millikan calculated the mass of an electron (charge/( charge/mass» to be 2 9. I 09 x 1 0- 8 g. b) The value -1 .602 x 1 0- 1 9 C is a common factor, detennined as follows: -3 .204 x 1 0- 1 9 C / -1 .602 X 1 0- 1 9 C 2.000 19 19 -4. 806 X 1 0- 1 9 C / -1 .602 X 1 0- 1 9 C 3 .000 -8 .0 1 0 X 1 0- C / -1 .602 X 1 0- C 5.000 - 1 .442 X 1 0- 1 8 C / - 1 .602 X 1 0- 1 9 C 9.000 =

=

=

=

2.23

Plan: The superscript is the mass number. Consult the periodic table to get the atomic number (the number of protons). The mass number - the number of protons the number of neutrons. For atoms, the number of protons and electrons are equal. Solution: # of Protons # of Neutrons # of Electrons Mass Number Isotope 3 6 Ar 18 18 18 36 3 8 Ar 18 20 18 38 18 22 18 40 Ar 40 =

2.25

Plan: The superscript is the mass number (A) and the subscript is the atomic number (Z, number of protons). The mass number - the number of protons the number of neutrons. For atoms, the number of protons the number of electrons. =

=

16

Solution: a) ' : 0 and '� O have the same number of protons and electrons (8), but different numbers of neutrons. ' : 0 and '� O are isotopes of oxygen, and ' : 0 has 1 6 - 8 = 8 neutrons whereas '� O has 1 7 - 8 = 9 neutrons. Same Z value

b) �� Ar and :� K have the same number of neutrons (Ar: 40 - 1 8 = 22; K: 41 - 1 9 = 22) but different numbers of protons and electrons (Ar = 1 8 protons and 1 8 electrons; K = 1 9 protons and 1 9 electrons). Same N value c) � Co and �� Ni have different numbers of protons, neutrons, and electrons. Co: 27 protons, 27 electrons and 60 - 27 = 33 neutrons; Ni : 28 protons, 28 electrons and 60 - 28 = 32 neutrons. However, both have a mass number of 60. Same A value 2.27

Plan: Combine the particles in the nucleus (protons + neutrons) to give the mass number (superscript, A). The number of protons gives the atomic number (subscript, Z) and identifies the element. Solution:

2.29

Plan: The subscript (Z) is the atomic number and gives the number of protons and the number of electrons. The superscript (A) is the mass number and represents the number of protons + the number of neutrons. Therefore, mass number - number of protons = number of neutrons. Solution: a) �82Ti c) ' ; B b) ;: Se 48 - 22 = 26 79 - 34 = 45 11 -5=6

2.3 1

Plan: To calculate the atomic mass of an element, take a weighted average based on the natural abundance of the isotopes: (isotopic mass of isotope 1 x fractional abundance) + (isotopic mass of isotope 2 x fractional abundance) Solution: 39.89% 60. 1 1 % . . = 69 .7 230 = 69 . 72 amu AtomiC mass of gallium = (68.9256 amu) + (70.9247 amu) 1 00% 1 00%

(

2.33

)

(

)

Plan: To find the percent abundance of each CI isotope, let x equal the fractional abundance of 3 5 CI and (1 equal the fractional abundance of 37 Cl. Remember that atomic mass = isotopic mass of 3 5 CI x fractional abundance) + (isotopic mass of 37 CI x fractional abundance). Solution: Atomic mass of CI = 3 5 .4527 amu 35 .4527 = 34.9689x + 36.9659( 1 - x) 35 .4527 = 34.9689x + 36.9659 - 36.9659x 35 .4527 = 36.9659 - 1 .9970x 1 .9970x = 1 .5 1 32 x = 0.75774 and 1 x = 0.24226 % abundance 3 5C I 75.774 % % abundance 3 7CI 24.226% -

=

=

17

-

x)

2.35

Plan: Review the section in the chapter on the periodic table. Solution : a) In the modern periodic table, the elements are arranged in order of increasing atomic number. b) Elements in a column or group (or family) have simi lar chemical properties, not those in the same period or row. c) Elements can be classified as metals, metal loids, or nonmetals.

2.38

Plan: Locate each element on the periodic table. The Z value is the atomic number of the element. Metals are to the left of the "staircase", nonmetals are to the right of the "staircase" and the metalloids are the elements that lie along the "staircase" l ine. Solution : 4A( 1 4) metalloid a) Germanium Ge 6A( l 6) nonmetal S b) Sulfur 8A( 1 8) nonmetal c) Helium He 1 A( I ) metal Li d) Lithium 6B(6) metal e) Molybdenum Mo

2.40

Plan: Review the section in the chapter on the periodic table. Remember that alkaline earth metals are in Group 2A(2) and the halogens are in Group 7A( 1 7); periods are horizontal rows. Solution : a) The symbol and atomic number of the heaviest alkaline earth metal are Ra and 88. b) The symbol and atomic number of the lightest metalloid in Group 5A( 1 5 ) are As and 33 . c) The symbol and atomic mass of the coinage metal whose atoms have the fewest electrons are Cu and 63.55 amu.

d) The symbol and atomic mass of the halogen in Period 4 are

Br

and 79.90 amu.

2.42

Plan: Review the section of the chapter on the formation of ionic compounds. Solution : These atoms wil l form ionic bonds, in which one or more electrons are transferred from the metal atom to the nonmetal atom to form a cation and an anion, respectively. The oppositely charged ions attract, forming the ionic bond.

2.44

Plan: Assign charges to each of the ions. Since the sizes are similar, there are no differences due to the sizes. Solution: Coulomb 's law states the energy of attraction in an ionic bond is directly proportional to the product of charges and inversely proportional to the distance between charges. The product of charges in MgO (+2 x -2 = -4) is greater than the product of charges in LiF (+ 1 x - 1 = - 1 ). Thus, MgO has stronger ionic bonding.

2.47

P lan: Locate these elements on the periodic table and predict what ions they wil l form. For A-group cations (metals), ion charge = group number; for anions (nonmetals), ion charge = group number minus 8. Solution : Potassium (K) is in Group l A( I ) and forms the K+ ion. Iodine (1) is in Group 7A( 1 7) and forms the r ion (7 - 8 = - 1 ).

2 .49

Plan: Use the number of protons (atomic number) to identify the element. Add the number of protons and neutrons together to get the mass number. Locate the element on the periodic table and assign its group and period number. Solution : a) Oxygen (atomic number = 8) mass number = 8p + 9n = 1 7 Period 2 Group 6A( l 6) Period 2 Group 7 A( 1 7) b) Fluorine (atomic number = 9) mass number = 9p + I O n = 1 9 c) Calcium (atomic number = 20) mass number = 20p + 20n = 40 Group 2A(2) Period 4

18

2.5 1

Plan: Determine the charges of the ions based on their position on the periodic table. Next, determine the ratio of the charges to get the ratio of the ions. Solution: Lithium [Group I A( 1 )] forms the Li+ ion; oxygen [Group 6A( 1 6)] forms the 0 2- ion (6 8 -2). The ionic compound that forms from the combination of these two ions must be electrically neutral, so two Li+ ions combine with one 0 2- ion to form the compound Li 2 0. There are twice as many Li+ ions as 02- ions in a sample of Li 2 0. 1 0 2. ion = 2.65 X 1 0 2 ° = 2.6 x I 020 02- ions Number of 0 2- ions = (5 .3 x I 0 2 0 Li + iOnS) 2 Li + ions

-=

]

(

2.53

Plan: The key is the size of the two alkali ions. The charges on the sodium and potassium ions are the same as both are in Group I A( I ), so there wil l be no difference due to the charge. The chloride ions are the same, so there wil l be no difference due to the chloride. Solution: Coulomb ' s law states that the energy of attraction in an ionic bond is directly proportional to the product of charges and inversely proportional to the distance between charges. (See also problem 2 .44.) The product of the charges is the same in both compounds because both sodium and potassium ions have a + I charge. Attraction increases as distance decreases, so the ion with the smaller radius, Na+, wil l form a stronger ionic interaction (NaCl).

2.55

Plan: Review the definitions of empirical and molecular formulas. Solution: An empirical formula describes the type and simplest ratio of the atoms of each element present in a compound whereas a molecular formula describes the type and actual number of atoms of each element in a molecule of the compound. The empirical formula and the molecular formula can be the same. For example, the compound formaldehyde has the molecular formula, CH 2 0. The carbon, hydrogen, and oxygen atoms are present in the ratio of I :2: 1 . The ratio of elements cannot be further reduced, so formaldehyde ' s empirical formula and molecular formula are the same. Acetic acid has the molecular formula, C 2 H 4 02 . The carbon, hydrogen, and oxygen atoms are present in the ratio of 2 :4:2, which can be reduced to I :2: I . Therefore, acetic acid ' s empirical formula is CH 2 0, which is different from its molecular formula. Note that the empirical formula does not uniquely identify a compound, because acetic acid and formaldehyde share the same empirical formula but are not the same compound.

2.56

Plan: Review the concepts of atoms and molecules. Solution: The mixture is similar to the sample of hydrogen peroxide in that both contain 20 billion oxygen atoms and 20 billion hydrogen atoms since both O 2 and H 2 02 contain 2 oxygen atoms per molecule and both H 2 and H 2 0 2 contain 2 hydrogen atoms per molecule. They differ in that they contain different types of molecules: H 2 0 2 molecules in the hydrogen peroxide sample and H 2 and O 2 molecules in the mixture. In addition, the mixture contains 20 billion molecules ( 1 0 billion H 2 and 1 0 billion O2 ) while the hydrogen peroxide sample contains 1 0 billion molecules.

2.57

Plan: Examine the subscripts and see if there is a common divisor. If one exists, divide all subscripts by this value. Solution: a) To find the empirical formula for N 2 H 4 , divide the subscripts by the highest common divisor, 2 : N 2 H 4 becomes NH2 b) To find the empirical formula for C 6 H ' 2 06 , divide the subscripts by the highest common divisor, 6: C 6 H I 2 06 becomes CH20

2.59

Plan: Locate each of the individual elements on the periodic table, and assign charges to each of the ions. For A-group cations (metals), ion charge = group number; for anions (nonmetals), ion charge = group number minus 8. Find the smallest number of each ion that gives a neutral compound.

19

Solution : a) Lithium is a metal that forms a + I (group I A) ion and nitrogen is a nonmetal that forms a -3 ion (group +3 -3 SA, 5 - 8 = -3). +I + 1 -3 The compound is Li3 N, lithium nitride. Li N Li3N b) Oxygen is a nonmetal that forms a -2 ion (group 6A, 6 - 8 = -2) and strontium is a metal that forms a +2 ion (group 2A). +2 -2 Sr 0 The compound is SrO, strontium oxide. c) Aluminum is a metal that forms a +3 ion (group 3A) and chlorine is a nonmetal that forms a -1 ion (group 7A, 7 - 8 = -1 +3 -3 +3 - 1 +3 - 1 The compound is AICI3 , alu minum chloride. AICI3 AI CI 2.6 1

Plan : Based on the atomic numbers (the subscripts) locate the elements on the periodic table. Once the atomic numbers are located, identify the element and based on its position, assign a charge. For A-group cations (metals), ion charge = group number; for anions (nonmetals), ion charge = group number minus 8. Find the smallest number of each ion that gives a neutral compound. Solution: a) 1 2 L is the element Mg (Z = 1 2). Magnesium [group 2A(2)] forms the Mg2 + ion. 9M is the element F (Z = 9). Fluorine [group 7 A( 1 7)] forms the F- ion (7-8 = 1 ) The compound formed by the combination of these two elements is MgF2, magnesiu m fluoride. b) 1 1 L is the element Na (Z = 1 1 ). Sodium [group IA( I )] forms the Na+ ion. 1 6M is the element S (Z = 1 6). Sulfur[group 6A( 1 6)] will form the S 2- ion (6-8 = -2). The compound formed by the combination of these two elements is Na 2 S, sodiu m sulfide. c) 1 7 L is the element CI (Z = 1 7). Chlorine [group 7 A( 1 7)] forms the Cl- ion (7-8 = - 1 ). 3 8 M is the element Sr 2 (Z = 38). Strontium [group 2A(2)] forms the Sr + ion. The compound formed by the combination of these two elements is SrC h , stronti u m chloride. -

.

2.63

P lan: Review the rules for nomenclature covered in the chapter. For metals, like many transition metals, that can form more than one ion each with a different charge, the ionic charge of the metal ion is indicated by a Roman numeral within parentheses immediately fol lowing the metal ' s name. Solution: a) Tin (IV) chloride = SnCl4 The (IV) indicates that the metal ion is Sn4+ which requires 4 cr ions for a neutral compound. b) FeBr) = iron(III) bromide (common name is ferric bromide); the charge on the iron ion is +3 to match the -3 charge of 3 Br- ions. The +3 charge of the Fe is indicated by ( I I I ) + 6 -6 +3 -2 c) cuprous bromide = CuBr (cuprous is + 1 copper ion, cupric is +2 copper ion) d) Mn 2 0) = manganese(III) oxide Use ( I I I ) to indicate the +3 ionic charge of Mn: Mn 2 03

2.65

Plan : Review the rules for nomenclature covered i n the chapter. Compounds must b e neutral. Solution: a) Barium [Group 2a(2)] forms Ba2+ and oxygen [Group 6A( 1 6)] forms 02- (6 - 8 = -2) so the neutral compound forms from one barium ion and one oxygen ion. Correct formula is BaO. b) Iron(Il) indicates Fe 2+ and nitrate is NO)- so the neutral compound forms from one iron(II) ion and two nitrate ions. Correct formula is Fe(N03h c) Mn is the symbol for manganese. Mg is the correct symbol for magnesium. Correct formula is MgS. Sulfide is the S 2- ion and sulfite is the SO)2- ion.

2.67

Plan : Acids donate H+ ion t o solution, s o the acid i s a combination o f H+ and a negatively charged ion. Binary acids (H plus one other nonmetal) are named hydro + nonmetal root + ic acid Oxoacids (H + an oxoanion) are named by changing the suffix of the oxoanion: -ate becomes -ic acid and -ite becomes -ous acid. Solution: a) Hydrogen sulfate is H S0 4-, so its source acid is H 2 S04. Name of acid is sulfu ric acid. b) HI0 3 , iodic acid (I03- is the iodate ion)

20

c) Cyanide is C� ; its source acid is d) H z S, hydrosulfuric acid

HCN hydrocyanic acid .

2.69

Plan: This compound is composed of two nonmetals. Rule I ("Names and Formulas of B inary Covalent Compounds") indicates that the element with the lower group number is named first. Greek numerical prefixes are used to indicate the number of atoms of each element in the compound. Solution : Disulfur tetrafluoride SZF4 di- indicates two S atoms and tetra- indicates four F atoms.

2.7 1

Plan: Break down each formula to the individual elements and count the number of each. The molecular (formula) mass is the sum of the atomic masses of all of the atoms. Solution: a) There are 1 2 atoms of oxygen in AI 2 (S0 4 h The molecular mass is: Al 2(26.98 amu) 53 .96 amu S 3(32.07 amu) 96.2 1 amu o 1 2( 1 6.00 amu) 1 92.0 amu 342.2 amu

b) There are 9 atoms of hydrogen in (N H 4 ) 2 H P04 . The molecular mass is: N 2( 1 4.0 1 amu) 28.02 amu H 9( 1 .008 amu) 9.072 amu P 1 (30.97 amu) 30.97 amu o 4( 1 6.00 amu) 64.00 amu 1 3 2 .06 amu

c) There are 8 atoms of oxygen in CU3(OHMC03) 2 ' The molecular mass is: Cu 3(63.55 amu) 1 90.6 amu o 8( 1 6.00 amu) 1 28.0 amu H 2( 1 .008 amu) 2.0 1 6 amu C 2( 1 2.0 1 amu) 24.02 amu 344.6 amu

2.73

P lan: Review the rules of nomenclature and then assign a name. The molecular (formula) mass is the sum of the atomic masses of all of the atoms. Solution: a) (NH4) z S04 28.02 amu 2( 1 4.0 1 amu) N 8.064 amu 8( 1 .008 amu) H 32.07 amu 1 (32.07 amu) S 64.00 amu 4( 1 6.00 amu) 0 1 3 2 . 1 5 amu

b) NaH z P04 Na H P 0 c) KHC03 K

H C 0

22.99 amu 2.0 1 6 amu 30.97 amu 64.00 amu

1 (22.99 amu) 2( 1 .008 amu) 1 (30.97 amu) 4( 1 6.00 amu)

1 1 9.98 amu

39. 1 0 amu 1 .008 amu 1 2.0 1 amu 48.00 amu

1 (39. 1 0 amu) 1 ( l .008 amu) 1 ( 1 2.0 1 amu) 3 ( 1 6.00 amu)

1 00. 1 2 amu

21

2. 7 5

2. 7 7

Plan: Use the chemical symbols and count the atoms of each type to give a molecular formula. Divide the molecular formula by the largest factor to give the empirical formula. Use the nomenclature rules in the chapter to derive the name. This compound is composed of two nonmetals. Rule ("Names and Formulas of Binary Covalent Compounds") indicates that the element with the lower group number is named first. Greek numerical prefixes are used to indicate the number of atoms of each element in the compound. The molecular (formula) mass is the sum of the atomic masses of all of the atoms. Solution: The compound's name is disulfur dichloride . (Note: Are you unsure when and when not to use a prefix? If you leave off a prefix, can you definitively identify the compound? The name s u lfur dichloride would not exclusively identify the molecule in the diagram because sulfur dichloride could be any combination of sulfur atoms with two chlorine atoms. Use prefixes when the name may not uniquely identify a compound.) The empirical formula is S 2I2 CI 2/2 or S C I . The molecular mass is amu) + amu) 1 35.04 amu .

1

2(32. 07

2(35.45

=

Plan: Use the chemical symbols and count the atoms of each type to give a molecular formula. D ivide the molecular formula by the largest factor to give the empirical formula. Use the nomenclature rules in the chapter to derive the name. This compound is composed of two nonmetals. Rule I ("Names and Formulas of Binary Covalent Compounds") indicates that the element with the lower group number is named first. Greek numerical prefixes are used to indicate the number of atoms of each element in the compound. The molecular (formula) mass is the sum of the atomic masses of all of the atoms. Solution : a) Formula is S03. Name is sulfur trioxide . ( 1 S atom and three 0 atoms) Molecular mass amu) + amu) = 80.07 amu b) Formula is N 2 0. Name is dinitrogen monoxide . N atoms and 1 0 atom) Molecular mass amu) + amu) 44.02 amu =

=

(32. 0 7 2(14. 0 1

3(16.00 (16.00

=

(2

2. 79

Plan: Review the discussion on separations. Solution: Separating the components of a mixture requires physical methods only; that is, no chemical changes (no changes in composition) take place and the components maintain their chemical identities and properties throughout. Separating the components of a compound requires a chemical change (change in composition).

2. 8 2

Plan: Review the definitions in the chapter. Solution : a) Distilled water is a compound that consists of H 2 0 molecules only. How would you classify tap water? b) Gasol ine is a homogeneous mixture of hydrocarbon compounds of uniform composition that can be separated by physical means (distillation). c) Beach sand is a heterogeneous mixture of different size particles of minerals and broken bits of shells. d) Wine is a homogenous mixture of water, alcohol, and other compounds that can be separated by physical means (distillation). e) Air is a homogeneous mixture of different gases, mainly N 2 , O2 , and Ar.

2. 84

Plan: Use the equation for the volume of a sphere in Part a) to find the volume of the nucleus and the volume of the atom. Calculate the fraction of the atom volume that is occupied by the nucleus. For Part b), calculate the total mass of the two electrons; subtract the electron mass from the mass of the atom to find the mass of the nucleus. Then calculate the fraction of the atom's mass contributed by the mass of the nucleus. Solution: a) Fraction of volume

=

Volume of Nucleus Volume of Atom

-------­

( �) 1t(2. 5 10-1 5 ( �) 1t(3.1 10-11 X

x

22

m

t

m)

3

=

5.2449 10-1 3 = X

5.2

X

1 0-1

3

b) Mass of nucleus = mass of atom - mass of electrons 6.64648 x 1 0-24 g - 2(9. 1 0939 X 1 0-2 8 g) 6.64466 X 1 0-24 g 2 6.64466 x 1 0 - 4 g ) ( Mas s of Nuc leus = 0.999726 1 7 = 0.999726 = . . Fraction of mass = M ass of Atom ( 6.64648 x 1 0-24 g ) As expected, the volume of the nucleus relative to the volume of the atom is small while its relative mass is large. =

2.86

=

Plan: Determine the percent oxygen in each oxide by subtracting the percent nitrogen from 1 00%. Express the percentage in grams and divide by the atomic mass of the appropriate elements. Then divide by the smaller ratio and convert to a whole number. Solution: I a) ( 1 00.00 - 46.69 N)% = 53.3 1 % 0 I mol 0 1 mol N ( 53 . 3 1 g 0 ) = 3.3326 mol N ( 46.69 g N ) = 3 .33 1 9 mol 0 1 6.00 g 0 1 4.0 1 g N

)

(

3 . 3 3 1 9 mol 0 ----- = 1 .0000 mol 0 3.33 1 9

3 .3326 mol N ---- = 1 .0002 mol N 3 .3 3 1 9

NO

1 : 1 N :O gives the empirical formula: II

( 1 00.00 - 36.85 N)% = 63 . 1 5% 0 1 mol N = 2.6303 mol N ( 36.85 g N ) 1 4.0 1 g N

)

(

2.6303 mol N 2.6303

=

)

(

( 63 . 1 5 g 0)

(

)

1 mol 0 = 3 .9469 mol 0 1 6.00 g 0

3 . 9469 mol 0 = 1 .500 1 mol O 2 .6303

1 .0000 mol N

I : 1 .5 N :O gives the empirical formula: III

)

( 1 00.00 - 25 .94 N)% = 74.06% 0 I mol N = 1 .85 1 5 moI N ( 2 5 .94 g N ) 1 4.0 1 g N

(

) ) J

1 :2.5 N :O gives the empirical formula: N 2 0s 5 3 .3 I g 0 ( 1 .00 g N ) = 1. 1 4 1 8 = 1 .14 g 0 46.69 g N II

( 1 .00 g N )

III

( 1 .00 g N )

( ( (

(

)

1 mol 0 = 4.6288 mol 0 1 6.00 g 0

4.6288 mol 0 = 2.5000 mol 0 1 . 85 1 5

1 . 85 1 5 mol N = 1 .0000 mol N 1 . 85 1 5

b)

( 74.06 g O )

63. 1 5 g 0 = 1 .7 1 37 36.85 g N

=

1 .7 1 g 0

74.06 g 0 = 2.8550 = 2 .86 g 0 25.94 g N

23

2.88

Plan: The mass percent comes from determining the kilograms of each substance in a kilogram of seawater. The percent of an ion is simply the mass of that ion divided by the total mass of ions. Solution: a) For chloride ions: 1 8980. mg C I - 0.00 1 g � 00% = .898% (1 cr Mass% cr = ) 1 I kg seawater I mg 1 000 g cr: 1 .898% 1 .056% Na+: 80/-: 0.265% 2 Mg +: 0.127% 2 Ca +: 0.04% 0.038% K+: HC03-: 0.014% Comment: Should the mass percent add up to I OO? No, the maj ority of seawater is H 2 0. b) Total mass of ions in 1 kg of seawater = 1 8980 mg + 1 0560 mg + 2650 mg + 1 270 mg + 400 mg + 380 mg + 1 40 mg = 34380 mg % Na+ = ( 1 0560 mg Na +/34380 mg total ions) ( 1 00) = 30.7 1 553 = 30.72% c) Alkaline earth metal ions are Mg2 + and Ca2 +. Total mass% = 0. 1 27 + 0.04 = 0. 1 67 = 0.17% Alkali metal ions are K+ and Na+. Total mass% = 1 .056 + 0.03 8 = 1 .094% Total mass percent for alkali metal ions is 6.6 times greater than the total mass percent for alkaline earth metal ions. Sodium ions (alkali metal ions) are dominant in seawater. d) Anions are cr, SO/-, and HC03-. Total mass% = 1 .898 + 0.265 + 0.0 1 4 = 2.177% Cations are Na+, Mg2 +, Ca2 +, and K+. Total mass% = 1 .056 + 0. 1 27 + 0.04 + 0.03 8 = 1 .26 1 0 = 1 .26% The mass fraction of anions is larger than the mass fraction of cations. Is the solution neutral since the mass of anions exceeds the mass of cations? Yes, although the mass is larger the number of positive charges equals the number of negative charges.

)(

[

2 .90

)( )

Plan: First, count each type of atom present to produce a molecular formula. Divide the molecular formula b y the largest divisor to produce the empirical formula. The molecular mass comes from the sum of each of the atomic masses times the number of each atom. The atomic mass times the number of each type of atom divided by the molecular mass times 1 00 percent gives the mass percent of each element. Solution: The molecular formula of succinic acid is C4H604• Dividing the subscripts by 2 yields the empirical formula C 2 H30 2 . The molecular mass of succinic acid is 4( 1 2.0 1 amu) + 6( 1 .008 amu) + 4( 1 6.00 amu) = 1 1 8.088 = 1 1 8.09 a m u . 4 ( 1 2 . 0 1 amu C ) 1 00% = 40.68 1 5 = 40.68% C %C= 1 1 8 .088 amu %H=

[ [( [(

6 1 .008 amu H 1 1 8 .088 amu

) )) ))

1 00% = 5 . 1 2 1 6 = 5. 122% H

4 1 6.00 amu 0 1 00% = 54. 1 969 = 54.20% 0 1 1 8.088 amu Check: Total = (40.68 + 5 . 1 22 + 54.20)% = 1 00.00% The answer checks. %0=

2.92

P lan: To find the formula mass of potassium fluoride, add the atomic masses of potassium and fluorine. Fluorine has only one naturally occurring isotope, so the mass of this isotope equals the atomic mass of fluorine. The atomic mass of potassium is the weighted average of the two isotopic masses: (isotopic mass of isotope 1 x fractional abundance) + (isotopic mass of isotope 2 x fractional abundance) Solution: 93 .258% . 6.730% Average atomIc mass of K = (3 8.9637 amu) = 39.093 amu + (40.96 1 8 amu 1 00% 1 00% The formula for potassium fluoride is KF, so its molecular mass is (39.093 + 1 8.9984) = 58.091 amu

)

(

24

{

)

2.94

)

(

Plan: First, count each type of atom present to produce a molecular formula. Determine the mass percent of each element. Mass percent = total mass of the element 1 00 . The mass of TNT times the mass percent of molecular mass of TNT each element gives the mass of that element. Solution: The molecular formula for TNT is C 7 Hs06N 3 . (What is its empirical formula?) The molecular mass of TNT is: C 7( 1 2.0 1 amu) 84.07 amu H 5( 1 .008 amu) 5.040 amu o 6( 1 6.00 amu) 96.00 amu N 3 ( 1 4.0 1 amu) 42.03 amu 227. 1 4 amu

( (

) )

The mass percent of each element is: 84.07 amu C= 1 00 = 37.0 1 % C 227. 1 4 aum 0=

H=

96.00 amu 1 00 = 42.26% 0 227. 1 4 aum

( ( ( (

N=

( (

)

5.040 amu 1 00 2.2 1 9% H 227 . 1 4 aum

)

=

42.03 amu 1 00 = 1 8.50% N 227. 1 4 aum

Masses: 37.0 1 % C kg C = ( I .00 Ibs ) = 0.370 Ib C 1 00% TNT kg H = kg 0 =

2.2 1 9% H 1 00% TNT 42.26% 0 1 00% TNT

J J( J( J (I .OO

1 .00 Ibs ) = 0.0222

Ib H

1 .00 Ibs ) = 0.4223

Ib 0

1 8.50% N Ibs ) = 0. 1 85 1b N 1 00% TNT Note: The percent ratio yields the mass of a substance in the compound. kg N =

2. 1 04

Plan: Remember that a change is physical when there has been a change in physical form but not a change in composition. In a chemical change, a substance is converted into a different substance Solution: 1 ) Initially, all the molecules are present in blue-blue or red-red pairs. After the change, there are no red-red pairs, and there are now red-blue pairs. Changing some of the pairs means there has been a chemical change. 2) There are two blue-blue pairs and four red-blue pairs both before and after the change, thus no chemical change occurred. The different types of molecules are separated into different boxes. This is a physical change. 3) The identity of the box contents has changed from pairs to individuals. This requires a chemical change. 4) The contents have changed from all pairs to all triplets. This is a change in the identity of the particles, thus, this is a chemical change. 5) There are four red-blue pairs both before and after, thus there has been no change in the identity of the individual units. There has been a physical change.

25

Chapter 3 Stoichiometry of Formulas and Equations FO LLOW-UP PROBL E M S

3. 1

a) Plan: The mass of carbon must be changed from mg to g. The molar mass of carbon can then be used to determine the number of moles. Solution: I O -3 g 1 mol C 2.6228 X 1 0-2 2 . 62 X 1 0-2 mol C 3 1 5 mg C 1 mg 1 2.0 1 g C Check: 3 1 5 mg is less than a gram, which is less than 1 1 1 2 mol of C. b) Plan: Avogadro's number is needed to convert the number of atoms to moles. The molar mass of manganese can then be used to determine the number of grams. Solution: 54.94 g n 1 mol Mn 2 2 .9377 x 1 0-2 3 .22 x 1 0 0 Mn Atoms 2 3 6.022 X 1 0 Mn Atoms 1 mol Mn

[ )( =

=

)=

[

2.94

x

)(

2 1 0- g M n

M )=

Check: The exponent, 20, from the Mn atoms is much smaller than that for Avogadro's number, 23, thus the mass is much smal ler than the molar mass of Mn. 3.2

a) P lan: Avogadro's number is used to change the number of molecules to moles. Moles may be changed to mass using the molar mass. The molar mass of tetraphosphorus decaoxide requires the chemical formula. Solution : Tetra 4, and deca 1 0 to give P 4 0 1 0 . The molar mass, .M., is the sum of the atomic weights, expressed in glmol : 1 23 .88 glmol P 4(30.97) 1 60.00 g/mol ° 1 O( 1 6.00) 283.88 glmol of P 4 0 l o 1 ol 22 283.88 g 4.65 x 1 0 molecules P40l O 2 1 .9203 2 1 .9 g P40 1 0 � 1 mol 6.022 x L O molecules Check: The exponents indicate there is less than 1 1 1 0 mole of P 4 0 l o . Thus the grams must be less than 1 1 1 0 the molar mass. b) Plan: Each molecule has four phosphorus atoms, so the total number of atoms is four times the number of molecules. Solution : P 23 1 .86 X 1 0 P atoms (4.65 x 1 0 22 P4 0 l0 molecule J\ 1 P 04 atoms 4 l0 molecule Check: There are more phosphorus atoms than molecules so the answer should be larger than the original number.

=

= =

== =

=

)(

[

)=

=

)=

3.3

Plan: The formula of ammonium nitrate and the molar mass are needed. The total mass of nitrogen over the molar mass times 1 00% gives the answer. Solution : The formula for ammonium nitrate is NH 4N0 3 . There are 2 atoms of N per each formula. a) Molar mass N H 4N0 3 (2 x 1 4 .0 1 ) + (4 x 1 .008) + (3 x 1 6.00) 80.05 glmol 2 x 1 4.0 1 glmol total mass of N (1 00 ) 3 5 .003 1 35.00% N ( 1 00 ) 80.05 glmol molar mass of N H 4 N0 3

= =

------ = =

26

=

b) Plan: Convert kg to grams. Use the mass percent found in (a) to find the mass ofN in the sample. Solution: (3 5 . 8 kg -1 03 g 35 . 00 g N = 1 .2530 x 1 04 = 1 .2 5 x 1 04 g Nitrogen I kg 1 00 g NH 4 N0 3 Note: The percent ratio yields the mass of nitrogen in the compound. Check: Nitrogen and oxygen are about the same mass. The difference is very slight and is neglected. Now 40% of the atoms remaining are N, so the answer should be about 40%.

{ )(

3 .4

Plan: The moles of sulfur may be calculated from the mass of sulfur and the molar mass of sulfur. The moles of sulfur and the chemical formula will give the moles af M. The mass of M divided by the moles of M will give the molar mass of M. Solution: ) ( 2.88 g S I mol S 2 mol M = 0.0599 mol M 32.07 g S 3 mol S (3 . 1 2 g M) / (0.0599 mol M) = 52. 1 = 52. 1 g M / mol M The element is Cr (52.00 glmo!); M is Chromiu m and M 2 S 3 is chromiu m(III) sulfide. Check: Given that, the starting masses are similar, but the final formula has 1 .5 times as many S ions as M ions. M should have a molar mass near 1 .5 times the molar mass of sulfur: 32 x 1 .5 = 48

(

3.5

)

)(

)

Plan: Two calculations are needed - one for carbon and one for hydrogen. This is because these are the only elements present in benzo[a]pyrene. If we assume there are 1 00 grams of this compound, then the masses of carbon and hydrogen, in grams, are numerically equivalent to the percentages. Using the atomic masses of these two elements, the moles of each may be calculated. Dividing each of the moles by the smaller value gives the simplest ratio of C and H. The smallest multiplier to convert the ratios to whole numbers gives the empirical formula. Comparing the molar mass of the empirical formula to the molar mass given in the problem allows the molecular formula to be determined. Solution: Assuming 1 00 g of compound gives 95.2 1 g C and 4.79 g H. Then find the moles of each element using their molar masses. I mol C = 95.2 1 g 7.92756 mol C 1 2.0 1 g C

c( (

) )

I mol = 4.75 1 98 mol H H 1 .008 g H Divide each of the moles by 4.75 1 98, the smaller value. 4.75 1 98 mol H = 7 .92756 mol C = 1 .6683 mol C '. 1 .000 mol H 4.75 1 98 4.75 1 98 The value 1 .668 is 5/3 , so the moles of C and H must each be multiplied by 3 . If it is not obvious that the value is near 5/3 , use a trial and error procedure whereby the value is multiplied by the successively larger integer until a value near an integer results. This gives C S H 3 as the empirical formula. The molar mass of this formula is: (5 x 1 2.0 1 glmol) + (3 x 1 .008 glmol) = 63 .074 glmol Dividing 252.30 glmol by 63.074 glmol gives 4.000. Thus, the empirical formula must be multiplied by 4 to give C 2oH1 2 as the molecular formula of benzo[a]pyrene. Check: Determine the molar mass of the formula given and compare it to the value given in the problem: .At (20 x 1 2.0 1 glmol) + ( 1 2 x 1 .008 glmol) = 252.296 glmo!. This is very close to the given value. 4.79 g H

=

27

3.6

Plan: The carbon in the sample is converted to carbon dioxide, the hydrogen is converted to water, and the remaining material is chlorine. The grams of carbon dioxide and the grams of water are both converted to moles. One mole of carbon dioxide gives one mole of carbon, while one mole of water gives two moles of hydrogen. Using the molar masses of carbon and hydrogen, the grams of each of these elements in the original sample may be determined. The original mass of sample minus the masses of carbon and hydrogen gives the mass of chlorine. The mass of chlorine and the molar mass of chlorine will give the moles of chlorine. Once the moles of each of the elements have been calculated, divide by the smallest value, and, if necessary, multiply by the smallest number required to give a set of whole numbers for the empirical formula. Compare the molar mass of the empirical formula to the molar mass given in the problem to find the molecular formula. Solution : Determine the moles and the masses of carbon and hydrogen produced by combustion of the sample. 1 2.0 I g C I mol CO 2 I mol C = = 0. 1 2307 g C 0.0 1 0248 mOl c 0.45 1 g C0 2 I mol C 44. 0 1 g CO 2 I mol CO 2

(

J(

(

J

J(

J

(

(

J

J

1 .008 g H 1 mol H 2 0 2 mol H 0.006904 g H 0.0068495 mol H 1 mol H 1 8.0 1 6 g H 2 0 I mol H 2 0 The mass of chlorine is given by: 0.250 g sample - (0. 1 2307 g C + 0.006904 g H ) 0. 1 20 g CI The moles of chlorine are: 1 mol CI 0. 1 20 g C I 0.0033850 mol CI. This is the smallest number of moles. 3 5 .45 g CI Dividing each mole value by the lowest value, 0.0033850: 0.0033850 mol CI 0.0068495 mol H 0.0 1 0248 mol C 2 .02 mol H ' 1 .00 mol CI 3 .03 mol C' ' 0.0033850 0.0033850 0.0033850 These values are all close to whole numbers, thus the empirical formula is C 3 H 2 CI. The empirical formula has the following molar mass: (3 x 1 2.0 1 glmol) + (2 x 1 .008 g/mol) + (3 5 .45 glmol) 73 .496 glmol C 3 H 2 CI Dividing the given molar mass by the empirical formula mass: ( 1 46.99 glmol) / (73 .496 glmol) 2.00 Thus, the molecular formula is two times the empirical formula, C 6 H4C12 . Check: Carbon is about one-fourth the mass of carbon dioxide, or 0. 1 1 grams of C in the compound. The mass of hydrogen is very small, thus, most of the remaining mass of the compound (0.250 - 0. 1 1 0. 1 4) must be chlorine. Chlorine is about three times as heavy as carbon, thus, there must be three carbons for each chlorine. Also, check that the molar mass of the molecular formula agrees with the given molar mass. (6 x 1 2.0 1 glmol) + (4 x 1 .008 glmol) + (2 x 35 .45 glmol) 1 46.992 glmol 0.06 1 7 g H 2 0

(

J

=

=

=

=

=

=

=

=

=

=

=

3.7

Plan: In each part it is necessary to determine the chemical formulas, including the physical states, for both the reactants and products. The formulas are then placed on the appropriate sides of the reaction arrow. The equation is then balanced. a) Solution: Sodium is a metal (solid) that reacts with water (liquid) to produce hydrogen (gas) and a solution of sodium hydroxide (aqueous). Sodium is Na; water is H 2 0; hydrogen is H 2 ; and sodium hydroxide is NaOH . Na(s) + H 2 0(l) � H 2 (g) + NaOH(aq) is the equation. Balancing wil l precede one element at a time. One way to balance hydrogen gives: Na(s) + 2 H 2 0(l) � H 2 (g) + 2 NaOH(aq) Next, the sodium will be balanced: 2 Na(s) + 2 H 2 0(l) � H 2 (g) + 2 NaOH(aq) On inspection, we see that the oxygens are already balanced. Check: Reactants (2 Na, 4 H , 2 0) Products (2 Na, 4 H, 2 0) =

28

b ) Solution: Aqueous nitric acid reacts with calcium carbonate (solid) to produce carbon dioxide (gas), water (liquid), and aqueous calcium nitrate. Nitric acid is HN03 ; calcium carbonate is CaC0 3 ; carbon dioxide is CO2 ; water is H 2 0; and calcium nitrate is Ca(N0 3 ) 2 ' The starting equation is HN0 3 (aq) + CaC03 (s) � CO 2 (g) + H 2 0(l) + Ca(N0 3 Maq) Initially, Ca and C are balanced. Proceeding to another element, such as N , or better yet the group of elements in N03 - gives the following partially balanced equation: 2 HN03 (aq ) + CaC0 3 (s) � CO 2 (g) + H 2 0(l) + Ca(N0 3 )z(aq) Now, all the elements are balanced. Check: Reactants (2 H, 2 N, 9 0, I Ca, I C ) Products (2 H , 2 N, 9 0, 1 Ca, I C) c) Solution: We are told all the substances involved are gases. The reactants are phosphorus trichloride and hydrogen chloride, while the products are phosphorus trifluoride and hydrogen chloride. Phosphorus trifluoride is PF 3 ; phosphorus trichloride is PCI 3 ; hydrogen fluoride is HF; and hydrogen chloride is HC!. The initial equation is: P CI 3 (g) + HF(g) � PF 3 (g) + HCI(g) Initially, P and H are balanced. Proceed to another element (either F or CI); if we wi ll choose CI, it balances as: PCI 3 (g) + H F(g) � PF 3 (g) + 3 HCI(g) The balancing of the Cl unbalances the H, this should be corrected by balancing the H as: P C h (g) + 3 HF(g) � PF 3 (g) + 3 HCl(g) Now, all the elements are balanced. Check: Reactants (1 P, 3 Cl, 3 H , 3 F) Products ( I P, 3 Cl, 3 H , 3 F) d) Solution: We are told that nitroglycerine is a liquid reactant, and that all the products are gases. The fonnula for nitroglycerine is given. Carbon dioxide is CO2 ; water is H 2 0; nitrogen is N 2 ; and oxygen is O 2 • The initial equation is: C 3 HSN 3 0 9(l) � CO 2 (g) + H 2 0(g) + N 2 (g) + 0 2 (g) Counting the atoms shows no atoms are balanced. One element should be picked and balanced. Any element except oxygen wil l work. Oxygen wil l not work in this case because it appears more than once on one side of the reaction arrow. We wil l start with carbon. Balancing C gives: C 3 HSN 3 0 9 (l) � 3 CO 2 (g) + H 2 0(g) + N 2 (g ) + 0 2 (g) Now balancing the hydrogen gives: C 3 HsN 3 0 9 (l) � 3 CO2 (g) + 5 /2 H 2 0(g) + N 2 (g) + 0 2 (g) Similarly, if we balance N we get: C 3 HsN 3 0 9 ( l) � 3 CO2 (g) + 5 /2 H 2 0(g) + 3/2 N 2 (g) + 0 2 (g) Clearing the fractions by multiplying everything except the unbalanced oxygen by 2 gives: 2 C3 HSN 3 0 9 (l) � 6 CO 2 (g) + 5 H 2 0(g) + 3 N lCg) + 0 2 (g) This leaves oxygen to balance. Balancing oxygen gives: 2 C 3 HSN 3 0 9( l) � 6 CO 2 (g) + 5 H 2 0(g) + 3 N 2 (g) + 1 12 0 2 (g ) Again clearing fractions by multiplying everything by 2 gives: 4 C 3 HSN 3 0 9 ( l) � 12 CO 2 (g) + 10 H2 0(g) + 6 N 2 (g) + 0 2 (g) Now all the elements are balanced. Check: Reactants ( 1 2 C 20 H 1 2 N 36 0 ) Products ( 1 2 C 20 H 1 2 N 36 0) =

=

=

3.8

a) P lan: The reaction, like all reactions, needs a balanced chemical equation. The atomic mass of aluminum is used to determine the moles of aluminum. The mole ratio, from the balanced chemical equation, converts the moles of aluminum to moles of iron. Finally, the atomic mass of iron is used to change the moles of iron to the grams of iron.

29

Solution: The names and formulas of the substances involved are : iron(I1I) oxide, Fe203 , and aluminum, AI, as reactants, and aluminum oxide, AIz03 , and iron, Fe. The iron is formed as a liquid; all other substances are solids. The equation begins as : Fe203 (s) + AI(s) � AIz03 (s) + Fe(l) There are 2 Fe, 3 0, and 1 AI on the reactant side and 1 Fe, 3 0, and 2 AI on the product side. Balancing aluminum: Fe203 (s) + 2 Al(s) � AI20 3 (s) + Fe(l) Fe203 (s) + 2 AI(s) � AIz03 (s) + 2 Fe(l) Balancing iron: Check: reactants: (2 Fe, 3 0, 2 AI) products: (2 F e, 3 0, 2 AI) Using the balanced equation and the atomic masses, calculate the grams of iron: =

( 1 3 5 g AI )

(

(J

1 mol AI 26.98 g AI

2 mol Fe 2 mol AI

(J

5 5 . 85 g F e 1 mol Fe

J

=

279.457

=

27 9 g Fe

Check: The number of moles of aluminum produces an equal number of moles of iron. Iron has about double the mass of Al (2 x 27 54). Thus, the initial mass of aluminum should give approximately 2 x 1 3 5 g ( 270) of Iron. b) P lan: The grams of aluminum oxide must be converted to moles. The formula shows there are two moles of aluminum for every mole of aluminum oxide. Avogadro ' s number will then convert the moles of aluminum to the number of atoms. Solution: 23 6.022 x 1 0 atoms AI 1 mol AI2 03 2 mol Al 22 22 1 . 1 8 X 1 0 a toms Al l . l 8 1 25 x 1 0 ( 1 . 00 g AI2 03 ) 1 0 1 .96 g Al203 I mol Al203 I mol Al =

=

(

)(

)(

)

=

=

Check: The molar mass of aluminum oxide is about 1 00, so one mole of aluminum oxide is about 1 1 1 00 the mass of aluminum oxide. Doubling the moles of aluminum oxide gives the moles of aluminum atoms. Multiplying 22 Avogadro ' s number by 21 1 00 gives about 1 .2 x 1 0 atoms. 3.9

Plan: (a) Count the molecules of each type, and find the simplest ratio. The simplest ratio leads to a balanced chemical equation. The substance with no remaining particles is the limiting reagent. (b) Use the balanced chemical equation to determine the mole ratio for the reaction. Solution: (a) The balanced chemical equation is B2(g) + 2 AB(g) � 2 AB2(g) The limiting reagent is AB since there is a B2 molecule left over (excess). (b) Moles of AB2 from AB : (1 . 5 mol AB Moles of AB2 from B 2 : (1 . 5 mol B 2

{ 2 mol AB 2 \ 2 moi AB

{

2 mo1 AB 1 mol B 2

2

J

)

=

=

1 .5 mol AB2

3 . 0 mol AB2

Thus A B i s the Limiting reagent and only 1.5 mol of AB 2 will form. Check: The balanced chemical equation says twice as many moles of AB are needed for every mole of B2. Equal numbers of moles means AB is not twice as great as B2. Thus, AB should be limiting. 3.10

Plan: First, determine the formulas of the materials in the reaction and begin a chemical equation. Balance the equation. Using the molar mass of each reactant, determine the moles of each reactant. Use mole ratios from the balanced equation to determine the moles of aluminum sulfide that may be produced from each reactant. The reactant that generates the smaller number of moles is limiting. Change the moles of aluminum sulfide from the limiting reactant to the grams of product using the molar mass of aluminum sulfide. To find the excess reactant amount, find the amount of excess reactant required to react with the limiting reagent and subtract that amount from the amount given in the problem.

30

Solution: The balanced equation is: 2AI(s) + 3 S(s) � AI 2 S3(s) Determining the moles of product from each reactant: I mol A1 2 S3 I mol AI ( 1 0.0 g AI ) = 0. 1 8532 mol A I 2 S3 26.98 g AI 2 mol AI

(

(

)( )(

)

)

1 mol S 1 mol A1 2 S3 = 0. 1 55909 mol AI 2 S 3 32.07 g S 3 mol AI Sulfur produces less product, thus it is limiting. The moles of product formed are calculated from the moles and the molar mass. 1 50. 1 7 g AI 2 S3 = 23.4 1 3 = 23.4 g AIzS3 (0. 1 55909 mol A1 2 S3 ) 1 mol AI 2 S3 The mass of aluminum used in the reaction is now determined : ( 1 5 .0 g S { I mol S 2 moI AI 26.98 g AI = 8 .4 1 258 g Al used \ 32.07 g S 3 mol S I mol AI Subtracting the mass of aluminum used from the initial aluminum gives the mass remaining. Un-reacted aluminum = 1 0.0 g - 8.4 1 285 g = 1 .5872 = 1 .6 g A I e x c e s s Check: The reactant ratios in the balanced chemical equation are the same as the mass ratio given in the problem. Thus, the substance with the larger molar mass should be limiting. This is the sulfur. An additional check is based on the aluminum calculation. If the sulfur were not the limiting reactant, the "remaining" aluminum would have been a negative number. ( 1 5.0 g S)

J

(

)(

3. 1 1

Plan : Determine the formulas, and then balance the chemical equation. The grams o f marble are converted to moles, a mole ratio (from the balanced equation) gives the moles of CO2 , and finally the theoretical yield of CO 2 is determined from the moles of CO2 and its molar mass. Solution : The balanced equation: CaC03(s) + 2 HCI(aq) � CaCI 2 (aq) + H 2 0(l) + CO 2 (g) The theoretical yield of carbon dioxide: I moi CaC03 44.0 1 g C0 2 I mol CO 2 = 4.39704 g C0 2 ( 1 0.O g Cac o3 ) 1 mol CO 2 1 00.09 g CaC03 1 mol CaC03 The percent yield: 3 .65 g CO 2 actual yield ( 1 00% ) = ( 1 00%) = 83.0 1 04 = 83.0 % 4.39704 g CO 2 theoretical yield Check: Initially, there are about 1 0/ 1 00 moles of marble (mass of marble/molar mass). Theoretically, about 1 1 1 0 the molar mass of carbon dioxide should form.

)

(

J

J(

J(

(

3. 1 2

)

)(

(

J

Plan: Multiply the molarity by the liters to determine the moles. Solution : 0.50 Ol 84 m L ) = 0.042 mol KI

(

�

KJ) [ \o:t }

Check: The molarity is 0.5, this ratio impl ies the moles should be 0.5 (84 mL) = 42 mmole (0.042) 3. 1 3

Plan: Use the molar mass to change the grams to moles. The molarity may then be used to convert to volume. Solution : 1 L 1 mol C 1 2 H 22 0 1 1 = 0. 1 1 95 1 = 0.1 20 L ( 1 35 g C 1 2 H 22 0 l d 342 .30 g C 1 2 H 22 0 1 1 3.30 mol C 1 2 H 22 0 I I Check: All units cancel except the volume units requested. The mass given is about 1 13 mole and the molarity term gives another 1 /3 ratio, thus the answer should be about ( 1 13 ) ( 1 13 ) = 1 19 L .

(

J

(

J

31

3.14

Plan: Determine the new concentration from the dilution equation ( Mconc)(Vconc) = ( Mdil)(Vdi l ) . Convert the molarity (moUL) to glm L in two steps (one-step is moles to grams, and the other step is L to mL.) Solution : ( m3 ) = M eo nc Vc o n e M M dil Vd m3 =

( 7. 5 0 M) 25. 0 500. ( 0. 3 75 L J ( 98. 09 (8) 0.10 0.10 3 (0. 0 )( 78.00 i1

=

0.375 J [ ) 0.036784 25/500 1120. 3. 1 5 3.4 3 3 ) 3. 84615 1 0 3. 8 )(

g H 2 S0 4 1 O -3 L mol H 2 S0 4 = I mL I mol H 2 S0 4 I = Check: The dilution wi ll give a concentration lower by calculation gives ( 1 /20) ( 1 00) (0.00 1 ) = 0.04.

3.15

3.16

= 3.68 x

1 0-

2

g/mL solution

Checking the calculation by doing a rough

P lan: The problem should be solved like Sample Problem to facilitate the comparison. A new balanced chemical equation is needed. A g sample of aluminum hydroxide, for direct comparison, is converted to moles. The mole ratio from the balanced equation converts from moles of AI(OH )3 to moles of HCI. F inally, the moles of acid reacting with the AI(OH ) 3 are compared to the x 1 0-3 mol of HCI that was shown in the Sample Problem to react with g of Mg(OH) 2 . Solution : Balanced equation: HCI(aq) + AI(OH Ms) � AICI 3 (aq) + H 2 0(l) I mol AI(OH) 3 mol H CI 3 X X 1 0- mo l HCI = -3 = 1 g AI(OH h g AI(OH ) 3 1 mol AI(OH ) 3 Magnesiu m hydroxide is less effective than aluminum hydroxide because it reacts with fewer x 1 0-3 ) moles of HCI. Check: The greater molar mass of AI(OH ) 3 is about and this compound has a larger mole ratio from the balanced equations. This gives x -3 ) = x 1 0-3 .

(3.4 10 (6/8) (1. 56/8,) 3. 8

3/2

(3. 4

a) Plan: The formula of lead( U ) acetate is needed. The moles of compound are converted to moles of lead; this value times the inverse of the molarity gives the volume of the solution. Solution : The formula is Pb(C 2 H 3 0 2 ) 2 which may be written as Pb(CH3COO) 2 . 1 mol Pb(C 2 H 3 0 2 h I 2 mol Pb + ) = = 0.267 L ( 2 mol Pb(C 2 H 3 0 2 h 1 mol Pb + Check: A reverse calculation may serve as a check (complete units are unnecessary): . m OI 1 m O I L = 0.4005 = mol L I mol b) Plan: The formulas are used for the balanced chemical equation. The molarity and the volume of the sodium chloride solution are used to determine the moles ofNaCI. Either the lead or the chloride ion is limiting - the one producing the fewer moles of product is limiting. Convert the lower number of moles of product to grams of product. Solution: Balanced reaction: Pb(C 2 H 3 0 2 Maq) + N aCI(aq) � PbCI 2 (s) + NaC 2 H 3 0 2 (aq) Because of the l : l ratio, there will be mol of PbCI 2 produced from mol of Pb 2+. The moles of PbCI 2 produced from the NaCI are: 1 O -3 mol NaCI --I mol PbCI 2 = mol PbCI 2 mol NaCI Im L The NaCI is limiting. The mass of PbCI 2 may now be determined using the molar mass. g PbCI 2 mol PbCI 2 ) = = 5 9.1 g PbC h mol PbCI 2

0.400

[

(0.267 ) ( 1 5 ) ( J

) ( 1. 5 0

(0. 2 125

) 0. 2 66667

0.400

2

( 3.40 1

L

0.400 2 J [ LL ) (125 mL ) ( 2 J 0.2 125 ( 278.1 J 59.0962 1 32

0.400

Check: There are 0.400 mol of lead ions; they wi ll require 2 x 0.400 0.800 mol of chloride ion. The volume of NaCI solution needed to supply the chloride ions is (0. 800/3 .4) 0.235 L (235 mL). The NaCI must be limiting because less than 235 mL are suppl ied. =

=

END-OF-C HAPTER PROBLEM S

3.2

Plan: The formulas are based on the mole ratios of the constituents. Avogadro's number al lows the change from moles to atoms. Solution : 1 2 mol C a) Moles of C atoms ( 1 mol Sucrose ) 1 2 mol C I mol C l2 H 22 0 " 2 6.022 x 1 0 3 C atoms 12 mol C 24 7.226 x 1 0 C atoms b) C atoms ( I mol C ' 2 H 22 0 , , ) 1 mol C ' 2 H 22 0" I mol C Plan: It is possible to relate the relative atomic masses by counting the number of atoms. Solution : a) The element on the left (green) has the higher molar mass because only 5 green balls are necessary to counterbalance the mass of 6 yel low balls. Since the green ball is heavier, its atomic mass is larger, and therefore its molar mass is larger. b) The element on the left (red) has more atoms per gram. This figure requires more thought because the number of red and blue balls is unequal and their masses are unequal. If each pan contained 3 balls, then the red balls would be lighter. The presence of six red balls means that they are that much I ighter. Because the red ball is l ighter, more red atoms are required to make 1 gram. c) The element on the left (orange) has fewer atoms per gram. The orange balls are heavier, and it takes fewer orange balls to make 1 gram. d) Neither element has more atoms per mole. Both the left and right elements have the same number of atoms per mole. The number of atoms per mole (6.022 x 1 0 23 ) is constant and so is the same for every element.

(

=

=

3 .6

3.7

(

J[

J

=

)

=

Plan: Locate each of the elements on the periodic table and record its atomic mass. The atomic mass of the element times the number of atoms present in the formula gives the mass of that element in one mole of the substance. The molar mass is the sum of the masses of the elements in the substance. Solution : a) The molar mass, M, is the sum of the atomic weights, expressed in g/mol : Sr 87.62 g Sr/mol Sr(OH ) 2 0 = (2 mol 0) ( 1 6.00 g O/mol 0) 32.00 g O/mol Sr(OH) 2 2.0 1 6 g H/mol Sr(0H)2 H (2 mol H ) ( 1 .008 g Hlmol H ) =

=

=

=

=

=

1 2 1 .64 g/mol of S r(OH) 2

b) M (2 mol N) ( 1 4.0 1 g N/mol N ) + ( 1 mol 0) ( 1 6.00 g O/mol 0) 44.02 g/mol of N 2 0 c) M ( I mol Na) (22.99 g Nalmol Na) + ( 1 mol CI) (35.45 g Cllmol Cl) + (3 mol 0) ( 1 6.00 g O/mol 0) 1 06.44 g/mol of NaCI0 3 d) M (2 mol Cr) (52.00 g Cr/mol Cr) + (3 mol 0) ( 1 6.00 g O/mol 0) 1 52.00 g/mol of C r2 0 3 =

=

=

=

=

=

3.9

Plan: Locate each of the elements on the periodic table and record its atomic mass. The atomic mass of the element times the number of atoms present in the formula gives the mass of that element in one mole of the substance. The molar mass is the sum of the masses of the elements in the substance. Solution: a) M ( 1 mol Sn) (I 1 8.7 g Sn/mol Sn) + (2 mol 0) ( 1 6.00 g O/mol 0) 1 50.7 g/mol of S n0 2 b) M ( l mol Ba) ( 1 37.3 g Balmol Ba) + (2 mol F) ( 1 9.00 g Flmol F) 1 75.3 g/mol of BaF 2 c) M = (2 mol AI) (26.98 g Allmol AI) + (3 mol S) (32.07 g Simol S) + ( 1 2 mol 0) ( 1 6.00 g O/mol 0) =

=

=

=

=

342 . 1 7g/mol of AI z ( S 04) 3

d) M ( I mol Mn) (54.94 g M n/mol Mn) + (2 mol CI) (35 .45 g Cllmol C I) =

33

=

1 25.84 g/mol of M nCI z

3. 1 1

Plan: The mass of a substance and its number of moles are re lated through the conversion factor of M, the mol ar mass expressed i n g/mol . The moles of a substance and the number of entities per mole are rel ated by the conversion factor, Avogadro ' s number. Solution : a) M of K M n04 = 3 9 . 1 0 + 54.94 + (4 x 1 6 . 00) = 1 5 8 .04 gimol of KMn04 Mass of KM n04 =

( 0 . 5 7 mol KMn04 )

(

1 5 8 . 04 g KMnO 4 1 mol K M n 0 4

)

= 90.08 = 9.0

x

I

1 0 g KM n0 4

b) M of Mg(NO) 2 = 2 4 . 3 1 + (2 x 1 4 . 0 I ) + (6 x 1 6 . 00) = 1 48 . 3 3 g/mol Mg(N03)2 Moles 0 f ° atoms =

(8. 1 8 g

)

Mg ( N O 3 ) 2

(

1 m o l Mg(N03 ) 2 1 48 . 3 3 g M g ( N 0 3 h

)(

6 mol ° atoms 1 mol Mg( N03 h

= 0 . 3 3 0 8 8 = 0.33 1 mol 0 atoms c ) M of C u S 0405 H20 = 63 . 5 5 + 3 2 . 07 + (9 x 1 6 .00) + ( l O x 1 . 008) = 249 .70 g/mol (Note that the waters of hydration are incl uded in the molar mass . )

(

3

o atoms = 8 . 1 x 1 O - g C u c mPd = 1 .758 1 x 1 0 3. 1 3

20

= 1 .8

X

)

10

(

20

1 mol Cu C mp d 249 .70 g Cu C mpd

)(

9 mol ° atoms 1 mol Cu Cmpd

0 atoms

)[

6 . 022 x 1 0

23

0 atoms

1 mol ° atoms

]

P lan: Determi n e the molar mass of each substance, then perform the appropri ate molar conversions. Solution : a) M of M nS04 = ( 5 4 . 94 g M n/mol M n ) + ( 3 2 . 0 7 g S/mo l S ) + [(4 mol 0) ( 1 6 . 0 0 g O/mo l 0)] = 1 5 1 . 0 1 gimol of M n S 04 M ass of M n S 04 = ( 0 . 64 mol MnSO 4 )

(

1 5 1 .0 \ g MnSO 4 I moi MnS0 4

)

= 96.65 = 97 g M n S 04

b) M of Fe(C l04)3 = ( 5 5 . 8 5 g Fe/mol Fe) + [(3 mol C I ) ( 3 5 .45 g C l/mol C I ) ] + [( 1 2 mol = 3 54 . 2 0 gimol of Fe(C I 04)3 Moles Fe( C I 04») = ( 1 5 . 8 g Fe(CI0 4 ) 3 )

(

1 mol Fe(C I 0 4 ) 3 3 54.20 g Fe(CIO 4 ) 3

0)

= 1 . 74 1 26 x 1 0

24

(

)[

)(

= 1 .74

X

10

24

( 1 6.00 g O/mol

0)]

)

2 = 0 . 044608 = 4.46 x 1 0- mol Fe(CI0 4h c) M of N H4N02 =[(2 mol N ) ( 1 4 . 0 1 g N/mol N)] + [(4 mol H ) ( 1 .008 g H/mol H ) ] + [ ( 2 m o l 0) ( 1 6 . 00 g O/mol 0 ) ] = 64 .05 gimol of N H 4N 02 23 1 mOI 2 mol N 6 . 022 x 1 0 N atoms N atoms = 92 . 6 g N H 4 N O ? - 64.05 g 1 mol N H 4 N 0 2 1 mol N

3. 1 5

)

]

N atoms

P l an : The formula o f each compound must b e determined from its name. The molar mass for each formula comes from the formula and atomic masses from the peri odic table. Avogadro ' s number i s also necessary to find the number of particles. S o l uti o n : 2 a) C arbonate i s a polyatomic a n i o n with t h e formu la, C O ) -. C opper (J) indicates C u +. The correct formula for this ionic compound is C U2CO). M of C u2C 03 = (2 x 63 . 5 5 ) + 1 2 . 0 1 + (3 x 1 6 . 00) = 1 8 7 . 1 1 gimo l Mass C U2CO) =

(8.4 1

mol C U 2 C03

)

(

1 8 7 . 1 1 g Cu 2 CO 3

I

mol C U 2 C03

)

= 1 5 7 3 . 5 9 5 = 1 .57

x

3 1 0 g CU 2 C03

b ) D i n i trogen pentaox ide has the formula N20S ' Di- indicates 2 N atoms and penta- i ndicates 5 ° atoms. M of N20s = ( 2 x 1 4 . 0 \ ) + (5 x 1 6 .00) = 1 08 . 02 gimol M ass N20S =

( 2 . 04

X

10

21

N 2 0S mOlecu les

= 0 . 3 65926 = 0.366 g N 2 0S

)

[

34

1

�3O l N 2 0S

6 . 02 2 x 1 0

N 2 0S molecules

J(

1 08 . 02 g N 2 0S 1 mol N 2 0S

)

c) The correct formula for this ionic compound is NaCI04. There are Avogadro ' s number of entities (in this case, formula units) in a mole of this compound . .M ofNaCI04 = 22.99 + 3 5 .45 + (4 x 1 6.00) = 1 22 .44 glmol Moles NaCI04 = ( 5 7 . 9 g NaCI02 ) FU = formula units FU NaCI04 = ( 5 7 . 9 g NaCI02 )

(

(

1 mol NaCIO 4

1 22 .44 g NaCI04

1 mol NaCI0 4

1 22 .44 g NaCI04

J[

J

= 0.47288 = 0.473 mol NaCl04

3 6.022 x 1 02 FU NaC I04

I

mol NaCl04

]

=

23 2 . 8477 1 1 5 x 1 0 = 2.85 X 10 23 F U NaCl04 d) The number of ions or atoms is calculated from the formula units given in part c. Note the unrounded initially calculated value is used to avoid intermediate rounding. 2 . 8477 1 1 5 x 1 0

2 . 8477 1 1 5 x 1 0

2 . 8477 1 1 5 x 1 0 2 . 8477 1 1 5 x 1 0

3. 17

23 23 23 23

mol NaCI04

mol NaCI04

mol NaCl04 mol NaCl04

[ [ ( (

1 Na+ lon 1 FU NaCI04

I CIO; Ion

I

FU NaCl04 1 Cl atom

1 FU NaCI04 4 0 atoms 1 FU NaCI0 4

]

]

J J

+ .

= 2.85 x 10 23 Na Ions = 2.85

X

1 0 23 Cl04- ions

= 2.85 x 10 23 CI atoms = 1 . 1 4 x 10

24

0 atoms

P lan: Determine the formula and the molar mass of each compound. The formula gives the number of atoms of each type of element present. Masses come from the periodic table. Mass percent = (total mass of element in the substancelmolar mass of substance) x 1 00. Solution: a) Ammonium bicarbonate is an ionic compound consisting of ammonium ions, NH/ and bicarbonate ions, HC0 3The formula of the compound is NH4HC0 3 .M of NH4HC03 = ( 1 4. 0 1 glmol) + (5 x 1 .008 glmol) + ( 1 2 .0 1 glmo!) + (3 x 1 6. 00 glmo!) = 79.06 glmol NH4HC0 3 In 1 mole of ammonium bicarbonate, with a mass of 79.06 g, there are 5 H atoms with a mass of 5 .040 g. (5 mol H ) (1 .008 g / mol H) x 1 00% = 6.374905 = 6.375% H 79.06 g / mol NH4 HC03 •

b) Sodium dihydrogen phosphate heptahydrate is a salt that consists of sodium ions, Na+, dihydrogen phosphate ions, H2P04-, and seven waters of hydration. The formula is NaH2P04·7H20. Note that the waters of hydration are included in the molar mass . .M of NaH2P04·7Hp = (22.99 glmol) + ( 1 6 x 1 .008 glmol) + (30.97g1mol) + ( 1 1 x 1 6.00 glmol) = 246.09 glmol NaH2P04°7H20 In each mole of NaH2P04·7H20 (with mass of 246.09 g), there are 1 1 x 1 6.00 glmol or 1 76.00 g of oxygen.

( 1 1- mol 0 ) ( 1 6.00 g / mol 0 ) -'-------'--'-------'-x 1 00 % = 7 1 . 5 1 855 = 71 .52% 0 246.09 g l mol

35

3. 1 9

Plan : Determine the formula of c i splat i n from the figure, and then calculate the molar mass from the formula. The molar mass i s necessary for the subsequent calculati ons. Solution : The form ula for c i splatin i s Pt(C IMNH3) 2 .M of Pt( C I M N H 3 h = 1 95 . 1 + (2 x 3 5 .45) + (2 x 1 4 .0 1 ) + (6 x 1 . 008) = 3 0 0 . 1 glmol

. . latm ( 2 8 5 . 3 g clsp

.

a) Moles cisplatm =

b)

H

a

to ms =

3.2 1

=

(0 . 98 m o l c l.

3 . 540936

x

10

spla

24

.

tm

= 3.5

) X

(

(

I mol ci splatin

.

. J(

.

300. 1 g clsp latm

6 mol H . 1 mol clsplatm 1 0 24 H atoms

J

6 . 02 2

. · I atm = 0 . 950683 1 = 0 . 950 7 mo I CISP

x

10

23 H

1 mol H

atoms

)

Plan: Determine the formulas for the compounds where needed. Determine the molar mass of each formula. Calculate the percent nitrogen by dividing the mass of nitrogen i n a mo l e of compound by the molar mass of the compound, and multiply the result by 1 00%. Then rank the values. Soluti o n : Mo lar Mass Cg/mol) Name Formu la 101.1 1 KN03 Potassium n itrate 80.05 N H4N03 Ammonium n itrate 1 32. 1 5 (NH4)2S04 Ammon i u m sulfate 60.06 U rea CO(NH2)2 Calcul ating the nitrogen percentages :

( 1 mol N ) ( 1 4 . 0 1 g / mol N )

Potassium nitrate

1 0 1 .l 1 g / mol

( 2 mol N ) ( 1 4 . 0 1 g / mol N )

Ammon i u m n itrate

80.05 g / mo l

)

(2 m o l N ( 1 4 . 0 1 g/mol N

Ammon i u m sulfate

1 3 2 . 1 5 g/mol

)

x

x

1 00 = 1 3 . 8 5 6 1 96 = 13.86% N

x

1 00 = 3 5 . 003 1 2 3 = 35.00% N

1 00

( 2 mol N ) ( 1 4 . 0 1 g / mol N )

-'-----'--'------"x

U rea

3 .22

)

60.06 g/ mol

= 2 1 .203 1 8 = 2 1 .20% N

1 00 = 4 6 . 65 3 3 = 46.65 % N

Plan: The volume must be converted from cubic feet to cubic centi meters (or vice versa) . The vol ume and the density w i l l give you mass, and the mass with the molar mass gives you mo les. P art (b) requi res a conversion fro m cubic dec i meters, i n stead of cubic feet, to cubic centi m eters. The density al lows you to change these cubic centimeters to mass, the molar mass al lows you to find moles, and finally Avogadro ' s number al lows you to make the last step. Solution : The molar mass of galena is 2 3 9 . 3 g/mol . 3 3 ( 1 2 in) ( 2 . 54 Cm) 7 46 g PbS 1 mol PbS 3 a ) Moles P b S = l . 00 ft PbS 3 3 3 2 3 9 . 3 g PbS ( 1 ft) ( I in) 1 cm 8 8 2 . 7 5 66886 b ) Lead atoms 3 (0. 1 m) 3 1 . 00 dm PbS 3 ( 1 dm) =

=

(

{ \

= 1 . 8773 1

)(

{\

(

x

10

=

883 mol PbS

)[

25

3 ( l cm) 2 3 ( 1 0 - m)

= 1 .88

X

)(

7 .46 g PbS 3 I cm

)( .

)(

)(

J(

1 mol PbS 2 3 9 . 3 g Pb S

1 0 25 Pb atoms

36

I mol Pb I mol PbS

)(

J

6 . 02 2

x

10

23

Pb atoms

I mo l Pb

)

3 . 24

P lan: Remember that the molecular formula te l l s the actual number of moles of each e l e ment i n one mo le of compound. Soluti o n : a) No, y o u c a n obtain t h e empirical formula from the number of m o l e s of e a c h type of atom i n a compound, but not the mo lecular formula. b ) Yes, you can obtain the mo lecular formu la from the mass percentages and the total number of atoms. Solution P l an� 1 ) Assume a 1 00 . 0 g samp le and convert masses (from the mass% of each element) to moles using molar mass. 2 ) I dentity the e lement with the lowest number of moles and use this number to divide i nto the number of moles for each e l e ment. You now have at least one elemental mole ratio (the one with the sma l lest number of moles) equal to 1 . 00 and the remai n i ng mole ratios that are l arger than one. 3) Examine the numbers to determine i f they are whole numbers. I f not, multi p l y each number by a whole n u mber factor to get whole numbers for each el ement. You w i l l have to use some j udgment to decide when to round. 4) Write the empirical formula usi ng the who l e numbers from step 3 . 5 ) Chec k the total n umber o f atoms i n the empirical formula. I f i t equals the total n umber o f atoms given then the empirical formula i s also the molecular formu la. I f not, then divide the total number of atoms given by the total n umber of atoms in the empirical formula. This should give a whole number. M ultiply the n u mber of atoms of each el ement in the empirical formul a by this whole number to get the mo lecular formula. I f you do not get a whole number when you divide, return to step 3 and revise how you multipl ied and rounded to get whole numbers for each element. c) Yes, you can determine the molecular formula from the mass percent and the n u mber of atoms of one element in a compound. S o lution plan : I ) Fol low steps 1 -4 i n part b. 2 ) C ompare the n u mber of atoms given for the one element to the number in the emp i rical formula. Determi ne the factor the number i n the emp irical formula must be multi p l i ed by to obtain the given n u mber of atoms for that e lement. M ultip ly the empirical formula by this number to get the molecular formula. d) No, the mass % will only lead to the empirical formula. e) Yes, a structural formula shows all the atoms i n the compound. S o l ution plan: Count the number of atoms of each type of e lement and record as the number for the molecular formula.

3 .25

Plan: Exami n e the number of atoms of each type in the compound. Divide al l atom n umbers by any common factor. The final answers must be the l owest whole-number values. S o l ution: a) C2H4 has a ratio of 2 carbon atoms to 4 hydrogen atoms, or 2 :4 . This ratio can be reduced to I :2, so that the empirical formula is CH 2 . The empirical formula mass i s 1 2 . 0 1 + 2( 1 . 0 0 8 ) 1 4.03 g/mol. b ) The ratio of atoms i s 2 : 6 : 2 , or 1 : 3 : I . T h e empirical formula i s CH 3 0 a n d i t s empirical formula mass i s 1 2 . 0 1 + 3 ( 1 .008) + 1 6 .00 3 1 .03 g/mot. c) S ince, the ratio of e lements cannot be further reduced, the molecular formula and empirical formula are the same, N 2 0S' The formula mass is 2 ( 1 4 . 0 1 ) + 5 ( 1 6.00) 1 08.02 g/mot. d) The ratio of e lements i s 3 atoms of barium t o 2 atoms of phosphorus t o 8 atoms of oxygen, or 3 : 2 : 8 . This ratio cannot be further reduced, so the empirical formula is also Ba 3 (P0 4b with a formula mass of 3 ( 1 3 7 . 3 ) + 2(30.97) + 8 ( 1 6 . 0 0 ) 60 1 . 8 g/mol. e) The ratio of atoms i s 4: 1 6, or 1 :4. The empirical formula i s TeI4, and the formula mass is 1 27 . 6 + 4( 1 2 6 . 9 ) 635.2 g/mol. =

=

=

=

=

3.27

P lan: Determine t h e molar mass o f each empirical formula. T h e molar mass of each compound divided b y its empirical formula mass gives the number of ti mes the empirical formula i s within the mo lecule. M ultiply the emp irical formula b y the number of times the empirical formula appears to get the molecular formula.

37

Solution : Only approximate whole number values are needed. a) CH2 has empirical mass equal to 1 4.03 glmol

(

42.08 g/mol 1 4.03 g / mol

)

=3

Multiplying the subscripts in CH2 by 3 gives C3H6 b) NH2 has empirical mass equal to 1 6 .03 glmol

(

32.05 g/mol 1 6 .03 g / mol

)

=2

Multiplying the subscripts in NH2 by 2 gives N 2 H4 c) N02 has empirical mass equal to 46.0 1 glmol

(

92.02 g/mol 46. 0 1 g / mol

)

=2

Multiplying the subscripts in N02 by 2 gives N 2 04 d) CHN has empirical mass equal to 27.03 glmol

(

)

1 3 5 . 1 4 g/mol = 5 27.03 g/mol

Multiplying the subscripts in CHN by 5 gives CsHsNs 3 .29

Plan: The empirical formula is the smallest whole-number ratio of the atoms or moles in a formula. All data must be converted to moles of an element. Using the smallest number of moles present, convert the mole ratios to whole numbers. Solution : a)

(

0.063 mol CI 0.063 mol C l

J

(

= I

0.22 mol 0 0.063 mol Cl

J

= 3.5

The formula is Cl , 0 3 .5, which in whole numbers (x 2) is CIz07 b) ( 2 .45 g Si )

(

(

1 mol Si 28 .09 g Si

0.08722 mol Si 0.08722 mol Si

J

J

( 1 2.4 g CI )

= 0.08722 mol Si

(

= 1

0.349788 mol Cl 0.08722 mol Si

The empirical formula is SiCI4• c) Assume a 1 00 g sample and convert the masses to moles.

( 1 00 g )

(

(

27.3% C 1 00%

2.273 1 mol C 2.273 1 mol C

J

J(

I mol C 1 2. 0 1 g C

J

(

4.5438 mol O 2.273 1 mol C

The empirical formula is CO 2 • 3.3 1

1 mol Cl 3 5 .45 g CI

J

)

= 0.349788 mol Cl

=4

( 1 00 g )

= 2.273 l moI C

= I

J

(

(

72.7% 0 1 00%

J(

1 mol 0 1 6.00 g 0

)

= 4.5438 mol 0

=2

P lan: The balanced equation for this reaction is: M(s) + F2(g) � MF2(s) since fluorine, like other halogens, exists as a diatomic molecule. The moles of the metal are known, and the moles of everything else may be found from these moles using the balanced chemical equation. Solution : a) Determine the moles of fluorine. Moles

F = ( 0.600 mol M )

(

2 mol

F

1 mol M

J

= 1 .20 mol F

38

F) ( 19.1 00 F ) = 40.=0 40.0

b) The grams o f M are the grams of M F2 m i n us the grams of F present. Grams M

=

46. 8

(1.20 = 24.0 0. 600

g (M + F)

-

mol

g

mol F

c) The molar mass i s needed to identify the el ement. M o l ar mass of M gMI mol M The metal with the c losest m o l ar mass to

3. 3 3

100

24.0 g M

g I mol g/mol i s calci u m .

P l an : Assume grams o f cortisol s o the percentages are n umerically equivalent t o the masses of each element. Convert each of the masses to moles by using the molar mass of each element involved. D i v i de all moles by the lowest number of moles and convert to whole numbers to determ ine the empirical formula. The empirical formula mass and the given molar mass w i l l then re late the empirical formula to the molecular formula. Solution :

(69. 6 ) ( 12.1 0 1 ) = 5. 7952 = (8. 3 4 ) ( 1.1008 . ) = 8.2738 = (22.1 ) ( 16.1 00 ) 1. 3 8125 738 ) 6. 00 ( 1.1.33 8125 952 J = 4.20 ( 1.8.328125 8125 ) = 1.00 ( 1.5.378125 5. 21 (12. 0 1 30 (1. 008 5 (16. 00 362.45

M o les C

mol C

g C

=

Moles H

g H

Moles °

g 0

mol

mol C

g C

mol H

mol

g H

mol °

mol °

=

g °

C

H

mol

H

mol 0

=

mal O

mol °

maI O

4.20

The carbon value i s not close enough to a whole n umber to round the value. The smallest number that may be multiplied by to get c l ose to a whole number i s (You may wish to prove thi s to yoursel f. ) A l l three ratios need to be multi p l i e d by five to get the empirical formula Of C2 1 H3 0 0S . The empirical formula mass i s : g C/mo l ) + g H/mol ) + g O/mo l ) glmol The empirical formula mass and the molar mass given are the same, so the empirical and the molecular formulas are the same . The molec u l ar formula is C 2 1 H 30 0S. =

3. 34

P l an : I n combustion analysis, fi nding the moles o f carbon and hydrogen i s rel atively s i mp l e because all o f the carbon present in the sampl e is found in the carbon of CO2, and all of the hydrogen present in the samp l e i s found i n the hydrogen of H 20 . The moles of oxygen are more difficult to fi nd, because additional O2 was added to cause the combustion reacti o n . The masses of CO2 and H20 are used to find both the mass of C and H and the moles of C and H . S ubtracting the masses of C and H from the mass of the sampl e gives the mass of O . Convert the mass of ° to moles of 0. Take the moles of C , H, and ° and divide by the smallest value, and convert to a who l e number t o g e t the empirical formula. Determ ine t h e empirical formula m a s s and compare i t to t h e mol ar mass given i n the prob lem to see how the empirical and mo lecular form ulas are rel ated. F i nally, determine the molecular formula. Solution: ( There i s n o intermediate ro unding. ) I n i tial mole determinati o n : Moles C

M o les H

( 44. 0 1 1 )( 18.02 = (0.0 10202 C ) ( 12.1 0 1 = (0.020422 ) ( 1. 008

= (0.449 = (0. 184

g CO2

)

g H 20

I

mol CO 2 g CO2

mo l H 2 0 g H20

Now determi ne the masses of C and H : Grams C

Grams H

mol

mol H

g C

mol C

I

) 0.0 10202 J( J ( 1 2 J = 0. 020422 ) = 0.122526 ) = 0.020585 I

I

mol C

mo l H

mol

H20

gC

g H

mol H

=

mol CO2

gH

39

mol C

mol H

- 0.122526 - 0.020585 0.0 16389 (0.0 16389 ( 16.1 00 J 0.0010243 0.0.00010243 20422 J 19.9 20 ( 0.0. 00010243 ( 9. 9 6 10 010243 J J 10 (12. 0I 20 (1.008 1 (16. 00 156.26

Determine the mass and then the moles of 0: g (C, H, and 0) gC gH= gO mol 0 = mol 0 g 0) Moles 0 = g0 Divide by the smal lest number of moles: (Rounding is acceptable for these answers.) mol O mol H mol C =I = mol ° mol ° mol ° Empirical formula = C , oH 2 0 0 Empirical formula mass = g C/mol) + g H/mol) + g O/mol) = glmol The empirical formula mass matches the given molar mass so the empirical and molecular formulas are the same. The molecular formula is C IO H 20 0 .

0.1595

10202 ( 0.0.00010243

3. 3 6 3. 3 7

=

=

=

Plan: Examine the diagram and label each formula. We wil l use A for red atoms and 8 for green atoms. Solution : The reaction shows A 2 and 8 2 molecules forming AB molecules. Equal numbers of A 2 and 8 2 combine to give twice as many molecules of AB. Thus, the reaction is A 2 + 8 2 4 AB. This is the answer to part b.

2

Plan: Balancing is a trial and error procedure. Do one blank/one element at a time. Solution : a) lQ Cu(s) + _ Ss(s) 4 � Cu 2 S(s) Hint: Balance the S first, because there is an obvious deficiency of S on the right side of the equation. Then balance the Cu. b) P 4 0 , o (s) + Q H 2 0( 1) 4 :! H 3 P04 ( 1) Hint: Balance the P first, because there is an obvious deficiency of P on the right side of the equation. Balance the H next, because H is present in only one reactant and only one product. Balance the ° last, because it appears in both reactants and is harder to balance. c) _B 2 0 3 (s) + Q NaOH(aq) 4 2. Na3 B0 3 (aq) + J. H 2 0( 1) Hint: Oxygen is again the hardest element to balance because it is present in more than one place on each side of the reaction. If you balance the easier elements first ( 8 , Na, H), the oxygen will automatically be balanced. d) 2. CH 3 N H 2 (g) + 0 2 (g) 4 2. CO 2 (g) + l H 2 0(g) + _N 2 (g) ) CH -± 3 N H 2 (g + 2. 0 2 (g) 4 :! CO 2 (g) + lQ H 2 0(g) + 2. N 2 (g ) Hint: You should balance odd/even numbers of oxygen using the "half' method, and then multiply al l coefficients by two. _

9/2

3. 3 9

Plan: The names must first be converted to chemical formulas. The balancing is a trial and error procedure. Do one blank/one element at a time. Remember that oxygen is diatomic. Solution : a) :! Ga(s) + J. 0 2 (g) 4 2. Ga2 0 3 (s) b) 2. C 6H ' 4 ( 1) + l2. 0 2 (g) 4 .ll CO 2 (g) + H 2 0(g) c) J. CaCI 2 (aq) + 2. Na3 P0 4 (aq) 4 Ca3 (P04 Ms) + Q NaCI(aq)

14

3.4 1

Plan : Convert the ki lograms o f oxygen to the moles o f oxygen. Use the moles o f oxygen and the mole ratios from the balanced chemical equation to determine the moles of KN0 3 . The moles of KN0 3 and its molar mass will give the grams. Solution : 3 mol KN0 3 mol 02 g 3 a) Moles KN0 3 = kg 02 ) = 2.22 x 1 0 mol KN 03 I kg g O2 mol O2 1 03 g mol O2 mol KN0 3 g KN0 3 kg O2 ) b) Grams KN0 3 = I kg g O2 mol O2 I mol KN0 3 = = 2.24 x 1 0 5 g KN0 3

(88.6 (88. 6 223958.65

[ 10 )( 32.I 00 )( 4 5

[ )( 32.1 00 ) ( 4 5 40

) 2215 )( 101.11

=

)

The beginning of the calculation is repeated to emphasize that the second part of the prob lem is s i mply an extension of the fi rst part. T here is no need to repeat the entire calculation, as only the fi nal step ti mes the answer of the fi rst part w i l l give the final answer to thi s part. 3 .43

P lan : F i rst, balance the equati on. Convert the grams of di borane to moles of diborane using its mo lar mass. Use mole ratios fro m the balanced chemical equation to determine the moles of the products. U se the moles and molar mass of each product to determi ne the mass formed. Solution : The balanced equation i s : B 2 H 6 (g ) + 6 H 2 0(l) � 2 H3B03(S) + 6 H 2 (g). M ass H 3 B03 =

M ass H 2

=

=

3 .45

(33.6 1

1 50.206

(33.6 1

=

(

I mol B 2 H 6

2 7 . 67 g B 2 H 6

1 50.2 g H 3 B0 3

g B2 H 6

1 4 . 69268

)

g B2 H 6

=

)

(

I

mol B2 H 6

2 7 . 6 7 g B2 H 6

1 4.69 g H 2

J(

J(

2 mol H 3 B03 I mol B2 H 6

6 mol

H2

1 mol B2 H 6

)(

J(

6 1 . 8 3 g H 3 B03 I mol H 3 B03

2.0 1 6 g H 2 I

mol H 2

)

J

Plan: Write the balanced equation by first writing the formulas for the reactants and products . Reactants : formula for phosphorus is given as P4 and formula for chlorine gas i s CI2 (chlorine occurs as a d i atomi c molecule). Products : formula for phosphorus pentachloride - the name indicates one phosphorus atom and five chlorine atoms to give the formula P C l s . Convert the mass of phosphorus to moles, use the mole ratio from the balanced chemical equati on, and fi n a l l y use the molar mass of chlorine to get the mass o f chlori ne. S o l ution : Formulas give the equati o n : P 4 + C I 2 � PCls Balancing the equati o n : P4 + 1 0 C I 2 � 4 PC I s Grams C h

3 .47

=

=

(355 g

P4

)

(

I

mol P4

1 23 . 8 8 g P4

J

(

1 0 mol C I 2 I mol P4

J(

70. 90 g C I 2 I mol C I 2

J

=

203 1 . 76

=

2.03

x

3 1 0 g Ch

Plan: Convert the given masses to moles and use the mole ratio from the balanced chemical equation to find the moles of CaO that w i ll form. The reactant that produces the least moles of CaO i s the I i m iting reactant . Convert the moles of CaO fro m the l i m iting reactant to grams using the molar mass. S o l ution : a) Moles CaO fro m Ca

b) Moles CaO from O 2

( o? ) (

I mol Ca

=

( 4 . 2 0 g ca )

40.08 g Ca

=

( 2 . 80 g

3 2 . 00 g 02

-

1 mol ° 2

)( )(

2

mol ca

) o J

o

=

2 mol Ca 2 mol c a

=

I mol 0 2

0 . 1 04790

0 . 1 7 5 00

=

=

0. 1 05 mol CaO

0. 1 75 mol CaO

c) Calciu m i s the l i m iting reactant si nce it wi l l form less calcium oxide. d ) The mass of C aO formed i s determined by the l i miting reactant, Ca. Grams CaO

3 .49

=

(4.20 g ca )

(

I mol Ca 4 0 . 0 8 g Ca

)(

2 mol CaO 2 mol Ca

)(

5 6 . 0 8 g ca

o

1 mol CaO

)

=

5 . 8 766

=

5.88 g CaO

P l an : First, balance the chemi cal equation. Determine which o f the reactants i s the l i miting reagent. Use the l i m iting reagent and the mo l e ratio from the bal anced chemical equation to determi ne the amount of materi al formed and the amount o f the other reactant used. The difference between the amount of reactant used and the i n itial reactant s upp l ied gives the amount of excess reactant remai ning. S o l ution : The balanced chemical equation for this reaction i s : 2 l C I 3 + 3 H 2 0 � r C I + H I03 + 5 H C I H i nt : Balance the equation by starting with oxygen. The other el ements are in multiple reactants and/or products and are harder to balance initially.

41

N ext, fi n d the l i m iting reactant by using the molar ratio to find the smaller number of mo les of H I 03 that can be produced from each reactant gi ven and excess of the other: Moles H I 03 from I C I 3 =

( 685 g

M o l e s H I 03 fro m H 2 0 =

( 1 1 7 .4 g

ICI3

)

(

H )- O

I

(

mol T C I 3

233.2 g ICI3

)

I

)(

mol H 2 °

1 8 .02 g H 2 0

1 mol H I03

)(

2 m o l IC I 3

)

= 1 .468696 = 1 .4 7 mol H I 03

1 mol H I03 . 3 mol H 2 0

)

= 2 . 1 7 1 66 = 2 . 1 7 mol H I 03

I C I 3 is the l i miting reagent and w i l l produce 1 .47 mol HI0 3 . Use the l i m iting reagent to fi n d the grams of H I03 formed. G rams H I 03 =

( 685 g

ICI3

)

(

I mol I C I 3 2 3 3 . 2 g lC I 3

J(

I mol H I 03 2 mol l C I 3

)(

1 7 5 . 9 g H I03 I mol H I03

J

= 2 5 8 . 3 5 5 = 258 g H I 0 3

The remai ning mass of the excess reagent can be cal culated from the amount of H20 comb i n i ng with the l i miting reagent.

( 685 g

Grams H20 required to react with 685 g I C I 3 :

ICI3

. = 7 9 . 3 9 8 = 79.4 g H20 reacted Remain i n g H 20 = 1 1 7 .4 g 79.4 g = 38.0 g H z O

)

(

1 mol I C I 3 233.2 g ICI3

)(

3 mol H 2 0 2 mol ICI3

)(

1 8 .02 g H 2 0 1 mol H 20

)

-

3.5 1

P l a n : Write the bal anced equation: formula for carbon is C, formu l a for oxygen i s O2 and formula for carbon dioxide is CO2, Determ ine the l i miting reagent by see ing which reactant wi l l yi e l d the smal ler amount of product. The l i miting reactant is used for a l l subsequent calculations. S o l ution : C(s) + 02(g) � CO2(g) Moles CO2 from C =

( 0 . 1 00 mo l C )

M o l e s CO2 from O2 =

( 8 . 00 g ° 2 )

(

(

(

) J(

1 mol CO 2 1 mol C I mol °2

3 2 . 00 g 02

)(

= 0 . 1 00 mo I C02 I mol CO2 I mol 02

)

)

= 0 . 2 5 000 = 0 . 2 5 0 mol CO2

The C is the l i m iting reactant and wi l l be used to determine the amount of CO2 that wi l l form . Grams CO2 =

c l ( 0 . 1 00 mol )

mol CO 2 1 mol C

44 . 0 1 g CO 2 I

mol CO2

= 4 .40 1 = 4.40 g CO z

Since the C is l i miti ng, the O z is in excess. The amount remai n i ng depends on how much combines with the l i miting reagent. . . O2 req U i red to react wIth 0 . 1 00 mo l of C = Remaining O2 = 8 . 00 g 3.53

-

( 0 . 1 00 mol C )

3 . 2 0 g = 4.80 g O z

(

I mol 02 I

mol C

)(

3 2 . 00 g O2 1 mol 0 2

)

= 3 .2 0 g O2

P l a n : The question asks for the mass of each substance present a t t h e end o f t h e reaction. "S ubstance" refers to both reactants and products. Solve this problem using multip l e steps. Recognizing that this is a l i miting reactant pro b l em, first write a bal anced chemical equation. U sing the mo l ar re lationsh ips from the balanced equation, determine whi c h reactant i s l i m iti ng. Any product can be used to pred ict the l i miting reactant; i n this case, AICI3 is used. Additional significant figures are retained unti l the last step . S o l ution : The balanced chemical equation i s :

AI(N 02Maq) + 3 N H4C I(aq) � A I C I3(aq ) + 3 N2(g) + 6 H 20(l) Now determi n e the l i miting reagent. We w i l l use the moles of A I C I 3 produced to determine which is l i m iting. Mole A I C l 3 from AI(N02)3 =

( 62 . 5 g A I ( N 02 )3 )

= 0 . 3 7 8 7 6 = 0 . 3 7 9 mol A I C I 3

(

l mol A l ( N 0 2 h

1 6 5 . 0 I g A I ( N 02 )3

42

)(

I

I

mol A I C I 3

mol Al ( N 0 2 ) 3

)

Mole AICI) from NH4CI = ( 54.6 g NH4CI )

(

1 mol NH 4 CI 53 .49 g NH4CI

)(

1 mol AICI 3 3 mol NH4CI

) 0. 34025 =

= 0.340 mol AICI)

Ammonium chloride is the limiting reactant, and it is important for all subsequent calculations. Mass of substances after the reaction: AI(N02») : AI(N02) 3 required to react with 54.6 g of NH4CI: ( 54.6 g NH 4 C I ) 1 mol NH4CI 1 mol AI(N02 h l 65 .0 1 g AI(N02 )3 5 3 .49 g NH4CI 3 mol NH4CI I mol AI(N02 )3 = 5 6 . 1 4474 = 56. 1 g AI(N02») AI(N02) 3 remaining: 62 . 5 g - 56. 1 g = 6.4 g A I(N 02 h

)(

(

)(

)

NH4CI: none left since it is the limiting reagent.

( )(

( 54.6 g NH4CI ) ( 54.6 g NH4CI

3.55

3.57

1 mol NH4CI 5 3 .49 g NH4CI 1 mol NH4CI 5 3 .49 g NH4CI

)( J(

1 mol AICI3 3 mol NH4CI 3 mol N 2 3 mol NH4CI

)( ) ( 28.02 J J 1 33 . 3 3 g AlCI3 1 mol AICI3 g N2

1 mol N2

= 45 .3656 = 45.4 g A ICI3

= 2 8 . 60 1 = 28.6 g N 2

Plan: Multiply the yield of the first step by that of the second step to get the overall yield. Solution : It is simpler to use the decimal equivalents of the percent yields, and then convert to percent using 1 00%. (0.65) ( 1 00%) = 5 3 . 3 = 53 %

(0. 82)

Plan: Balance the chemical equation using the formulas of the substances. Determine the yield (theoretical yield) for the reaction from the mass of tungsten(VI) oxide. Use the density of water to determine the actual yield of water in grams. The actual yield divided by the yield j ust calculated (with the result multiplied by 1 00%) gives the percent yield. Solution: (Rounding to the correct number of significant figures will be postponed until the final result.) The balanced chemical equation is: W0 3 (s) + 3 H2(g) � W(s) + 3 H20(l) Theoretical yield of H20 :

( 4 1 .5 g W03 )

(

1 mol W03 23 1 .9 g W03

( 00

J )

(

3 mol H 2 0 1 mol W03

Actual yield, in grams, of H20 :

( 9.5

(

0

mL H 2 0 )

1.

Calculate the percent yield: Theoretical Yield

J

g H20

I mol H 2 0

J

= 9.6743 9 g H20

g H20 = 9.50 g H 2 °

1 mL H 2 0

Actual Yield

J

( 18.02

x 1 00% =

(

9.50 g H 2 0 9.67439 g H20

J

x 1 00% = 98. 1 974 = 98.2%

43

3 . 59

quantitieswiofl l form. ( o d on. Sinceof products tyhe balancedof thechemicalcculalaequati of amounts d e t g. Onltefigures lsiPlimganin:itifinWricant ) . t resul final the l unti postponed be l wi Sol u(tigo)n: CI2(g) C H3C I (g) HCI (g) CH4 Mole HCI from CH4 = g CH4)( molgCH4CH4 ) ( molmol CH4 ) = Mole HCI from C I2 = g C1 2 ) ( molgCICI2 2 )( molmol CI 2 ) = mol Chlorine is the l i miting reactant. Grams CH3CI = ( g CI 2 ) ( molgCICI2 ) ( molmol ) ( mol ) ( ) =ning of the= calculation i s repeated to emphasize that the The begi n extensi to repeatto thithsepartenti. re calc answeroofn ofthethfirste firstpartpart.wil lThere give theis nofinalneedanswer first stemust p is tobedetermi nneed.theFichemi c, altheformul as soCF4a balis anced lSolPliman:uittiinTheogn:reactant determi n al l y mass ng toonthise: correct number of significant figures ( Roundi The bal a nced chemi c al equati (CN)2(g) F2(g) CF4(g) N F3(g) mol ( CNh mo l C 4 F4 Mol e CF4 from ( CN)2 = ( g(CN)2) ( g (CNh )( F ) = Mole CF4 from F2 = ( g F ) ( I molg F2 )( molmolCF4F2 ) = mol CF4 F2 is the l i miting reactant, and wi l be used to calculate the yield. Grams CF4 = g F )( molg F )( molmolCF4F )( g CF4F4 ) = = n: The spheres represent partimolcelessofofsolsoluutete/volandumethe(amount solute solution iSolPltsaconcentrat i o n. Mol a ri t y = L) a)b) ution: hashas more more solsolvutente added because it contmoleaculins es because sol v ent c)d) hashas aa hil ogwerherconcentrati mol arity, because moles it has fewer moles ty), because on (and imolt hasarimore P n aI cases, the de I n ltl. on f mo lant' y Lmolofesols solutIuOten ) b . molar mass i s used to convert moles to grams. theSolliters.umoltioThen:ar mass. a) Grams Ca( C2H302)2 = mL)[ mLL J( mol aL C 0 )( J = =

reactants are present, we must determine which is R un ing to the correct number

80.0% �

+

+

1 1 6.04

( 1 8.5

1

1

2

�

7

2

+

1 52.04

( 80.0

2

F2

2

2 7

38.00

I

I

80.0% 1 00%

I F2 38.00 2

2 7

3 .074558 mol C

0.60 1 50

88.0 1

I mol

2

52.9383

C

of of solution.

--..J!!J..:.

CH 3 CI

chemical equation can be written. The determined from the limiting reactant. will be postponed until the final result.)

2 I mol (CN) 2

Box C Box B Box C Box B

3 . 65

CH3CI

2

80.0

80.0

0.606488

mol

second part of the problem is simply an ulation as only the final step(s) times the

of

+

1 . 1 53367

50.48 g CH 3 CI 1 CH 3 CI

CH 3 CI CI 2

24.5 g C H 3 CI

24.4924

3.64

CH 3 CI

1

1

I 70.90

43.0

3 .6 1

1

1 70.90

(43.0

CH 3 C I

I

52.9

g

C

F4

per given volume o f

determines

2 more spheres than Box A contains.

have displaced two solute molecules. of solute per volume of solution. of solute per volume of solution.

fi

I

.

0

(M

=

.

.

.

WI'11 e Important. Volume must be expressed In

The chemical formulas must be written to determine

( 1 75 .8

5 .7559

1 0- 3

0.207

I

5.76 g Ca(C 2 H 3 0 2 ) 2

44

C ( 2 H3 2 )2 1

1 58. 1 7

1 mol

g

Ca(C 2 H 3 0 2 h Ca(C 2 H 3 0 2 h

(2 1 . 1 g KI f

)

1 mol KI \ 1 66.0 g KI 0. 1 27 1 08 moles Kl 1 O -3 L Volume (SOO. mL -O.SOO L I mL 0. 1 27 1 08 mol KI = 0.2S42 1 6 = 0.254 M KI Molarity KI

b ) Moles KI

=

{ J

=

c ) Moles NaCN 3 .67

=

=

O . S OO L

=

(

=

J

0.8S0 mol NaCN ( 1 4S.6 L ) 1L

1 23 . 76

=

=

1 24 mol NaCN

Plan: These are dilution problems. Dilution problems can be solved by converting to moles and using the new volume, however, it is much easier to use MI V I M2 V2. Part (c ) may be done as two dilution problems or as a mole problem. The dilution equation does not require a volume in liters; it only requires that the volume units match. Solution: a) MI 0.2S0 M KCI V I 3 7.00 mL M2 ? V2 I SO.OO mL (0.2S0 M)(37.00 mL ) (M2)( I SO.0 mL ) MI VI = M2V2 (0.2S0 M)(37.00 mL ) M2 M2 0.06 1 667 0.06 1 7 M KCI I SO.O mL b ) MI 0.0706 M (NH 4 hS0 4 V I 2S . 7 1 mL M2 ? V2 SOO.OO mL = I (M2)( I SOO.0 mL 2V2 (0.0706 M)(2S .7 1 mL M VI M ) ) (0.0706 M)(2S .7 I mL ) M2 0.003630 0.00363 M (NH4) 2 S04 M2 SOO.O mL =

=

=

=

=

=

_

=

=

=

=

=

=

=

-

_

=

=

c ) When working this as a mole problem it is necessary to find the individual number of moles of sodium ions in each separate solution. (Rounding to the proper number of significant figures will only be done for the final answer. ) 3 1 mol Na + 0.288 mol NaCl 1 O- L (3.S8 mL ) Moles Na+ from NaCl solution I mol NaCl I mL IL 0.00 1 03 1 04 mol N a+ 3 2 mol Na + 6.S 1 x 1 0 -3 mol Na 2 S0 4 1O- L Moles Na+ from Na2 S0 4 solution (soo. mL ) 1 mol Na 2 S0 4 I mL 1L 0.006S I O mol Na+ ( 0.00 1 03 1 04 + 0.006S 1 0) mol Na + I mL --3- 0.0 1 497486 0.0 1 50 M Na+ ions Molarity of Na+ ( 3 . S 8 + SOO. ) mL 1 0- L =

J[ ]

(

=

=

][ ]

[

]( )

=

=

3 .69

]

[

[

=

]

[

=

Plan: Use the density of the solution to find the mass of I L of solution. The 70.0% by mass translates to 70.0 g solutell OO g solution and is used to find the mass of HN0 3 in I L of solution. Convert mass of HN0 3 to moles to obtain moles/L, molarity. Solution: 70.0 g HN?3 1 .4 1 g Solution I mL 987 g HN03 / L a) Mass HN0 3 per liter 3 I mL 1 0- L 1 00 g SolutI O n =

(

(

1 .4 1 g Solution . b ) Molanty of HN0 3 = I mL I S .66 1 7 1 5.7 M HN03 =

=

(J )( J (--)( I mL 1 0 -3 L

J 3 ( J

70.0 g HN 0 . 1 00 g SolutI On

4S

=

I mol HN0 3 63 .02 g HN0 3

)

3.7 1

cal aciequatid wioln togivfienthed the e toes molof acies,dandalongusewiththe tbalheamolncedarichemi ofdcalrequiciumred.carbonat the mass Plmolan:esConvert the of y t mol The aci c ri o hydrochl of volSoluumetion:required. The molarity of the solution is given in the calculation as mollL. HCI(aq) CaC03(s) CaCI2(aq) CO2(g) H20(l) Volume required = g cac0 { �0��1 �����J [ �:o�:c�J ( 0.383 �I JUO�) volumeUseof the reactininogn.whiUsechtheis themolliamriittyinandg reactant. on tofordetermi calaequati write andne thebalamolnceetshofe chemi step i stotodetermi Pleachan: ofThethefirstreactants de u prel as each tSolhe ulitimoin:ting reactant to determine the mass of barium sulfate that wil form. The bal2(aq)ancedNa2S04(aq) chemical equatiBaS04(s) on i s : NaCI(aq) BaCI The mole and l imiting reactant calculations are: [-mol Moles BaS04 from BaCI2 = mL ) ( mol BaCI J [ molmol a J Moles BaS04 from Na2S04 = mL) [--) [ molLNa )( molmol ) mol Sodium sulfate is the limiting reactant. [ mL ) ( moI l J( molmol )[233.mol4 g ) Grams BaS04 = = = firstof thepartHCIofthaleoprobl etmh theis amolsimaplriety.dilution problem (MI VI = M2V2). The second part requires the molSolPlan:uatirTheomass ng wi a) MI =n:M VIM= M2V2 VI = M)(VIM2 =) = M V2gal=) gal gal) V VI = gallons (unrounded) Instructiner.ons:AddBeslsureowlytoandwearwitgoggl contai h mixeisntgo protectgalloyour n of eyes!MPourHCIapproxi into thematwatelyer. Digallutelotnso of water gallonsintowitthhewater. Volume needed = g H I ( molgHCIHCI J( mol HCI J ( ) = ne andthis themassmoltoedetermi s of watneer theare mass requirofed.watWeercanpresentassumeandanyconvert masstheof mass narceitonemolhydrates ofe wiThel usemolThees ofmass g),narcei andofusewater (tPlhweean:hydrate. wil bepresent. converted to moles. Finally, the ratio of the moles of hydrate to moles of watSoluetir owin:l give the amount of water ) n e hydrat e Moles narceme. hydrate = ( g narceme. hydrate ) [ mol gnarcei narceine hydrate = mol narceine hydrate 2

�

+

+

( 1 6.2

=

3 .73

845 . 1 923

=

3

+

�

+

+

(25.0 mL) ( 68.0

( 68.0 mL)

1 1 .7

?

(3.5 M)(5.0 I 1 .7 M

-

_

1 O-3 L 1

2

1 O-3 L 0. 1 60 1L 1 1 O-3 L 0.055 1 1 mL

0.055

3.5 ( 3 . 5 M)(5 .0

( 1 1 .7

3 .76

BaS04

I

B CI2

Na2S04

BaS04

Na2S04

0.00400

BaSO4

1

1

1

=

=

0.00374

BaS04

BaS04

1

=

5.0

l .4957

I

C

(9.55

22.38725

1

2 SO4

I

L

1 .5

b)

Na2S04

2

0.87 g BaS04

0.8729 1 6

3 .75

HCI

1

1

845 mL HCl solution

)

1 36.46

3.0

1 1 .7

1L

1 l .7

22.4 mL muriatic acid solution

1 00

1 00

1 499.52

0.200 1 9

46

1 mL 1 O-3 L

5 .0

BaS04

BaS04

Moles H 2 0 =

( 1 00 g n arcei. n e hydrate )

(

1 0 . 8% H ?- O 1 00% narceine hydrate

J

(

1 mol H 2 ° 1 8 . 02 g H 2 0

)

= 0 . 5 99 3 3 mol H 20 The rati o of water to hydrate i s : ( 0 . 5 99 3 3 mol) / ( 0 . 200 1 9 mo l ) = 3 Thus, there are three water molecules per mole of hydrate. The formula for narceine hydrate is narceineo3 H 2 0 3.77

Plan : Determi n e the formula, then the molar mass o f each compo und. Determ ine the mass o f hydrogen i n each formula. The mass of hydrogen divided by the molar mass of the compound (with the result multi p l i ed by 1 00%) w i l l give the mass percent hydrogen . Ranki ng, based on the percents, i s easy. Sol ution : N ame C h e m ical M o l ar mass Mass percent H formula (glmol ) [( mass H ) / ( molar mass)] x 1 00% Ethane C2H6 30.07 [ ( 6 x 1 . 008) / ( 3 0 . 07)] x 1 00% = 2 0 . 1 1 % H Propane C3Hg 44.09 [ ( 8 x 1 . 008) / (44 . 09)] x 1 00% = 1 8 .29% H Cetyl pal mitate C32 H 6 402 480.83 [ ( 64 x 1 . 008) / (48 0 . 83 )] x 1 00% = 1 3 .42% H Ethano l C 2 H sO H 46.07 [ ( 6 x 1 . 008) / (46 . 0 7 )] x 1 00% = 1 3 . 1 3 % H B enzene C6H 6 78 . 1 1 [ ( 6 x 1 . 008) / ( 7 8 . 1 1 )] x 1 00% = 7 . 743% H The hydrogen percentage decreases i n the fo l l owing order: Ethane > Propane > Cetyl palmitate > Ethanol > Benzene

3.8 1

P l an : I f 1 00 . 0 g of d i nitrogen tetroxide reacts with 1 00 . 0 g of hydrazine ( N 2 H 4) , what i s the theoretical yi eld of ni trogen if no side reaction takes p l ace? F i rst, we need to ident i fy the l i miting reactant. The l i miting reactant can be used to calcu late the theoretical yie l d . Determ ine the amount of l i miting reactant required to produce 1 0 . 0 grams of N O . Reduce the amount of l i miting reactant by the amount used to produce NO. The reduced amount of l i miting reactant is then used to calculate an "actual yield." The "actual" and theoretical yields w i l l give the max i m u m percent yield. Solution : Determ i n i n g the l im i t i n g reactant : Nz from N z04 =

( 1 00 . 0 g

N ? 04 -

)

(

I mo I N 2 04 9 2 . 02 g N 2 0 4

NZ04 is the l i m it i ng reactant. . . Theoretical Yield of Nz =

( 1 00 . 0 g N 2 04 )

(

)(

3 mol N 2 1 mol N 2 0 4

I mol N 2 ° 4 92 . 02 g N 2 04

)(

( 1 0. 0 g NO )

(

I mol N O 30.0 1 g NO

)(

= 3 . 2 60 1 6 mo I N z

3 mol N 2 1 mol N 2 04

= 9 1 .3497 g Nz ( unrounded) H o w much l i miting reactant used to produce 1 00 . 0 g NO? G rams N ?04 used = -

)

2 mol N 2 ° 4 6 mol N O

)(

)(

2 8 . 02 g N 2 I mol N 2

92.02 g N 2 0 4 1 mol N 2 0 4

)

)

= 1 0 . 22 1 g Nz04 ( unrounded)

Determi n e the "actual y i e l d . " A m o u n t of N z04 avai lable t o produce N 2 = 1 00 . 0 g NZ04 - m a s s of N 204 required t o produce 1 0 . 0 g N O 1 00 . 0 g - 1 0 .22 1 g = 8 9 . 7 7 9 g NZ04 ( unrounded)

(

"Actual yie ld" of N -? = 8 9 . 7 7 9 g N 2 0 4

{

I mol N 2 ° 4 92.02 g N 2 0 4

)(

3 mol N 2 1 mo I N 2 0 4

)(

Theoretical yield = ["Actual yield" / theoreti cal yield] x 1 00% [ ( 8 2 . 0 1 28 5 g N2) / ( 9 1 . 3497 g N2)] x 1 00% = 8 9 . 7 790 = 89.8%

47

2 8 . 02 g N 2 I mol N 2

)

3 . 82

Plan: Count the number of each type of molecule i n the reactant box and i n the product box. S ubtract any molecules of excess reagent ( molecules appearing in both boxes) . The remain i ng material is the overal l equation. This will need to be s i mp l i fi ed i f there i s a common factor amon g the substances i n the equation. The balanced chemical equation is necessary for the remainder of the problem. Solution: a) The contents of the boxes give: B 2 -7 AB3 2 B2 B2 i s i n excess, so two molecules need to be removed from each side. This gives:

6 AB2 + 5 6 + 6 +3 6 + (5. 0 { J 5. 0 (3 . 0 { J 6. 0 (5 . 0 {\ 5. 0 3.0

AB2 B 2 -7 AB3 Three i s a common factor among the coeffic ients, and a l l coeffi c i ents need to be divided by thi s value to give the fi nal balanced equati o n : 2 AB2 B2 -7 2 AB 3 b) B2 was i n excess, thus AB2 is the l i miting reactant. c) Moles of A B 3 from

M o les of AB3 from

AB2

82

2 mol A B 3 2 mol A B 2

mol A B 2

=

2 mo1 A B 3 I mol B 2

mol B 2

=

=

mol A83

mol A83

=

AB2 is the l i miting reagent and maximum is 5.0 mol A B3 . d)

Moles of

82 that reacts with

The un-reacted B2 is

3. 8 5

mol

mol - 2 . 5 mol

=

AB 2

mol A B 2

=

I mol B 2

2 mol A B 2

I)

=

2 . 5 mol B2

0.5 mol B2 .

P l an : Count t h e total number of spheres i n each box. T h e number i n b o x A d ivided by the volume change in each part wi l l give the number we are looking for and allow us to match boxes. S o l ution : The number i n each box i s : A 1 2, B C and D a ) When the volume i s tri pled, there should b e spheres i n a box. This i s box C . b ) When the volume i s doubled, there should be 1 212 spheres i n a box. This i s box B . c) When the volume i s q uadrupled, there should b e spheres i n a box. This i s box D . =

=

6, 12/3 4, 4 3. 12/46 3 =

=

=

=

=

3.89

Plan: T h i s prob lem may be done as two d i l ution problems with the two fi nal molarities added, or, as done here, it may be done by calculating, then adding the moles and dividing by the total volume. S o l ution : M KBr

=

Total M o l e s K B r

M o les K B r from Solution

( 0.053 �t }0.200 L ) + ( 0. 078 t 0.200 L + 0. 5 50 L m

KBr

M KBr

3. 92

KBr

I

=

1 ++ } 0. 5 50 L )

Volume Solution I

Total Volume

M oles K B r from S olution 2

Volume S olution 2

=

0.071333

0.071 M KBr

=

Plan: Deal with the methane and propane separate ly, and combine the results. Balanced equations are needed for each hydrocarbon. The total mass and the percentages w i l l give the mass of each hydrocarbon . The mass of each hydrocarbon i s changed to moles, and through the balanced chemical equation the amount of CO2 produced by each gas may be found. S u m m i ng the amounts of CO2 gives the total from the m ixture . S o l ution : The balanced chemical equations are : M ethane : CH 4 (g) 2 02(g) -7 CO2(g) 2 H20(l) C 3 H g (g) 02(g) -7 CO2(g) H20(l) Propan e : M ass of CO2 from eac h : M et h ane:

(200

++ 5 3 + + 4 ( 25.0% ) ( ) ( -J 100% 16.04

· . g M Ixture

I mol C H 4

g CH4

48

I mol

CO 2

I mol C H 4

J ( 44. 0 1

CO 2 CO 2

g

I mol

J

=

1 3 7 1 88 g C 02 .

(--)(

I mol C 3 Hg 75.0% P ropane: ( 200 .g M·Ixture) 1 00% 44.09 g C 3 Hg Total CO2 = 1 37. 1 88 g + 449. 1 83 g = 586.3 1 8 = 586 g CO2 3 .93

)(

3 mol CO2 I mol C 3 Hg

)(

)

44.01 g CO2 = 449. 183 g CO2 1 mol CO2

Plan: lfwe assume a 1 00-gram sample of fertilizer, then the 30: 1 0: 1 0 percentages become the masses, in grams, ofN, P20 5 , and K20. These masses may be changed to moles of substance, and then to moles of each element. To get the desired x:y:1.0 ratio, divide the moles of each element by the moles of potassium. Solution: A 1 00-gram sample of 30: I 0: I 0 fertilizer contains 30 g N, 1 09 P20 5 , and 109 K20. I mol N = 2. 1 4 1 3 mol N (unrounded) Moles N = ( 30 g N) 1 4. 0 1 g N

(

( (

Moles P = (l O g P20 5 )

)

)( )(

I mol P20 S 141.94 g P20 S

)

2 mol P = 0. 1 4090 mol P (unrounded) I mol P2 0S

)

1 mol K20 2 mol K = 0.2 1 23 1 mol K (unrounded) 94.20 g K20 I mol K20 This gives a ratio of 2 . 14 1 3:0.14090:0.2 1 23 1 The ratio must be divided by the moles ofK and rounded. (2. 1 4 1 3/0.2 123 1 ):(0. 14090/0.2123 1 ):(0.2 1 23 1 10.2 1 23 I ) 1 0.086:0.66365: 1.000 1 0:0.66: 1.0 Moles K = ( 1 0 g K20)

3 .95

Plan: Assume 1 00 grams of mixture. This means the mass of each compound, in grams, is the same as its percentage. Find the mass of C from CO and from CO2 and add these masses together. Solution: 1 00 g of mixture = 35 g CO and 65 g CO2. 1 mol C 1 2.01 g C 1 mol CO = 1 5.007 g C (unrounded) C from CO = ( 35.0 g CO) 28.01 g CO I mol CO I mol C

(

C from CO2 = ( 65.0 g C02) Mass percent C = 3 .97

[

(

)(

I mol CO2 44.0 I g CO2

)

)(

)(

I mol C I mol CO2

)(

)

)

12.0 I g C = 17 . 738 gC (UnrOUnded) I mol C

( 1 5.007 + 1 7.738)g x 100% = 32.745 = 32.7% C 1 00 g Sample

Plan: Determine the molecular formula from the figure. Once the molecular formula is known, use the periodic table to determine the molar mass. Convert the volume in (b) from quarts to mL and use the density to convert from mL to mass in grams. Take 6.82% of that mass and use the molar mass to convert to moles. Solution: a) The formula of citric acid obtained by counting the number of carbon atoms, oxygen atoms, and hydrogen atoms is C6Hs07. Molar mass = (6 x 12.01 ) + (8 x 1 .008) + (7 x 1 6.00) = 192.12 g/mol b) Determine the mass of citric acid in the lemon juice, and then use the molar mass to find the moles. l m L 1 .09 g 6.82% l moI C 6Hg�7 IL Moles C6H g0 7 = (1.50 qt) 1 00% 1 92. 1 2 g aCId mL 1 .057 qt 1O-3 L = 0.549 1 04 = 0.549 mol C6Hs07

(

)( )( )( ) (

49

)

3 .99

Plan: Use the mass percent to find the mass of heme in the sample; use the molar mass to convert the mass of heme to moles. Then find the mass of Fe in the sample. Solution : 6.0% heme . a) Grams of heme ( 0.45 g hemoglobIn ) 0.0270 = 0.027 g heme 1 00% hemoglobin =

(

(

)

=

I mol heme I 4.3 7963 X 1 0-s 4.4 x 10-5 mol heme 616.49 g heme ) 1 mol Fe 55.85 g Fe c) Grams of Fe = (4.3 7963 x 1 0 - 5 mol heme . 1 mol heme I mol Fe 2.44602 x 1 0-3 2.4 X 1 0-3 g Fe l mol hemin 65 1 .94 g hemin d) Grams of hemin = (4.37963 x 1 0 -s mol heme 1 mol heme 1 mol hemin 2. 85526 x 1 0-2 2.9 X 10-2 g hemin b) Mole of heme = ( 0.027 g heme )

3 . 1 02

=

=

=

=

{

{

)(

)

)(

=

)

Plan: Determine the molecular formula and the molar mass of each of the compounds. From the amount of nitrogen present and the molar mass, the percent nitrogen may be determined. The moles need to be determined for part (b). Solution: a) To find mass percent of nitrogen, first determine molecular formula, then the molar mass of each compound. Mass percent is then calculated from the mass of nitrogen in the compound divided by the molar mass of the compound, and multiply by 1 00%. Urea: CH4N 2 0, oM = 60.06 g/mol 2(1 4.0 1 glmol 1 00% 46.6533 46.65% N in urea %N 60.06 g/mol CH 4 N 2 0 Arginine: C6H I SN402, oM 1 75 .22 g/mol 4(1 4.0 1 g/mol N) %N = I 00% 3 1 9 8265 3 1 98% N in a r g inin e 1 75.22 glmol C6 H IsN 4 02 Ornithine: C s H 1 3N202, oM 1 33 . 1 7 glmol 2(1 4.0 I glmol 1 00% 2 1 .04077 = 2 1.04% N in ornithine %N 1 33 . 1 7 g/mol C sH 13 N 2 02 =

=

b) Grams ofN

=

=

(

(

( (

=

N) J N)

J(

=

=

J

=

I mol C SH I3 N 2 0 2 1 33 . 1 7 g C S H I 3 N 2 0 2 30. 1 30390 = 30.13 g N

( 1 43 . 2 g C 5 H 1 3 N 2 0 2 )

3 . 1 06

=

J

=

=

.

.

=

1 mol C H 4N 2 0 1 mol C S H I3 N 2 0 2

J(

2 mol N I mol C H 4N 2 0

J(

1 4.0 1 g N 1 mol N

J

Plan: The balanced chemical equation is needed. From the balanced chemical equation and the masses we can calculate the limiting reagent. The limiting reagent wi ll be used to calculate the theoretical yield, and finally the percent yield. Solution : Determine the balanced chemical equation: ZrOCI2"8H20(s) + 4 H2C204"2H20(s) + 4 KOH(aq) � K2Zr(C204)3( H2C204)"H20(S) + 2 KCI(aq) + 20 H20(l) Determine the limiting reactant: I mol product Moles product from ZrOCI2"8 H20 ( 1 .60 g Zr cmP d ) I mol Zr cmpd 322.25 g Zr cmpd 1 mol Zr cmpd 0.004965 1 mol product (unrounded)

(

=

=

50

J(

J

(

Moles product from H2C204"2H20 =

)(

)

1 mol H2C204 " 2H20 1 mol Product 1 26.07 g H 2C204 " 2H 20 4 mol H2C204 " 2H20 = 0.0 1 03 1 1 7 mol product (unrounded) Moles product from KOH = irrelevant because KOH is stated to be in excess. The ZrOCIz"8H20 is limiting, and will be used to calculate the theoretical yield: 1 mol product 54 1 .53 g Product 1 mol Zr cmpd G rams pro d uct = ( 1 . 60 g Zr cmp d ) 322.25 g Zr cmpd 1 mol Zr cmpd 1 mol product = 2.68874 g product (unrounded) Finally, calculating the percent yield: 1 .20 g Actual Yield . Percent YIeld = x 1 00% = 44.63 1 = 44.6% Yield x 1 00% = 2.68874 g Theoretical Yield

( 5 .20 g H 2 C204 " 2H20 )

(

(

)(

)

(

51

)

)(

)

.

Chapter 4 The Major Classes of Chemical Reactions FOLLOW-UP PROBLEMS

4. 1

Plan: We must write an equation showing the dissociation of one mole of compound into its ions. The number of moles of compound times the total number of ions formed gives the moles of ions in solution. If the moles of compound are not given directly, they must be calculated from the information given. Solution: a) One mole of KCI04 dissociates to form one mole of potassium ions and one mole of perchlorate ions. KCI04(s) � K+(aq) + CI04-(aq) Therefore, 2 moles of solid KCI04 produce 2 mol of K+ ions and 2 mol of CI04- ions. b) Mg(C2H 3 02)z(S) �Mg2 +(aq) + 2 C 2H 302-(aq) First convert grams ofMg(C 2 H 302)2 to moles of Mg(C 2 H 302)2 and then use molar ratios to determine the moles of each ion produced. 1 mol Mg(C 2H 02 ( 354 g Mg(C 2 H 3 0 2 h) 1 42.40 g Mg(C H3 0h ) = 2.48596 mol (unrounded) 2 3 2 2) The dissolution of 2.48596 molMg(C 2 H 302)z(S) produces 2.49 mol Mg2+ and (2 x 2.48596) =

4.97 mol C2 H302-

I

(

(NH4)2Cr04(S) � 2 NH/(aq) + CrO/-(aq) c) First convert formula units to moles and then use molar ratios as in part b). (�H 4h Cr0 4 3 . 1 2 1 886 mol (unrounded) ( 1 .88 x I 0 2 4 Formula Units ) 6.022I mol x 1 0 Formula Units The dissolution of 3 . 1 2 1 886 mol (NH 4) 2 Cr04(S) produces (2 x 3. 1 2 1 886) 6.2 4 mol NH/ and 3.1 2 mol Cr042 -.

]

[

=

=

NaHS04(s) � Na\aq) + H S04-(aq) d) The solution contains ( 1 .32 L solution) (0.55 mol NaHSOiL solution) = 0.726 mol ofNaHS04 and therefore 0.73 mol ofNa+ and 0.73 mol HS04-. Check: The ratio of the moles of each ion in the solution should equal the ratio in the original formula. 4.2

4.3

Plan: Each mole of acid will produce one mole of hydrogen ions. It is convenient to express molarity as its definition (moles/L). Solution: HBr(/) � H+(aq) + Br-(aq) 3 + Moles H+ = ( 45 1 mL ) 1 0- L 3 .20 mol H Br I mol H = 1 .4432 = 1.44 mol H+ L I mol H Br I mL

[ ](

J[

]

Plan: Determine the ions present in each substance on the reactant side. Use Table 4. 1 to determine if any combination of ions is not soluble. If a precipitate forms there will be a reaction and chemical equations may be written. The molecular equation simply includes the formulas of the substances, and balancing. In the total ionic equation, all soluble substances are written as separate ions. The net ionic equation comes from the total ionic equation by eliminating all substances appearing in identical form (spectator ions) on each side of the reaction arrow. Solution: a) The resulting ion combinations that are possible are iron(III) phosphate and cesium chloride. According to Table 4. 1 , iron(III) phosphate is a common phosphate and insoluble, so a reaction occurs. We see that cesium chloride is soluble.

52

Total ionic equation: Fe 3 +(aq) + 3 C reaq) + 3 Cs+(aq) + PO /-(aq) ---7 FeP04(s) + 3 cr(aq) + 3 Cs\aq) Net ionic equation: Fe 3 +(aq) + P043-(aq) ---7 FeP04(s) b) The resulting ion combinations that are possible are sodium nitrate (soluble) and cadmium hydroxide (insoluble). A reaction occurs. Total ionic equation: 2 Na+(aq) + 2 OW(aq) + Cd2+(aq) + 2 N0 3-(aq) ---7 Cd(OH)z(s) + 2 Na\aq) + 2 N0 3-(aq) Note: The coefficients for Na+ and OH- are necessary to balance the reaction and must be included. Net ionic equation: Cd2+(aq) + 2 OH-(aq) ---7 Cd(OH)z(s) c) The resulting ion combinations that are possible are magnesium acetate (soluble) and potassium bromide (soluble). No reaction occurs. d) The resulting ion combinations that are possible are silver chloride (insoluble, an exception) and barium sulfate (insoluble, an exception). A reaction occurs. Total ionic equation: 2 Ag+(aq) + SO/-(aq) + Ba2 +(aq) + 2 cr(aq) ---7 2 AgCI(s) + BaS04(s) The total and net ionic equations are identical because there are no spectator ions in this reaction. 4.4

Plan: According to Table 4.2, both reactants are strong. Thus, the key reaction is the formation of water. The other product of the reaction is soluble. Solution: Molecular equation: 2 HN0 3 (aq) + Ca(OHMaq) ---7 Ca(N0 3 Maq) + 2 H 20(l) Total ionic equation: 2 H\aq) + 2 N0 3-(aq) + Ca2 +(aq) + 2 O W(aq) ---7 Ca2+(aq) + 2 N0 3 -(aq) + 2 H20(l) Net ionic equation: 2 H\aq) + 2 OW(aq) ---7 2 H 20(l) which simplifies to: H+(aq) + OJr(aq) ---7 H20(1)

4.5

Plan: A balanced chemical equation is necessary. Determine the moles ofHCl, and, through the balanced chemical equation, determine the moles of Ba(OH)2 required for the reaction. The moles of base and the molarity may be used to determine the volume necessary. Solution: The molarity of the HCl solution is 0. 1 0 1 6 M. However, the molar ratio is not 1 : 1 as in the example problem. According to the balanced equation, the ratio is 2 moles of acid per 1 mole of base: 2 HCI(aq) + Ba(OH)z(aq) ---7 BaCI2 ( aq) + 2 H20(l) L 1 O 3 L 0. 1 0 1 6 mol HCI I mol Ba(OH h Vol ume = ( 50.00 mL ) L 2 mol HCI 0. 1 292 mol Ba(OH) 2 I mL 0.0 1 96594 = 0.0 1 966 L Ba(OH)2 solution

[ )(

=

4.6

)(

)(

)

Plan: Apply Table 4.3 to the compounds. Do not forget that the sum of the O.N . ' s (oxidation numbers) for a compound must sum to zero, and for a polyatomic ion, the sum must equal the charge on the ion. Solution: a) Sc = +3 0 -2 In most compounds, oxygen has a -2 O.N ., so oxygen is often a good starting point. If each oxygen atom has a -2 O.N., then each scandium must have a +3 oxidation state so that the sum of O.N. 's equals zero: 2(+3) + 3(-2) = o. b) Ga = +3 CI = - 1 In most compounds, chlorine has a -I O.N., so chlorine is a good starting point. If each chlorine atom has a -I O .N., then the gallium must have a +3 oxidation state so that the sum of O.N . 's equals zero: 1 (+3) + 3 (- 1 ) O. c) H + 1 P =+5 0 = -2 The hydrogen phosphate ion is HPO/-. Again, oxygen has a -2 O.N . Hydrogen has a + 1 O.N. because i t i s combined with nonmetals. The sum of the O.N. 's must equal the ionic charge, so the fol lowing algebraic equation can be solved for P: 1 (+ 1 ) + 1 (P) + 4(-2) = -2; O.N. for P +5 . d) 1=+3 F = -1 The formula o f iodine trifluoride i s IF3 . In all compounds, fluorine has a -I O.N., so fluorine is often a good starting point. If each fluorine atom has a -I O.N . , then the iodine must have a +3 oxidation state so that the sum of O.N. 's equal zero: 1 (+3) + 3(-1 ) = O. =

=

=

=

53

4.7

4.8

Plan: Use Table 4.3 and assign O.N.'s to each element. A reactant containing an element that is oxidized (increasing O.N.) is the reducing agent, and a reactant containing an element that is reduced (decreasing O.N.) is the oxidizing agent. (The O.N.'s are placed under the symbols of the appropriate atoms.) Solution: a) 2 Fe(s) + 3 Ch(g) � 2 FeCI3(s) Fe = +3 O.N . : Fe = O Cl = O Cl =- 1 Fe is oxidized from 0 to +3 ; Fe is the reducing agent. Cl is reduced from 0 to - 1 ; CI2 is the oxidizing agent. b) 2 C2H 6(g) + 7 02(g ) � 4 CO2(g) + 6 H20(l) O.N . : C = -3 0=0 C = +4 H = +I H = +1 0 = -2 0 = -2 C is oxidized from -3 to +4; C2H6 is the reducing agent. o is reduced from 0 to -2; O2 is the oxidizing agent. H remains + 1 5 CO(g) + 120s(s ) � 12(s) + 5 CO2(g) c) O.N . : C = +2 1 = +5 1 = 0 C = +4 o = -2 0 = -2 0 = -2 C is oxidized from +2 to +4; CO is the reducing agent. I is reduced from +5 to 0; 1205 is the oxidizing agent. o remains -2 Plan: To classify a reaction, compare the number of reactants used versus the number of products formed. Also examine the changes, if any, in the oxidation numbers. Recall the definitions of each type of reaction: Combination: X + Y � Z; decomposition: Z � X + Y Single displacement: X + YZ � XZ + Y double displacement: WX + YZ � WZ + YX Solution: a) Combination; Sg(s) + 1 6 F2(g) � 8 SF4(g) O.N. : S=0 F=0 S = +4 F = -1 Sulfur changes from 0 to +4 oxidation state; it is oxidized and S8 is the reducing agent. Fluorine changes from 0 to - I oxidation state; it is reduced and F2 is the oxidizing agent. b) Displacement; 2 CsI(aq) + CI2(aq) � 2 CsCl(aq) + Iz(aq) O.N . : Cs = + 1 Cl = O Cs = + I I = O I = -I C l = -1 Total ionic eqn: 2 Cs+ (aq) + 2 qaq) + Ch(aq) � 2 Cs+ (aq) + 2 Cqaq) + 12(aq) Net ionic eqn: 2 qaq) + CI2(aq) � 2 Cqaq) + IzCaq) Iodine changes from - I to 0 oxidation state; it is oxidized and CsI is the reducing agent. Chlorine changes from 0 to -I oxidation state; it is reduced and CI2 is the oxidizing agent. c) Displacement; 3 Ni(N03)2 + 2 Cr(s) � 2 Cr(N03Maq) + 3 Ni(s) O.N . : Ni = +2 Cr = O Cr = +3 Ni = O N = +5 N = +5 0 = -2 0 = -2 2 3 Total ionic eqn: 3 Ni+ (aq) + 6 N03-(aq) + 2 Cr(s) � 2 Cr+ (aq) + 6 N03-(aq) + 3 Ni(s) 2 3 Net ionic eqn: 3 Ni+ (aq) + 2 Cr(s) � 2 Cr+ (aq) + 3 Ni(s) Nickel changes from +2 to 0 oxidation state; it is reduced and Ni(N03)2 is the oxidizing agent. Chromium changes from 0 to +3 oxidation state; it is oxidized and Cr is the reducing agent.

54

END-OF-CHAPTER PROBLEMS 4.2

4.5

4.8

4. 1 0

4.12

Plan: Review the definition of electrolytes. Solution: Ions must be present in an aqueous solution for it to conduct an electric current. Ions come from ionic compounds or from other electrolytes such as acids and bases. Ions must be present in an aqueous solution for it to conduct an electric current. Ions come from ionic compounds or from other electrolytes such as acids and bases. Plan: Write the formula for magnesium nitrate and note the ratio of magnesium ions to nitrate ions. Solution: The box in (2) best represents a volume of magnesium nitrate solution. Upon dissolving the salt in water, magnesium nitrate,Mg(N0 3 )2, would dissociate to form oneMg2 + ion for every two N0 3- ions, thus forming twice as many nitrate ions. Only box (2) has twice as many nitrate ions (red circles) as magnesium ions (blue circles). Plan: Compounds that are soluble in water tend to be ionic compounds or covalent compounds that have polar bonds. Solution: a) Benzene is likely to be insoluble in water because it is non-polar and water is polar. b) Sodium hydroxide, an ionic compound, is likely to be soluble in water since the ions from sodium hydroxide wil l be held in solution through ion-dipole attractions with water. c) Ethanol (CH 3 CH20 H) will likely be soluble in water because the alcohol group (-O H) wil l hydrogen bond with the water. d) Potassium acetate, an ionic compound, will likely dissolve in water to form sodium ions and acetate ions that are held in solution through ion-dipole attractions to water. Plan: Substances whose aqueous solutions conduct an electric current are electrolytes such as ionic compounds and acids and bases. Solution: a) An aqueous solution that contains ions conducts electricity. CsI is a soluble ionic compound, and a solution of this salt in water contains Cs+ and r ions. Its solution conducts electricity. b) H Br is a strong acid that dissociates completely in water. lts aqueous solution contains H + and Br- ions, so it conducts electricity. Plan: To determine the total moles of ions released, write a dissolution equation showing the correct molar ratios, and convert the given amounts to moles if necessary. Solution: a) Recall that phosphate, PO/ -, is a polyatomic anion and does not dissociate further in water. K3 P04(S) � 3 K +(aq) + PO/ -(aq) 4 moles of ions are released when one mole of K3 P04 dissolves, so the total number of moles released is (0.83 mol K3 P04) (4 mol ions/mol K3 P04) 3 3 2 3.3 mol of ions b) NiBr203 H20(s) � Ni2 +(aq) + 2 Br -(aq) Three moles of ions are released when I mole ofNiBr203 H20 dissolves. The waters of hydration become part of the larger bulk of water. Convert the grams ofNiBr203H20 to moles using the molar mass (be sure to include the mass of the water): 3 mol Ions ) 1 mol NiBr2 3H 2 0 ( 8.11 x 10- g NiBr2 3H 2 0 272.54 g NiBr2 3H 2 0 1 mol NiBr2 3 H 2 0 8.93 1 0-5 mol of ions 8.9271 x 1 0- 5 =

3

=

°

=

(

.

=

°

°

X

55

J(

°

J

c) FeCI 3(s) � Fe 3+(aq) + 3 Cr(aq) Recall that a mole contains 6.022 x 1 023 entities, so a mole of FeCI 3 contains 6.022 x 1 0 23 units of FeCl 3, (more easily expressed as formula units). Since the problem specifies only 1 .23 x 1 021 formula units, we know that the amount is some fraction of a mole. 4 moles of ions are released when one mole of FeCI 3 dissolves. 4 mo l I ons I mol FeCI 3 1.23 x 102 \ F.U. FeCI 3 2 3 6.022 x 1 0 F. u. FeC1 3 1 mol FeCI 3 3 = 8. 1 7004 x 1 0- = 8.17 x 10-3 mol of ions

)[

(

4.14

J

)(

Plan: To determine the moles of each type of ion released, write a dissolution equation showing the correct molar ratios, and convert the given amounts to moles if necessary. Solution: I mol of AIH and 3 mol of cr per mole of AICI 3 dissolved

[ )( [ I )( )[ )[ 1

-3 Moles A13+ = ( 1 00. mL) 1O L I mL 3 Moles Cr = (100. mL) 10- L mL

)[ )[ )

2.45 mol AICI 3 L

2.45 mol AICI 3 L

) )

1 mol A1 3+ = 0.2 45 mol Ae+ 1 mol AICI 3

3 mol C I= 0.735moI C r 1 mol AlCI 3

6.022 x 1 02 AI 3+ = 1.47539 X 1023 = 1.48 X 1023 Ae+ ions I mol AI + 6.022 x l O 2 3 Cl= 4.426 1 7 X 1 023 = 4.43 X 1 023 cr ions cr ions = 0.735 mol CImol CIb) Li2 S04(s) � 2 Li\aq ) + SO/-(aq) 2 mol of Lt and 1 mol of SO/- per mol of Li 2S04 dissolved

(

:

A13+ ions = 0.245 mol AI 3+

(

)

(

Moles Li+ = (1.80 L) 2.59 g Li2S0 4 I L

(

M a I es SO42- -(I . 80 L) 2.59 g Li2S04 1L

J( ( J

1 mol Li 2 S0 4 109.95 g L i2S0 4 I mol Li2 S04 109.95 g L i2S04

[J

J[

2 mol Li+ 1 mol Li 2 S04

I mol SO�-

)

= 0.08480 = 0.0848 mol Lt

)

= 0.04240 = 0.042 4 mol S0421 mol Li 2 S04 6.022 x 1O Li+ = 5. 1 06787 x 1 022 = 5.1 1 X 1 022 Li+ ions Li+ ions = 0.084802 mol Li+ I mol LI 6.022 x 1 02 3 O�= 2.5 5339 X 1 022 = 2.55 X 1022 SO/- ions S042- ions = 0.04240 I mol SO�_ 1 mol S04 + c) KBr(s) � K (aq ) + Br-(aq) I mol of L i + and I mol of Br- per mole ofKBr dissolved 1O-3L 1 .68 x 1 022 F. u.KBr I K+ . = 3.78 x 102 1 K + Ions K+ ·IOns -- ( 225 mL) I F.U.KBr L 1 mL -

(

[--)[ [ )[ )[ )[

1 O-3 L Br- ·Ions - ( 225 m L) -1 mL

(

(

X

1 02 \ K+

Moles Br- = 3.78 x 1 02 1 Br-

)[ )[

1 .68 X I 022 F.u.KBr L

1 mol K+

6.022

x

)

)

�

)[

(

Moles K+ = 3 .78

�:

)[

) )

I Br= 3.78 x 10 2 1 Br- .Ions I F.U.KBr

)

= 6.27698 X 1 0-3 = 6.28 X 10-3 mol K+ 2 3 1 0 K+

)

1 mol Br= 6.27698 X 1 0-3 = 6.28 X 1 0-3 6.022 x 1 02 3 Br-

56

mol Br-

4.16

Plan: The acids in this problem are all strong acids, so you can assume that all acid molecules dissociate completely to yield W ions and associated anions. One mole of H CI04, HN03 and H C I each produce one mole of H + upon dissociation, so moles H + moles acid. Molarity is expressed as moles/L instead of as M. Solution: 0.25 mOl 0.3 5 mol H+ a) Moles H + mol HCI04 (1.40 L) IL =

=

b) Moles H + mol HN03 =

c) Moles H + mol H C I = =

( ) 3 ) (1.8 ) (100 )( ( 7.6 ) ( 0.056 ) 0.4256 =

=

mL

=

L

L I mL

o.72 mOl IL

--

mOl IL

=

=

=

1.296 x 10-3 1.3 x 10=

3

mol H+

0.43 mol H+

4.23

P lan: Use Table 4. 1 to predict the products of this reaction. Ions not involved in the precipitate are spectator ions and are not included in the net ionic equation. Solution: Assuming that the left beaker is AgN03 (because it has gray Ag+ ion) and the right must be NaCI, then the N03- is blue, the Na+ is brown, and the cr is green. (Cr must be green since it is present with Ag+ in the precipitate in the beaker on the right.) Molecular equation: AgN03(aq) + NaCI(aq) � AgCI(s) + NaN03(aq) Total ionic equation: Ag+(aq) + N03-(aq) + Na+(aq) + C r( aq) � AgCI(s) + Na\aq) + N03-(aq) Net ionic equation: Ag\aq) + Cr(aq) � AgCI(s)

4.24

Plan: Check to see if any of the ion pairs are not soluble according to the solubil ity rules in Table 4.1 Ions not involved in the precipitate are spectator ions and are omitted from the net ionic equation. a) Molecular: Hg2(N03Maq) + 2 KI(aq) � Hg212(s) + 2 KN03(aq) Total ionic: Hg2 2+(aq) + 2 N03-(aq) + 2 K\aq) + 2 l(aq) � H g212(s) + 2 K+(aq) + 2 N03-(aq) Net ionic: H g/+(aq) + 2 l(aq) � Hg212(s) Spectator ions are K+ and N03-. b) Molecular: FeS04(aq) + Ba(OHMaq) � Fe(OHMs) + BaS04(s) Total ionic: Fe2\aq) + SO /-(aq) + Ba2+(aq) + 2 OW( aq) � Fe(OHMs) + BaS04(s) Net ionic: This is the same as the total ionic equation, because there are no spectator ions.

4.26

Plan: A precipitate forms if reactant ions can form combinations that are insoluble, as determined by the solubility rules in Table 4.1. Create cation-anion combinations other than the original reactants and determine if they are insoluble. Any ions not involved in a precipitate are spectator ions and are omitted from the net ionic equation. Solution: a) NaN03(aq) + CuS04(aq) � Na2S04(aq) + Cu(N03Maq) No precipitate will form. The ions Na+ and SO/- will not form an insoluble salt according to solubility rule #1: All common compounds of Group fA ions are soluble. The ions Cu2+ and N03- will not form an insoluble salt according to the solubil ity rule #2: All common nitrates are soluble. There is no reaction. b) A precipitate wil l form because silver ions, Ag+, and iodide ions, r, will combine to form a solid salt, silver iodide, Agl. The ammonium and nitrate ions do not form a precipitate. Molecular: NH4I(aq) + AgN03(aq) � AgI (s) + NH4N03(aq) Total ionic: NH /(aq) + l(aq) + Ag\aq) + N03-(aq) � AgI(s) + NH /(aq) + N03 -(aq) Net ionic: Ag+(aq) + l(aq) � AgI(s)

4.28

Plan: Write a balanced equation for the chemical reaction described in the problem. By applying the solubility rules to the two possible products (NaN03 and PbI2), determine that2 PbI2 is the precipitate. By using molar relationships, determine how many moles of Pb(N03)2 (and thus Pb + ion) are required to produce 0.628 g of PbI2·

57

Solution: The reaction is: Pb(N03Maq) + 2 NaJ(aq) � PbI2(s) + 2 NaN03(aq). I J mol PbI I mol .Pb 2 + 2 2 M Pb + = ( 0.628 g PbI 2 ) 46 1 .0 g Pbl 2 I mol PbI 2 35.0 mL =

4.30

(

0.03892 1 6 0.0389 M Pb2+ =

)(

][

)( ) 10 L I mL -3

--

Plan: The balanced equation for this reaction is AgN03(aq) + cr(aq) � AgCI(s) + N03-(aq). First, find the moles of AgN03 and thus the moles of Cr present in the 25 .00 mL sample by using the molar ratio in the balanced equation. Second, convert moles of CI- into grams, and convert the sample volume into grams using the given density. The mass percent of cr is found by dividing the mass of CI- by the mass of the sample volume and mUltiplying by 1 00. Solution: 1 0 3 L 0.3020 mol AgN03 I mol C I35 .45 g C I 0.467098 g C I (unrounded) (43 .63 mL ) L I mL I mol AgN0 3 1 mol CI-

[ )(

Mass of sample = ( 25 .00 mL ) Mass% CI =

Mass C I Mass Sample

x

( 1 .04 ) g

mL

1 00%

=

=

) [.

)[

26.0 g sample

0.467098 g C I 26.0 g Sample

x

1 00%

)

=

=

1 .79653 1.80% CI =

4.36

Plan: Remember that strong acids and bases can be written as ions in the total ionic equation but weak acids and bases cannot be written as ions. Omit spectator ions from the net ionic equation. Solution: a)KOH is a strong base and H I is a strong acid; both may be written in dissociated form. K1 is a soluble compound since all Group I A( I ) compounds are soluble. Molecular equation: KOH(aq) + H I (aq) � KJ(aq) + H20(!) Total ionic equation: K\aq) + OW(aq) + H\aq) + qaq) � K\ aq) + qaq) + H20(l) Net ionic equation: OW(aq) + H +(aq) � H20(!) The spectator ions are K+(aq) and qaq) b) N H3 is a weak base and is written in the molecular form. HCI is a strong acid and is written in the dissociated form (as ions). N H4C I is a soluble compound, because all ammonium compounds are soluble. Molecular equation: N H3(aq) + HCI(aq) � NH4CI(aq) Total ionic equation: N H3(aq) + H +(aq) + Creaq) � NH/ (aq) + Creaq) Net ionic equation: NH3(aq) + H+(aq) � NH / (aq) CI- is the only spectator ion.

4.38

Plan: Write an acid-base reaction between CaC03 and HC!. Solution: Calcium carbonate dissolves in HCI(aq) because the carbonate ion, a base, reacts with the acid to form CO2(g). Total ionic equation: 2 CaC03(s) + 2H +(aq) + 2 cr(aq) � Ca +(aq) + 2 cr(aq) + H20(l) + CO2(g) Net ionic equation: CaC03(s) + 2H\aq) � Ca2\aq) + H20(!) + CO2(g)

4.40

Plan: Write a balanced equation and use the molar ratios to convert the amount of KOH to the amount of CH3COOH. Solution: The reaction is: KOH(aq) + C H3COOH(aq) � KCH3COO(aq) + H20(l) 0. 1 1 80 mol KOH 1 0-3 L l mol CH 3 COOH ( I I mL M = ( 25.98 mL L I mL l I mol KOH l 52.50 mL 1 0-3 L

(

=

)[ )

]

l

0.058393 1 4 0.05839 M CH3COOH =

58

]( )

4.45

Plan: An oxidizing agent has an atom whose oxidation number decreases during the reaction. Solution: a) The S in SO/- (i.e., H2S04) has O.N. = +6, and in S02, O.N. (s) = +4, so the S has been reduced (and the r oxidized), so the H2S04 is an oxidizing agent. b) The oxidation numbers remain constant throughout; H2S04 transfers a proton to F to produce HF, so it acts as an acid.

4.46

Plan: Consult Table 4.3 for the rules for assigning oxidation numbers. Solution: a) NH20H: (O.N. for N) + 3(+ 1 for H) + 1 (-2 for 0) = 0 O.N. for N = -1 b) N2H4: 2(0.N. for N) + 4(+ 1 for H) = 0 O.N. for N = -2 c) NH/: (O.N. for N) + 4(+ 1 for H) = + 1 O.N. for N = -3 d) HN02: (O.N. for N) + 1 (+ 1 for H) + 2(-2 for 0) = 0 O.N. for N = +3

4.48

Plan: Consult Table 4.3 for the rules for assigning oxidation numbers. Solution: a) AsH). H is combined with a nonmetal, so its O.N. is + 1 (Rule 3). The O.N. for As is -3 . b) H)As04. The O.N. of H in this compound is + I , or +3 for 3 H 's. Oxygen's O.N . is -2, with total O.N. of -8 (4 times -2), so As needs to have an O.N. of +5 : +3 + (+5) + (- 8) = 0 c) AsCh . Cl has an O.N. of- 1 , total of -3, so As must have an O.N. of +3 . a)As = -3 b)As = +5 c) As = +3

4.5 0

Plan: Consult Table 4.3 for the rules for assigning oxidation numbers. Solution: a) MnO/-: (O.N. for Mn) + 4(-2 for 0) =-2 O.N. for Mn = +6 b) Mn203 : O.N. for Mn = +3 { 2(0.N. for Mn) } + 3(-2 for 0) = 0 O.N. for Mn = +7 c) KMn04: 1 (+ 1 for K) + (O.N. for Mn) + 4(-2 for 0) = 0

4.5 2

Plan: Oxidiz ing agent: substance that accepts the electrons released by the substance that is oxidized; the oxidation number of the atom accepting electrons decreases. The oxidiz ing agent undergoes reduction. Reducing agent: substance that provides the electrons accepted by the substance that is reduced; the oxidation number of the atom providing the electrons increases. The reducing agent undergoes oxidation. First, assign oxidation numbers to all atoms. Second, recognize that the agent is the compound that contains the atom that is gaining or losing electrons, not just the atom itself. Solution: 2 a) 5 H2C204(aq ) + 2 Mn04-(aq) + 6 H+ (aq) � 2 Mn + (aq ) + \ 0 CO2(g ) + 8 H20(l) H = +1 Mn = +7 H = +1 Mn = +2 C = +4 H = +1 0 = -2 0 = -2 0 = -2 C = +3 0 = -2 Hydrogen and oxygen do not change oxidation state. The Mn changes from +7 to +2 (reduction). Therefore, Mn04- is the oxidizing agent. C changes from +3 to +4 (oxidation), so H 2 C 2 04 is the reducing agent. 2 b) 3 Cu(s ) + 8 H \aq) + 2 N03-(aq) � 3 Cu + (aq) + 2 NO(g ) + 4 H20(l) Cu = O H = +1 N = +5 Cu = +2 N = +2 H = +I 0 = -2 0 = -2 o = -2 Cu changes from 0 to +2 (is oxidized) and Cu is the reducing agent. N changes from +5 (in N03-) to +2 (in NO) and is reduced, so N03- is the oxidizing agent.

4.5 4

Plan: Oxidiz ing agent: substance that accepts the electrons released by the substance that is oxidized; the oxidation number of the atom accepting electrons decreases. The oxidiz ing agent undergoes reduction. Reducing agent: substance that provides the electrons accepted by the substance that is reduced; the oxidation number of the atom providing the electrons increases. The reducing agent undergoes oxidation. First, assign oxidation numbers to all atoms. Second, recognize that the agent is the compound that contains the atom that is gaining or losing electrons, not just the atom itself.

59

Solution: 2 a) 8 H +(aq) + 6CI- (aq) + Sn(s) + 4N03- (aq) � SnC16 - (aq) + 4N02(g) + 4H20(l) + H = +1 N = +4 Sn = +4 H = + I cr = - 1 Sn = 0 N = +5 CI = - I 0 = -2 0 = -2 0 = -2 Oxidizing agent is N03- because nitrogen changes from +5 O.N. in N03- to +4 O.N. in N02. Reducing agent 2 is Sn because its O.N. changes from 0 as the element to +4 in SnCI6 -. 2 b) 2Mn04- (aq) + I OCr (aq) + 1 6W(aq) � 5CI2(g) + 2Mn2 +(aq) + 8H20(l) Mn = +7 Mn + = +2 H = +l H+ = + 1 CI = O CI- = -1 O=� O=� 2 Oxidizing agent is Mn04- because manganese changes from +7 O.N. in M n04- to +2 O.N. in M n +. Reducing agent is CI- because its O.N. changes from - I in cr to 0 as the element to C12.

4.56

P lan: S is in Group 6A ( 1 6), so its highest possible O.N. is +6 and its lowest possible O.N. is 6 - 8 = -2. Remember that a reducing agent has an atom whose O.N. increases while an oxidizing agent has an atom whose O.N. decreases. Solution: a) The lowest O.N. for S [(Group 6A( 1 6) ] is 6 - 8 = -2, which occurs in 2S 2-. Therefore, when S 2- reacts in an oxidation-reduction reaction, S can only increase its O.N. (oxidize), so S - can only function as a reducing agent. b) The highest O.N. for S [(Group 6A( 1 6) ] is +6, which occurs in SO/-. Therefore, when SO/- reacts in an oxidation-reduction reaction, the S can only decrease its O.N. (reduce), so SO /- can only function as an oxidizing agent. c) The O.N. of S in S02 is +4, so it can increase or decrease its O.N. Therefore, S0 2 can function as either an oxidizing or reducing agent.

4.62

Plan: Recall the definitions of each type of reaction: Combination: X + Y � Z; decomposition: Z � X + Y Single displacement: X + YZ � XZ + Y double displacement: WX + YZ � WZ + YX Solution: combination a) 2 Sb(s) + 3 C h( g) � 2 SbCI3(s) decomposition b) 2 AsH3(g) � 2 As(s) + 3 H2(g) c) 3 Mn(s) + 2 Fe(N03Maq) � 3 Mn(N03Maq) + 2 Fe(s) displacement

4.64

Plan: Two elements as reactants often results in a combination reaction while one reactant only often indicates a decomposition reaction. Review the types of reactions in Section 4.6 Solution: a) N2(g) + 3 H2(g) � 2 NH3(g) L\

b) 2 NaCI03(s) � 2 NaCI(s) + 3 02(g) c) Ba(s) + 2 H20(l) � Ba(OHMaq) + H2(g) 4.66

Plan: Review the types of reactions in Section 4.6 Solution: a) Cs, a metal, and 12, a nonmetal, react to form the binary ionic compound, CsI. 2 Cs(s) + 12(s) � 2 CsI(s) b) AI is a stronger reducing agent than Mn and is able to displace M n from solution, i.e., cause the reduction from Mn2+(aq) to Mn o(s). 2 AI(s) + 3 MnS04(aq) � AI2(S04h(aq) + 3 Mn(s) c) Sulfur dioxide, S02, is a nonmetal oxide that reacts with oxygen, O2, to form the higher oxide, S03. L\

2 S02(g) + 02(g) � 2 S03(g) It is not clear from the problem, but energy must be added to force this reaction to proceed.

60

d) Propane is a three-carbon hydrocarbon with the formula C3 HS. It burns in the presence of oxygen, Oz, to form carbon dioxide gas and water vapor. Although this is a redox reaction that cou ld be balanced using the oxidation number method, it is easier to balance by considering only atoms on either side of the equation. First balance carbon and hydrogen (because they only appear in one species on each side of the equation), and then balance oxygen . C3Hs(g) + 50z(g) .-, 3COz(g) + 4HzO(g) e) Total ionic equation: z 2 Al(s) + 3 Mn + (aq) + 3 SOl-(aq) .-, 2 AI3+ (aq ) + 3 S Ol-(aq) + 3 M n (s) Net ionic equation: z 3 2 AI(s) + 3 Mn + (aq) .-, 2 AI + (aq) + 3 Mn(s) Note that the molar coefficients are not simplified because the number of electrons lost ( 6 e-) must equal the electrons gained (6 e-). 4.68

Plan: Write a balanced equation; convert the mass ofHgO to moles and use the molar ratio from the balanced equation to find the moles and then the mass of 02 . Perform the same calculation to find the mass of the other product. Solution: The balanced chemical equation is 2 HgO(s) � 2 Hg(l) + Oz(g) I 03 g I mol ° 2 32 .00 g O 2 1 mol HgO Mass Oz = (4.27 kg HgO) 1 kg 2 1 6.6 g HgO 2 mol HgO 1 mol 02 The other product is mercury. 2 mol Hg 200.6 g Hg 1 mol HgO 1 03 g Mass Hg = (4.27 kg HgO) 1 kg 2 1 6.6 g HgO 2 mol HgO 1 mol Hg = 3 .95458 = 3 . 9 5 kg Hg

( )(

4.70

)(

( )(

)(

)(

)

)(

=

315 .420 = 31

5

g

O2

)( ) 1 kg 1 03 g

Plan: To determine the reactant in excess, write the balanced equation ( metal + Oz .-, metal oxide), convert reactant masses to moles, and use molar ratios to see which reactant mak es the smaller (" limiting") amount of product. Use the limiting reactant to calculate the amount of product formed . Solution: The balanced equation is 4 Li(s) + Oz(g) .-, 2 LizO (s)

( (

. . . . . .. a) Moles LlzO If LI IImltmg = ( 1 . 62 g LI ) Moles Liz O if Oz limiting

=

(6.00 g ° 2 )

Imol Li . 6.94 1 g LI

I mol ° 2 32.00 g 02

)( )(

2 mol Li 2 0 4 mol LI .

2 mol Li 20 1 mol 02

) )

=

. 0. 1 1 66979 mol LI2 0 (unrounded)

=

. 0.375 mol LI2 0 (unrounded)

Li is the limiting reactant; O2 is in excess. b) 0. 1 1 66979 = 0.117 mol LizO c) Li is limiting, thus there will be none remaining (0 g Li). 2 moI Li 2 0 29.88 g Li 2 0 _ . I mol Li . . Grams LlzO = ( 1 .62 g LI ) - 3 . 4869_ - 3 . 4 9 g L 12 O 6.94 1 g Li 4 mol Li 1 mol Li 2 0

(

(

)(

)( )(

)(

)

)

1 mol 0 2 32 .00 g O 2 1 mol Li 1 .867 1 66 g Oz (unrounded) 6.94 1 g Li 4 mol Li I mol 0 2 Remaining Oz = 6.00 g Oz - 1 .867 1 66 g Oz = 4. 1 3283 = 4.13 g O2

Grams Oz used = ( 1 .62 g Li )

61

=

4.73

Plan: To find the mass of Fe, write a balanced equation for the reaction, determine whether Al or Fe203 is the limiting reactant, and convert to mass. Solution: 2 AI(s) + Fe203(S) � 2 Fe(s) + AI203(s) When the masses of both reactants are given, you must determine which reactant is limiting. 1 03 g I mol Al 2 mol Fe = 37.064 mol Fe (unrounded) Mole Fe (from AI) = ( 1 .00 kg AI) I kg 26.98 g Al 2 mol Al

[ )(

)(

(

)

)

2 mol Fe Mole Fe (from Fe2 03) = (2.00 mol Fe20 3 ) = 4.00 mol Fe 1 mol Fe20 3 Fe203 is limiting, so 4.00 moles of Fe forms. 55.85 g Fe Mass = ( 4.00 mol Fe) = 223 .4 = 223 g Fe 1 mol Fe Though not required by the problem, this could be converted to 0.223 kg. 4.74

4.75

(

)

P lan: Convert the mass of Fe in a 1 25-g serving to the mass of Fe in a 737-g sample. Use molar mass to convert mass to moles and use Avogadro's number to convert moles of Fe to moles of ions. Solution: Fe(s) + 2 H+(aq) � Fe2+ (aq) + H2 (g) a) O.N .: 0 +1 +2 0 2 2 2 1 mol Fe + 6.022 x 1 0 3 Fe + ions 1 O- 3 g 1 mol Fe 49 mg Fe 2 s b) Fe + ions = ( 737 g auce) 2 1 25 g Sauce 1 mg 55.85 g Fe 1 mol Fe I mol Fe + 2 2 2 = 3 . 1 1 509 x 1 0 1 = 3.1 X 1 0 1 Fe + ions per jar of sauce

(

)[

)

P lan: Convert the mass of glucose to moles and use the molar ratios from the balanced equation to find the moles of ethanol and CO2. The amount of ethanol is converted from moles to grams using its molar mass. Solution: ° ° 1 mol C6H1 206 2 mol C2HsOH 46.07 g C2 HsOH Mass 0 f C 2HS H - ( 1 0 . 0 g C6H1 2 6 ) 1 80. 1 6 g C6H1 2 06 1 mol C6 H1 206 1 mol C2HsOH = 5 . 1 1 43 = 5.1 1 g C2HsOH 1 mol C6H1 206 2 mol CO2 22.4 L CO2 Volume CO2 = ( 1 0.0 g C6 HI 2 06 ) 1 80. 1 6 g C6H1 2 06 I mol C6HI 2 06 1 mol CO2 = 2 .4866785 = 2.49 L CO2 -

4.80

)[

)[ )(

(

(

)(

)(

)(

)(

)

)

Plan: For part (a), assign oxidation numbers to each element; the oxidizing agent has an atom whose oxidation number decreases while the reducing agent has an atom whose oxidation number increases. For part (b), use the molar ratios, beginning with Step 3, to find the moles ofN02 , then moles of NO, then moles ofNH3 required to produce the given mass of HN03. Solution: a) Step I . 4NH3(g) + 502(g) � 4NO(g) + 6H2 0(l) O.N.: N = -3 0=0 N = +2 H = +1 H = +1 0 = -2 ° 0 = -2 N oxidized from -3 to +2 by O2, and is reduced from 0 to -2. Oxidizing agent

=

O2

Reducing agent

=

O2

Reducing agent

=

NH3

2NO(g) + 02(g) � 2N02(g) N = +2 0 = 0 N° = +4 ° = -2 = -2 ° N oxidized from +2 to +4 by O2 , and is reduced from 0 to -2.

Step 2. O.N.:

Oxidizing agent

=

62

NO

Step 3 . 3 N02(g) + H20(l) � 2 HN03(l) + NO(g) O.N.: N=+4 H=+ l N=+2 H=+1 O=� O=� N=� O=� 0=-2 N oxidized from +4 to +5 by N02, and N is reduced from +4 to +2. Oxidizing agent

( )(

=

N02

Reducing agent

J(

b) Mass of N H3 : (3 .0 x 1 0 4 kg HN0 3 ) 10 3 g I mol HN0 3 3 moI N0 2 lkg 63 .02 g HN0 4 2 mol HN0 3 = J .2 1 604 X 1 0 4= 1 .2 X 104 kg NH3 4.82

N02

J(

2 mol NO 2 mol N0 2

J(

4 moI NH 3 4 moiNO

)(

17.03 g N H 3 I mol NH 3

J( ) � 3 10 g

P lan: Write a balanced equation and use the molar ratio between Na202 and CO 2 to convert the amount of Na202 given to an amount of CO 2 . Solution : The reaction is: 2 Na20 2 (s) + 2 CO 2(g) � 2 Na2C03(S) + OzCg). 1 mol Na202 44.0 1 g CO2 2 mol CO2 L Air Volume ( 80.0 g Na202 ) 77.98 g Na202 2 mol Na202 J mol CO2 0.0720 g CO2 = 627.08 = 627 L Air

)(

(

=

4.86

=

)(

)(

J

Plan: Balance the equation to obtain the correct molar ratios. Convert the mass of each reactant to moles and use the molar ratios to find the limiting reactant and the amount of CO2 produced. Solution : a) Balance the equation to obtain the correct molar ratios. This is not a redox reaction as none of the O.N. 's change. Here is a suggested method for approaching balancing the equation. - Since PO/- remains as a unit on both sides of the equation, treat it as a unit when balancing. - On first inspection, one can see that Na needs to be balanced by adding a "2" in front of NaHC03. This then affects the balance of C, so add a "2" in front of CO2. - Hydrogen is not balanced, so change the coefficient of water to "2," as this will have the least impact on the other species. - Verify that the other species are balanced. /';.

Ca( H2P04)z(S) + 2 NaHC03(s) ----7 2 CO2(g) + 2 H20(g) + CaHP04(s) + Na2 HP04(S) Determine whether Ca(H2P04)2 or NaHC03 limits the production of CO2. In each case calculate the moles of CO2 that might form. J mol NaHC0 3 2 mol CO2 31% Mole CO2 (NaH C03) = ( 1 .00 g ) 1 00% 84.0 I g NaHC0 3 2 mol NaHC0 3 3 = 3 .690 x 1 0- mol CO 2 ( unrounded) 2 mol CO2 I mol Ca( H2 P04 )2 35% Mole CO2 (Ca( H 2P04 ) 2) = ( l .00 g ) 1 00% 234.05 g Ca( H2P04 h ) 1 mol Ca( H2 P0 4 h = 2.9908 x 10-3 mol CO 2 (unrounded) S ince Ca(H2P04)2 is limiting, 3.03 x 1 0-3 mol CO2 wi ll be produced. b) Volume CO2 (2.9908 X 1 0- mol CO 2) (37.0 Llmol CO2)= 0. 1 1 06596= 0.1 1 L CO2

J(

( )(

( )(

=

4.88

i(

J

)

Plan: To determine the empirical formula, find the moles of each element present and divide by the smallest number of moles to get the smal lest ratio of atoms. To find the molecular formula, divide the molar mass by the mass of the empirical formula to find the factor by which to multiple the empirical formula. Solution: a) Determine the moles of each element present. The sample was burned in an unknown amount of O2, therefore, the moles of oxygen must be found by a different method. I mol CO2 I mol C = 4.27 1 756 X 10-3 mol C (unrounded) Moles C ( 0. 1 880 g CO2 ) 44.0 I g CO2 ) 1 mol CO2 =

(

i(

63

J

I mol H 2 0 ( 2 mol H = 3 .052 1 64 1 0-3 mol H (unrounded) ( 1 8.02 g H 2 0 J 1 mol H 2 0 J 1 mol Bi 2 0 3 )( 2 mol Bi ) = 6. 1 03004 x 1 0-4 mol Bi (unrounded) Moles Bi = ( 0. 1 422 g Bi 2 0 3) ( 466.0 g Bi 2 0 3 1 mol Bi 2 0 3 X

Moles H = ( 0.02750 g H 2 0)

Subtracting the mass of each element present from the mass of the sample will give the mass of oxygen originally present in the sample. This mass is used to find the moles of oxygen. 1 2.0I g C Mass C = (4.27 1 756 x lO- 3 mOl c ) = 0.05 1 3038 g C 1 mol C 1 .008 gH MassH = (3 .052 1 64 xl0-3 mOIH ) = 0.0030766 g H ImolH 209.0 gBi Mass B i = (6. 1 03004 x 1 0-4 mol Bi ) Imol Bi =0. 1 27553 g Bi

( (

] )

[

j

Mass ° = 0.22 1 05 g sample - (0.05 1 3038 g C + 0.0030766 g H + 0. 1 27553 g Bi) = 0.039 1 1 66 g O Moles ° = (0.039 1 1 66 g 0) Imol ° = 0.0024448 mol ° 1 6.00 g ° Divide each of the moles by the smallest value (moles Bi). C = (4.27 1 756 1 0-3 mol) / (6. 1 03004 x 1 0-4 mol) = 7 H = (3 .052 1 64 1 0-3 mol) / (6. 1 03004 x 1 0-4 mol) = 5 0 = (2.4448 1 0- 3 mol) / (6. 1 03004 x 1 0-4 mol) 4 Bi (6. 1 03004 x 1 0-4 mol) / (6. 1 03004 x 1 0-4 mol) I Empirical formula = C7Hs04Bi b) The empirical formula mass is 362 g/mol. Therefore, there are 1 086 / 362 = 3 empirical formula units per molecular formula making the molecular formula = 3 x C 7Hs04Bi = C2IHIS012Bi3. c) Bi(OH ) 3 (s) + 3 H C 7Hs0 3 (aq) � Bi(C 7Hs0 3Ms) + 3 H 20(l) 1 mol Bi(O�h 26 0 . 0 g �i(OHh 1 mg 1 00% 1 0-3 g 1 mol Active 3 mol B i d) ( 0.600 mg) . I mg 1 086 g 1 mol Active I mol BI I mol BI(OHh 1 0 3 g 88.0% = 0.48970 = 0.490 mg Bi(OH)3

(

X

X

=

X

=

=

[ )(

4.90

J

)(

)(

)[ ) ( )

)(

-

Plan: Write balanced equations and use the molar ratios to convert mass of each fuel to the mass of oxygen required for the reaction. Solution: a) Complete combustion of hydrocarbons involves heating the hydrocarbon in the presence of oxygen to produce carbon dioxide and water. Ethanol: C 2HsOH (l) + 3 0 2 (g) � 2 CO 2(g) + 3 H 20(l) Gasoline: 2 CsHls(l) + 25 0 2(g) � 1 6 CO 2 (g) + 1 8 H 20(g) b) The amounts of each fuel must be found: 90% l mL 0.742 g Gasoline = (l.OO L) = 667.8 g gasoline ( unrounded) 1 00% 1 0- 3 L ImL 0.789 g Ethanol = (I.OO L) 1 0% I mL = 78.9 g ethanol 1 00% 1 0- 3 L 1 mL I mol Cs Hls 25 mol 0 2 3 2.0 0 g 0 2 Mass O 2 (gasoline) (667.8 g CsH1s) 1 1 4.22 g CsHIS 2 mol Cs HIS I mol 0 2 = 2338.64 g O 2 (unrounded) ( 32.00 g O 2 Mass O 2 (ethanol) ( 78.9 g C 2HsOH) I mol C 2 HsOH ( 3 mol 0 2 46.07 g C 2HsOH I I mol C 2 HsOH l 1 mol 0 2 = 1 64.4 1 g O 2 (unrounded)

( )( J( ) ( J( J ( ) ( =

=

l

64

J(

)

J(

)

)

)

Total O2 = 2338.64 g O2 + 1 64.4 1 g O2 = 2503.05 = 2.50 x 103 g O2 I mo l 0 2 22.4 L c) (2503 .05 g 0 2 ) = 1 752. 1 35 = 1.75 x 103LOz 32.00 g 0 2 1 mol 0 2 d) (1 752. 1 35 L Oz

4.92

)( ) ( )( 1 00% ) = 83 83 .42 = 8.38 20.9%

x 103 L air

Plan: From the molarity and volume of the base NaOH, find the moles of NaOH and use the molar ratios from the two balanced equations to convert the moles ofNaOH to moles of HBr to moles of vitamin C. Use the molar mass of vitamin C to convert moles to grams. Solution: Mass vitamin C : 3 l moI C6Hg 06 1 1 76. 12g C6Hg 06 I mg (43 .20 mL NaOH) 1 O- L 0. 1 350 mol NaOH I mol HBr l mL lL I mol NaOH 2 mol H Br ) I mol C6Hg 06 1 0 -3 g = 5 1 3 .5659 = 5 1 3 .6 mg C6Hs 06 Yes, the tablets have the quantity advertised.

4.93

( )(

(

)(

)(

)( )

Plan: Remember that oxidation numbers change in a redox reaction. For the calculations, use the molarity and volume ofHCI to find the moles of HCI and use the molar ratios from the balanced equation to convert moles of HCI to moles and then grams of the desired substance. Solution: a) The second reaction is a redox process because the O.N . of iron changes from 0 to +2 (it oxidizes) while the O.N. of hydrogen changes from + 1 to 0 (it reduces). b) Determine the moles ofHCI present and use the balanced chemical equation to determine the appropriate quantities. 3.00 mol HCI 1 mol Fe 2 0 3 1 59.70 g Fe 2 0 3 Mass Fe203 = ( 2.50 x I 03 L ) L 6 mol HCI 1 mol Fe20 3

(

)

)(

)(

= 1 99625 = 2.00 x 105 g FeZ03 3.00 mol HCI 2 mol FeCI3 1 62.20 g FeCI3 Mass FeC I 3 = ( 2.5 0 x 1 0 3 L ) L 6 mol HCI I mol FeC I 3 = 405500 = 4.06 x 105 g FeCI3 c) Use reaction 2 like reaction 1 was used in part b. 3.00 mo l HCI 1 mol Fe 55.85 g Fe Mass Fe = ( 2.50 x 1 0 3 L ) 2 mol HCI 1 mol Fe L = 209437.5 = 2.09 x 105 g Fe . 3 .00 mol HCI I mol FeCI2 1 26.75 g FeCI2 Mass FeCI2 = ( 2.50 x 1 0 3 L ) L 2 mol HCI 1 mol FeCI2 = 4753 1 2.5 = 4.75 x 105 g FeCh d) Use 1 .00 g Fe203 to determine the mass of FeCI3 formed (reaction I ), and 0.280 g Fe to determine the mass of FeCI2 formed (reaction 2). 2 mol FeCI3 1 62.20 g FeCI 3 1 mol Fe 2 0 3 Mass FeCh = ( 1 .00 g Fe20 3) 1 mol FeCI 3 1 59.70 g Fe20 3 1 mol Fe20 3 = 2.03 1 3 g FeCI3 (unrounded) 1 mol Fe 1 mol FeCI2 1 26.75 g FeCI2 Mass FeCI2 = ( 0.280 g Fe) 55.85 g Fe I mol Fe I mol FeCI2 = 0.635452 g FeCI2 (unrounded) Ratio = (0.635452 g FeCI2) / (2.03 1 3 g FeCI3) = 0.3 1 2830 = 0.313

(

(

(

(

)(

(

)(

)(

)(

65

)(

)(

)(

)(

)(

)

)

)(

)

)

)

Chapter 5 Gases and the Kinetic-Molecular Theory FOLLOW-UP PROBLEMS

5. 1

2 Plan: Use conversion factors in Table 5 . 1 to convert pressure in torr to units of mmHg, pascals and Ib/in . Solution : Peo , = 579.6 torr

( )(

) )[

Converting from torr to mmHg:

p = ( 579.6 torr )

1 mmHg = 579.6 torr 1 torr

Converting from torr to pascals:

P = ( 579.6 torr

I atm 760 torr

4 = 7.727364 x 1 0 = 7.727 X 1 04 Pa

(

5 1 .0 1 325 x 1 0 pa latm

)[

)

)

2 1 atm 1 4.7 Ib/in = 1 1 .2 1 068 = 1 l .2 Ib/in2 760 torr 1 atm Check: For conversion to mmHg, the value of the pressure should stay the same. The order of magnitude for each conversion corresponds to the calculated answer. For conversion to pascals the order of magnitude calculation is 1 0 2 x 1 0 5 / 1 0 2 = 1 0 5 . For conversion to Ib/in 2 the order of magnitude calculation is 1 0 2 x 1 0 ' / 1 02 = 1 0 ' . Converting from torr to Ib/in 2 :

5.2

Plan: Given in the problem is an initial volume, initial pressure, and final pressure for the argon gas. The final volume can be calculated from the relationship P, V, = P2 V2 . Unit conversions for mL to L and atm to kPa must be included. Solution: 3 3 1 0- L 1 atm 1 0 pa P , = 0.87 1 atm; V, = ( 1 05 mL ) = 0. 1 05 L; P2 = ( 26.3 kPa ) 1 mL 1 kPa 1 .0 1 325 x 1 0 5 Pa = 0.25956 atm � ( 0.87 1 atm ) ( 0. 1 05 L ) V2 = ( V ) = = 0.352346 = 0.352 L I ( 0.25956 atm ) P2 Check: As the pressure goes from 0.87 1 atm to 0.25956 atm, it is decreasing by a factor of about 3 and the volume should increase by the same factor. The calculated volume of 0.352 L is approximately 3 times greater than the initial volume of 0. 1 05 L.

[ J

5.3

P = ( 579 . 6 torr )

( )

[

J

(

)

Plan: The problem asked for a temperature with given initial temperature, initial volume, and final volume. The relationship to use is V /T , = VzlT2• The units of volume in both cases are the same, but the initial temperature must be converted to Kelvin. Solution: 3 3 V, = 6.83 cm ; T , = O°C + 273 = 273 K; V2 = 9.75 cm ; T 2 = ? � = V2 T2 T, 75 cm 3 V2 T2 = T, - 389.7 1 4 390. K ( 273 K ) 6.83 �n 3 �

[ J

-

t �

-

Check: The volume increases by a factor of about 1 .4 so the temperature must have i ncreased by the same factor. The initial temperature of 273 K times 1 .4 is 380 K, so the answer 390 K appears to be correct.

66

5 .4

Plan: In this problem, the amount of gas is decreasing. Since the container is rigid, the volume of the gas will not change with the decrease in moles of gas. The temperature is also constant. So, the only change will be that the pressure of the gas will decrease since fewer moles of gas will be present after removal of the 5 .0 g of ethylene. To calculate the final pressure, use the relationship n/P I = n21P2. Since the ratio of moles of ethylene is equal to the ratio of grams of ethylene, there is no need to convert the grams to moles. (This is illustrated in the solution by listing the molar mass conversion twice.) Solution: �=� PI P2

( J

n2 --( 793 torr) P2 --( .pJ ) _ nJ

(

1 mol C2H 4 ( (35.0 - 5 .0) g C 2 H 4 ) 28.05 g C 2 H 4

(

J

J

-;-----'----�.:....:....

= 679.7 1 4 = 680. torr I mol C 2 H 4 (35.0 g C2H 4 ) 28.05 g C2H 4 Check : The amount of gas decreases by a factor of 6/7. Since pressure is proportional to the amount of gas, the pressure should decrease by the same factor, 6/7 x 793 = 680. 5.5

5.6

5.7

--

•

Plan: From Sample Problem 5 . 5 the temperature of 2 1 °C and volume of438 L are given. The pressure is 1 .37 atm and the unknown is the moles of oxygen gas. Use the ideal gas equation to calculate the number of moles of gas. Solution: ( 1 .37 atm) (438 L ) = 24.847 mol O2 n = PV / RT = 0.082 1 atm L ( (273 . 1 5 + 2 1 ) K ) mol K Mass of O2 = (24.847 mol O2) x (32 .00 glmol) = 795 . 1 04 = 7 9 5 g O2

(

)

0

0

Plan: The pressure is constant and, according to the picture, the volume approximately doubles. The volume change may be due to the temperature andlor a change in moles. Solution: The balanced chemical equation must be 2 CD ---j C2 + D2 . Thus, the number of mole of gas does not change (2 moles both before and after the reaction). Only the temperature remains as a variable to cause the volume change. Using V I / T I = V2 / T2 with V2 = 2 V ) , and T I = (-73 + 273 . 1 5) K gives: (2VI ) (-73 + 273 . 1 5 ) K V2 400.30 K - 273 . 1 5= 127. 1 5 = 127°C = T2 = TI ( VI ) VI MP Plan: Density of a gas can be calculated using a version of the ideal gas equation, d RT Two calculations are required, one with T = O°C = 273 K and P = 380 torr and the other at STP which is defined as T = 273 K and P = I atm. Solution: Density at T = 273 K and P = 380 torr ( 44.0 1 g/mol ) ( 3 80 torr) I atm = 0.981 783 = 0.982 giL d= 760 torr 0.082 1 atm L (273 K ) mol K Density at T = 273 K and P = I atm. (Note: The I atm is an exact number and does not affect the significant figures in the answer.) ( 44.0 1 g/mol ) ( 1 atm) = 1 .9638566 = 1 .96 giL d= 0.082 1 atm L (273 K ) mol K The density of a gas increases proportionally to the increase in pressure.

( J

(

(

= --

0

0

0

0

)

(

J

)

67

Check: In the two density calculations, the temperature of the gas is the same, but the pressure differs by a factor of two. The calculation of density shows that it is proportional to pressure. The pressure in the first case is half the pressure at STP, so the density at 380 torr should be half the density at STP and it is .

5.8

Plan: Use the ideal gas equation for density, d Solution: Molar mass = =

dRT -P

( l.26 g/L) =

28.95496 29.0 g/mol =

( 0.082 1

.AtP

, and solve for molar mass.

= --

RT

)

(

atm 0 L ( ( I O.O + 273. 1 5) K ) 1 0 l .325 kPa mol 0 K 1 atm ( 1 02.5 kPa )

J

Check: Dry air would consist of about 80% N2 and 20% O2. Estimating a molar mass for this mixture gives (0.80 x 28) + (0.20 x 32) 28.8 g/mol, which is close to the calculated value. =

5.9

1

Plan: Calculate the number of moles of each gas present and then the mole fraction of each gas. The partial pressure of each gas equals the mole fraction times the total pressure. Total pressure equals atm since the problem specifies STP. This pressure is an exact number, and wil l not affect the significant figures in the answer. No intermediate values, such as the moles of each gas, will be rounded. This will avoid intermediate rounding. Solution: 1 mol He = 1 .37397 mol He nH e = ( 5.50 g He ) 4.003 g He

( J ( 5.0 )( 1 J 0.7433 1 20. 1 8 n Kr = (35.0 g Kr) ( J = 0.4 1 766 83.80

nN e = I

g Ne

mol Ne g Ne

I mol Kr g Kr

=

mol Ne mol He

Total number of moles of gas = l.37397 + 0.7433 1 + 0.4 1 766 = 2.53494 mol P A = X A X PIOla l 1 .37397 mol He PH e = ( 1 atm ) = 0.5420 1 = 0.542 atm He 2.53494 mol 0.7433 1 mol Ne atm) = PNe = (I 0.29322 = 0.293 atm Ne 2.53494 mol 0.4 1 766 mol PKr = ( I atm ) = 0 . 1 64 76 = 0 . 1 65 atm Kr 2.53494 mol Check: One way to check is that the partial pressures add to the total pressure, 0.542 + 0.293 + 0. 1 65 = 1 .000 atm, which agrees with the total pressure of atm at STP.

( ( (

5. 1 0

) ) Kr)

1

Plan: The gas collected over the water will consist of H2 and H20 gas molecules. The partial pressure of the water can be found from the vapor pressure of water at the given temperature (Table 5.2). Subtracting this partial pressure of water from total pressure gives the partial pressure of hydrogen gas collected over the water. Calculate the moles of hydrogen gas using the ideal gas equation. The mass of hydrogen can then be calculated by converting the moles of hydrogen from the ideal gas equation to grams. Solution : From Table 5.3, the partial pressure of water is 1 3 .6 torr at 1 6°C. P = 752 torr - 1 3 .6 torr = 738.4 = 738 torr H2 The unrounded partial pressure (738.4 torr) will be used to avoid rounding error. ( 738.4 torr ) ( 1 495 m ) 1 atm -Moles of hydrogen = n = PV/RT = 0.082 1 atm 0 L 760 torr Im (( 273. 1 5 + 1 6) K) mol o K = 0.06 1 1 86 mol H2 (unrounded)

(

)

68

L

(

J[10-3LL )

Mass of hydrogen

= ( 0.06 1 1 86 mol H 2 ) ( 2.0I mol1 6 gHH2 2 J

=

0. 1 2335 1

=

0. 1 23 g H 2

Check: Since the pressure and temperature are close to STP, and the volume is near 1 .5 L, the molar volume at STP (22.4 Llmol) may be used to estimate the mass of hydrogen. ( 1 moll22.4 L) ( 1 .5 L) (2 g/mol) 0. 1 3 g, which is close to the calculated value. =

5.1 1

P lan: Write a balanced equation for the reaction. Calculate the moles of HCI(g) from the starting amount of sodium chloride using the stoichiometric ratio from the balanced equation. Find the volume of the HCI(g) from the molar volume at STP. Solution : The balanced equation is H 2S04(aq) + 2 NaCI(aq) -j Na2S04(aq) + 2 HCI(g). 3 I mol NaCI 2 mol HCI ( 0. 1 1 7 kg NaCI ) 11 0k gg 58.44 2.00205 mol H C I g NaCI 2 mol NaC I

[ )(

(

J( J= )( � )

I L 22.4 L 4.4846 X 1 0 4 4.48 X 1 0 4 mL Hel I mol HCI 1 0- L Check: 1 1 7 g NaCI is about 2 moles, which would form 2 moles of HCI(g). Twice the molar volume is 44.8 L, which is the answer as calculated.

A t S T P : ( 2.00205 m o l HCI )

5. 1 2

=

=

P lan: Balance the equation for the reaction. Determine the I imiting reactant by finding the moles of each reactant from the ideal gas equation, and comparing the values. Calculate the moles of remaining excess reactant. This is the only gas left in the flask, so it is used to calculate the pressure inside the flask. There will be no intermediate rounding. Solution: The balanced equation is N H3(g) + HCI(g) -j N H4CI(s). The stoichiometric ratio ofNH3 to HCI is 1 : 1 , so the reactant present in the lower quantity of moles is the limiting reactant. ( 0.452 atm ) ( 1 0.0 L ) PV Moles ammonia 0. 1 8653 mol N H3 0.082 1 atm · L RT 273 . 1 5 + 22 ) K ) (( mol · K ( 7.50 atm ) ( 1 55 mL ) 1 O-3 L 0.052249 mol HCI Moles hydrogen chloride 0.082 I atm · L ( 27 1 K ) I mL mol · K The HCI is limiting so the moles of ammonia gas left after the reaction would be 0. 1 8653 - 0.052249 0. 1 3428 1 mol NH 3 ( 0. 1 3428 1 mOI ) 0.082 1 atm · L ( ( 273 . 1 5 + 22 ) K ) mol · K nRT . Pressure ammOnIa ( 1 0.0 L ) V 0.325387 0.325 atm NH3 Check: Doing a rough calculation of moles gives for N H3 (0.5 x 1 0) 1 ( 0. 1 x 300) 0. 1 7 mol and for HCI (8 x 0. 1 )/(0. 1 x 300) 0.027 mol which means 0. 1 4 mol NH3 is left. Plugging this value into a rough calculation of the pressure gives (0. 1 4 x 0. 1 x 300)/ 1 0 0.4 atmospheres. This is close to the calculated answer.

= =( --

=(

=

=

=

--

=

=

)

=

)

[ )= --

(

)

=

69

=

=

5. 1 3

Plan: Graham' s Law can be used to solve for the effusion rate of the ethane since the rate and molar mass of helium is known, along with the molar mass of ethane. In the same way that running slower increases the time to go from one point to another, so the rate of effusion decreases as the time increases. The rate can be expressed as I 1time. Solution: Rate He M Mc, H ' = Rate C 2 H 6 He

(

�

mol H e 1 .2 5 min

0.0 1 0

)

( 3 0 .07

( 4 . 003

g/mol ) g/mol )

Time for C2H 6 = 3 . 4 2 5 9 7 = 3 .43 min Check: The ethane should move slower than the helium since ethane has a larger molar mass. This is consistent with the calculation that the ethane molecule takes longer to effuse. The second check is an estimate. The square root of 30 is estimated as 5 and the square root of 4 is 2. The time 1 .2 5 min x 5/2 = 3 . 1 min, which validates the calculated answer of 3 .42 min. END-OF-CHAPTER PROBLEMS 5.1

5 .6

a) The volume of the liquid remains constant, but the volume of the gas increases to the volume of the larger container. b) The volume of the container holding the gas sample increases when heated, but the volume of the container holding the liquid sample remains essentially constant when heated. c) The volume of the liquid remains essentially constant, but the volume of the gas is reduced. The ratio of the heights of columns of mercury and water are inversely proportional to the ratio of the densities of the two liquids. h H ,o

h Hg

h 5 .8

d Hg

d H ,o

= � xh Hg = d H ,o

(

1 3 .5 g/mL

1 . 00 g / m L

]

( 725 mmH g )

( l( ) 1 0- m 3

I

rum

� 1 O -2 m

= 9 7 8 . 7 5 = 979 c m H2 O

Plan: Use the conversion factors between pressure units: I atm = 760 mmHg = 760 torr = 1 0 1 . 32 5 kPa = 1 .0 1 32 5 bar Solution: 760 mmHg a) ( 0.745 atm ) = 566.2 = 566 mmHg 1 atm b)

( 99 2 torr )

c)

( 3 6 5 kPa )

d) ( 804 5. 1 4

",0

=

( (

(

1 .0 1 3 2 5 760

bar torr

] ]

l atm 1 0 1 . 3 2 5 kPa

mmH ) g

(

1 0 1 .325 760

]

= 1 . 3 2 2 5 6 = 1 .3 2 bar = 3 . 60227 = 3.6 0 a tm

kP a mmHg

]

= 1 07. 1 9 1 = 1 07 kP a

At constant temperature and volume, the pressure of the gas i s directly proportional to the number of moles of the gas. Verify this by examining the ideal gas equation. At constant T and V, the ideal gas equation becomes P = n(RTN) or P = n x constant.

70

5.16

a) A s the pressure on a gas increases, the molecules move closer together, decreasing the volume. When the pressure is tripled, the volume decreases to one third of the original volume at constant temperature (Boyle's Law). b) As the temperature of a gas increases, the gas molecules gain kinetic energy. With higher energy, the gas molecules collide with the walls of the container with greater force, which increases the size (volume) of the container. lf the temperature is increased by a factor of 2.5 (at constant pressure) then the volume will i ncrease by a factor of 2.5 (Charles's Law). c) As the number of molecules of gas increase, the force they ex ert on the container increases. This results in an increase in the volume of the container. Adding two moles of gas to one mole increases the number of moles by a factor of three, thus the volu m e increases by a factor of three (Avogadro's Law).

5. 1 8

Plan: This is Charles's Law. Charles's Law states that at constant pressure and with a fixed amount of gas, the volume of a gas is directly proportional to the absolute temperature of the gas. The temperature must be lowered to reduce the volume of a gas. Solution:

� =�

at constant n and P

T-?

=

T

I

�

-

VI T I = 1 98°C + 273 = 47 1 K; V2 = 2.50 L T 2 = ? 2.50 L = 230.88 K - 273 = - 42. 1 2 T 2 = 47 1 K = 42°C 5. 1 0 L

T I T2 VI = 5. 1 0 L;

5.20

( )

Plan: Since the volume, temperature, and pressure of the gas are changing, use the combined gas law. Solution: TI V2

5.22

=

VI

T2 T2

( )(�) P2 T

I

P I = 1 53 .3 kPa; =

( 25.5

q( 298273 KK )( 1 01 53.3 k Pa ) = 35.3437 = l .325 kPa

35.3 L

Plan: Given the volume, pressure, and temperature of a gas, the number of moles of the gas can be calculated using the ideal gas equation, n = PV/RT. The gas constant, R = 0.082 1 Loatm/moloK, gives pressure in atmospheres and temperature in Kelvin. The given pressure in torr must be converted to atmospheres and the temperature converted to Kelvin. Solution: I atm = 0.300 atm; V = 5.0 L; T = 27°C + 273 = 300 K P = (228 torr) PV = nRT or n = PV/RT 760 torr (0.300 atm)(5 .0 L) = 0.06090 1 = 0 . 06 1 mol chlorin e n PV = RT (0.082 1 L . atm )(300 K) mol - K =

5.24

-

)

(

Plan: Solve the ideal gas equation for moles and convert to mass using the molar mass of ClF3 · Volume must be converted to L , pressure to atm and temperature to K. Solution: l atm = 0.9 1 974 atm; v = 0.207 L PV = nRT or n = PV/RT P = (699 mmHg) 760 mmHg T = 45°C + 273 = 3 1 8 K

(

)

71

PV (0.9 1 974 atm)(0.207 L) = 0.0072923 mol CIF) R T - (0.082 1 L - atm )(3 1 8 K) mol - K 92.45 g CIF) = 0.674 1 7 = 0.674 g CIF3 mass CIF) = (0.0072923 mol CIF) ) 1 mol CIF) n-

_

(

J

5 .28

The molar mass of Hz is less than the average molar mass of air (mostly Nz, Oz, and Ar), so air is denser. To collect a beaker of Hz(g ), invert the beaker so that the air will be replaced by the l ighter Hz. The molar mass of COz is greater than the average molar mass of air, so COz(g) is more dense. Collect the COz holding the beaker upright, so the l ighter air will be displaced out the top of the beaker.

5.3 1

Plan: Using the ideal gas equation and the molar mass of xenon, 1 3 1 .3 g/mol, we can find the density of xenon gas at STP. Standard temperature is O°C and standard pressure is 1 atm. Do not forget that the pressure at STP is exact and wil l not affect the significant figures. Solution: ( 1 3 1 .3 g/mol ) ( 1 atm ) = 5 . 85 8 1 = 5.86 gIL d = M P I RT = L · atm 0.082 1 ( 273 K ) mol · K

5.33

(

)

Plan: Apply the ideal gas equation to determine the number of moles. Convert moles to mass and divide by the volume to obtain density in giL. Do not forget that the pressure at STP is exact and wil l not affect the significant figures. Solution : ( I atm ) ( 0.0400 L ) = 1 .78465 x 1 0-) = 1 .78 X 1 0-) mol AsH 3 PV n= - = RT L · atm ( 273 K ) 0.082 1 mol · K ( 1 .78465 X 1 0-3 mol )( 77.94 g/mol ) mass d= = 3 .47740 = 3.48 giL volume ( 0.0400 L )

)

(

5.35

Plan : Rearrange the formula PV = (m I M)RT to solve for molar mass: M = mRT I P V . Convert the mass in ng to grams and volume in il L to L. Temperature must be in Kelvin and pressure in torr. Solution : l atm =0.5 1 0526 atm P = (388 torr ) T = 45°C + 273 = 3 1 8 K 760 torr { 1 O -9 g = 2.06 X 1 0-7 g { 1 O -6 L = 2.06 X 1 0-7 L Y = (0.206 ,uL mass = (206 ng \ I� \ 1� L - atm (2.06 X 1 0 -7 g)(0.082 1 )(3 1 8 K) T R = mol e K M= � = 5 1 . 1 390 = 5 1 . 1 g/mol PY (0.5 1 0526 atm)(2.06 x 1 0 -7 L )

(

[

J

)

j

72

J

5.37

Plan: Use the ideal gas equation to determine the number of moles of Ar and O2. The gases are combined (nTOT = n Ar + no) into a 400 mL flask (V) at 27°C (T) . Determine the total pressure from nTOT, V, and T. Pressure must be in units of atm, volume in units of L and temperature in K. Solution: PV PV = nRT n=RT ( 1 .20 atm ) ( 0.600 L ) PV Moles Ar = - = = 0.0 1 7539585 mol Ar (unrounded) L o atm RT ) ( ( 273 + 227 K ) 0.082 1 mol o K ( 50 1 torr ) ( 0.200 L ) PV 1 atm = 0.0040 1 4680 mol O 2 (unrounded) Moles O2 = - = L atm RT (( 273 + 1 27 ) K ) 760 torr 0.082 1 mol o K

(

(

)

)

0

(

]

)

NTOT = n Ar + no = 0.0 1 7539585 mol + 0.0040 1 4680 mol = 0.02 1 554265 mol ( 0.02 1 554265 mol ) 0.082 1 L o atm (( 273 + 27 ) K ) mol K I mL nRT . P mixture = = -------"--------"------400 mL V 1 0-3 L = 1 .32720 = 1 .33 atm

(

--

5.41

( )

Plan: The problem gives the mass, volume, temperature, and pressure of a gas, so we can solve for molar mass using M = mRTIPV. The problem also states that the gas is a hydrocarbon, which by, definition, contains only carbon and hydrogen atoms. We are also told that each molecule of the gas contains five carbon atoms so we can use this information and the calculated molar mass to find out how many hydrogen atoms are present and the formula of the compound. Convert pressure to atm and temperature to K. Solution: ( 0.482 g ) 0.082 1 L atm (( 273 + 1 0 1 ) K ) 760 torr mol K = 7 1 .8869 g/mol (unrounded) M = mRTIPY = ( 767 torr ) ( 0.204 L ) 1 atm The carbon accounts for [5 ( 1 2 g/mol) ] = 60 g/mol, thus, the hydrogen must make up the difference (72 - 60) = 1 2 glmol . A value of 1 2 glmol corresponds to 1 2 H atoms. (Since fractional atoms are not possible, rounding is acceptable.) Therefore, the molecular formula is CsH12 .

(

5 .43

0

)

0

0

(

]

Plan: Since you have the pressure, volume and temperature, use the ideal gas equation to solve for the total moles of gas. Solution: PV = n RT a) ( 850. torr ) ( 2 1 L ) I atm = 0.8996 1 = 0. 9 0 mol gas n = PY I RT = L atm 0.082 1 (( 273 + 45 ) K ) 760 torr mol o K b) The information given i n ppm is a way of expressing the proportion, or fraction, of S0 2 present in the mixture. Since n is directly proportional to Y, the volume fraction can be used in place of the mole fraction used in equation 6 5 . 1 2. There3 are 7.95 x 1 0 3 parts S0 2 in a million parts of mixture, so volume fraction = (7.95 x 1 0 3 I I X 1 0 ) 7.95 X 1 0- . 3 Therefore, Pso , = volume fraction x PTOT = (7.95 x 1 0- ) (850. torr) = 6.7575 = 6.76 torr.

(

0

(

)

]

=

73

occupies 22.that4 Lwilat l L ofesgasof phosphorus me of gases molaor nvoltoudetermi fromththee balstandard es ofcoxygen thecmol Plan: Weand canuse find 5.44 STP) mol e h t e n equati nced a from o rati metri o hi stoi e h t react Sol utiwion:thPthe4(S) oxygen. + 5 02 (g) p40J Q ( s ) Mass P4 = (35. 5 L O 2 )( 22.1 mol4 L OO22 )( 51 molmol OP42 )( 123.I mol8 8 gP4P4 ) = 39.2655 5. 46 reactant. Plan: To findThe thesmalmassler number ofPH3, ofwrimolte thees ofbalproduct anced equati on andthe findl i m ittheingnumber ofSolmolveesforofPH3 produced byngeach i n di c ates reagent. mol e s of Hz usi the standard mol a r vol u me (or use i d eal gas equati o n). Solution:P4(S) + 6 Hz(g) 4 PH3(g) Moles hydrogen = (83. 0 L ) (� 22.4 L ) = 3. 705357 mol Hz (unrounded) PH3 from P4 = (37. 5 g P4 ) ( 123.I mol88 gP4P4 )( 41 moImolPHP4 3 ) = 1. 2 1085 mol PH3 PH 3 from Hz (3. 7 05357 mol Hz ) ( 46molmol PHH 23 ) = 2.470238 mol PH 3 P4 is the li miting reactant. Mass PH3 = (37. 5 g P4 )( 123.1 mol8 8 gP4P4 )( 41 molmol PHP4 3 )( 33.I mol99 gPHPH 3 ) = 41 . 15676 3 Pl an: Fionrst,andwrithente thethebalstoianced equatic oratin. oThefrommolthees balof hydrogen produced cantobedetermi calculantede thefrommolthees ofidealalugasminum 5.48 equati c hi o metri a nced equati o n i s used that reacted. TheTablproble 5.e2mreports specifipressure es "hydrogen gas(25.col2letorr) cted andover28°C water,(28." so3 torr), the partiso atakel pressure of waterof themusttwofirst bevaluessubtracted. at 26°C the average Solutioton:2obtain the+ 6 partial pressure2 of water +at 327°e. Hz(watge)r vapor = Hydrogen pressure = total pressure -pressure of Moles of hydrogen: (751 mmHg) - [(28. 3 + 25.2) torr / 2] = 724.25 torr (unrounded) 10-3 L ) = 0. 00138514 mol Hz PY =nRT n = -PYRT = ( (724.2L5o torratm)()35.( 8 mL+ ) ) ( 760I atmtorr )( -I mL 0. 0821 mol o K 273 27 K Mass of Al = (0. 00138514 mol H 2 ) ( 32 molmol HAl2 )( 26.I mol98 gAl l ) 0. 024914 = (l

�

= 39.3

g P4

�

=

= 4 1 .2

A I (s)

H C I (aq)

�

g PH3

AICI3(aq )

r

j

A

=

0.024 9

g

AI

5. 5 0 toPlafindn: Tomolfindes ofmLSOz,ofSand02, wriusetthee theidbalealagasncedequati equationon,to convert theume.given mass ofP4S3 to moles, use the molar ratio find vol Sol utio n:P4S3( ) + 8 Oz(g) P40I (S) + 3 SOz(g) S 0 P4S, 3 mol SO 2 l mol Moles SOz = ( 0. 800 g P4S3 ) ( 220.09 g P4S3 )( I mol P4S3 ) = 0. 0 10905 mol SOz �

J

74

nRT Volume S02 -P 286.249

=

=

5.5 1

=

=

)

( 0.0 1 0905 mol S02 ) 0.082 1 L o atm (( 273 + 32 ) K )

(

mol K 725 torr 0

286 mL S02

(

760 torr 1 atm

J[ ) I mL 1 0-3 L

Plan: First, write the balanced equation. Given the amount of xenon hexafluoride that reacts, we can find the number of moles of silicon tetrafluoride gas formed. Then, using the ideal gas equation with the moles of gas, the temperature and the volume, we can calculate the pressure of the silicon tetrafluoride gas. Solution: 2 XeF 6 (S) + Si02(s) -? 2 XeOF4(l) + SiF4(g) 1 mol SiF4 I mol XeF6 0.0040766 mol SiF4 Mole SiF4 n ( 2.00 g XeF6 ) 245 .3 g XeF6 2 mol XeF6

==

(

J

(

(-'--

J=

----'-) (( 273

( 0.0040766 mol SiF4 ) 0.082 1 L atm K . nRT -------- --mol -Pressure SIF4 P = V 1 .00 L 0.099737 0.0997 atm SiF4

= -- = = =

0

0

+

25 ) K )

------

5 .54

At STP (or any identical temperature and pressure), the volume occupied by a mole of any gas will be identical. This is because at the same temperature, all gases have the same average kinetic energy, resulting in the same pressure.

5.57

Plan: The molar masses of the three gases are 2.0 1 6 for H2 (Flask A), 4.003 for He (Flask B), and 1 6.04 for CH4 (Flask C). Since hydrogen has the smallest molar mass of the three gases, 4 g of Hz will contain more gas molecules (about 2 mole' s worth) than 4 g of He or 4 g of CH4• Since helium has a smaller molar mass than methane, 4 g of He will contain more gas molecules (about I mole' s worth) than 4 g of CH4 (about 0.25 mole's worth). Solution: a) PA > PD > Pe The pressure of a gas is proportional to the number of gas molecules. So, the gas sample with more gas molecules will have a greater pressure. b) EA ED Ee Average kinetic energy depends only on temperature. The temperature of each gas sample is 273 K, so they all have the same average kinetic energy. c) rateA > rateD > ratee When comparing the speed of two gas molecules, the one with the lower mass travels faster. d) total EA > total ED > total Ee Since the average kinetic energy for each gas is the same (part b of this problem) then the total kinetic energy would equal the average times the number of molecules. Since the hydrogen flask contains the most molecules, its total kinetic energy will be the greatest. e) dA dD de Under the conditions stated in this problem, each sample has the same volume, 5 L, and the same mass, 4 g. Thus, the density of each is 4 gl5 L 0.8 giL. =

=

5.58

=

=

=

To find the ratio of effusion rates, calculate the inverse of the ratio of the square roots of the molar masses (equation 5 . 1 4, Graham' s Law). 352.0 g/mol Molar Mass UF6 Rate H2 1 3 .2 1 3 7 = 13.21 2.0 1 6 g/mol Rate UF6 Molar Mass H 2

=

5 .60

a) The gases have the same average kinetic energy because they are at the same temperature. The heavier Ar atoms are moving slower than the lighter He atoms to maintain the same average kinetic energy. Therefore, Curve 1 better represents the behavior of Ar. b) A gas that has a slower molecular speed would effuse more slowly, so Curve 1 is the better choice. c) Fluorine gas exists as a diatomic molecule, F2, with .M = 38.00 glmol. Therefore, F2 is much closer in size to Ar (39.95 glmol) than He (4.003 glmol), so Curve 1 more closely represents Fz 's behavior.

75

squareon.roots of the molar masses oftithemeratiforotheof theF2 effusi calcoulnateratesthetoinverse on orates, ratio ofuseeffusi Plan: Toonfind5.14).the Then 5. 62 (equati the find effusi of rati the Sol uti o n: g/mol = 3. 08105 (unrounded) Rate He Mol ar Mass F2 4.38.00030 g/mol Rate F2 Molar Mass He 3. 08105 Time F2 Time F2 = 1 4.0 1 878 = Rate He Ti me F2 1. 00 4. 5 5 min He Rate F2 Time He ofar mass of number, ting oftosome consiandsneon phosphorus of theonelofement ar formof effusi isearelmolatievcule rates phosphorus 5. 64 phosphorus Plan: White atoms. mol the e n determi phosphorus e t whi h t Use the mol ar mass of white phosphorus, determine the number of phosphorus atoms, in From e phosphorous. tmol whi one e cul e of whi t e phosphorus. Sol ution: Rate Px Mol ar Mass e Rate N e = 0.404 = Molar Mass NPx Ne 20.18 g/mol (0.404)2 = MMololaarr Mass Mass Px Molar Mass Px g/mol 0.163216 = Mol20.18ar Mass Px Molar Mass Px = 123. 6398 gimol ( 123.mol6398Px g )( 30.mol97 gPP ) = 3. 992244=4 mol P/mol Px or 4 atoms P/molecule Px Thus, so Px = P 5. 66 The Intermol the realon pressure pressure,ng tosoTabl it causes n. size eofculthear attracti intermolonseculcause ar attracti is relatedtotobethe constantidealAccordi e 5 .4,a a N , 1 . 39devi, atio2.32 and aco, = 3. 5 9. Therefore, CO2 experiences greater negative deviation i n pressure than the other two gases: N2 < Kr< CO2. 5. 6 8 Nfarther itrogenapart.gas behaves more iddefined eal l y atasI atm thanstingatof500gasatmmolbecause at loactweri npressures they ofgasthmol ehculer gases are An i d eal gas is consi e cul e s that dependentl e ot mol ecules.andWhenthe gasvol umolmeeofculthees aremolfareculapart, eallyo, nbecause i ntermolnerevolculuame. r attractions are less important es is atheysmalactleri dfracti of the contai 5. 7 1 4:PlIan:ratiUseo . DithveidIdeal GasmassEquati onbytotfind the number ofesmolto eobtai s ofnO2.molMolar mass, es of O2g/mol.combine with Hb in a e t h e of Hb h e number of mol SolPV=utinoRn:T Moles O2 = PVRT = (743L torratm) (1. 5 3 mL ) ) ( 760I atmtorr J [I1O-3 L J ( 0.0821 mol K ) ( (273 37 K ) = 5. 8 7708 10-5 mol O2 (umounded) Moles Hb = ( 5. 87708 10.5 mol O2 ) ( 41 molmol HbO2 ) = 1.46927 1 0-5 mol Hb (unrounded) Mol ar mass hemoglobin = (1. 00 g Hb) I (1.46927 10-5 mol Hb) = 6.806098 1 04 1 4.0

min

x,

x,

I

4

4.

atoms per molecule,

less than

a

0

0

negative

a.

=

mL

+

X

X

X

X

X

76

=

6.81

X

1 04

g/mol

a K, =

5 . 73

Plan: Convert the mass of CI2 to moles and use the ideal gas law and van der Waals equation to find the pressure of the gas. Solution: 1 03 g I mol CI 2 a) Moles Ch: ( 0.5850 kg CI 2 ) ___ = 8.25 1 0578 mol I kg 70.90 g CI 2 Ideal gas equation: PY = nRT L - atm 8.25 1 0578 mol 0.082 1 (( 273 + 225 ) K ) mol - K IGL = nRTN = --'P ----'� 1 5 .00 L = 22.490 1 = 22.5 atm -

b)

_

[ p :: } +

Y - nb )

( )( (

=

)

-

)

---

nRT

2 nRT n a atm- e From Table 5.4: a = 6.49 2 Y nb y mof n = 8.25 1 0578 mol from Part (a) P YDW -

_

(

)

L b = 0.0562 mol 2

[

2

atm - L ( 8.25 1 0578 mol CI2 ) 0.082 1 L - atm (( 273 + 225 ) K ) ( 8.25 1 0578 mol Cl2 ) 6.49 mol 2 mol - K P yDW = ----------'-------,--:------:--2 ( 1 5.00 L ) 1 5.00 L - ( 8.25 1 0578 mol CI2 ) 0.0562 �

5.75

= 2 1 .24378 = 21.2 atm

(

mol

)

)

Plan: Partial pressures and mole fractions are calculated from Dalton's Law of Partial Pressures: P A = XA(Ptota l) Solution: a) Convert each mole percent to a mole fraction by dividing by 1 00%. PNitrogen = XNitrogen PTotal = (0.786) ( 1 .00 atm) (760 torr / I atm) = 597.36 = 597 torr Nz 1 59 torr Oz P Oxygen = XOxygen PTotal = (0.209) ( 1 .00 atm) (760 torr / I atm) = 1 58.84 P C arOOn Di oxide = XCarOOn Di oxide PTotal = (0.0004) ( 1 .00 atm) (760 torr / I atm) = 0.304 = 0.3 torr COz P Water = XWater PTotal = (0.0046) ( 1 .00 atm) (760 torr / atm) = 3 .496 = 3.5 torr Oz b) Mole fractions can be calculated by rearranging Dalton's Law of Partial Pressures: XA = P AlPtotal and multiply by 1 00 to express mole fraction as percent. PTotal = (569 + 1 04 + 40 + 47) torr = 760 torr [(569 torr) / (760 torr) ] x 1 00% = 74.8684 = 74.9 mol% Nz N2: O2: [( 1 04 torr) / (760 torr) ] x 1 00% = 1 3 .6842 = 1 3.7 mol% Oz [(40 torr) / (760 torr) ] x 1 00% = 5.263 = 5.3 mol% COz CO2: [(47 torr) / (760 torr)] x 1 00% = 6. 1 842 = 6.2 mol% COz H20: c) Number of molecules 0[ 02 can be calculated using the Ideal Gas Equation and Avogadro's number. PY = nRT ( 1 04 torr ) ( 0.50 L ) I atm PY - 0.0026883 mol O2 Moles O2 = - = L - atm RT (( 273 + 37 ) K ) 760 torr 0.082 1 mol - K 6.022 x 1 0 23 molecules 0 2 Molecules O2 = ( 0.0026883 mol O 2 ) I mol O 2 21 Z1 = 1 .6 1 89 X 1 0 = 1.6 X 1 0 molecules Oz =

I

(

)

(

(

77

j_

J

5 . 77

Plan: For part a, since the volume, temperature, and pressure of the gas are changing, use the combined gas law. For part b, use the ideal gas equation to solve for moles of air and then moles ofN2. Solution: 1 atm P V P 2 V2 = 1 .842 1 atm; VI = 208 mL; P I = ( 1 400. mmHg ) a) I I 760 mmHg T2 TI T I = 286 K; P2 = l atm; T2 = 273 K; V2 = ? 2 298 K 1 .842 1 atm = 399.23 mL = 4 x l 0 m L V2 = V I � � = ( 208 mL) 286 K latm TI P2

( ( )(

=

( )(

)

(

)

)

( 1 .842 1 atm) ( 0.208 L ) = 0.0 1 63 1 8 mol air L · atm ( 286 K ) 0.082 1 mol · K 77% N 2 = 0.0 1 25649 = O. 0 13 mol N2 Mole N2 = ( 0.0 1 63 1 8 mol ) 1 00%

PV b ) Mole air = n = - = RT

5 .78

(

J

(

)

)(

)( ) )[ ) ( J(

The balanced equation and reactant amounts are given, so the first step is to identify the limiting reactant. 2 mol N02 8.95 g c u 1 mol Cu = 1 .394256 mol N02 (unrounded) Moles N 02 from Cu = ( 4.95 cm 3 ) 63 .55 g Cu 1 mol Cu cm 3

(

)(

)

2 mol N02 68.0% HN0 3 1 cm 3 1 .42 g 1 mol HN0 3 1 00% 1 mL mL 63 .02 g 4 mol HN0 3 = 1 .7620 mol N02 (unrounded) Since less product can be made from the copper, it is the limiting reactant and excess nitric acid will be left after the reaction goes to completion. Use the calculated number of moles ofN02 and the given temperature and pressure in the ideal gas equation to find the volume of nitrogen dioxide produced. Note that nitrogen dioxide is the only gas involved in the reaction. L · atm ( ( 273.2 + 28.2) K ) ( 1 .394256 mol N0 2 ) 0.082 1 760 torr mol ·K V = nRT I P = ( 735 torr) 1 atm = 35 .67427 = 3 5.7 L N02 Moles N02 from HN0 3 = ( 230.0 mL)

)

(

5.82

( )

Plan: The empirical formula for aluminum chloride is AICh (Ae+ and Cn The empirical formula mass is 1 33 .33 glmol). Calculate the molar mass of the gaseous species from the ratio of effusion rates. This molar mass, divided by the empirical weight, should give a whole number multiple that will yield the molecular formula. Solution: Molar Mass He Rate Unk --= 0. 1 22 = Molar Mass Unk 0. 1 22 = Molar mass Unknown = 268.9465 glmol The whole number multiple is 268.946511 33.33, which is about 2. Therefore, the molecular formula of the gaseous species is 2 x (AICI3) = A12C16.

5 . 84

Plan: First, write the balanced equation for the reaction: 2 S02 + O2 � 2 S03' The total number of moles of gas will change as the reaction occurs since 3 moles of reactant gas forms 2 moles of product gas. From the volume, temperature and pressures given, we can calculate the number of moles of gas before and after the reaction using ideal gas equation. For each mole of S03 formed, the total number of moles of gas decreases by mole. Thus, twice the decrease in moles of gas equals the moles of S03 formed.

78

1 /2

Solution : Moles of gas before and after reaction ( 1 .95 atm ) ( 2 . 00 L ) PV Initial moles 0.05278 1 1 6 mo l (u nrounded ) · RT 0.082 1 L atm ( 900. K ) mol · K ( 1 .65 atm ) ( 2 .00 L ) PV . Fmal moles 0.04466098 mol (unrounded) atm RT ' L 0.082 1 ( 900. K ) mol · K Moles of S03 produced 2 x decrease in the total number of moles 2 x (0.05278 1 1 6 mol - 0.04466098 mol) 0.0 1 624036 1 .62 x 1 0-2 mol Check: Jf the starting amount is 0.0528 total moles of S02 and 02, then x + y 0.0528 mol, where x mol of S02 and y mol of O2. After the reaction : (x - z) + (y - 0.5z) + z = 0.0447 mol Where z mol of S03 formed mol of S02 reacted 2(mol of O2 reacted). Subtracting the two equations gives: x - (x - z) + Y - (y - 0.5z) - z 0.0528 - 0.0447 z 0.0 1 63 mol S03 The approach of setting up two equations and solving them gives the same result as above. =

=

=

-

=

=

=

(

(

)

=

)

=

=

=

=

=

=

=

=

=

=

=

5.88

a) A preliminary equation for this reaction is CxHyNz + n O 2 --j 4 CO2 + 2 N2 + 1 0 H 20. Since the organic compound does not contain oxygen, the only source of oxygen as a reactant is oxygen gas. To form 4 volumes of CO2 would require 4 volumes of O2 and to form 1 0 volumes of H 20 would require 5 volumes of O 2 , Thus, 9 volumes of O2 was required. b) Since the volume of a gas is proportional to the number of moles of the gas, we can equate volume and moles. From a volume ratio of 4 CO2 :2 N2: 1 0 H20 we deduce a mole ratio of 4 C:4 N :20 H or I C: 1 N : 5 H for an empirical formula of CHsN.

5 .90

Plan: To find the factor by which a diver's lungs would expand, find the factor by which P changes from 1 25 ft to the surface, and apply Boyle 's L aw. To find that factor, calculate Pseawater at 1 25 ft by converting the given depth from ft-seawater to mmHg to atm and adding the surface pressure ( 1 .00 atm). Solution : 2 1 2 in 2.54 cm 1 0- m I � 4 = 3 . 8 1 X 1 0 nunH 20 P (H20) ( 1 25 ft ) 3 1 ft 1 III 1 cm 10 m 3 . 8 1 X 1 0 4 mmH 2 0 1 3 . 5 g/m L 2935 . 1 1 1 1 mmHg h Hg 1 .04 g/m L h Hg

_

( )(

=

( I

)(

)( ) _

)

=

atm 3 .86 1 988 atm (unrounded) 760 mm Hg Ptotal ( 1 .00 atm) + (3 .86 1 988 atm) 4.86 1 988 atm (unrounded) Use Boyle 's Law to find the volume change of the diver's lungs: P

( Hg)

=

( 2935 . 1 1 1 1 1 mmHg )

=

PIVI

=

=

P2V

=

4.86 1 988 atm 4.86 VI P2 VI 1 atm To find the depth to which the diver could ascend safely, use the given safe expansion factor ( 1 .5) and the pressure at 1 25 ft, P 1 2 5 , to find the safest ascended pressure, P safe. P 1 2 5 / Psafe 1 .5 Psa fe P 1 2 5 / 1 . 5 = (4.86 1 988 atm) / 1 .5 3 .24 1 325 atm (unrounded) Convert the pressure in atm to pressure in ft of seawater using the conversion factors above. Subtract this distance from the initial depth to find how far the diver could ascend. V2

_

=

=

=

=

79

hH 2 0

(

( 4.86 1 988 - 3 .24 1 325 atm ) 760 mmHg

h (Rg): =

hHg

dHg

dH 2 0

)

1 23 1 .7039 mmHg 1 atm 1 3 . 5 g/mL hH 2 0 1 23 1 .7039 mmHg 1 .04 g/mL

(

J(

_

-3 ( 1 5988.464 mmH 2 0 ) 1 0 m I .094 Yd 1 mm

1m

)( J

Therefore, the diver can safely ascend 52.5

3 ft 1 yd

ft to

=

=

52.474 1

ft

a depth of ( 1 25 - 52.474 1 )

=

72.5259

=

73 ft.

5 .97

Plan: Deviations from ideal gas behavior are due to attractive forces between particles which reduce the pressure of the real gas and due to the size of the particle which affects the volume. Compare the size and/or attractive forces between the substances. Solution: a) Xenon would show greater deviation from ideal behavior than argon since xenon is a larger atom than xenon. The electron cloud of Xe is more easily distorted so intermolecular attractions are greater. Xe's larger size also means that the volume the gas occupies becomes a greater proportion of the container's volume at high pressures. b) Water vapor would show greater deviation from ideal behavior than neon gas since the attractive forces between water molecules are greater than the attractive forces between neon atoms. We know the attractive forces are greater for water molecules because it remains a liquid at a higher temperature than neon (water is a liquid at room temperature while neon is a gas at room temperature). c) Mercury vapor would show greater deviation from ideal behavior than radon gas since the attractive forces between mercury atoms is greater than that between radon atoms. We know that the attractive forces for mercury are greater because it is a liquid at room temperature while radon is a gas. d) Water is a liquid at room temperature; methane is a gas at room temperature (think about where you have heard of methane gas before - Bunsen burners in lab, cows' digestive system). Therefore, water molecules have stronger attractive forces than methane molecules and should deviate from ideal behavior to a greater extent than methane molecules.

5 . 1 00

Plan: V and T are not given, so the ideal gas equation cannot be used. The total pressure of the mixture is given. Use P A X A X P total to find the mole fraction of each gas and then the mass fraction. The total mass of the two gases is 35.0 g. Solution: Ptotal P krypton + Pc arbo n diox ide 0.708 atm The NaOR absorbed the CO2 leaving the Kr, thus P krypton 0.250 atm P c arbon diox ide P total - P kry pton 0.708 atm - 0.250 atm 0.458 atm Determining mole fractions: P A X A X Ptotal Peo 2 0.458 atm Carbon dioxide: X 0.64689 (unrounde d ) 0.708 atm Ptota) 0.250 atm Krypton : X PKr 0.353 1 07 (unrounded) 0.708 atm Ptotal =

=

=

=

=

=

=

=

=

=

---

Re i ative mass fract;oo

=

=

�

l

=

(

( 0.353 1 07 ) 83 .80 g ( 0.64689 )

=

(

Kr) j )

mo i 44.01 g CO 2 mol

�

1 .039366 (uomuoded)

3 5 .0 g x g CO2 + ( 1 .039366 x) g Kr 3 5 .0 g 2.039366 x Grams CO2 x (35.0 g) / (2.039366) 1 7. 1 62 1 95 8 1 1 7.2 g CO2 Grams Kr 35.0 g - 1 7. 1 62 g CO2 1 7.837804 1 9 1 7.8 g Kr =

=

=

=

=

=

=

80

=

5. 1 03

�

3 RT M Set the given relationships equal to each other.

a) Derive

U

=

rms

..!.

--

mu2

2

�(l!...-) T 2

Multiply each side by 2 and divide by m.

NA

2 (�) T

=

�

=

m

NA

3 RT

�

- --

mNA

Solve for u by taking the square root of each side; substitute molar mass, M, for mNA (mass of one molecule x Avogadro's number of molecules). u

,m.,

-

�3RT

--

M

�

rate2 � ....; M2 rate, At a given T, the average kinetic energy is equal for two substances, with molecular masses ml and m2:

b) Derive Graham's L aw

E

k

=

..!.

/

2

-2 mjUj

..!!!..!....-

mju

I

U 22

_

m2

U

/

--

/

m2u

2 -2 m2u 2

=

�

----..

U2

=

�

Uj

The average molecular speed, u , is directly proportional to the rate of effusion. Therefore, substitute "rate" for each "u." In addition, the molecular mass is directly proportional to the molar mass, so substitute M for each m:

� f.M:

5 . 1 07

=

rate2 rate,

Plan: Find the number of moles of carbon dioxide produced by converting the mass of glucose in grams to moles and using the stoichiometric ratio from the balanced equation. Then use the T and P given to calculate volume from the ideal gas equation. Solution: a) C6H I 206(S) + 6 02(g) -; 6 C O2(g) + 6 H 20(g) 6 mol C O2 mol C 6 H 1 2 0 6 = 0 . 599467 mol CO2 Moles CO2: ( 1 8 . 0 g C6 H I 2 0 6 ) mol C6 H , 2 06 1 80. 1 6 g C6 H , 2 06

(

(I

)

)( I

)

atm (0.599467 mOI) 0.082 1 L · ( ( 27 3 + 3 5 ) K ) nRT = mol-.,-· ---'K ----'-----;V = ( 760 torr ) atm ( 780. torr ) P = 14.76992 = 14.8 Liters CO2 This solution assumes that partial pressure of 02 does not interfere with the reaction conditions. --

-

-

-

-

81

I

b) Plan: From the stoichiometric ratios in the balanced equation, calculate the moles of each gas and then use Dalton's law of partial pressures to determine the pressure of each gas. Solution : 6 mol 1 mol C 6 H 12 0 6 Moles CO2 Moles O2 ( 9.0 g C 6 H 12 0 6 ) 1 80. 1 6 g C 6 H 12 0 6 I mol C 6 H 12 0 6 0.299734 mol CO2 mol O 2 At 35°C, the vapor pressure of water is 42.2 torr. No matter how much water is produced, the partial pressure of H2 0 wi II stil l be 42.2 torr. The remaining pressure, 780 torr - 42.2 torr 73 7.8 torr (unrounded) is the sum of partial pressures for O2 and CO2. Since the mole fractions of 02 and CO2 are equal, their pressures must be equal, and be one-half of sum of the partial pressures just found. =

Pwater

=

42.2

=

torr

(737.8 torr) / 2 368.9

5.1 1 1

=

=

)(

(

=

=

3.7 x 1 0 2 torr Poxygen

=

=

)

Pcarbon dioxide

Plan: To find the number of steps through the membrane, calculate the molar masses to find the ratio of effusion rates. This ratio is the enrichment factor for each step. Solution : Molar Mass 2 3 8 UF6 352.04 g/mol 1 ��� 3 2 Rate 23 8 UF6 349.03 g/mol Molar Mass 5 UF6 =

__ __ __ __

1 .004302694 enrichment factor (unrounded) Therefore, the 23abundance of 23 5 UF6 after one membrane is 0. 72% x 1 .004302694; Abundance of 5 U F6 after "N" membranes 0.72% * ( 1 .004302694)N Desired abundance of 23 5 UF6 3 .0% 0.72% * ( 1 .004302694)N Solving for N : 4. 1 6667 ( 1 .004302694)N In 4. 1 6667 In ( 1 .004302694)N In 4. 1 6667 N * In ( 1. 004302694) N (In 4. 1 6667) / (In 1 .004302694) 332.392957 332 steps =

=

=

=

=

= =

=

=

5. 1 12

=

Plan: The amount of each gas that leaks from the balloon is proportional to its effusion rate. Using 45% as the rate for H2, the rate for O2 can be determined from Graham's Law. Solution : Rate 0 2 Molar Mass H 2 2.0 1 6 g/mol Rate O 2 Rate H 2 Molar Mass 0 2 32.00 g/mol 45 = Rate O2 0.250998(45) 1 1 .2949 (unrounded) Amount of H 2 that leaks 45%; 1 00-45 = 55% H2 remains Amount of O2 that leaks 1 1 .2949%; 1 00- 1 1 . 2949 88.705% O2 remains � 88.705 1 .6 1 28 1 .6 55 H2 =

=

=

=

=

=

=

=

=

82

Chapter 6 Thermochemistry: Energy Flow and Chemical Change FOLLOW-UP PROBLEMS

6. 1

Plan: The system is the reactant and products of the reaction. Since heat is absorbed by the surroundings, the system releases heat and q is negative. Because work is done on the system, w is positive. Use equation 6.2 to calculate 11E. Solution : 1 .055 kJ 4. 1 84 kJ I1E = q + w = ( -26.0 kcal ) + ( + 1 5 .0 Btu ) = -92.959 = - 93 kJ 1 kcal I Btu Check: A negative I1E seems reasonable since energy must be removed from the system to condense gaseous reactants into a liquid product.

(

(

)

)

6.2

Plan: Since heat is a "product" in this reaction, the reaction is exothermic (f1H < 0) and the reactants are above the products in an enthalpy diagram. Solution:

6.3

Plan: Heat is transferred away from the ethylene glycol as it cools. Table 6.2 lists the specific heat of ethylene glycol as 2.42 J/gK. This value becomes negative because heat is lost. The heat released is calculated using equation 6.7. Solution: �T = 37.0°C - 25.0°C = 1 2°C = 1 2.0 K 1 J I L � q = c X mass X �T = ( 2 .42 J/gK ) ( 5 .50 L ) � ( l 2.0 K ) m L 1 0- L 10 J = - 1 77.289 = -1 77 kJ

[ l ( )l

[

6.4

[ �1

Plan: To find �T, find the T final by applying equation 6.7. The diamond loses heat (-q d iamon d ) whereas the water gains heat (q w ater) . Although the Celsius degree and Kelvin degree are the same size, be careful when interchanging the units. To be safe, always convert the Celsius temperature to Kelvin temperatures. Use the initial temperatures, masses, and specific heat capacities to solve the expression below. Solution: -q d iamon d = q water

-( m Cd iamo nd � T)

=

m Cwater �T

(

( 1 0.25 carat ) 0.2000 g

)

= 2.050 g 1 carat = 74.2 1 + 273 . 1 5 347.36 K Tinit (diamond) = 27.20 + 273 . 1 5 = 300.35 K Tinit (water) - (2.050 g) (0.5 1 9 J/g-K) (T final - 347.36) = (26.05 g) (4. 1 84 J/g-K) (T final - 300.35) (-1 .06395 J/ K) (T final - 347.36) = ( 1 08.9932 J/ K) (T final - 300.35) - 1 .06395 T final + 369.5737 = 1 08.9932 T final - 32736. 1 08 33 1 05 .68 1 7 = 1 1 0.057 1 5 Tfina l

mass of diamond

=

=

83

T final = 300.80446 K �Td iamon d = 300.80446 - 347.36 = -46.55554 = -46.56 K �Twater = 300.80446 - 300.35 = 0.45446 K = 0.45 K

Check: Rounding errors account for the slight differences in the final answer when compared to the identical calculation using Celsius temperatures. The temperature of the diamond decreases as the temperature of the water increases. The temperature of the water does not increase significantly because its specific heat capacity is large in comparison to the diamond, so it takes more heat to raise I g of the substance by I OC.

6.5

Plan: The bomb calorimeter gains heat from the combustion of graphite, so -qgraphi te = q c alorimeter Convert the mass of graphite from grams to moles and use the given kllmol to find qgrap h ite ' The heat lost by graphite equals the heat gained from the calorimeter, or L'lT multiplied by C calorimeter ' Solution: - (mol graphite x kllmol graphite) = Ccalorimeter �Tcalorimeter I mol C -393.5 kJ = Ccalorimete/2 . 6 1 3 K) - ( 0.8650 g C ) I mol C 1 2.0 1 g C -28.34 1 1 7 = Ccalorimeter(2 .6 1 3 K) Ccalorimeter = 1 0.8462 2 = 10.85 kJ/K

(

6.6

)(

)

Plan: To find the heat required, write a balanced thermochemical equation and use appropriate molar ratios to solve for required heat. Solution: Mf = - 1 37 kJ C2H4(g) + H2(g) -7 C2H 6 (g) I mol C 2 H6 - 1 37 kJ H eat = ( 1 5 .0 kg C 2 H 6 ) 1 0 3 g = -6.83405 X 1 0 4 = --6.83 X 1 0 4 kJ I kg 30.07 g C 2 H6 I mol C 2 H6

[ )(

)

)(

6.7

Plan: Manipulate the two equations so that their sum will result in the overall equation. Reverse the first equation (and change the sign of M!); reverse the second equation and multiply the coefficients (and M!) by two. Solution: Mf = -(223 .7 kl)= -223.7 kJ 2 �lO(g) + 3/2 02(g) -7 N20S(s) 2 N02(g) -7 2 NOEg) + Olg} Mf = -2(-57 . 1 kl) = 1 1 4.2 kJ Total: 2 N02(g) + 1 12 02(g) -7 N20S(s) Mf = -1 09.5 kJ

6.8

Plan: Write the elements as reactants (each in its standard state), and place one mole of the substance formed on the product side. Balance the equation with the following differences from "normal" balancing - only one mole of the desired product can be on the right hand side of the arrow (and nothing else), and fractional coefficients are allowed on the reactant side. The values for the standard heats of formation ( � H ; ) may be found in the appendix. Solution: a) C(graphite) + 2 H2(g) + 1 /2 02(g) -7 C H) O H ( l) Mf; = -238.6 kJ b) Ca(s) + 1 /2 02(g) -7 CaO(s) Mf ; = --635. 1 kJ c) C(graphite) + 1 14 Sg(rhombic) -7 CS 2 ( l) Mf ; = 87.9 kJ

6.9

Plan: Apply equation 6.8 to this reaction, substitute given values, and solve for the Mf; (C H) O H ). Solution: Mf;omb = 'L Mf; (products) - 'L Mf; (reactants) Mf;omb = [ Mf; (C02(g» + 2 Mf; (H20(g» ] - [ Mf; (CH)OH(l) + 3/7 Mf; (02(g» ] -63 8.5 kJ = [ 1 mol(-393 .5 kllmol) + 2 mol(-24 1 .826 kllmol)] - [ Mf ; (CH)OH(l) + 3/2(0)]

-638.5 kJ = (-877. 1 52 kl) - Mf ; (CH)OH( l) Mf; (CH)OH(l) = -23 8.652 = -238.6 kJ Check: You solved for this value in Follow-Up 6.8. Are they the same? 84

END-OF-CHAPTER PROBLEMS

6.5

The change in a system' s energy is M q + w. If the system receives heat, then its qfinal is greater than qinitial so q is positive. Since the system performs work, its Wfinal < Winitial so W is negative. The change in energy is (+425 J) + (- 425 J) 0 J. =

=

6. 7

C(s) + 02(g) � CO2(g) + 3 . 3 x 1 0 1 0 J ( 1 .0 ton) 1 J a) M(kJ) (3 . 3 x 1 0 1 0 3.3 X 107 kJ 10 J =

b) M(kcal) c) M(Btu) 6. 1 0

6. 1 1

J) [ � ) ( J[ � ) ( J =

=

=

(3.3

(3 . 3

x x

10

10

10

10

J)

J)

1

cal

4 . 1 84

Btu 1 05 5 J 1

1

J

10

=

cal cal

3 . 1 2 7 96

=

X

X

1 06

3.1

X

7 . 8 87

10

7

=

=

7.9

X

106 kcal

107 Btu

a) Exothermic, the system (water) i s releasing heat in changing from liquid to solid. b) E ndothermic, the system (water) is absorbing heat in changing from liquid to gas. c) Exothermic, the process of digestion breaks down food and releases energy. d) Exothermic, heat is released as a person runs and muscles perform work. e) Endothermic, heat is absorbed as food calories are converted to body tissue. f) Endothermic, the wood being chopped absorbs heat (and work). g) Exothermic, the furnace releases heat from fuel combustion. Alternatively, if the system is defined as the air in the house, the change is endothermic since the air's temperature is increasing by the input of heat energy from the furnace. An exothermic reaction releases heat, so the reactants have greater H (Hini tial) than the products (Hfinal) . /).}f Hfinal - Hinitial < O. =

Reactants

!

Products 6. 1 3

-

Mf � ( ) , (exothwn;,)

a) Combustion of methane : CH 4 (g) + 2 02(g) � CO2(g) + 2 H20(g) + heat C H 4 + 2 O2 (initial)

!

-

Mf � ( ) , (oxothenn;,)

85

b) Freezing of water: H20(l) � H20(s) + heat H20(l) (initial) M! = (-), (exothermic)

6. 1 5

a) Combustion of hydrocarbons and related compounds require oxygen (and a heat catalyst) to yield carbon dioxide gas, water vapor, and heat. C2HsOH(l) + 3 02(g) � 2 CO2 (g) + 3 H20(g) + heat C2HsOH + 3 O2 (initial)

2 CO2 + 3 H20 (final)

!

tlli � ( - ), (exothenn;c)

b) Nitrogen dioxide, N02, forms from N2 and O2. 1 /2 N2(g) + 02(g) + heat � N02(g) N02 (final)

f

tlli � (+), (endothenn;c)

1 12 N2 + O2 (initial)

6. 1 8

To determine the specific heat capacity of a substance, you need its mass, the heat added (or lost), and the change in temperature.

6.20

Plan: The heat required to raise the temperature of water is found by using the equation q = c x mass x LH . The specific heat capacity, Cwate" is found in Table 6.2. Because the Celsius degree is the same size as the kelvin degree, �T = 1 00.oC - 20.oC = 80.oC = 80. K.

(

q(J) = c x mass x �T = 4. 1 84 6.22

:

g C

}

1 2.0 g) ( ( I OO. - 20.) OC ) = 40 1 6.64 = 4.0 x 1 03 J

q(J) = c x mass x �T Tj = 3 .00°C Tr = ? 3 10 J 4 q = (85.0 kn = 8.50 x 1 0 J I kJ 4 8.50 x 1 0 J = (0.900 J/g0C) (295 g) (Tr - 3 .00)OC ( 8.50 x 1 04 J ) (T r - 3 . OO)OC = ----'----:-----'-.,... J O (295 g

( )

mass = 295 g

{ :�� J

(Tr - 3.00tC = 320. 1 5°C (unrounded) Tr = 323°C

86

c = 0.900 J/gOC

6.24 Since the bolts have the same mass, and one must cool as the other heats, the intuitive answer is [(7; : T, ) 1 [(l OO" C + 55" C )] 2 6.26 The heat l ost by Both the water origiarenal lconverted y at 82°e toi s gaimassnedusibyngthethewater thatty. is originally at 22°e. Therefore volumes densi Mass of85 mL = ( 85 mL ) ( I1.OmLO g ) = 85 g Mass of 165 mL ( 165 mL ) ( \. o� ) 165 g x mass84 Jx/g0C)(82°e water)=82)c x°emass(4.184 x (22°e water) J/g g) (85 -(4.1 0C) ( 165 g) (Tf -22)Oe 165 82) Tr -6970[ 85](Tf[ -22) ] ( Tr -3630 -+ 853630Tr= 165165 Tr+ 6970 85 Tr 10600. 250. T f Tr= (10600. /250. ) 42.4 on has a positive because thi s reaction requires the input of energy to break the oxygen-oxygen 6. 3 1 The bond:reacti02(g) + energy 2 0(g substanceochanges from the gaseous state to the l i q ui d state, energy i s rel eased so woul d be negative for 6. 3 2 Asthe acondensati n of I mol of water. The value of f..H for the vapori z ati o n of2 mol of water woul d be twi c e the value of H20(g) for the condensati on of 1 mol of water an opposite sign (+f..H) . 2 H20(l)vapor+ butEnergywoul d have 2 H20(g) H20(l) + Energy The enthalo npof2 y formol1 moles ofli e ofqwater would be opposite i n sign to and one-half the value for the conversi uid H20condensi to H20ngvapor. 6. 3 3 a)b) ThiBecause s reactif..Honi si sa state functiobecause tlHenergy i s negatirequi ve. red for the reverse reaction, regardless of how the change n, the total occurs, magni tudethe butreactidi foferent sigtten,n ofmeani the forward reacti okJn. iTherefore, speci fi c for n as wri n g that 20. 2 rel easedmorewhenenergy118 wioflal bemolrele eofased.sulfur c)reacts. The Inis thisthe issame case, 3. 2 moles of sul fur react and we therefore expect thatsmuch ( 3. 2 molSg ) ( ( 118-20.) mol2 kJSg ) 517 12 5 2 x 1 d) The mass of Ss requires conversion to mol e s and then a calculation identical to c) can be performed. ( 20. 0 g Sg ) ( 256.I mol5 6 gSgSg J(( 11-28 )0.mol2 kJSg ) 1 2 5974 12 6 90.29 kJ 6. 3 5 a) 112 N2(g) + 112 02(g) b) Mf. ( 1. 5 0 g NO) ( 30.1 mol0 1 gNONO J ( -I 90mol.29NOkJJ 5129957 4 5 1 �

-ql osl

=

�

77.50C

qgai n ed '

=

-q losl

=

=

qgai n ed

tJ. T

C

=

tJ.T

=

( Tf -

=

=

=

=

42°C

f..Hrx n ,

�

)

f..H

f..H

f..Hc ond

=

�

�

f..Hvap

(-)

=

( +) 2 [ f..Hc ond]

exothermic

f..H

tlHrx n

=

f..Hrx n =

-

.

=

=

� NO(g)

tlH

0 2 kJ

.

=

f..Hrx n =

rx n

-

.

-

= -

.

kJ

=

=

87

-4

.

=

-

.

kJ

=

+20.2 kJ.

6.37

6.42

6.44

For the reaction written, 2 moles of H202 release 1 96. l kl of energy upon decomposition. tillrxn = - 1 96. 1 kJ 2 H202(l) � 2 H20(l) + 02(g) 1 mol H202 1 03 g - 1 96. 1 kJ - -2 . 1 097 x 1 0 6 - -2 . 1 1 Heat - q - ( 732 kg H 2 0 2 -1 kg 34.02 g H202 2 mol H 202

) [ )(

J

(

J

x

6 1 0 kJ

To obtain the overall reaction, add the first reaction to the reverse of the second. When the second reaction is reversed, the sign of its enthalpy change is reversed from positive to negative. till = -635. 1 kJ Ca(s) + 1 12 02(g) � GaGW till = - 1 78.3 kl GaGW + COlg) � CaC03W till = -8 1 3.4 kJ Ca(s) + 1 /2 02(g) + CO2(g) � CaC03 (s) till = 1 80.6 kJ N2(g) + 02(g) � 2NO(g) till = - 1 1 4.2 kJ + Oig) � 2N02{g} tillrxn = +66.4 kJ N2(g) + 2 02(g) � 2 N02(g) In Figure P6.44, A represents reaction 1 with a larger amount of energy absorbed, B represents reaction 2 with a smaller amount of energy released, and C represents reaction 3 as the sum of A and B .

2NO(g)

6.47

The standard heat of reaction, t:Jf:n , is the enthalpy change for any reaction where all substances are in their standard states. The standard heat of formation, .:1H ; , is the enthalpy change that accompanies the formation of one mole of a compound in its standard state from elements in their standard states. Standard state is I atm for gases, 1 M for solutes, and pure state for liquids and solids. Standard state does not include a specific temperature, but a temperature must be specified in a table of standard values.

6.48

a) 1 12 Ch(g) + Na(s) � NaCI(s) The element chlorine occurs as C12, not Cl. b) H2(g) + 1 12 02(g) � H20( l) The element hydrogen exists as H2, not H, and the formation of water is written with water as the product in the liquid state. c) No changes

6.49

Formation equations show the formation of one mole of compound from its elements. The elements must be in their most stable states ( till ; =0) a) Ca(s) + CI2(g) � CaCI2(s) b) Na(s) + 1 12 H2(g) + C(graphite) + 3/2 02(g) � NaHC03 (s) c) C(graphite) + 2 CI2(g) � CCI4(l) d) 1 12 H2(g) + 1 12 N2(g) + 3/2 02(g) � HN0 3 (l)

6.5 1

The enthalpy change of a reaction is the sum of the tillf of the products minus the sum of the t:Jff of the reactants. Since the t:Jff values (Appendix B) are reported as energy per one mole, use the appropriate coefficient to reflect the higher number of moles. till :n = Im [ t:Jf; (products) ] - In [ till; (reactants) ] a) till:xn = { 2 t:Jf; [ S02(g)] + 2 till; [ H20(g) ] } - {2 till; [ H2S(g) ] + 3 t:Jf; [ 02(g) ] } = 2 mol(-296.8 kJ/mol) + 2 mol(-24 1 .826 kl/mol) - [2 mol(-20.2 kl/mol) + 3(0.0) ] = -1 036.8 kJ

b) The balanced equation is CH4(g) + 4 CI2(g) � CCI4(l) + 4 HCI(g) till;", = { I .:1H; [ CCI4(l)] + 4 t:Jf; [ HCI(g)] } - { 1 till; [CH4(g) ] + 4 t:Jf; [CI2(g) ] } t:Jf:xn = I mol(- 1 39 kJ/mol) + 4 mol(-92.3 1 kJ/mol) - [ I mol(-74.87 kl/mol) + 4 mol(O) ] = -433 kJ

88

6.53

!:l.H:n = Lm [ Mf; (products)] - Ln [ !:l.H; (reactants)] !:l.H:n - 1 46.0 kJ Cu20(s) + 1 12 02(g) � 2 CuO(s) !:l.H :n = {2 mol ( !:l.H; , CuO(s» } - { I mol ( Mf; , Cu20(s» + 1 12 mol ( Mf; , 02(g» } kJ - 1 46.0 kJ 2 mol ( !:l.H; , CuO(s» - [ 1 mol (- 1 68.6 ) + 1 /2 mol (0) ] mol - 1 46.0 kJ = 2 mol ( !:l.H; , CuO(s» + 1 68.6 kJ 3 1 4.6 kJ A LJ O tin ' C U O(S ) -157.3 kJ/mol I 2 mol =

=

=

6.56

-

=

-

2 PbS04(s) + 2 H20(!) � Pb(s) + Pb02(s) + 2 H2S04(!) a) !:l.H:" { I mol ( Mf ; , Pb(s» + I mol ( !:l.H; , Pb02(s» + 2 mol ( !:l.H; , H2S04(!) } - {2 mol ( !:l.H; , PbS04(s» + 2 mol ( Mf; , B20(!) } kJ kJ kJ = [ 1 mol (0 - ) + 1 mol (-276.6 - ) + 2 mol (-8 1 3 .989 - ) ] mol mol mol kJ kJ - [ 2 mol (-9 1 8.39 - ) + 2 mol (-285.840 - ) ] = 503.9 kJ mol mol b) Use Hess' s Law to rearrange equations ( 1 ) and ( 2) to give the equation wanted. Reverse the first equation (changing the sign of Mf:,, ) and multiply the coefficients (and !:l.H:,, ) of the second reaction by 2 . 2 PbS04(s) � Pb(s) + Pb02(s) + 2-8G;,W tili" = -(-768 kJ) tili" = 2{- 1 32 kJ) 2-8G;,(g) + 2 B20 fD � 2 B2S04(£L Reaction: 2 PbS04(s) + 2 B20(!) � Pb(s) + Pb02(s) + 2 H2S04(!) Mf:xn 504 kJ =

=

6.57

a) C l sH 36 02(S) + 26 02(g) � 1 8 CO2(g) + 1 8 H20(g) b) tili"comb = { 1 8 mol ( Mf; CO2(g)) + 1 8 mol ( !:l.H; H20(g» } - { I mol ( !:l.H; C l sH 36 02(S» + =

26 mol ( Mf; 02(g» } 1 8 mol (-393.5 kJ/mol) + 1 8 mol (-24 1 .826 kJ/mol) - [ 1 mol (-948 kJ/mol) + 26 mol (0 kJ/mol) ]

= -1 0,488 kJ

c) q(kJ) = ( 1 .00 g C l sH 36 02 = -36.9 kJ

mol CI s H 36 02 ( - 1 0, 488 kJ /l 2184.4 7 CI s H 36 02 J I I mol CI sH 36 02 J

q(kcal) = (-36.9 kJ

[

/l 4.11 kcal J 84 kJ

=

-8.81 kcal

]

- 8.8 1 kcal = 96.9 kcal 1 .0 g fat The calculated calorie content is consistent with the package information. d) q(kcal) = ( 1 1 .0 g fat )

6.58

a) A first read of this problem suggests there is insufficient information to solve the problem. Upon more careful reading, you find that the question asks volumes for each mole of helium. T = 273 + 1 5 = 288 K or T = 273 + 30 303 K L atm 0.082 1 ( 288 K ) V R T mol K IS = = 23 .6448 = 23.6 Ll mol P n ( 1 .00 atm) V30 n

=

RT P

(

=

(

0

0

0.082 1

)

)

L o atm (303 K ) mol K ( 1 .00 atm ) 0

=

=

=

24.8763 = 24 . 9 L/mol

89

b) Internal energy is the sum of the potential and kinetic energies of each He atom in the system (the balloon). The energy of one mole of hel ium atoms can be described as a function of temperature, E nRT, where n mole. Therefore, the internal energy at l 5°C and 30°C can be calculated. The inside back cover lists values of R with different units. 1 87 J nRT ( I mol) J/moloK) c) When the bal loon expands as temperature rises, the balloon performs work. However, the problem specifies that pressure remains constant, so work done on the surroundings by the balloon is defined by the equation : When pressure and volume are multiplied together, the unit is Loatm. Since we would like to express work in Joules, we can create a conversion factor between Loatm and 1 . IJ ? 2 Pa L atm m-Is

= 3/2 1 E = 3/2 = (3/2) .00 (8. 3 14 (303 -288)K = 187.065PY= w = -P�Y. 2 s a 101325 kg/m [ ) p ) [ 10-13 m3 )][ kg ( [ 1 ) ) ( ( 763 448 8 6 0 0 atm 1. 23. 24. = w=-P�Y ) 1 ( =-124. 7 8 = d) = M + P�Y = (187. 065 J) + (124. 7 8 J) = 31 1. 8 45 = e) = =

=

_

f)

1 .2

qp

till qp

x

2

10 J

3.1

310 J.

x

2 10 J

0

)

When a process occurs at constant pressure, the change in heat energy o f the system can be described by a state function called enthalpy. The change in enthalpy equals the heat (q) lost at constant pressure: M

6.66

�E - w = + w) -w = (q

qp

Chemical equations can be written that describe the three processes. Assume one mole of each substance of interest so that units are expressed as kJ . till ; till :x,. kJ H2(g) � CH4(g) ( I ) C(graphite) CH4(g) � C(g) R (g) till :,. kJ MfDatoJ11 till :,. kJ MfDatom ( 3 ) H 2(g) � H (g) The third equation is reversed and its coefficients are multiplied by to add the three equations. till :,. kJ C(graphite) + �W � GR4W till :,. kJ �W � C(g) � till :", kJ 4-:Hfgt � 2--#;ltrl­

(2)

+2

2

=

+4

+

C(graphite) � C(g)

6. 7 3

till = + P�Y =

Ml:n

= -74.9 = = 1660 = = 432 = -74.92 = 1660 = -2(432 kJ = -864 = = 72l.l = MfD ato m

72 1

kJ per one mol C(graphite)

a) The heat of reaction is calculated from the heats of formation found in Appendix B . The Ml; 's for all of the species, except SiCI4, are found in Appendix B. Use reaction with its given Ml:xn ' to find Ml; [ SiC I4(g)) . SiCI4(g) 2 H20(g) � Si02(s) 4HC I(g) Ml:,. Ml; [ H20(g) ] } [ SiCI4(g)] [ HCI(g) ] } [ Si02(s) ] kJ) } kJ kJ) kJ) { �H; [ SiCI4(g)] kJ) } kJ - { Ml ; [ SiCI4(g)] kJ) } kJ { M; [ SiCI4(g)] Ml; [ SiCI4(g)] kJ/mol (unrounded) The heats of reaction for the first two steps can now be calculated. ( I ) Si C s) � SiCI4(g) Ml; [ SiCI4(g)] till° rxn l [ Si Cs) ] Ml ; [ C I2(g)] } MfDrxn l 2(0) ] -657.0 kJ (2) Si02(s) 2C(graphite) 2CI2(g) � SiCI4(g) 2CO(g) Ml; [ C(gr) ] �H ; [ C h(g) ] } MfDrxn2 [ CO(g)]} � [ Si02(g) ] [ SiCI4(g)] 32.9 kJ kJ kJ) MfD rxn2 2(0) }

3,

(3) = + + - {till; +2 + 4 �H; { Ml; + 2(-241. 826 - 139. 5 = (-910. 9 + 4(-92. 3 1 + (---483. 652 -139. 5 = -1280.14 + (---483.652 1 140. 64 = = -656. 9 88 = + 2CI2(g) - { Ml; + 2 = -656.+ 9 88 kJ - [0 + + = -656.988 = + +2 = {Ml; +2 + 2 till; {M; = -656. 9 88 + 2(-1 10. 5 - { (-910.9 kJ) + 2(0) + = 32. 9 12 = 90

b) Adding reactions 2 and 3 yields: (2) �ts1 + 2C(graphite) + 2CI2(g) � 8iG4tgj + 2 C O ( g) f1ffO rxn = 3 2 .9 1 2 kJ (3) 8iGl4tgj + 2H20(g) � £iG;,fst + 4 HC I(g) f1ffOrxn = - 1 39.5 kJ 2 C(gr) + 2 Cb(g) + 2 H20(g) -> 2 C O (g) + 4 H CI(g) f1ffO rxn2+3 = -1 06.588 kJ kJ 06.588 1 -106.6 = = 2+3 f1ffO rxn Confirm this result by calculating Mi:. using Appendix B values. 2 C(gr) + 2 C b (g) + 2 H20(g) -> 2 CO(g) + 4 HC I(g) f1ffO rxn2+3 = { 2 Mi; [ CO(g) ] + 4 Mi ; [ HCI(g)] } - { 2 Mi; [ C( gr) ] + 2 Mi ; [ CI2(g) ] + 2 Mi; [ H20(g)] } f1ffO rxn2+3 = 2(- 1 1 0.5 kJ) + 4(-92.3 1 kJ) - [ 2(0) + 2(0) + 2(-24 1 .826 kJ) ] = -1 06.588 = -1 06.6 kJ 6.76

a) LlT = 8 1 9°C - O°C = 8 1 9°C = 8 1 9 K 3 w = PLl V = IlRLlT = ( 1 mol) x (8.3 1 4 J/mol o K) x (8 1 9 K) = --6809. 1 66 = -6.8 1 x 1 0 J b) q = (mass)(c)( LlT) 6.809 1 66 X 1 0 3 J LlT = --q"---­ (mass)(c) 28.02 g N 2 I mO I N 2 ( l . O O J/g o K) 1 mol N 2

[

Jl

(

6.77

Only reaction 3 contains N 204(g) , and only reaction 1 contains N 203(g) , so we can use those reactions as a starting point. N20 S appears in both reactions 2 and 5, but note the physical states present: solid and gas. As a rough start, adding reactions 1 , 3, and 5 yield the desired reactants and products, with some undesired intermediates: N203(g) � NO(g) + N02(g) Reverse ( 1 ) f1ffO rxn 1 = -(-39.8 kJ) = 39.8 kJ 4 N 02(g) � 2 N204 (g) Multiply (3) by 2 f1ffO rxn3 = 2(-57.2 kJ) = - 1 1 4.4 kJ Reverse (5) f1ffO rxns = -(-54. 1 kJ) = 54. 1 kJ lliQs(s) � N2�(g} N203(g) + 4N 02 (g) + N20 S( S) � NO(g) + N02( g) + 2 N204(g) + N20S( g) To cancel out the N20S(g) intermediate, reverse equation 2. This also cancels out some of the undesired N 02(g) but adds NO(g) and 02 (g) . Finally, add equation 4 to remove those intermediates: N203(g) � NG(gj + NQ;o(gj Reverse ( 1 ) f1ffO rxn 1 = -(-39.8 kJ) = 39.8 kJ Multiply (3) by 2 4-NG;o(gt-� 2 N204(g) f1ffO rxn3 = 2(-57.2 kJ) = - 1 1 4.4 kJ Reverse (5) N20S(s) � N;oG�(gj f1ffO rxn s = -(-54. 1 kJ) = 54. 1 kJ Reverse (2) N;oG�(gt-� NG(gj + �(gj + G;o(gj f1ffO rxn2 = --(-1 1 2.5 kJ) = 1 1 2.5 (4) 2 �+O(g) + G;"fgt-� 2-NG;ofrlf1ffOrxn4 = - 1 1 4.2 kJ Total: N 203(g) + N 20s(s) � 2 N204(g) Mi,:" = -22.2 kJ

6.79

a) The balanced chemical equation for this reaction is CH 4(g) + 2 02(g) � C O2(g) + 2 H20(g) Instead of burning one mole of methane, ( 25.0 g

CH 4 )

(

1 mol CH 4 1 6 .04 g CH 4

J

= 1 .5586 mol CH4 (unrounded) of methane

are burned. CH4(g) + 2 02(g) -> C O 2 (g) + 2 H20(g) f1ffOc omb = [ I mol ( Mi; C02(g» + 2 mol ( Mi; H20(g» ] - [ I mol ( Mi; C H4 (g» + 2 mol ( Mi; 02(g» ] f1ffO c omb = 1 mol (-393.5 kJ/mol) + 2 mol (-24 1 .826 kJ/mol) - [ 1 mol (-74.87kJ/mol) + 2mol (0.0 kJ/mol) ] = -802.282 kJ/mol CH4 (unrounded) ) -802.282 kJ 3 = - 1 250.4 = -1.25 x 1 0 kJ ( 1 .5586 mol C H 4 1 mol C H 4

(

)

91

b) The heat released by the reaction is "stored" in the gaseous molecules by virtue of their specific heat capacities, c, using the equation AH = mc�T. The problem specifies heat capacities on a molar basis, so we modify the equation to use moles, instead of mass. The gases that remain at the end of the reaction are CO2 and H20. All of the methane and oxygen molecules were consumed. However, the oxygen was added as a component of air, which is 78% N2 and 2 1 % O2, and there is leftover N2. 1 mol CO 2 = 1 .5586 mol Moles of C02(g) = ( 1 .5586 mol CH4 ) 1 mol CH4

( )(

J J

2 mol H 2 O = 3 . 1 1 72 mol 1 mol CH4 Mole fraction N2 = (79% 1 1 00%) = 0.79 Mole fraction O2 = (2 1 % I 1 00%) = 0.2 1 Moles ofN2(g) = (3 . 1 1 72 mol O2 used) (0.79 mol N2 1 0.2 1 mol O2) = 1 1 .7266 mol N2 (unrounded) Q = (mol)(c)(�T) 1 250.4 kJ ( 1 03 JI kJ) = 1 .5586 mol CO2 (57.2 J I mol°C) (Tr - O.O)OC + 3 . 1 1 72 mol H20 (36.0 J I mol°C) (T r - O.O)OC + 1 1 .7266 mol N2 (30.5 J I mol°C) (Tr - O.O)OC 1 .2504 x 1 06 J = « 89. 1 5 1 9 + 1 1 2.2 1 92 + 357.66 1 3) J 1°C)Tr = (559.0324 J 1°C)Tf Tr = ( 1 .2504 x 1 0 6 J) I (559.0324 J 1°C) = 2236.72 = 2.24 x l030C Moles of H20(g) = ( 1 .5586 mol CH4

92

Chapter 7 Quantum

Theory

and Atomic

Structure The value for the speed of light will be 3 .00 x 1 08 mls except when more significant figures are necessary, in which cases, 2.9979 x 1 08 mls will be used. FOLLOW-UP PROBLEMS

7. 1

Plan: Given the frequency of the light, use the equation c = AV to solve for wavelength. Solution: 3 x 08 = 4 1 4. 938 = 4 15 nm A = c I v = . 00 1 m/s 7.23 x 1 01 4 S - 1 1 0-9 m

(�) ( A)

3 . 00 x 1 08 m/s I = 4 1 49 . 3 8 = 4 1 5 0 A 7.23 x 1 01 4 S - I 1 0 - 1 0 m Check: The purple region of the visible light spectrum occurs between approximately 400 to 450 nm, so 4 1 5 nm is in the correct range for wavelength of purple light.

A c/v =

7.2

=

Plan: To calculate the energy for each wavelength we use the formula E = hc I A Solution: ( 6.626 x 1 0 -34 J s)(3 .00 X 1 08 m/s ) 1 7 = 2 X 1 0- 1 7 J = 1 .9878 X 1 0E = hc I A = 1 x 1 0-8 m •

E

=

hc I A =

( 6.626 x 1 0-34 J s)(3 .00 5 X 1 0- 7 m •

1 08 m/s )

X

=

3 .9756 X

1 0- 1 9 = 4

X

1 0- 1 9 J

( 6.626 x 1 0 -34 J . s)(3 .00 X 1 08 m/s ) 21 1 = 1 .9878 X 1 0= 2 X 1 0-2 J 1 x 1 0-4 m As the wavelength of light increases from ultraviolet (uv) to visible (vis) to infrared (ir) the energy of the light decreases. Check: The decrease in energy with increase in wavelength follows the inverse relationship between energy and wavelength in the equation E = hc I A .

E

7.3

=

hc I A =

P lan: With the equation for the de Broglie wavelength, A = hlmu and the given de Broglie wavelength, calculate the electron speed. Solution: 6.626 X 1 0 -34 J S kg · m 2 /s 2 = 7273.3 7.27 x 1 03 mls u=himA= J ' m ( 9 1 ' x 1 0 -" kg ) ( ' OO nm

[

•

{ �:m )1

[

Check: Perform a rough calculation to check order of magnitude: 1 0 -34 = 1 X 1 04

[

( 1 0 -" ) ( I 00 )

[ l O,-" )1

93

)

=

7.4

Plan: Following the rules for / (integer from 0 to n - I) and m, (integer from -/ to +i) write quantum numbers for n = 4. Solution: / = 0, 1 , 2, 3 For n = 4 For / = 0, m, = ° For / = 1 , m, = -1, 0, 1 For / = 2, m, = -2, -1, 0, 1 , 2 For / = 3 , m, = -3, -2, -1, 0, 1, 2, 3 2 Check: The total number of orbitals with a given n is n . For n = 4, the total number of orbitals would be 1 6. Adding the number of orbitals identified in the solution, gives I (for / = 0) + 3 (for / = 1 ) + 5 (for / = 2) + 7 (for / = 3) = 16 orbitals.

7.5

Plan: Identify n and / from the subshell designation and knowing the value for /, find the m, values. The subshells are given a letter designation, in which s represents / = 0, p represents / = 1 , d represents / = 2,/ represents / = 3 . Solution· m, values / value n value Sublevel name 1 - 1 , 0, 1 2 2p -3 , -2, - 1 , 0, 1 , 2, 3 3 5 Sf Check: The number of orbItals for each sublevel equals 21 + 1 . Sublevel 2p should have 3 orbitals and sublevel Sf should have 7 orbitals. Both of these agree with the number of m, values for the sublevel.

7.6

Plan: Use the rules for designating quantum numbers to fill in the blanks. For a given n, / can be any integer from 0 to n- l . For a given /, m, can be any integer from - / to + /. The subshells are given a letter designation, in which s represents / = 0, p represents 1 = 1 , d represents 1 = 2,/ represents / = 3. Solution: The completed table is: / m, n Name 4 0 a) I 4p 1 b) 2 0 2p 2 c) 3 -2 3d 2 d) 0 0 2s Check: All the given values are correct deSIgnatIons.

END-OF-CHAPTER PROBLEMS

7.2

a) Figure2 7.3 describes the2 electromagnetic spectrum by wavelength and frequency. Wavelength increases from left ( 1 0- nm) to right ( 1 0 1 nm). The trend in increasing wavelength is: x-ray < ultraviolet < visible < infrared < microwave < radio waves . b) Frequency is inversely proportional to wavelength according to equation 7. 1 , so frequency has the opposite trend: radio < microwave < infrared < visible < ultraviolet < x-ray. c) Energy is directly proportional to frequency according to equation 7.2. Therefore, the trend in increasing energy matches the trend in increasing frequency: radio < microwave < infrared < visible < ultraviolet < x-ray. High­ energy electromagnetic radiation disrupts cell function. It makes sense that you want to limit exposure to ultraviolet and x-ray radiation.

7.4

In order to explain the formula he developed for the energy vs. wavelength data of blackbody radiation, Max Planck assumed that only certain quantities of energy, called quanta, could be emitted or absorbed. The magnitude ofthese gains and losses were whole number multiples of the frequency: M = nhv.

94

7. 6 Pl1 Isan: WavelAssume ength thati s reltheatednumber to frequency through thesigequati onfigures. c Recall that a Hz i s a reci procal second, or 9 " 60" has three nificant cSol ution: 3. 00 x l08 m/s 3 Hz I (�H Z I ( 960. kH Z) ( 101 kHz ) ) 3. 00 x 108 m/s [ 1 �m 1 (nm) 3 H Z ] [ � ] 10 9 m ( 960. kH z ) [ 101kHz Hz 3. 00 x 108 m/s I ( I O 3 H Z ][ S - ] IO- m J ( 960. kH Z) [ 101 kHz Hz. . SolPlan:uhvtiFrequency on: i s related to energy through the equation hv. N ote that 1 Hz 1 10-34 Jos) 10 1 0 10-23 Si nce energy is directly proporti onal to frequency hv) and frequencyhcand wavelength are inversel y related (v it fol l ows that energy is inversely rel ated to wavel ength ) . As wavelength decreases, energy increases. In terms of i ncreasing energy the order is Plan: a) The shortest wavell eeastngthenergeti c photon has the longest wavelength nm). b) The most energetic photon has the 00 x 108 m/s [� l 1. 23 9669 10 1 5 a) v nm 10-9 m 1 nm ] hc ( 10-34 J s)( 108 m/s) [ -10-9 m. m/s [ 1 1 1. 3 636 101 5 b) v 00 10-10 m hc ( 1 0-34 J s)( 108 m/s ) [ 1 ] 9 1 10 00 10-1 0 m The number ishigrelheratedenergy to the(hienergy l evelvingofantheabsorpti electron.on spectrum. An electronAn electronenergy toenergy changeas from ldrops owerquantum energy (l o w to g h gi it from a hi g her energy l e vel to a l o wer one gi v i n g an emi s si o n spectrum. a) b) c) d) = AV .

I = S- .

= AV

A ( m) = � =

= 3 1 2.5 = 3 1 2 m

v

A

�

=

v

II = 3 . 1 25 x l O = 3.1 2 x l Ol l nm

=

I A

A (A) = �

12 12 = 3 . 1 25 x I 0 = 3. 1 2 x 1 0 A

v

E=

7.8

E=

E = ( 6 . 626

X

(3 . 6

X

I S- ) = 2 . 3 8 5 x

= 2 .4

X

=

1 0-

23

(E =

7. 1 0

= Ci A ) ,

red


O. Since the Kelvin temperature is always positive, I'1Gsys must be negative (I'1Gsys < 0) for a spontaneous process.

!:Jl :xn positive a n d L\S�., positive. The reaction is endothermic ( M/:" > 0) and requires a lot of heat from its surroundings to be spontaneous. The removal of heat from the surroundings results in I'1S:urr
1 . Q depends on initial conditions, not equi l i bri um conditions, so its val ue cannot be pred i cted from /:;. C o.

20.53

T h e standard free energy change, not confuse th i s with

t,G; , the

t,Go,

occurs w h e n a l l components o f t h e system are i n t h e i r standard states ( do

standard free energy of fonnati o n ) . Standard state is defined as I atm for gases,

I M for s o l utes, and pure so l i ds and l i quids. Standard state does not spec i fy a temperature because standard state can occur at any temperature . t,Co = /:;.G when a l l concentrations equal I M and a l l partial pressures equal 1 atm . T h i s occurs because the val ue of Q = 1 and In Q = 0 in the eq uation t,C = t,C o + RT In Q.

20.54

For e a c h reaction, fi rst fi n d

t,Go, t h e n calculate K fr o m t,Go = - RT

fro m Appen d i x B . a)

t,Go =

[1

mol

( t,C; ( N 0 2 (g) )] - [ I

[

mol

I n K. Calculate

t,G:,. using t h e t,G;

( t,C; (N O(g)) ) + 12 m o l ( t,G; ( 02(g)) ]

(86.60 kJ ) + 12 mol (0 kJ ) ] = -35 .6 kJ ( unrounded) t,Go -35.6 kJ / mo l . ) -1 03 J ) = 1 In K = -- = 4.3689 ( unrounded ) -RT - ( 8.3 1 4 J / mol K ) ( 298 K ) I kl K = e l 4 3 68 9 = 1 .739 1 377 x 1 0 6 = 1 . 7 1 0 6 b ) t,Co = [ 1 mo l ( t,G; ( H 2 (g) ) ) + 1 mol ( t,C; ( C I2(g) ) ) ] - [2 mol ( t,G; ( H C I (g) ) ) ] = [ I mol (0) + I mol ( O )kJ ] - [2 mol (-95.30 kJ/mol ) ] = 1 90.60 k J t,Go 1 90.60 kJ / mo l 1 03 J ) = In K = = -76.930 ( unrounded ) W - RT - ( 8.3 1 4 J / mo l K ) (2 9 8 K ) 34 K = e-7 6 9 3 0 = 3 .88799 x L O-34 = 3.89 1 0c ) t,Co = [2 mol ( t,G; ( C O (g) ) ) ] - [2 mol ( t,G; (C( graph ite ) ) ) + I mol ( t,G; ( 0 2 (g) ) ) ] = [2 mo l (- 1 37.2 kl/mol ) ) - [2 mol (0) + 1 mol (0) kJ ] = -274.4 kJ t,Go -274.4 kJ /mol 1 03 J ) = = In K = 1 1 0.75359 ( unrounded ) - RT - ( 8.3 1 4 J / mol o K ) (298 K ) W 11 . 5 K = e 0 7 3 59 = 1 .2579778 x 1 04 8 = 1 .26 1 0 48 = [ I mol

(5 1

k J ) ] - [ I mol

[

0

X

[

)[

0

X

[

)[

X

N ote : You may get a d i fferent answer depending on how you rounded in earl ier calculations.

296

val ues

20.56

The solubility reaction for Ag2 S is Ag2 S(s) + H 2 0(l) =+ 2 Ag+(aq) + HS-(aq) + O W(aq) /lGo = [2 mol ( /lG; Ag\aq)) + 1 mol ( /lG; H S-(aq ) ) + 1 mol ( /lG; O W (aq)] - [ 1 mol ( /lG; Ag2 S(s )) + I mol ( /lG; H 2 0(l))] = [(2 mol) (77. 1 1 1 kJ/mol) + ( l mol) ( 1 2.6 kJ/mol) + ( I mol) (- 1 57.30 kJ/mol)] - [( 1 mol) (-40.3 kJ/mol) + ( 1 mol) (-237. 1 92 kJ/mol)] = 287.0 1 4 kJ (umounded) /lGo 287.0 1 4 kJ / mol 1 03 J. In K = -= = - 1 1 5.8448 675 (umounded) -RT - ( 8.3 1 4 J /mol K ) ( 298 K ) 1 kJ K = e-1 1 5. 844867 5 = 4.888924 1 x 1 0-5 1 = 4. 89 1 0-5 1

[

][ ]

•

X

20.58

Calculate /lG:.. , recognizing that 1 2 (s), not 1 2 (g), is the standard state for iodine. Solve for Kp using the equation /lGo = -RT In K. /lG:n = [(2 mol) ( /lG; (ICI))] - [( 1 mol) ( /lG; ( 1 2 )) + ( 1 mol) ( /lG; (Cl 2 ))] /lG:.. = [(2 mol) (-6.075 kJ/mol)] - [( 1 mol) ( 1 9.38 kJ/mol) + ( I mol ) (0)] /lG:. = -3 1 . 5 3 kJ I 03 J -3 1 .53 kJ / mol = 1 2.726 1 69 (umounded) In Kp = /lGo I -RT = - (8.3 1 4 J / mol · K ) (298 K ) I kJ Kp = e 1 2 726 1 6 9 = 3.3643794 x l Os = 3.36 1 0 5

][ ]

[

X

In K = -(8.3 1 4 J/mol ·K) (298 K) In ( 1 .7 1 0-5) = 2.72094 x 1 04 Ilmol = 2.7 1 04 J/mol The large positive /lGo indicates that it would not be possible to prepare a solution with the concentrations of lead and chloride ions at the standard state concentration of 1 M A Q calculation using I M solutions will confirm this: PbCI 2 (s) =+ Pb 2+(aq) + CI - (aq) 2 Q = [Pb +] [Cr] 2 = ( I M) ( I M) 2 =1 Since Q > Ksp, it is impossible to prepare a standard state solution of PbCI 2 .

20.60

/lGo = -RT

20.62

a) The equilibrium constant, K, is related to /lGo through the equation /lGo = -RT In K. /lGo = -RT In K = -(8.3 1 4 J/mol·K) (298 K) In (9. 1 x 1 0-6 ) = 2.875776 x 1 0 4 = 2.9 X 1 04 J/mol b) Since /lG:n is positive, the reaction direction as written is nonspontaneous. The reverse direction,

x

X

formation

of reactants, is spontaneous, so the reaction proceeds to the left. c) Calculate the value for Q and then use to find /lG. 2 2 2 2 Fe 2 + Hg 2 + [ 0.0 1 0 ] [ 0.025 ] = 1 .5625 x 1 0-4 ( umounded) Q 2 ] ] [ [ 0.20 0.0 1 0 Fe3 + Hg� + =

[ J[ J [ r[ ]

=

RT In Q = 2.875776 1 04 J/mol + (8.3 1 4 Ilmol·K) (298) In ( 1 .5625 x 1 0-4 ) = 7 .044 1 87 1 03 = 7.0 1 03 J/mol Because /lG29 8 > 0 and Q > K, the reaction proceeds to the left to reach equilibrium.

/lG = /lGo +

X

X

20.64

X

Formation of 0 3 from O 2 : 3 0 2 (g) =+ 2 0 3 (g) or per mole of ozone: 3/2 0 2 (g) =+ 0 3 (g) a) To decide when production of ozone is favored, both the signs of /lH; and /lS; for ozone are needed. From Appendix B , the values of llH; and 5" can be used: llH ; = [ I mol 0 3 ( llH; 0 3 )] - [3/2 mol ( llH; O2 )] llH; = [ I mol( 1 43 kJ/mol] - [3/2 mol(O)] = 1 43 kllmol /lS ; = [ 1 mol 0 3 ( 5" 0 3 )] - [3/2 mol O 2 ( 5"0 2 )] 297

""S; = [ 1 mol (23 8.82 J/mol-K] - [3/2 mol (205 .0 llmol-K)] = -68.68 J/mol-K (unrounded). The positive sign for !'1f1; and the negative sign for M; indicates the formation of ozone is favored at no temperature. The reaction is nonspontaneous at all temperatures. b) At 298 K, ""Go can be most easily calculated from ""G; values for the reaction 3/2 02(g) =+ 03(g). From ""G; : ""Go = [ 1 mol 03 ( ""Gj 03)] - [3/2 mol ( ""G,} O2)] ""Go = [ 1 mol ( 1 63 kllmol 03)] - [3/2 mol (0)] = 1 63 kJ for the formation of one mole of 03. c) Calculate the value for Q and then use to find ""G. 0 3 ] [ 5 X 1 0 -7 atm [ = 5 . 1 95664 x 1 0-6 (unfounded) Q= 3 ti ti 3- = [ [ 02 ] 0.2 1 atm ] 3 ""G = ""Go + RT In Q = 1 63 kllmol + (8.3 1 4 J/mol-K) (298) ( l kJ I 1 0 J) In ( 5 . 1 95664 x 1 0-6) = 1 32.85368 = 1 x 1 0 2 kJ/mol

]

_ _

20.67 (a) (b) (c) (d) (e) ( f)

!'1f1rxn

""Srxn

+

0 + ( -) 0 +

( +) -

0 ( ) -

+

""Grxn

Comment

-

Spontaneous

( +)

-

Spontaneous Not spontaneous Spontaneous

+

Not spontaneous

(-)

T""S > !'1f1

a) The reaction is always spontaneous when ""Grxn < 0, so there is no need to look at the other values other than to check the answer. b) Because ""Grxn = !'1f1 - T ""S = -T ""S, M must be positive for ""Grxn to be negative. c) The reaction is always nonspontaneous when ""Grxn > 0, so there is no need to look at the other values other than to check the answer. d) Because ""Grxn = !'1f1 T M = !'1f1, !'1f1 must be negative for ""Grxn to be negative. e) Because ""Grxn = !'1f1 TM = T""S, M must be negative for ""Grxn to be positive. f) Because T ""S > !'1f1 the subtraction of a larger positive term causes ""Grxn to be negative. -

-

-

,

20.69

.

a) For the reactIOn, K = K=

[ Hb - CO] [ Hb - 02 ]

[ Hb - CO][02 ] [ since the problem states that [ 0 2] = [ CO ] ; the K expression simplifies to: Hb - 02 ][ CO ]

][ )

The equilibrium constant, K, is related to ""Go through the equation ""Go = -RT In K. ""Go - 1 4 kJ /mol 1 03 J In K = -- = -- = 5 .43 1 956979 ( unrounded) RT - ( 8.3 1 4 J /mol - K ) ( (273 + 37)K ) l kJ

[

3 K = e 5 4 1 9569 79 8 = 228 .596 = 2.3

x

1 02 =

[ Hb - CO] [ Hb - 02 ]

�---=-

b) By increasing the concentration of oxygen, the equilibrium can be shifted in the direction of Hb-02• Administer oxygen-rich air to counteract the CO poisoning.

298

20.72 a) 2 N20S(g) + 6 F2(g) 4 NF3(g) + 5 02(g) b) Use the values from Appendix B to determine the value of t:J.Go. t:J.G:n =[(4 mol) (t:J.G; (NF3» + (5 mol) (t:J.G; (02»] - [( 2 mol) (t:J.G; (N20S» + (6 mol) (t:J.G; (F2»] t:J.G:n =[(4 mol) (-83.3 kl/mol» + (5 mol) (0 kl/mol) ] - [(2 mol) ( 1 18 kl/mol) + (6 mol) (0 kl/mol)] -569.2 t:J.G:n = =-569 kJ c) Calculate the value for Q and then use to find t:J.G. _ [ NF3 1 [ 02 f - [ O. 25atm t[ O.50atm f = 47.6837 (unrounded) Q2 [ N20S f [ F2 ]6 [ O.20atm ] [ O.20atm ]6 3 + (I kJ I 10 J) (8.3 14 J/mol-K) ( 298) In ( 47.6837) t:J.G =t:J.Go + RT In Q =-569.2 kl/mol 2 =-559.625 =-5.60 10 kJ/mol 20.75 a) The chemical equation for this process is 3 C(s) + 2 Fe203(S) 3 CO2(g) + 4 Fe(s) tili:n =[(3 mol) (tili; (C02» + (4 mol) (tili; (F e»] - [(3 mol) (tili; (C» + (2 mol) (tili; (F e203»] tili:n =[(3 mol) (-393.5 kl/mol) + (4 mol) (0)] - [(3 mol) (0) + (2 mol) (-825.5 kl/mol)] 470.5 kJ t:J.S:n =[(3 mol) (S;(C02» + (4 mol) (S;(Fe»] - [(3 mol) (S;(C» + (2 mol) (S;(Fe203»] t:J.S:n =[(3 mol) (213.7 J/mol-K) + (4 mol) (27.3 J/mol-K) ] - [(3 mol) (5.686 J/mol-K) + (2 mol) (87.400 J/mol-K)] M:n =558. 4 42 =558.4 JIK b) The reaction will be spontaneous at higher temperatures, where the -Tt:J.S term will be larger in magnitude than tili. c) t:J.G;98 =tili:n - T t:J.S:n =470.5 kl - [(298 K) (558.442 JIK) (1 kl I 103 J)] = 304.084 = 304.1 kJ Because t:J.G is positive, the reaction is not spontaneous. d) The temperature at which the reaction becomes spontaneous is found by calculating t:J.G:n =0 =tili:n - T t:J.S:n tili:n =T t:J.S:n ° 470.5 kJ [ 103 J 1 = 842.5 225896 =842.5 T = tili = 558.442 J/K 1 kJ MO �

_

x

�

=

K

20.77 a) The balanced chemical equation is N20S(s) + H20(/) 2 HN Oi/) Calculate t:J.G:n for the reaction and see if the value is positive or negative. t:J.G:n =[(2 mol) (t:J.G; (HN03»] - [(1 mol) (t:J.G; (N20S» + (1 mol) (t:J.G; (H20»] t:J.G:n =[(2 mol) (-79.914 kJ/mol)] - [(1 mol) (1 14 kl/mol) + (1 mol) (-237.192 kl/mo!)] t:J.G:n =-36.636 =-37 kl Yes, the reaction is spontaneous because the value of t:J.G:n is negative. b) The balanced chemical equation is 2 N20s(s) 4 N02(g) + 02(g) The value of t:J.G:n indicates the spontaneity of the reaction, and the individual tili:n and t:J.S:n values are necessary to determine the temperature. t:J.G:n =[(4 mol) (t:J.G; (N02» + (1 mol) (t:J.G; (02 )) ] - [(2 mol) (t:J.G; (N20s )) ] t:J.G:n =[(4 mol) (51 kl/mol» + (I mol) (0)] - [(2 mol) (1 14 kl/mol) ] t:J.G:n =-24 kl Yes, the reaction is spontaneous because the value of t:J.G:n is negative. �

�

299

MI:" = [ (4 mol) (MI; (N02» + ( 1 mol) (MI; (02»] - [( 2 mol) (MI; (N20 S))] MI:" = [(4 mol) (33 .2 kl/mol) + (I mol) (0)] - [(2 mol) (-43 . lkJ/mol)] MI:,, = 2 1 9.0 kJ fhl:" = [(4 mol) (S"(N0 2» + ( 1 mol) (S"(02»] - [(2 mol) (S"(N20 S))] i1S:n = [(4 mol) (239.9 J/mol oK) + (I mol) (205 J/mol oK)] - [(2 mol) ( 1 78 J/moloK)] fhl :" = 808.6 JIK

[

MIo - 2 1 9.0 kJ 1 03 J = 270.83 8 = 2 70. 8K 808.6 J/K 1 kJ i1So c) The balanced che mical e quati on is 2 N 20 S( g) 44 N02(g) + 02( g) MI:" = [(4 mol) ( MI; (N02» + (I mol) (MI; (02)]- [ ( 2 mol) (MI; (N20 S))] MI:" = [(4 mol) (3 3 .2 kJ/mot) + (I mol) (0)] - [(2 mol) ( llkJ/mol)] MI:,, = 1 1 0.8 = III kJ fhl :" = [( 4 mol) (S"(N02» + (I mol) (S"(02»]- [(2 mol) (S°(N20 S))] fhl:" = [(4 mo t) (239.9 J/moloK) + (I mol) (205 J/mol oK)] - [(2 mol) (346 J/moloK)] fhl :n = 472.6 = 473 JIK T-

]

MIo l l O.8 k J l O 3 J = 234.4477 = 234 K = 472.6 J/K 1 kJ fhl o The te mpe rat ure is d iffe rent because the val ues fo r N 20S vary w ith physical state .

[

T=

20.8 1

]

a) Kp = 1 .00 when i1G = 0; co mb ine th is with i1G = MI- Tfhl. F irst, calculate MIand fhl, using values in the Append ix. MfD = [(2 mol NH ) (MI; N H ) ] - [( 1 mol N 2) (MI; N 2) + (3 mol H2) (MI; H 2)] 3 3 = [ ( 2 mol NH 3 ) (-45.9 kJ/mol)] - [( I mol N 2) (0) + ( 3 mol H 2) (0)] = -9 1 .8 kJ t1S" = [(2 mol NH ) ( SO N H ) ] - [( 1 mol N 2 ) ( SO N 2) + (3 mol H 2) ( SO H 2)] 3 3 = [(2 mol NH 3 ) ( 1 93 J/moloK)] - [( 1 mol N 2 ) ( l 9 l .50 J/mol oK) + (3 mol H 2) ( 1 30.6 J/moloK)] = -1 97.3 J/ K ( unro unded) i1G = 0 ( at e quil ib rium) i1G = 0 = MI- Tfhl MI= Tfhl -9 1 .8 kJ 1 0 3 J MIo = 465.28 1 = 465 K T - 1 97.3 J/K 1 kJ i1So b) U se the relationsh ip s: i1G = MI- Tfhl and i1G = -RT I n K w ith T = (273 + 400.) K 673 K i1G = MI- Ti1S= (-9 1 . 8 kJ) ( 1 0 3 J 1 1 kl) - (673 K) (- 1 97.3 JIK) i1G = 4.09829 x 1 04 J ( un rounded) i1Go = -RT I n K 4.09829 X 1 0 4 ll mol In K = i1Go I -RT = = -7.3 2449 (unrounded) - ( 8.3 1 4 J/ mol o K)( 673 K ) 44 = e -7 .3 2 9 = 6.59 1 934 x l O -4 = 6.59 X 10-4 c) The reaction rate is h igher at the h igher te mperature. The time re quired (kinetics) overshadows the lower yield (the rmodynamic s). _

_ _

[

]

=

K

[

]

300

Chapter 21 Electrochemistry: Chemical Change and Electrical Work FOLLOW-UP PROBLEMS 21.1

Plan: Follow the steps fo r balancin g a redox reacti on in acidic s ol uti on : 1 . Divide into half- reactions 2. Fo r each half- reaction balance a) Ato ms othe r than 0 and H, b) 0 ato ms with H2 0 , c) H a to ms with H+ and d) Charge with e -. 3. Multiply each half- reac ti on by an integer that will make the n umbe r of electrons l os t e qual to the nu mber o f electrons gained . 4. Add the half- reactions and cancel s ub stance s appearing as both reactants and p roducts. Then, add anothe r step fo r basic solution: 5. Add hyd roxide ion s to neutralize H+ . Cancel wate r. Solution: 1 . Divide into half- reactions: group the reac tan ts and p roduc ts wi th si milar ato ms . Mn0 4-(aq) � MnO /-(aq) naq) � lO ) -(aq) 2. For each half- reaction balance a) A to ms othe r than 0 and H Mn and r are balanced so no chan ge s needed b) 0 ato ms with H 2 0 , Mn0 4-(aq) � MnO/-(aq) 0 already balanced naq) + 3 H20( l) � rO) -(aq) Add 3 H20 to balance oxygen c) H ato ms with H+ Mn0 4-(aq) � MnO/-(aq) H al ready balanced naq) + 3 H2 0( l) � rO )-(aq) + 6 H +(aq) Add 6 H+ to balance hydro gen d) Cha rge with eMn0 4-(aq) + e- � Mn0 42-(aq) Total charge of reactants is -I and of p roducts is -2, so add I e- to reactants to balance charge: naq) + 3 H2 0( l) � rO) -(aq) + 6 H +(aq) + 6 e - Total charge is -I fo r reactants and +5 for p roducts, so add 6 e- as p roduct: 3. Multiply each half- reac tion by an inte ger that will make the n umbe r of electrons lost e qual to the n umbe r of elec tron s gained . One electron is gained and 6 are lost so reductio n must be multiplied by 6 fo r the n umbe r of elec tron s to be e qual. 6 {M n0 4-(aq) + e - � MnO /-(aq) } naq) + 3 H2 0( l) � rO)-(aq) + 6 H \aq ) + 6 e4. Add half- reactions and cancel s ubstance s appearing as both reactants and p roducts . 6 Mn0 4-(aq) + �- � 6 Mn042-(aq) nag) + 3 H20 CD � rO)-Cag) + 6 H \ag) + �Ove rall: 6 Mn0 4-(aq) + naq ) + 3 H2 0( l) � 6 MnO /-(aq) + rO)-(aq) + 6 H\aq) 5 . Add hyd roxide ions to neutralize H+ . Cancel wate r. The 6 H+ are neutralized by adding 6 O Ir. The same nu mbe r of hydroxide ions mus t be added to the reactants to keep the balance of 0 and H ato ms on both side s of the reaction. 6 Mn0 4-(aq) + naq) + 3 H2 0( l) + 6 O Ir(aq) � 6 MnO /-(aq) + lO)-(aq) + 6 H +(aq) + 6 OI1(aq) The neutralization reaction p roduce s wa ter: 6 { H+ + O Ir � H2 0 } . 6 Mn0 4-(aq) + naq) + 3 H2 0( l) + 6 O Ir(aq) � 6 MnO/-(aq) + 10) -(aq) + 6 H2 0( l)

301

Cancel water: 6 Mn0 4-(aq) + naq) + ��GtI1 + 6 OW(aq) -76 MnO /-(aq) + I0 3-(aq) + 6-H2 0( l) Balanced reaction i s 2 6 Mn0 4-(aq) + naq) + 6 OW(aq) -76 Mn0 4 -(aq) + I0 3-(aq) + 3 H2 0( l) Balanced reaction includin g spectato r ion s i s 6 KMn0 4(aq) + KI(aq) + 6 KO H(aq ) -7 6 K2 Mn0 4(aq) + KI0 3 (aq) + 3 H 2 0( l) Check: Check balance of atom s and charge: Reactants: P roducts: 6 Mn atoms 6 Mn atoms 1 I ato m I I ato m 30 0 ato ms 30 0 atoms 6 atoms 6 H atoms - 1 3 charge - 1 3 charge 2 1 .2

Plan: G iven the solution and electrode co mpo sition s, the two half cells involve the transfer of electrons I) between chromium in C r2 0 - and C r3 + and 2) between Sn and Sn2+ . The negative electrode is the anode so the tin half-cell i s where oxidation occurs. The graphite e lectrode with the chromium io n/chromate solution is where reduction occurs. In the cell dia gram, show the electrode s and the solutes involved in the half-reactions. I nclude the salt bridge and wi re connection between electrode s. Set up the two half-reactio ns and balance. ( Note that the Cr 3 +/Cr20 - half-cel l i s i n acidic solution.) W rite the cell notation placing the anode half-ce ll first, then the salt bridge , then the cathode half-cell. Solution: Cell dia gram: Voltmete r

/

/

ft

\\

Salt bridge

Sn ( )

C (+)

-

Cr 3 + , W C r20 7 2-

Sn2+

Balanced e quation s: Anode i s Sn/Sn2+ half-cell. Oxidation of Sn produces Sn2+ : Sn(s) -7Sn2 aq) All that needs to be balanced is charge: Sn (s) -7Sn2 aq) + 2 eCathode i s the C r3 +/C r2 0 7 2- half-cell. Check the oxidation number of chromium i n each substance to determine which i s reduced. C r3 + oxidation number i s +3 and chromium in Cr2 0 7 2- ha s oxidation number +6. Going from +6 to +3 involve s gain of electron s so C r2 0 - i s reduced. C rp -(aq) -7C r3 +( aq) Balance C r: C r2 0 -(aq) -72 C r3 +(aq) Balance 0: Cr2 0 -(aq) -72 C r3+(aq) + 7 H 2 0( l) Balance H : Cr2 0 -(aq) + 1 4 H +(aq) -72 C r3 aq) + 7 H2 0( l) Balance charge: C r2 0 -(aq) + 1 4 H + (aq) + 6 e- -72 C r3 aq) + 7 H2 0( l)

\ \

/ / l / l

l

\

\

302

Add two half-reactions2multiplying the tin half-reaction by 3 to equalize the number of electrons transferred. 3 {Sn(s) Sn \aq) + 2 e-} CrzO/-(aq) + 14 H\aq) + 6 e- 2 Cr3\aq) + 7 HzO(!) 3 Sn(s) + CrzO/-(aq) + 14 H +(aq) 3 Sn2+(aq) + Cr3\aq) + 7 HzO(!) Cell notation: Sn(s) I SnZ\aq) II H +(aq), CrzO/-(aq), Cr3+(aq) I C(graphite) 21. 3 Plan: Divide the reaction into half-reactions showing that Br2 is reduced and y3+ is oxidized. Use the equation E;ell = E;o''''''I< - E:', Oe to solve for E:,lOde . O Solution: Half-reactions: Reduction (cathode): Brz(aq) + 2 e- 2 Br-(aq) E:o,,,

C I-

a

Mn04-

Mn04-

CI-

From C I-,

to M n04-, �

305

21.7

a) Divide into half-reactions: CI03-(aq) -7 Cnaq) qaq) -712(s) 0 H I C 03-(aq) -7 Cnaq) 2 qaq) -7I2(s) H20 0 IO}-(aq) -7 Cnaq) + H20(l) C 2 qaq) -7I2(s) H+ H CIO}-(aq) + 6 H\aq) -7 Cnaq) + H20(l) 2 qaq) -7 12(s)

Balance elements other than and

chlorine is balanced iodine now balanced Balance by adding add 3 waters to add 3 0's to product 3 no change Balance by adding 3 add 6H+ to reactants no change Balance charge by adding eCIO}-(aq) + 6 H+(aq) + 6 e- -7 Cnaq) + 3 H20(l) add 6 e- to reactants for a -I charge on each side 2 qaq) -7I2(s) + 2 ee- to products for a -2 charge on each side Multiply each half-reaction by an integer to equalize the numberaddof2electrons CIO}-(aq) + 6 H+(aq) + 6e- -7 CI-(aq) + 3 H20(l) multiply by 1 to give 6 emultiply by 3 to give 6 e3 {2 qaq) -7 12(S) + 2 e-} Add half-reactions to give balanced equatiol] in acidic solution. 3 31 I Check balancing: C 03-(aq) + 6H+(aq) + 6 qaq) -7 Cnaq) + HP(l) + 2(s) Reactants: I CI Products: CI 3I 0 30 6 6H 6T

H 61

-I

-1

charge Oxidizing agent is CI03- and reducing agent is 1-. b) Divide into half-reactions: Mn04-(aq) -7 Mn02(s) SO/-(aq) -7 SO/-(aq) 0 H Mn04-(aq) -7 Mn02(S) SO/-(aq) -7 SO/-(aq) 0 H20 Mn04-(aq) -7 Mn02(S) + 2 H20(l) SO/-(aq) + H20(l) -7 SO/-(aq) H+ H Mn04-(aq) + 4 H+(aq) -7 Mn02(s) + 2 H20(l) SO/-(aq) + H20(l) -7 SO/-(aq) + 2 H+(aq)

Balance elements other than and

charge

is balanced is balanced Balance by adding add 2 H20 to products add H20 to reactants Balance by adding add 4 H+ to reactants add 2 H+ to products Balance charge by adding eMn04-(aq) + 4 H+(aq) + 3 e- -7 Mn02(S) + 2 H20(l) add 3 e- to reactants for a 0 charge on each side 2 SO/-(aq) + H20(l) -7 S04 -(aq) + 2 H\aq) + 2 e- add 2 e- to products for a -2 charge on each side Multiply each half-reaction by an integer to equalize the number of electrons multiply by 2 to give 6e2 {Mn04-(aq) + 4 H+(aq) + 3 e- -7Mn02(s) + 2 H20(l)} 3 {SO/-(aq) + H20(l) -7 SO/-(aq) + 2 H+(aq) + 2 e-} multiply by 3 to give 6eAdd half-reactions and cancel substances 2that appear as both reactants and products 2 Mn04-(aq) + &-H+(aq) + 3 S03 -(aq) + -7 2 Mn02(s) + 4=H20(l) + 3 SO/-(aq) + M4"� The balanced equation in acidic solution is: 2 Mn04-(aq) + 2 H+(aq) + 3 SO/-(ag) -7 2 Mn02(S) + H20(l) + 3 SO/-(aq) To change to basic solution, add OH- to both sides of equation to neutralize H+. 2 Mn04-(aq) + 2 H+(aq) + 2 OW(aq) + 3 S032-(aq) -7 2 Mn02(s) + H20(l) + 3 SO/-(aq) + 2 OW(aq) Mn04-(aq) + H20( l) + 3 SO/-(aq) -7 2 Mn02(S) + mGfl1 + 3 SO/-(aq) + 2 OW(aq) Balanced2equation in basic solution: 2 Mn04-(aq) + H20(l) + 3 S032-(aq) -7 2 Mn02(s) + 3 SO/-(aq) + 2 OW(aq) J-H;oGfA

�

306

Mn S

I

Check balancing: Reactants:

Products: 2Mn 2Mn 18 0 18 0 2H 2H 3S 3S -8 charge -8 charge Oxidizing agent is Mn04- and reducing agent is SO/-. c) Divide into half-reactions:

Mn04-(aq) � Mn2\aq) HZ02(aq) � 02(g) Balance elements other than 0 and H Mn04-(aq) � Mn2+(aq) Mn is balanced H20Z(aq) � 02(g) N o other elements to balance Balance 0 by adding H20 add 4 H20 to products Mn04-(aq) � Mn2+(aq) + 4 HzO(l) HZ02(aq) � 02(g) o is balanced Balance H by adding H+ add 8 H+ to reactants Mn04-(aq) + 8 H\aq) � Mn2\aq) + 4 H20(l) add 2 H + to products H202(aq) � 02(g) + 2 H+(aq) Balance charge by adding e add 5 e- to reactants for +2 on each side Mn04-(aq) + 8 W(aq) + 5 e- � Mn2+(aq) + 4 H20(l) add 2 e- to products for 0 charge on each side H202(aq) � 02(g) + 2 H+(aq) + 2 eMultiply each half-reaction by an integer to equalize the number of electrons multiply by 2 to give 1 0 e2 {Mn04-(aq) + 8 H+(aq) + 5 e- � Mn2+(aq) + 4 H2 0( l)} multiply by 5 to give 1 0 e5 {H202(aq) � 02 ( g) + 2 H+(aq) + 2 e -} Add half-reactions and cancel substances that appear as both reactants and products 2 Mn04-(aq) + M-H+(aq) + 5 H20Z(aq) � 2 Mn2\aq) + 8 H20(l) + 5 02(g) + -W-H"'taqj The balanced equation in acidic solution 2 2 Mn04-(aq) + 6 H+(aq) + 5 H20Z(aq) � 2 Mn +(aq) + 8 H20(l) + 5 02 ( g) Check balancing: Reactants: Products: 2 Mn 2Mn 18 0 18 0 16 16 H +4 charge +4 charge Oxidizing agent is Mn04- and reducing agent is H202.

H

21 . 1 0

a) Balance the reduction half-reaction: balance 0 N03-(aq) � NO(g) + 2 H 2 0(l) balance H N03-(aq) + 4 H+(aq) � NO(g) + 2 H20(l) balance charge N03-(aq) + 4 H+(aq) + 3 e- � NO(g) + 2 H20(l) Balance oxidation half-reaction: balance Sb 4 Sb(s) � Sb406 (s) balance 0 4 Sb(s) + 6 H20(l) � Sb406(s) balance H 4 Sb(s) + 6 H20(l) � Sb406(s) + 1 2 H+(aq) balance charge 4 Sb(s) + 6 H 2 0( l) � Sb406 (s) + 1 2 H\aq) + 1 2 eMultiply each half-reaction by an integer to equalize the number of electrons Multiply by 4 to give 1 2 e4{ N03-(aq) + 4 H+(aq) + 3 e- � N O( g) + 2 H 2 0( l)} Multiply by 1 to give 1 2 eI {4 Sb(s) + 6 H 20(l) � Sb406 (s) + 1 2 H+(aq) + 1 2 e- } Add half-reactions. Cancel common reactants and products. 4 N03-(aq) + M-H+(aq) + 4 Sb(s) + �G( l) � 4 NO(g) + 8-HzO(l) + Sb406(s) + �"'taqj Balanced equation in acidic solution: 4 N03-(aq) + 4 H\aq) + 4 Sb(s) � 4 NO(g) + 2 H20(l) + Sb406(s) Oxidizing agent is N 03- and reducing agent is Sb.

307

b) Balance reduction half-reaction: balance 0 Bi03-(aq) Bi 3+\aq) + 3 H320(l) balance H Bi03-(aq) + 6 H+(aq) Bi \aq) 3++ 3 H 20(l) balance charge to give +3 on each side Bi 0(l) e6 (aq) + 3 H (aq) + 2 Bi0 -(aq) + H 2 3 half-reaction: Balance oxidation balance 0 Mn22+(aq) + 4 H 20(l) Mn04-(aq) balance H Mn2\+ aq) + 4 H 20(l) Mn04-(aq) + 8 H +\aq) balance charge to give +2 on each side Mn + 4 H 2 0(l) Mn04-(aq) + 8 H (aq) + 5 e(aq) Multiply each half-reaction by an integer to equalize of electrons 3+(aq) +the3 Hnumber Multiply by 5 to give 1 0 eBi 0(l)} 5 {Bi0 3-(aq) + 6 H \ aq) + 2 e2 Mul tiply by 2 to give 1 0 e2 {Mn2+(aq) + 4 H 2 0(l) Mn04-(aq) + 8 H +(aq) + 5 e-} Add half-reactions. Cancel H 20 and H + in2 reactants and products. 3 Bi03-(aq)in acidic + W-H +(aq) + 2 Mn \ aq) + �G(l) 5 Bi +(aq) + B.-H 2 0(l) + 2 Mn0 4-(aq) + � Balanced5reaction solution: 2 5 Bi 3 +(aq) + 7 H 2 0( l) + 2 Mn0 4-(aq) 5 Bi0 3 -(aq) + 1 4 H+(aq) + 2 Mn \ aq) 2 Bi0 - is the oxidizing agent and Mn + is the reducing agent. c) Balance the3 reduction half-reaction: balance 0 Pb(OH) -(aq) Pb(s) + 3 H 20(l) balance H Pb(OH)33-(aq) + 3 H+(aq) Pb(s) + 3 H 2 0(l) Pb(OH)3-(aq) + 3 H \aq) + 2 e- Pb(s) + 3 H 20(l) balance charge to give 0 on each side Balance the oxidation half-reaction Fe(OH hCs) + H 20(l) Fe(O HMs) balance 0 Fe(OHhCs) + H 20(l) Fe(O HMs) + H \+ aq) balance H Fe(O H hCs) + H 20(l) Fe(O H)3(S) + H (aq) + ebalance charge to give 0 on each side Multiply each half-reaction by an integer to equalize the number of electrons I {Pb(O H)3-(aq) + 3 H \aq) + 2 e- Pb(s) + 3 H 20(l)} Multiply by I to give 2 eMultiply be 2 to give 2 e2 {Fe(OHh(s) + H 2 0(l) Fe(O HMs) + H +(aq) + e-} Add the two half-reactions. Cancel 0 and H Pb(OH)3-(aq) + �H +(aq) + 22 Fe(OHhCs) + ;!...H;;G(l) Pb(s) + �H20(l) + 2 Fe(O HHs) + ;!...H"� Pb(s) + H 20(l) + 2 Fe(O H)3(S) + H \ aq) + 2 Fe(O Hh(s) 3-(aq)sides Add one Pb(OH) OH- to both to neutralize H +. Pb(OH)3-(aq) + H\eq) OH-(aq) + 2 Fe(OHhCs) Pb(s) + H 20(l) + 2 Fe(OHMs) + OW(aq) GfI) + 2 Fe(O HhCs) Pb(s) + H;;GfI) + 2 Fe(O H Ms) + OW(aq) BalancedPb(OH) reaction3-(aq) in basic+ H;;solution: Pb(OH)3-(aq) + 2 Fe(OHhCs) Pb(s) + 2 Fe(OHMs) + OW(aq) Pb(OH)3- is the oxidizing agent and Fe(OH)2 is the reducing agent. a) Balance reduction half-reaction: balance 0 N03-(aq) N0+2(g) + H 20(l) balance H N03-(aq) + 2 H (aq) N02(g) + H 20(l) balance charge to give 0 on each side N0 -(aq) + 2 H \ aq) + e- N0 2 (g) + H 2 0(l) 3 Balance oxidation half-reaction: Au(s) + 4 Cr(aq) AuCI4-(aq) balance CI Au(s) + 4 Cr(aq) AuCI4-(aq) + 3 ebalance Multiply each half-reaction by an integer to equalize the number of electrons charge to on each side Multiply by 3 to give e3 {N0 3-(aq) + 2 H +(aq) + e- N0 2 (g) + H 2 0(l)} Multiply be 1 to give 3 e1 {Au(s) + 4 Cr(aq) AuCI 4-(aq) + 3 e-} Add half-reactions. Au(s)agent + 3 N0 3-(aq) + 4 Cr(aq) + 6 H +(aq) AuCI 4-(aq) + 3 N02 (g) + 3 H 2 0( l) b) Oxidizing is and reducing agent is c) The HCI provides chloride ions that combine with the unstable gold ion to form the stable ion, AuCLt-. -?

-?

-?

-?

-?

-?

-?

-?

-?

M-H"

-?

-?

-?

-?

-?

-? -?

-?

-?

W.

-?

-?

=i=

-?

-?

-?

2l . 1 2

-?

-?

-?

-?

-4

-?

-?

N03-

3

-?

-?

Au.

308

21.13 a) is the anode because by convention the anode is shown on the left. b) is the cathode because by convention the cathode is shown on the right. c) is the salt bridge providing electrical connection between the two solutions. d) is the anode, so oxidation takes place there. Oxidation is the loss of electrons, meaning that electrons are the anode.a positive charge because it is the cathode. e)leavingis assigned gains mass because the reduction of the metal ion produced the metal. 21.16 An active electrode is a reactant or product in the cell reaction, whereas an inactive electrode is neither a reactant nor a product. An inactive electrode is present only to conduct electricity when the half-cell reaction does not include a metal. Platinum and graphite are commonly used as inactive electrodes. 21.17 a) The metal is being oxidized to form the metal cation. To form positive ions an atom must always lose electrons, so this half-reaction is always an oxidation. b) The metal ion is gaining electrons to form the metal B, so it is displaced. c) The anode is the electrode at which oxidation takes place, so metal is used as the anode. d) Acid oxidizes metal B and metal B oxidizes metal A, so acid will oxidize metal A and when metal A is placed in acid. The same answer results if strength of reducing agents is considered. The fact that metal A is a better reducing agent than metal B indicates that if metal B reduces acid then metal A will also reduce acid. 21 .l8 a)Oxidation: Zn(s) Zn2+(aq) + 2e- (oxidation takes place at the negative electrode) 2 Reduction: Sn \aq) + 2e- Sn(s) Overall reaction: Zn(s) + Sn2+(aq) Zn2+(aq) + Sn(s) b) Voltmeter e e A

E

C

A

E f) E

A

B

A

b ubbles will form

�

�

�

\\

Zn () 1M Zn2+

�

Salt bridge

Sn (+)

-

It Amon flow

ICatIon t. Sn1 M2+ flow

21 .20 a) Electrons flow from the anode to the cathode, so left to right in the figure. By convention, the anode appears on the left and the cathode on the right. b) Electrons Oxidationenter occurstheatreduction the anode,half-cell, which isthethe electrode in the half-cell. c) half-cell in this example. d) Electrons are consumed in the reduction half-reaction. Reduction takes place at the cathode, electrode. e) The anode is assigned a negative charge, so the electrode is negatively charged. Metal is oxidized in the oxidation half-cell, so the electrode will decrease in mass. g) The solution must contain nickel ions, so any nickel salt can+ be added. is one choice. h) KN03 is commonly used in salt bridges, the ions being K Other salts are also acceptable answers. because an inactive electrode could not replace either electrode since both the oxidation and the i) reduction half-reactions include the metal as either a reactant or a product. j ) Anions will move toward the half-cell in which positive ions are bei n g produced. The oxidation half-cell produces Fe2+, so salt bridge anions move (nickel half-cell) (iron half-cell). Fe(s)2+ Fe2+(aq) + 2 ek) Oxidation half-reaction: Reduction half-reaction: Ni (aq) +22 e- Ni(s)2 Overall cell reaction: Fe(s) + Ni \aq) Fe \aq) + NiCs) from the iron half-cell to the nickel half-cell, iron

nickel

nickel

iron iron

f)

1 M NiS04

and N03-.

Neither

from right �

to left

�

�

309

21.22 fn cell notation, the oxidation components of the anode compartment are written on the left of the salt bridge and the reduction components of the cathode compartment are written to the right of the salt bridge. A double vertical line separates the anode from the cathode and represents the salt bridge. A single vertical line separates species of different phases. Anode I Cathode a) Al is oxidized,3+so it is the3+ anode and appears first in the cell notation: AI(s)IAI (aq)IICr (aq)ICr(s) reduced, so Cu is the cathode and appears last in the cell notation. The oxidation of S02 does not b)include Cu2+ ais metal , so an inactive electrode must be present. H ydrogen ion must be included in the oxidation half­ cell. 21.25 A negative E:ell indicates that the cell reaction is not spontaneous, > O. The reverse reaction is spontaneous with E;'II > O. 21.26 Similar to other state functions, the sign of E O changes when a reaction is reversed. Unlike and EO is an intensive property, the ratio of energy to charge. When the coefficients in a reaction are multiplied by a factor, the values of and are multiplied by the same factor. However, E O does not change because both the energy and charge are mUltiplied by the factor and their ratio remains unchanged. 21.27 a) Divide the balanced equation into reduction and oxidation half-reactions and add electrons. Add water and hydroxide ion to the half-reaction that includes oxygen. Oxidation: Se2-(aq) -7Se(s) + 2 eReduction: 2 SO/-(aq) + 3 H20(l) + 4 e--7S2032-(aq) + 6 OI1(aq) b) E ;'II = E �""ode - E:node E'�node = E�,,'ux'e - E :ell = -0.57 V - 0.35 V = 21.29 The greater (more positive) the reduction potential, the greater the strength as an oxidizing agent. a) 3From Appendix D:2 Fe +(aq) + e--7 Fe +(aq) EO = 0.77 V EO = 1.07 V Br22(l) + 2 e- -7 2Br-(aq) EO = 0.34 V Cu +(aq) + e- -7 Cu(s) + When placed in order of decreasing strength as oxidizing agents: b) 2From Appendix D: E O = -2.87 V Ca +(aq) + 2e- -7 Ca(s) Cr20l-(aq) + 14H\aq) 6e- -7 2Cr3\aq) + 7H20(l) EO = 1.33 V EO = 0.80 V Ag\aq) + e- -7 Ag(s) When placed in order of increasing strength as oxidizing agents: + 21.31 EOcell = Ecafhod E aOnode O e EO val u es are found in Appendix D . Spontaneous reactions have E:ell> O. a) Oxidation: Co(s)+ -7C02\aq) + 2 eEO = -0.28 V Reduction: 2 H (aq) + 2 e- -72 H2(g) E O = 0.00 V Overall reaction: Co(s) + 2 H+(aq) -7C0 +(aq) + H 2(g) E :ell = 0.00 - (-0.28 V) = Reaction is under standard state conditions because E :ell is positive. b) Oxidatio n: 2 {Mn2+(aq) + 4 H 20(l) -7Mn04-(aq) + 8 H\aq) + 5 e-} EO = +1.51 V 5 {Br2(l) + 2 e- -72 Br-(aq)} Reduction: 2 E O = +1.07 V Overall: 2 Mn \aq) + 5 Br2(l) + 8 H20(l) -72 Mn04-(aq) + 10 Br-(aq) + 16 H+(aq) E ;ell = 1.07 - 1.51 V = Reaction is under standard state conditions with E ,�ell O. tlGo

tlGo,!lff'

tlGo, !lff'

S",

S"

-0.92 V

3

Br2 > Fe + > C u 2 .

Ca2+


AI > Mn > Zn > Cr > Fe > Ni > Sn > Pb > Cu > Ag > H g> Au Metals with potentials lower than that of water (-0. 8 3 can displace hydrogen from water by reducing the hydrogen in water. These can displace H 2 from water: Li, Ba, Na, AI, and Mn Metals with potentials lower than that of hydrogen (0. 0 0 can displace hydrogen from acids by reducing the in acid. These can displace H from acid: Li, Sa, Na, AI, Mn, Zn, Cr, Fe, Ni, Sn, and Pb Metals with potentials above 2that of hydrogen (0. 0 0 cannot displace (reduce) hydrogen. These cannot displace H 2 : Cu, Ag, Hg, and Au 21.102 a) Use the stoichiometric relationships found in the balanced chemical equation to find mass of A1203 . Assume that 1 metric ton AI is an exact number. 2 AI203 (in Na3AIF6) + 3 C(gr) 4 AI(l) + 3 CO2(g) AI ) ( 2 mol AI 2 0 3 )( 10l. 9 6 g AI 2 0 3 ) [ 1 kg ] [_1 t_ ] mass AI203 (I t AI ) [ 1013 tkg ] [ 101 kg3 g ] ( 26.1 mol 9 8 g AI 4 mol AI I mol AI 2 03 103 g 103 kg 1.8895478 metric tons AI203 Therefore, are consumed in the production of 1 ton of pure AI. b) Use a ratio of3 mol C: 4 mol Al to find mass of graphite consumed. 1 t ] � ]( 1 mol AI )( 3 mol C )( 12. 0 1 g C)[ �] [ _ mass C (I t AI) [� ][ 3 3 1 t 1 kg 26.98 g AI 4 mol AI 1 mol C 10 g 10 kg 0.3338584 Therefore, are consumed in the production of 1 ton of pure AI, assuming 100% efficiency. c) The percent yield with respect to Ah03 is because the actual plant requirement of l.89 tons AI203 equals the theoretical amount calc ulated in part (a). d) The amount of graphite used in reality to produce 1 ton of AI is greater than the amount calculated in (b). In other words, a 100% efficient reaction takes only 0. 3 339 tons of graphite to produce a ton of AI, whereas real production requires more graphite and is less than 100% efficient. Calculate the efficiency using a simple ratio: (0. 4 5 t) (x) (0. 3 338584 t) (100%) x 74. 19076 =

=

max

X

=

]

=

=

-2.62 kJ /g

�

�

�

�

�

�

�

�

EO .

V)

V)

V)

�

=

=

= 1 .890 1 .890 tons of AI 203

=

=

0.3339 tons C 0.3339 tons of C =

1 00%

=

=

=

74 %

320

W

e) For every 4 moles of Al produced, 3 moles of CO2 are produced. Al 3 mol C O 4 moles C = ( I t AI ) [ 1013 tkg )[ 10I kg3 g )( 26.1 mol 9 8 g Al )( 4 mol Al2 ) = 2.7798 10 mol CO2 (unrounded) The problem states that 1 atm is exact. Use the ideal gas law to calculate volume, given moles, temperature and pressure. ( 2.7798 x 104 mol C O 2 )( 0. 0 8206L atm/mol K ) ( ( 273 + 960. ) K 10-3 m 3 ) V = nRT P = l �m IL = 2.81260] x 103 = 21.103 a) The reference half-reaction is: Cu2\aq) + 2 e- Cu(s) = 0. 3 4 Before the addition of the ammonia, = O. The addition of ammonia lowers the concentration of copper ions through the formation of the complex Cu(NH 3)/+. The original copper ion concentration is and the copper ion concentration in the solution containing ammonia is The Nernst equation is used to determine the copper ion concentration in the cell containing ammonia. = 0. 0 592n log ] 0.129 = 0. 0 0 0. 0 5922 log [Cu2+ [Cu2+ ] X

I

[

•

2.813

X

)][

•

3 3 10 m

�

Ecell

EO

V

[CU2+] original"

[C u 2+] . mmonia '

E

EO

V

_

Q

V

V

V

_

ammonia

] 0.129 = 0. 05922 log [Cu2+ [ 0. 0 100 ] ] (0.129 (-2 /0. 0 592) log [Cu2+ [ 0. 0 100 ] V

_

V

original

ammonia angma I

V)

.

.

ammonia

=

] --4.358108108 = log [Cu2+ [ 0. 0 100 ]

onglna I .

.

ammonia ongIna I .

.

Cu2+ ] 4.3842154 10-5 = [[ 0.0100 ] 10-7 (unrounded) 4.3842154 This is the concentration of the=copper ion thatx is not in the complex. The concentration of the complex and of the uncomplexed ammonia must be determined before may be calculated. The original number of moles of copper and the original number of moles of ammonia are found from the original volumes and molarities: . . moles of copper = ( 0. 0 100 mol CU(N03 h ) [ I mol Cu2+ )[ 10-3 L ) ( 90 . 0 m L ) OngInal 1 mol Cu(N03 h 1 mL L 4 = 9.00 x 10- mol . . moles ofammoma. = ( 0. 5 00 mol NH 3 )[ 10-3 L ) ( 10. 0 mL ) = 5. 00 x I0-3 mol NH 3 OngInal I mL L Determine the moles of copper still remaining uncomplexed. Remaining mol of copper = [ 4. 3 842154 x L10-7 mol Cu2+ ) [ 10-I mL3 L ) ( 100. 0 mL ) = 4.3842154 x 10-8 mol Cu ammonia

X

onglnaI .

.

M

[C u 2+] ammonia

Kr

--

C u2+

321

The difference between the original moles of copper and the copper ion remaining in solution is the copper in the complex (= moles of complex). The molarity of the complex may now be found. Moles copper in complex = (9.00 x 10-2 4 -4.3842154 x 10-8) mol Cu2+ = 8.9995615 10-4 mol Cu + (unrounded) 2 4 mol Cu + ) 1 mol CU (NH 3 )�+ (-1 mL ) Mo Ianty. f comp I ex = ( 8. 9995615100.102 0 mL I mol Cu + 10-3 L 3 = 8. 9995615 10- MCu(NH )/+ (unrounded) The concentration of the remaining ammonia is 3found as follows: mol N�3 ) ( 5. 0 0 x 10-3 mol NH 3 ) - ( 8. 9995615 10-4 mol c U 2 + ) ( 14 mol Cu + (-1 mL ) Molarity of ammonia = 100.0 mL 10-3 L = is:0.014001753 Mammonia (unrounded) The Kr equilibrium Cu2\aq) + 4 NH 3(aq) Cu(NH 3)/+(aq) )�+ J - [ [8. 9995615 x 1O-3 J 3 Kr - [CuCu(NH = 5. 34072 10" = [ 2 + ] [NH J 4. 3 842154 x 1O-7 J [0. 0 14001753 t b) The Kr wi II be used to determine the new concentration of free copper ions. Moles uncomplexed ammonia before the addition of new ammonia = (0.014001753 mol NH3 1 L)3 (10-3 Lli mL) (100. 0 mL) = 0.001400175 mol NH 3 Moles ammonia added = 5. 00 x 10- mol NH3 (same as original mol of ammonia) From the stoichiometry: 4 NH3(aq) Cu2\aq) Cu(NH + 3)/+(aq) 0.0014001753 mol Initial moles: 4. 3 842154 x 10-8 mol 8.9995615 x 10-4 mol Added moles: 5. 0 0 x 10mol Cu2+ is limiting: -(4.3842154 x 10-8 mol) -4 (4. 3 842154 10-8 mol) +(4. 3 842154 x 10-8 mol) 0 After the reaction: 0. 006400 mol 9. 00000 10-4 mol Determine concentrations before equilibrium: [Cu2+] = 0 [NH3] = (0. 006400 mol NH3 / 1 1O. 0 mL) (1 mL 1 10-3 L) = 0.0581818 MNH [Cu(NH3=)/+]0. 0=08181818 x 10-4 mol CU(NH3)/+ 1 1 10.0 mL) (1 mL 1 10-3 L) 3 (9.00000MCu(NH )/+ Now allow the system2 to come to equilibrium:3 Cu(NH 3)/+(aq) 4 NH3(aq) Cu \aq) + 0. 0 581818 0. 0 08181818 Initial molarity: 0 Change: +x +4x x Equilibrium: [ x 0. 0 581818 + 4 x 0. 008181818 - x )�+ J [0. 008181818 - x] = 5.34072 x 10 " 3 Kr- [ CuCu(NH 2 + J [NH 3 J [x][O. 0 581818 4x]4 Assume -x and +4x are negligible when compared to their associated numbers: [0. 0 08181818] = 5. 34072 x 10 " Kr= [x][O. 0 581818 t 2 x = [Cu +] = 1. 3 369 x 10-9 Cu2+ X

[

X

0

X

)

X

!:;

_

_

X

X

X

!:;

_

+

M

322

5.3

X

1 0- 1 1

Use the Nernst equation to determine the new cell potential: [ Cu 2 + ] ammonia E= log [ Cu 2 + ]

0.00 V 0. 05922 V - 0. 0 5922 V log [ 1. 3[0.3690 100]10-9 J 0. 203467 c) The first step will be to do a stoichiometry calculation of the reaction between copper ions and hydroxide ions. - ) [ 10-3 L ) Moles O W ( 0.500 mol NaOH )[ 1 mol OH (I O.o ) 5. 0 0 10-3 mol OW L I mol NaOH 1 mL The initial moles of copper ions were determined earlier: 9. 0 0 x 10-4 mol Cu2+ The reaction: + 2 0W(aq)3 Cu2+ (aq ) Cu(OHMs) 9. 0 0 x 10-4 mol Initial moles: 5.00 x 10- mol Cu2+ is limiting: -(9. 0 0 x 10-4 mol) -2 (9. 0 0 x 10-4 mol) 0 0. 0032 mol After the reaction: Determine concentrations before equilibrium: [Cu2+ ] 0 [NH 3 ] (0. 0 032 mol OH- / 100. 0 mL) (1 mL / 10-3 L) 0. 0 32 M O W Now allow the system to come to equilibrium: + 2 0W(aq) Cu(OHMs) Cu2+(aq ) Initial molarity: 0. 0 32 0. 0 Change: +x +2x x 0. 0 32+ 2 x Equilibrium: Ksp [Cu2+ ] [OW] 2 2. 2 10-20 Ksp [x][0. 0 32 + 2 ] 2 2. 2 10-20 Assume 2x is negli § ible compared to 0. 0 32 Ksp [x ] [ 0. 0 32 ] 2 2.2 x 10- 0 x [Cu2+] 2.1487375 10-1 7 2.1 10-1 7 _

original

X

E= E=

= 0.20 V

mL

=

=

X

---t

=

=

=

!::;

=

X

=

X

=

=

=

=

=

X

=

X

M.

M

X

=

Use the Nernst equation to determine the new cell potential: [ Cu 2 + J hydroxide E log [ Cu 2 + J

0.00 V 0. 05922 V x 1 O- J - 0.05922 V log [ 2.1487375 [0. 0 100] 0.4 34169 d) Use the Nernst equation to determine the copper ion concentration in the half-cell containing the hydroxide ion. [ Cu 2 + J 5 0 V 2 0. f 0. 0 0 V - � log _

=

original 17

E= E

=

E

=

=

0.43 V

[

Cu 2 +

[ Cu 2 + J

droX ide

original

0. 3 40 0. 0 5922 V I og [0. 0 100] [ Cu 2 + J (0. 340 V) (-2 /0. 0 592) g [0. 0 100] =

_

=

hydroxide

hydroxide

10

323

- 1 1 .486486

3 .262225 6

=

X

[

10 g

1 0-1 2

Cu 2 +

=

]

hydroxide

[ 0. 0 1 00 ]

[ C u 2 + ] hydroxide [ 0. 0 1 00 ]

[ C u 2+hydrox i de = 3 .2622256 X 1 0-1 4 M (unrounded) Now use the Ksp relationship : Ksp [ C u2+] [O Hl 2 . 2 X 1 0-20 Ksp = [ 3 .2622256 X 1 0-1 4 ] [OHlZ = 2 . 2 x 1 0-20 [OHlZ = 6 . 743 862 x 1 0-7 [OHl = 8 .2 1 2 1 x 1 0-4 = 8 . 2 X 1 0-4 M OI1 = 8.2 x 1 0-4 M NaOH =

2 1 . 1 05

=

The half-reactions are (from the Appendix): E = 0.00 V Oxidaton: H z (g) � 2 H +(aq) + 2 eReduction: E = 0 . 80 V 2 (Ag+(aq) + 1 e- � Ag(s)) Ece ll = 0 . 8 0 V - 0.0 V = 0 . 8 0 V 2 Ag+ (aq) + H (g) � 2 Ag(s) + 2 H+(aq) Overall : The hydrogen ion concentration 2can now be found from the Nernst equation. E = EO

_

0. 0592 V 2

0.9 1 5 V = 0.80 V

0.9 1 5 V

_

_

log Q 0 . 0592 V 2

0.80 V =

log

0 . 0592 V

_

2

/

1 . 3 0276

x

= log 1 0 -4

=

[H

+

[ Ag + r PH2

log

(0.9 1 5 V - 0 . 8 0 V) (-2 0.0592 V)

-3 . 8 85 1 3 5

[H+ r [H

+

r

[ 0 . 1 00 ] 2 ( 1 .00 )

= log

[ H: r

[ 0. 1 00 ] ( 1 . 00 )

r

[ 0 .0 1 00 ]

[H + r

[ 0 .0 1 00 ]

[ H+] = 1 . 1 4 1 3 85 1 X 1 0-3 M (unrounded) pH = -log [ H+] = -log ( 1 . 1 4 1 3 8 5 1 x 1 0-3)

=

2 .94256779

324

=

2 .94

Chapter 22 The Transition Elements and Their Coordination Compounds FOLLOW-UP PROBLEMS

22. 1

Plan: Locate the element on the periodic table and use its position and atomic number to write a partial electron configuration. Add or subtract electrons to obtain the configuration for the ion. Partial electron configurations do not include the noble gas configuration and any filledjsublevels, but do include outer level electrons (n-Ievel) and the n- l level d orbitals. Remember that ns electrons are removed before n-l electrons. Solution: a) Ag is in the fifth row of the periodic table, so n = S , and it is in group I B( l l ). The partial electron configuration of the element is Ss 1 4d1 0. For the ion, Ag+ , remove one electron from the Ss orbital. The partial electron configuration of Ag+ is 4dl O • b) Cd is in the fifth row and group 2B( 1 2), so the partial electron configuration of the element is Si4i o. Remove two electrons from the Ss orbital for the ion. The partial electron configuration of Cd2+ is 4dl O • c) Ir is in the sixth row and group The partial electron configuration of the element is 6isd7 . Remove two electrons from the 6s orbital and one from Sd for ion Ir3+ . The partial electron configuration of Ir3 + is 5,1 . Check: Total the electrons to make sure they agree with configuration. a) Ag+ should have 47 - 1 = 4 6 e-. Configuration has 36 e- (from Kr configuration) plus the 1 0 electrons in 4d1 o. This also totals 46 e-. b) Cd2+ should have 48 - 2 = 4 6 e-. Configuration is the same as Ag+, so 46 e- as well. c) 1r3 + should have 77 - 3 = 7 4 e-. Total in configuration is S4 e- (noble gas configuration) plus 1 4 e- ( in/­ sublevel) plus 6 e- (in the partial configuration) which equals 74 e-.

8B(9).

22.2

Plan: Name the compound by following rules outlined in section 22.2. Use Table 22.6 for the names of ligands and Table 22.7 for the names of metal ions. Write the formula from the name by breaking down the name into pieces that follow naming rules. Solution : a) The compound consists of the cation [Cr(H 2 0)sBr] 2- and anion cr. The metal ion in the cation is chromium and its charge is found from the charges on the ligands and the total charge on the ion. total charge = (charge on Cr) + S(charge on H 2 0) + (charge on Br-) -2 = (charge on Cr) + S(O) + (-1 ) charge on Cr = +3 The name of the cation will end with chromium(I I I) to indicate the oxidation state of the chromjum ion since there is more than one possible oxidation state for chromium. The water ligand is named aqua (Table 22.6). There are five water ligands, so pentaaqua describes the (H 2 0)s ligands. The bromide ligand is named bromo. The ligands are named in alphabetical order, so aqua comes before bromo. The name of the cation is pentaaquabromochromium(I I I). Add the chloride for the anion to complete the name: pentaaquabromochromiu m(III) chloride.

b) The compound consists of a cation, barium ion, and the anion hexacyanocobaltate(IIl). The formula of the anion consists of six (from hexa) cyanide (from cyano) ligands and cobalt (from cobaltate) in the +3 oxidation state (from (I I I)). Putting the formula together gives [Co(CN)6r+. To find the charge on the complex ion, calculate from charges on the ligands and the metal ion: total charge = 6( charge on CN-) + (charge on cobalt ion) = 6(- 1 ) + (+3 ) = -3 The formula of complex ion is [CO(CN )6] 3-. Combining this with the cation, Ba2+ , gives the formula for the compound: Ba3[Co(CN)6h. The three barium ions give a +6 charge and two anions give a -6 charge, so the net result is a neutral salt.

32S

22.3

Plan: The given complex ion has a coordination number of 6 (en is bidentate), so it will have an octahedral arrangement of ligands. Stereo isomers can be either geometric or optical. For geometric isomers, check if the ligands can be arranged either next to (cis) or opposite (trans) each other. Then, check if the mirror image of any of the geometric isomers is not superimposable. If mirror image is not superimposable, the structure is an optical isomer. Solution: The complex ion contains two NH} ligands and two chloride ligands, both of which can be arranged in either the cis or trans geometry. The possible combinations are \ ) cis-NH} and cis-Cl, 2) trans-NH} and cis-C!, and 3) cis­ NH} and trans-Cl. Both NH} and Cl trans is not possible because the two bonds to ethylenediamine can be arranged only in this cis-position, which leaves only one set of trans positions. +

+

NH3

J 1

CI H2N " , / ( / Co , H2N Cl NH3

Cl

"'-.. 1 ,/ NH3 ( / Co " H2N 1 NH3

+

H2N

Cl

trans-NH} cis-Cl cis-NH} trans-CI cis-NH ) cis-Cl The mirror images of the second two structures are superimposable since two of the ligands, either ammonia or chloride ion, are arranged in the trans position. When both types of ligands are in the cis arrangement, the mirror image is not a superimposable optical isomer' +

+

cis-NH} cis-Cl There are four stereo isomers of [Co(NH}M en)Cl 2 t

cis-NH} cis-Cl

22.4

Plan: Compare the two ions for oxidation state of the metal ion and the relative ability of ligands to split the d-orbital energies. Solution: The oxidation number of vanadium in both ions is the same, so compare the two ligands. Ammonia is a stronger } field ligand than water, so the complex ion [V(NH3)6f+ absorbs visible light of higher energy than [V(H 2 0)6] + absorbs.

22.5

Plan: Determine the charge on the manganese ion in the complex ion and the number of electrons in its d-orbitals. Since it is an octahedral ligand, the d-orbitals split into three lower energy orbitals and two higher energy orbitals. Check the spectrochemical series for whether CW is a strong or weak field ligand. If it is a strong field ligand, fill the three lower energy orbitals before placing any electrons in the higher energy d-orbitals. If it is a weak field ligand, place one electron in each of the five d orbitals, low energy before high energy, before pairing any electrons. After filling orbitals, count the number of unpaired electrons. The complex ion is low-spin if the ligand is a strong field ligand and high-spin if the ligand is weak field. Solution: Figure the charge on manganese: total charge = (charge on Mn) + 6(charge on CW) charge on Mn -3 - [6(- 1 )] +3 The electron configuration of Mn is [Ar]4i3tf; the electron configuration of Mn3 + is [Ar]3d'. The ligand is CW, which is a strong field ligand, so the four d electrons will fill the lower energy d-orbitals before any are placed in the higher energy d-orbitals: =

=

326

H igher energy d-orbitals

IT]

It . I t it I are unpaired in [Mn(CN)6] 3-. The complex is

L ower energy d-orbitals Two electrons

ligand.

low spin

since the cyanide ligand is a strong field

END--OF-CHAPTER PROBLEMS

22. 1

a) All transition elements in Period 5 will have a "base" configuration of [Kr]5i, and will differ in the number of d electrons (x) that the configuration contains. Therefore, the general electron configuration is li2i2p 63s23p 64i3dlo4p 6 Si4tf .

b) A general electron configuration for Period 6 transition elements includes/sublevel electrons, which are lower in energy than the d sublevel. The configuration is li2i2l3i3l4i3dt 04lsi4dtOSp6 6i4j4Stf . 22.4

a) One would expect that the elements would increase in size as they increase in mass from Period 5 to 6. Because there are 1 4 inner transition elements in Period 6, the effective nuclear charge increases significantly. As effective charge increases, the atomic size decreases or "contracts." This effect is significant enough that Zr4+ and Hr+ are almost the same size but differ greatly in atomic mass. b) The size increases from Period 4 to 5, but stays fairly constant from Period 5 to 6. c) Atomic mass increases significantly from Period 5 to 6, but atomic radius ( and thus volume) hardly increases, so Period 6 elements are very dense.

22.7

a) A paramagnetic substance is attracted to a magnetic field, while a diamagnetic substance is slightly repelled by one. b) Ions of transition elements often have unfilled d-orbitals whose unpaired electrons make the ions paramagnetic. Ions of main group elements usually have a noble gas configuration with no partially filled levels. When orbitals are filled, electrons are paired and the ion is diamagnetic. c) The d-orbitals in the transition element ions are not filled, which allows an electron from a lower energy d orbital to move to a higher energy d-orbital. The energy required for this transition is relatively small and falls in the visible wavelength range. All orbitals are filled in a main-group element ion, so enough energy would have to be added to move an electron to a higher energy level, not just another orbital within the same energy level. This amount of energy is relatively large and outside the visible range of wavelengths.

22.8

a) V: li2i2p63i3p64i3� b) Y: li2i2p63 s23p64i3dt04p6si 4d' c) Hg: [Xe]6i4l'4SdtO

22. 1 0

Check: 2 + 2 + 6 + 2 + 6 + 2 + 3 23 eCheck: 2 + 2 + 6 + 2 + 6 + 2 + 1 0 + 6 + 2 + 1 Check: 54 + 2 + 14 + 1 0 80 e=

=

39 e­

=

Transition metals lose their s orbital electrons first in forming cations. a) The two 4s electrons and one 3d electron are removed to form Sc 3 + : Sc: [Ar]4i3i ; Sc 3 + : [Ar] or li2i2p63 s2 3p6 . There are no u npaired electrons. b) The single 4s electron and one 3d electron are removed to form Cu2+ : Cu: [Ar]4s 1 3dI O; ci+ : [Ar]3tf. There is one unpaired electron . c) The two 4s electrons and one 3d electron are removed to form Fe3 + : Fe: [Ar]4S2 3Ji; Fe 3 + : [Ar]3tf. There are five unpaired electrons since each of the five d electrons occupies its own orbital. d) The two 5s electrons and one 4d electron are removed to form Nb 3+ : Nb: [Kr]5s 24d3 ; Nb 3 + : [Kr]4d2• There are two unpaired electrons.

327

22. 12 The elements in Group 6B(6) exhibit an oxidation state of +6. These elements include . Sg (Seaborgium) is also in Group 6B(6), but its lifetime is so short that chemical properties, like oxidationW states within compounds, are impossible to measure. 22.14 Transition elements in their lower oxidation states act more like metals. The oxidation state of chromium in CrF2 is +2 and in CrF6 is +6 (use -1 oxidation state of fluorine to find oxidation state of Cr). exhibits greater metallic behavior than CrF6 because the chromium is in a lower oxidation state in CrF2 than in CrF6. 22.16 Oxides increases. The oxidation state of chromiumof transition in CrO) ismetals +6 andbecome in CrO less is +2,basicbased(oronmorethe acidic) -2 oxidasatioxidation on state ofstate oxygen. The oxide of the higher oxidation state, produces a more acidic solution. 22.19 The coordination number indicates the number of ligand atoms bonded to the central metal ion. The oxidation number represents the number of electrons lost to form the ion. The coordination number is unrelated to the oxidation number. 22. 2 1 Coordination number of two indicates geometry. Coordination number offour indicates either or geometry. Coordination number of six indicates geometry. 22. 24 a) The oxidation state of nickel is found from the total charge on the ion (+2 because two CI- charges equals -2) and the charge on ligands: charge on nickel +2 - 6(0 charge on water) +2 Name nickel as nickel(II) to indicate oxidation state. Ligands are six (hexa-) waters (aqua). Put together with chloride anions to give b) The cation is [Cr(en))]n+ and the anion is CI04-, the perchlorate ion (see Chapter 2 for naming polyatomic ions). The charge on the cation is +3 to make a neutral salt in combination with 3 perchlorate ions. The ligand is ethylenediamine, which has 0 charge. The charge of the cation equals the charge on chromium ion, so chromium(IIl) is included in the name. The three ethylenediamine ligands, abbreviated en, are indicated by the prefix tris because the name of the ligand includes a numerical indicator, di-. The complete name is c) The cation is K+ and the anion is [Mn(CN)6] 4-. The charge of 4- is deduced from the four potassium ions in the formula. The oxidation state ofMn is - {6(-1)} +2. The name ofCN" ligand is cyano and six ligands are represented by the prefix hexa. The name of manganese anion is manganate(II). The -ate suffix on the complex ion is used to indicate that it is an anion. The full name of compound is 22. 2 6 The charge of the central metal atom was determined in 22. 24 because the Roman numeral indicating oxidation state is part of the name. The coordination number, or number of ligand atoms bonded to the metal ion, is found by examining the bonded entities inside the square brackets to determine if they are unidentate, bidentate, or polydentate. a) The Roman numeral "II" indicates a oxidation state. There are 6 water molecules bonded to Ni and each ligand is un identate, so the coordination number is b) The Roman numeral "III" indicates a oxidation state. There are 3 ethylenediamine molecules bonded to Cr, but each ethylenediamine molecule contains two donor N atoms (bidentate). Therefore, the coordination number is c) The Roman numeral indicates a oxidation state. There are 6 unidentate cyano molecules bonded to Mn, so the coordination number is 22. 2 8 a) The cation is K+, potassium. The anion is [Ag(CN)2r with the name dicyanoargentate (I) ion for the two cyanide ligands and the name of silver in anions, argentate(I). The Roman numeral indicates the oxidation number on Ag. O. N . for Ag I - {2(-I)} + 1 since the complex ion has a charge of - I and the cyanide ligands are also - I .+ The complete name is b) The cation is Na , sodium. Since there are two + 1 sodium ions, the anion is [CdCI 4] 2- with a charge of 2-. The anion is the tetrachlorocadmate(II) ion. With four -1 chloride ligands, the oxidation state of cadmjum is +2 and the name of cadmium in an anion is cadmate. The complete name is Cr, Mo, and

C r F2

C r03,

linear

tetrahedral

square planar

octahedral

=

=

hexa a q u a n ic kel(II) chloride.

tris( ethylened iamine ) c h ro m i u m ( I I I ) perchlorate . -4

=

potassium hexacyanomanganate ( I I ) .

+2

6.

+3

6.

"II"

+2

6.

(1)

= -

=

potassium dicyanoargentate(I).

sodi u m tetrachlorocad mate(I I ) .

328

c) The cation is [Co(NH 3 MH 2 0)Br] 2+. The 2+ charge is deduced from the 2Br- ions. The cation has the name tetraamineaquabromocobalt(III) ion, with four ammonia ligands (tetraammine), one water ligand (aqua) and one bromide ligand (bromo). The oxidation state of cobalt is +3: 2 - {4(0) + 1(0) + The oxidation state is indicated by following cobalt in the name. The anion is Br-, bromide. The complete name is I (-I ) } .

(m),

tetraa mmineaqu abro mocobalt( I I I ) bromide.

22. 3 0 a) The cation is tetramminezinc ion. The tetraammine indicate four NH3 ligands. Zinc has an oxidation state of +2, so the charge on the cation is +2. The anion is SO/-. Only one sulfate is needed to make a neutral salt. The formula of the compound is b) The cation is pentaamminechlorochromium(lII) ion. The ligands are NH from pentaammine, and one chloride from chloro. The chromium ion has a charge of +3, so the complex ion3 has a charge equal to +3 from chromium, plus 0 from ammonia, plus -1 from chloride for a total of +2. The anion is chloride, Two chloride ions are needed to make a neutral salt. The formula of compound is c) The anion is bis(thiosulfato )argentate(I). Argentate(I) indicates silver in the + 1 oxidation state, and / bis(thiosulfato) indicates 2 thiosulfate ligands, S -. The on thesalt.anion s +1 plusof2(-2) to equalis -3. 0 The cation is sodium, Na+ . Three sodium ions are2 needed tototal makecharge a neutral The iformula compound [Zn (NH3)4] S04.

5

[ C r(NH3)sC I ] CI2 .

cr.

N a 3 [Ag(S203)z] '

23. 3 2 Coordination compounds act like electrolytes, i. e . , they dissolve in water to yield charged species. However, the complex ion itself does not dissociate. The "number of individual ions per formula unit" refers to the number of would form per 2coordination compound upon dissolution in water. a)ionsThethatcounter ion is S04.4 -, so the complex ion is [Zn(NH 3)4f+ . Each ammine ligand is unidentate, so the coordination number is Each molecule dissolves in water to form one SO/- ion and one [Zn(NH 3 )4] 2+ ion, so 2 form per formula unit. b) The counter ion is so the complex ion is [Cr(NH 3 )sCI] 2+ . Each ligand is unidentate, so+ the coordination number is Each molecule dissolves in water to form two ions and one [Cr(N H 3 )sCl f ion, so form per formula unit. + c) The counter ion is Na , so the complex ion is [Ag(S203 h] 3-. Assuming that+ the thiosulfate ligand is unidentate, the4coordination number is 2. Each molecule dissolves in water to form 3 Na ions and one [Ag(S203)2] 3- ion, so form per formula unit. 22. 3 4 Ligands that form linkage isomers have two different possible donor atoms. a) The nitrite ion because it can bind to the metal ion through either the nitrogen or one of the oxygen atoms - both have a lone pair of electrons. Resonance Lewis structures are [:'.O=== N -O:] 6. :].. .. [:o-N=== .. b) Sulfur dioxide molecules because both the sulfur and oxygen atoms can bind metal ions because they both have lone pairs. · ·0 S O·. . c) Nitrate ions have. three oxygen atoms, all with a lone pair that can bond to the metal ion, but all of the oxygen atoms are equivalent, so there are The nitrogen does not have a lone pair to use to bind metal ions. : O N O: ions

c r,

cr

6.

3

ions

fo r m s lin kage isomers

-

� ..

for m linkage isomers

.

====

====

no linkage isomers.

:O-N=== O..· .. : 0I :

..

[

.. .. II .. . 0.. -

329

-

j

..

ions

22.36

a) Platinum ion, Pt2+, is a r1 ion so the ligand arrangement is square planar. A and geometric isomer exist for this complex ion: H H H H C H3",-NI "' Br CH3",-NI "' Br Pt/ Pt/ CH3-N/ '" Br Br/ '"N--H H/ HI ICH3"'H Isomer exist because the mirror imagesisomer No optical isomers of both compounds are superimposable on the original molecules. In general, a square planar molecule is superimposable on its mirror image. b) A and geometric isomer exist for this complex ion. No optical isomers exist because the mirror images of both compounds are superimposable on the original molecules. H H H H", I ", I F H--N F H --N '" / '" / Pt Pt / ""/ Cl Cl '"N-- H H --N H/ HI IH "' H Isomerc isomers exist for this molecule,isomer c) Three geometri although they are not named or because all the ligands are different. A different naming system is used to indicate the relation of one ligand to another. H H H H H H ", I ", I ", I F H --N F H--N Cl H --N '" / '" / '" Pt/ Pt Pt / ""/ "'" F Cl / ""-O H H Cl O H -- O HI HI HI Types of isomers for coordination compounds are coordination isomers with different arrangements ofligands and counterions, linkage isomers with different donor atoms from the same ligand bound to the metal ion, geometric isomers with differences in ligand arrangement relative to other ligands, and optical isomers with mirror images that are not superimposable. a) Platinum ion, Pt2+, is a dB ion, so the ligand arrangement is square planar. The ligands are 2 and 2 Br-, so the arrangement can be either both ligands or both ligands to form geometric isomers. cis

trans

CIS

cis

trans

trans

CIS

cis

trans

--

--

22.38

trans

trans

cis

2-

330

cr

b) The complex ion can form linkage isomers with the N02 ligand. Either the N or an 0 may be the donor. 22NH3 NH3 I / NH3 I / NH3 H3N-Cr ONO H3N;;Cr--N02 / H3N 1 H3N 1 NH3 NH3 --

c) In the octahedral arrangement, the two iodide ligands can be either trans to each other, 1800 apart, or cis to each other, 900 apart. 2+ 2+ NH3 1 /1 H3N-Pt--I H3N/ 1 NH3 22.40 a) Four empty orbitals of equal energy are "created" to receive the donated electron pairs from four ligands. The four orbitals are hybridized from an s, two p, and one d-orbital from the previous n level to form 4 dsi orbitals. b) One s and three p-orbitals become four Sp3 hybrid orbitals. 22.43 a) The crystal field splitting energy is the energy difference between the two sets of d-orbitals that result from the bonding of ligands to a central transition metal atom. b) In an octahedral field of ligands, the ligands approach along the and axes. The d and d orbitals are located along the and axes, so ligand interaction is higher in energy than the other orbital-ligand interactions. The other orbital-ligand interactions are lower in energy because the dxy, dyz, and dxz orbitals are located between the and axes. c) In a tetrahedral field ofligands, the ligands do not approach along the and axes. The ligand interaction is greater for the dxy, dyz. and dxz orbitals and lesser for the d and d orbitals. The crystal field splitting is reversed, and the dxy, dyz, and dxz orbitals are higher in energy than the d and d orbitals. 22.45 If � is greater than electrons will preferentially pair spins in the lower energy d-orbitals before adding as unpaired electrons to the higher energy d-orbitals. If � is less than electrons will preferentially add as unpaired electrons to the higher d-orbitals before pairing spins in the lower energy d-orbitals. The first case gives a complex that is low-spin and less paramagnetic than the high-spin complex formed in the latter case. 22.47 To determine the number of d electrons in a central metal ion, first write the electron configuration for the metal atom. Examine the formula of the complex to determine the charge on the central metal ion, and then write the ion's configuration. a) Electron configuration ofTi: [Ar]4i3tf Charge on Ti: Each chloride ligand has a -I charge, so Ti has a +4 charge {+4 + 6(-1) } 2- ion. Both of the 4s electrons and both 3d electrons are removed. Electron configuration ofTi4+: [Ar] Ti4+ has no d electrons. b) Electron configuration of Au: [Xe]6s'4j45io Charge on Au: The complex ion has a -1 charge ([ AuCI n since K has a + 1 charge. Each chloride ligand has a -I charge, so Au has a +3 charge {+ 3 + 4(-1)} 1- ion. The4 6s electron and two d electrons are removed. Electron configuration of Au3+: [Xe]4/45Jl Au3+ has electrons. x,

x,

y,

y,

x,

y,

z

x

z

z

x,

x

2

-

y, y

2

z

z

x

Epairing,

2

-

y

2

z

2

2

-

y

2

z

2

Epairing"

=

=

8d

331

2

c) Electron configuration of Rh: [Kr]Si4d7 Charge on Rh: Each chloride ligand has a -1 charge, so Rh has a +3 charge {+ 3 + The Ss electrons and one 4d electron are removed. Electron configuration of Rh3 + : [Kr]4Ji Rh3 + has 6 d electro n s . 22 . 49

6(-1)}

=

3- ion.

a) Ti: [Ar]4i3cf. The electron configuration of Ti 3 + is [Ar]3i . With only one electron in the d-orbitals, the titanium(llI) ion cannot form high and low spin complexes - all complexes will contain one unpaired electron and have the same spin. Co: [ar]4i3d7 . The electron configuration of C02+ is [Ar]3d7 and will form high and low-spin complexes with 7 electrons in the d-orbital. c) Fe: [Ar]4i3Ji. The electron configuration of Fe2+ is [Ar]3Ji and will form high and low-spin complexes with 6 electrons in the d-orbital . d) Cu: [Ar]4S I 3dIO. The electron configuration of Cu2+ is [Ar]3d 9 , so in complexes with both strong and weak field ligands, one electron will be unpaired and the spin in both types of complexes is identical. Cu2+ cannot form high and low-spin complexes.

b)

(a)

(b)

LL

L_

11 11 L

11 11 11 low

high - spin

(c)

LL 11 L L high - spin

22 . 5 1

(d)

11 11 11 low

-

spin

-

spin

li L . 11 1L 11

To draw the orbital-energy splitting diagram, first determine the number of d electrons in the transition metal ion. Examine the formula of the complex ion to determine the electron configuration of the metal ion, remembering that the ns electrons are lost first. Determine the coordination number from the number of ligands, recognizing that 6 ligands result in an octahedral arrangement and 4 ligands result in a tetrahedral or square planar arrangement. Weak-field ligands give the maximum number of unpaired electrons (high-spin) while strong-field ligands lead to electron pairing (low-spin). a) Electron configuration of Cr: [Ar]4S I 3d5 Charge on Cr: The aqua ligands are neutral, so the charge on Cr is +3 . Electron configuration of Cr3 + : [Ar]3d 3 Six ligands indicate an octahedral arrangement. Using Hund's rule, fill the lower energy t2 g orbitals first, filling empty orbitals before pairing electrons within an orbital.

332

b) Electron configuration ofCu: [Ar]4s i 3di O Charge on Cu: The aqua ligands are neutral, so Cu has a +2 charge. Electron configuration9 ofCu2+: [Ar]3d 9 Four ligands and a d configuration indicate a square planar geometry (only filled d sublevel ions exhibit tetrahedral geometry). Use Hund's rule to fill in the 9 d electrons. Therefore, the correct orbital-energy splitting diagram shows one unpaired electron. c) Electron configuration of Fe: [Ar]4s23d 6 Charge on Fe: Each fluoride ligand has a - 1 charge, so Fe has a +3 charge to make the overall complex charge equal to -3 . Electron configuration of Fe3+: [Ar]3d 5 Six ligands indicate an octahedral arrangement. Use Hund's rule to fill the orbitals. is a weak field ligand, so the splitting energy, �, is not large enough to overcome the resistance to electron pairing. The electrons remain unpaired, and the complex is called high-spin. F

(b)

(a)

-L L L 22.53

Figure 22.2 1 describes the spectrum of splitting energy, �. N02- is a stronger ligand than NH3, which is stronger than H20. The energy oflight absorbed increases as �3 increases. [Cr(H 2 0)6 1 3+

22.55

22.60


8 3 decay through ex decay. b) The NIZ ratio for i! Cr is (48 - 24)/24 1 .00. This number is below the band of stability because N is too low and Z is too high. To become more stable, the nucleus decays by converting a proton to a neutron, which is positron decay. Alternatively, a nucleus can capture an electron and convert a proton into a neutron through electron capture. c) The N/Z ratio for �� Mn is (50 - 25)/25 = 1 .00. This number is also below the band of stability, so the nuclide undergoes positron decay or electron capture. =

23 . 1 4

Stability results from a favorable NIZ ratio, even numbers of N and/or Z, and the occurrence of magic numbers. The NIZ ratio of �� Cr is ( 52 - 24)/24 = 1 . 1 7, which is within the band of stability. The fact that Z is even does not account for the variation in stability because all isotopes of chromium have the same Z. However, �� Cr has 28 neutrons, so N is both an even number and a magic number for this isotope only.

337

23 . 1 8

N o, it is not valid to conclude that tl/2 equals 1 minute because the number of nuclei is so small (6 nuclei). Decay rate is an average rate and is only meaningful when the sample is macroscopic and contains a large number of nuclei, as in the second case. Because the second sample contains 6 x 1 0 12 nuclei, the conclusion that tll2 = 1 minute is valid.

23 .20

Specific activity of a radioactive sample is its decay rate per gram. Calculate the specific activity from the number of particles emitted per second (disintegrations per second = dps) and the mass of the sample. Specific activity = decay rate per gram. I Ci = 3 .70 x 1 0 1 0 dps 1 .66 x 1 0 6 dPS 1 �g 1 Ci Specific Activity = = 2.8945 X 1 0-2 = 2.89 X 1 0-2 Ci/g 1 .5 5 mg 1 0- g 3 .70 x 1 0 1 0 dps

[

23 .22

][ ][

]

The rate constant, k, relates the number of radioactive nuclei to their decay rate through the equation A = kN. The number of radioactive nuclei is calculated by converting moles to atoms using Avogadro's number. The decay rate is 1 .39 x 1 0 5 d/yr or more simply, 1 .39 x 1 0 5 yr- I (the disintegrations are assumed). Decay rate = -(llN / Llt) = kN 1 .00 x 1 0. 1 2 mOI 6.022 x 1 0 2 3 atom - 1 .39 x 1 0 5 atom =k I mol 1 .00 yr 1 .39 x 1 0 5 atom /yr = k (6.022 x l O " atom) k = ( 1 .39 x 1 0 5 atom /yr) / 6.022 x 1 0 " atom k = 2.30820 X 1 0-7 = 2 3 1 X 1 0-7 y r- I

[

_

][

]

.

23 .24

Radioactive decay is a first-order process, so the integrated rate law is In � = kt Nt 3 To calculate the fraction of bismuth-2 1 2 remaining after 3 .75 x 1 0 h, first find the value of k from the half-life, then calculate the fraction remaining with No set to 1 (exactly). tll2 = 1 .0 1 yr t = 3 .75 X 1 0 3 h k = (In 2) / (tid = (In 2) / ( 1 .0 1 yr) = 0.686284 yr- I (umounded) 1 In _- = (0.686284 yr- I ) (3 .75 x 1 0 3 h) ( I day / 24 h) ( 1 yr / 365 days) Nt 1 In - = 0.293 785958 (unrounded) Nt I - = 1 .34 1 4967 (unrounded) Nt Nt = 0.745436 (unrounded) Multiplying this fraction by the initial mass, 2.00 mg, gives 1 .490872 = 1 .49 mg of bismuth-2 1 2 remaining after 3 .75 x 1 0 2 h.

23 .26

Lead-206 is a stable daughter of 23 8 U. Since all of the 206 Pb came from 23 8 U, the starting amount of 23 8 U was (270 /lmol + 1 1 0 /lmol) = 380 /lmol = No. The amount of 23 8 U at time t (current) is 270 /lmol = Nt. Find k from the first-order rate expression for half-life, and then substitute the values into the integrated rate law and solve for t. tll2 = (In 2) / k k = (In 2) / tll2 = (In 2) / (4.5 x 1 0 9 yr) = 1 .540327 x 1 0- 1 0 yr- I (unrounded) N In o = kt Nt

3 80 /lmol = ( 1 .540327 x 1 0- 10 yr- I )t 270 /lmol 0.34 1 749293 = ( 1 .540327 x 1 0- 1 0 yr- I )t t = (0.34 1 749293) / ( 1 .540327 x 1 0- 10 yr- I ) = 2.2 1 868 x 1 09 = 2.2 X 1 09 y r In

338

23 .28

Use the conversion factor, I Ci = 3 .70 x 1 0 1 0 disintegrations per second (dps). 6 X I 0 - 1 l mCi --1 0 -3 Ci 3 .70 x 1 0 1 0 dP S --. . 60 s 1 000 mL A ctlVlty = = 1 26.0 = 1 x mL 1 mCi 1 Ci I min I .OS7 qt

)[

[

)(

)[

)

)(

10

2

dpm/qt

23 .32

Protons are repelled from the target nuclei due to the interaction of like (positive) charges. Higher energy is required to overcome the repulsion.

23 .33

a)

I � B + � He

--7

�n + X

Since the charge on the left, S + 2 = 7, the charge on the right must = 7 Element X has a = 7 which is nitrogen. The mass is 1 4 on each side. lO B + ' He --7 I n + 1 3 N 2 0 5 7 b) Si + H --7 �� P + X Since the charge on the left, 1 4 + I = I S , the charge on the right must = I S . P-29 already has a charge of I S so X must have = 0, a neutron. Si + H --7 �� P + � n The mass on each side = 30 c) X + ; He --7 2 � n + 2 Cf The charge on the right = 0 + 98 = 98. The charge on the left must = 98. He-4 has a charge of 2, so element X has a charge of 98 - 2 = 96. Element 96 is Cm. 2 Cm + ; He --7 2 � n + 2 Cf The mass of Cm is 242 so that the mass on each side = 244

Z

�� � �� �

Z

��

��

��

23.37

Ionizing radiation is more dangerous to children because their rapidly dividing cells are more susceptible to radiation than an adult' s slowly dividing cells.

23 .38

a) The rad is the amount of radiation energy absorbed per body mass in kg. 3 .3 x 1 0-7 J 2.20 S Ib 1 rad = S .39 X 1 0-7 = 5.4 X 1 0-7 rad 1 kg 1 3S Ib 1 X 1 0-2 J / kg b) Conversion factor is 1 rad = 0.01 Gy (S .39 x 1 0-7 rad) (0.0 1 Gy/ I rad) = S .39 x 1 0-9 = 5.4 X 1 0-9 Gy

23 .40

)[

)(

[

)

[ X ](

a) Convert the given information to units of J /kg. I rad = 0.0 1 J /kg = 0.0 I Gy 6.0 x 1 0 5 � 8.74 x 1 0- 1 4 J /� 0 . 0 1 GY 1 rad = 7.49 1 4 X 1 0- 10 = 7.5 X Dose = 70. kg I rad 0.0 I g

(

)

)(

)(

) [ :r )

=

( )[ )( )[

23 .44

1 0- 1 0 G y

b) Convert grays to rads and multiply rads by RBE to find rems. Convert rems to mrems. I rad I em rem = rads x RBE = 7 .49 1 4 x 1 0- 1 0 GY ( 1 .0) = 7.49 1 4 x 1 O-5 = 7.5 x I0-5 mrem 0.0 1 Gy 1 0 rem c) 1 rem = 0.0 1 Sv Sv (7.S X 1 0-5 mrem) ( 1 0-3 rem / 1 mrem) (0. 0 1 Sv / rem) 7.49 1 4 x 1 0- 1 0 = 7.5 X 1 0- 10 Sv. Use the time and disintegrations per second (8q) to find the number of 60Co atoms that disintegrate, which equals the number of � particles emitted. The dose in rads is calculated as energy absorbed per body mass. I rad 60 S 47S 8q 1 0 3 g l dP S S .OS x 1 0- 14 J 27.0 = 2.447 X 1 0-3 = 2.45 X 1 0-3 ra d min ) Dose = ( . . 1 mill 0.0 I I .S 88 g I kg I Bq 1 dlslllt. g

(

23 .42

)

=

)

( )[

X

]

N AA does not destroy the sample while chemical analyses does. N eutrons bombard a non-radioactive sample, "activating" or energizing individual atoms within the sample to create radioisotopes. The radioisotopes decay back to their original state (thus, the sample is not destroyed) by emitting radiation that is different for each isotope.

339

oxygenin theinformal formalddehyde ehydeproduct. comes fromThe methanol because thethe oxygen isaciotoped reactant in the methanol reactant 23.45 The appears oxygen i s otope i n chromi c appears i n waterdehyde. product, not the formaldehyde product. The isotope traces the oxygen in methanol to the oxygen ithen formal 23.48 Apply the appropriate conversions from the chapter or the inside back cover. 6 ev ) a) Energy (0.0 1861 MeV) [ 10I MeV 6 eV ) [ 1.6021 xeV10- 1 9 ) 2 .981 322 10-1 5 b) Energy (0. 0 1861 MeV)[ 101 MeV 23. 5 0 Mass Calculof27 ate �m,IH convert the27 mass deficit to27.MeV,2 11275andamu divide by 59 nucleons. atoms x 1. 0 07825 Mass of32Totalneutrons 32 x59.1.0408665 32.27728 amu 88555 amu mass Mass defect �m 59. 4 88555 -58.933198 0. 5 55357 amurCo 0. 5 55357 glmol 59CO amu (931. 5 MeV] CO ) 59 a) B m· d'mg energy [ 0. 5 55357 59 nucleons 1 amu 8 768051619 5 MeV ] 517.3 150 b) B inding energy [ 0. 5 553571 atoamum 59 CO ) ( 931.I amu c) Use �E �mc2 Binding energy [ 0. 5 55357molg 59 co )[ 101 �gg ) ( 2. 99792 108 m s )2 kg ·I m 10I � J 4.9912845 101 0 andisfissia spontaneous on, radioactiprocess ve partiinclewhis arechemiunstabl tted,ebutnucltheei process leoadiactinvgetopartithecemiles andssion is 23. 5 3 Indiffbotherent.radiRadioactioactive vdecay e decay emi t radi energy.idesFitossibreak on occurs as thelerresul t dofes,hiradigh-energy bombardment ofenergy. nuclei with small particles that cause the nucl i n to smal nucli o acti v e parti c l e s, and Infissia ochain andn reacti orgen, alnucll fissieusoncaneventsleadareto splnotitthetingsame. Thelargecolnucllisioeni ibetween the ofsmalwaysl partito produce cle emit several ed in the the l a of the n a number different products. 23. 5 6 The water serves to slow the neutrons so that they are better able to cause a fission reaction. Heavy water (�H 2 0neutrons or D20)areis avai a betterlablemoderator because iotndoesprocess. not absorb neutrons asdoeswelnotl asoccur light natural water l(:y Hin20)greatdoes, so more to i n i t i a t e the fissi However, D20 abundance, so production of 020 adds to the cost of a heavy water reactor. In addition, if heavy water does absorb a neutron, it becomes i.e., it contains the isotope tritium, �H , which is radioactive. 23.60 a) Use the valCmues giv�enPuin the Heproblem to calculate the mass change (reactant -products) for: �mass (kg) [243. 0614 amu -(4.0026 + 239.0522) amu] [ 1.66054amu10-24 g )[ 101 kgg ) 1.095956 10-29 4 = 1 .861 x 1 0 eV

=

J =

=

= =

=

X

=

= .

=

=

X

=

= 8 . 768 M e V I

= 4.99 128

X

1010

[ j(,]( )

/

S

kJ

2:

2

I mol

+�

X

=

=

X

= 1.1

X

2 1 0- 9

kg

340

nue I eon

= 51 7.3 MeV I atom

tritiated,

-t

J

=

=

2:�

t o- 1 5

=

=

X

X

=

=

=

= 2 .98 1

-

3-

J

b) E = �mc 2 = ( 1 .095956

X

1 0-29 kg )( 2.99792

X

1 0 8 m/s

t

[ %] 1J kg m 0

= 9.84993 x 1 0- 1 3 = 9.8 X t o- 13 J

S2 1 3 23 c) E released = (9.84993 x 1 0- J/reaction) (6.022 x 1 0 reactions/mol) ( 1 kJ / 1 0 3 J ) = 5 .93 1 6 X 1 0 8 = 5.9 X 1 0 8 kJ/mol This is approximately 1 million times larger than a typical heat of reaction. 22.62

Determine k for 1 4C using the half-life (5730 yr): k = (In 2) / tl/2 = (In 2) / (5730 yr) = 1 .2096809 x 1 0-4 yr- I (unrounded) Determine the mass of carbon in 4.38 grams of CaC0 3 : I mol CaC 0 3 1 2.0 1 g C I mol C mass = ( 4.38 g caC0 3 ) = 0.52556 g C (unrounded) 1 mol C 1 00.09 g CaC0 3 1 mol CaC0 3 The activity is: (3.2 dpm) / (0.52556 g C) = 6.08874 dpmog- ' Using the integrated rate law:

(

In

( �: )

6.08874 dpm g- I 1 5 .3 dpm g- I t = 76 1 6.98 = 7.6 x 1 03 y r 23 .65

[

)

= -( l .2096809 X 1 0-4 yr- I )t

Determine how many grams of AgCI are dissolved in 1 mL of solution. The activity of the radioactive Ag+ indicates how much AgCI dissolved, given a starting sample with a specific activity ( 1 75 nCi/g). 1 .25 X 1 0-2 Bq 1 dPS 1 Ci 1 nCi 1 g AgCl Concentration = 1 mL I Bq 3 .70 X 1 0 0 dps 1 75 nCi 1 0-9 Ci = 1 .93050 x 1 0-6 g AgCI/mL (unrounded) Convert glmL to moUL (molar solubility) using the molar mass of AgCI. 1 mol AgC I 1 mL 1 .93050 x 1 0 .6 g AgCI Molarity = 1 43 .4 g AgCI 1 0-3 L mL = 1 .34623 X 1 0-5 = 1 .3 5 X t o-5 M AgCI

)( )[

[

)(

[

23 .66

)

No = 1 5.3 dpm g- 1 (the ratio of I 2 e : 14 C in living organisms)

= -kt In

)(

)(

)(

)[

)

)( )

a) Find the rate constant, k, using any two data pairs (the greater the time between the data points, the greater the reliability of the calculation). Calculate tl/2 using k. In

(�J

= -kt

(

)

495 photons / s = -k(20 h) 5000 photons / s -2.3 1 2635 = -k(20 h) k = 0. 1 1 563 h- ' (unrounded) tll2 = (In 2) / k = (In 2) / (0. 1 1 563 h- I ) = 5.9945 = 5.99 h (Assuming the times are exact, and the emissions have three significant figures.) In

34 1

2. 0

2. 0

b) The percentage of isotope remaining is the fraction remaining after h (Nt where t = h) divided by the initial amount (No), i.e., fraction remaining is N/No. Solve the first order rate expression for NtlNo, and then subtract from to get fraction lost. In

( �J

100%

= -kt

(��) -(0.1 1563 h-I) (2.0 (��) 0.793533 ( �� ] 100% 79.3 533% In

=

=

-0.23126 (unrounded)

(unrounded)

x

=

(unrounded)

100% - 79.3533% 20. 6467%

The fraction lost is

23. 6 8

h) =

=

= 21%

of the isotope is lost upon preparation.

The production rate of radon gas (volume/hour) is also the decay rate of 22 6Ra. The decay rate, or activity, is proportional to the number of radioactive nuclei decaying, or the number of atoms in g of 22 6Ra, using the relationship A = kN. Calculate the number of atoms in the sample, and find k from the half-life. Convert the activity in units of nuclei/time (also disintegrations per unit time) to volume/time using the ideal gas law. 2�: Ra � � He + 2�! Rn k = (In / tl/2 = (In / yr) h/yr)] = x h- I (unrounded) 6 22 amu / atom or g / mol. The mass of Ra is x ) Ra atoms mol Ra = x N= g Ra Ra atoms (unrounded) mol Ra g Ra x 1 0 21 Ra atoms) = x Ra atoms / h (unrounded) A = kN = x 6 22 This result means that x Ra nuclei are decaying into 222 Rn nuclei every hour. Convert atoms of 222 Rn into volume of gas using the ideal gas law. moles = x Ra atoms / h) ( l atom Rn / atom Ra) mol Rn / x 1 0 23 Rn) = x mol Rn / h (unrounded) L atm x mol Rn / h K) mol · V = nRT / P = atm 9 = x = 4.904 X 1 0- L / h Therefore, radon gas is produced at a rate of x Llh. Note: Activity could have been calculated as decay in moles/time, removing Avogadro's number as a multiplication and division factor in the calculation.

1 . 000

2)

2) [(1599 (8766 4. 9451051 10-8 226. 025402 226.2025402 ) 2.6643023 102 1 (1.000 ( 226.1025402 ) [ 6. 022 1 10 3 1 . 3 175254 101 4 (4. 9451051 10-8 h-I) (2.4 6643023 1. 3 18 101 (1 . 3 175254 101 4 1 (1 6. 022 2.1878536 10-10 (2.1878536 10-10 ) ( 0. 08206 K ) (273.15 1 4. 904006 10-9 4. 904 10-9 •

23. 7 5

2 1 2 (3 32 00 106 K) 2. 0709066 10-1 7 ( 23 ) (8.3146. 022 102K)(1. 3 1 . 7 975048 101 7 (2. 00 (2. 99792 108 1.7975048 1017 )[ ) ( 1 . 0078 J ) 2 3 3 1 10 6. 022 10 2. 0709066 10-17 J 1. 4 525903 107

a) Kinetic energy = ] / mv2 = ( / ) m RT/MH) = ( / ) (RT / NA) x J / mol · = Energy = = 2.07 X 1 0- 1 7 J/ato m : H X x atom / mol b) A kilogram of I H will annihilate a kilogram of anti-H ; thus, two kilograms will be converted to energy: x Energy = mc 2 = kg) x m/s) \J / (kg·m 2/s2 )) = J (unrounded) x gH I mol H J I kg H atoms H atoms = I kg H mol H g atoms H x x =

[

X

= 1 .45

X

1 07

H atoms

342

[

)[

c) 4 : H

�

� He + 2 � P

�m

=

(Positrons have the same mass as electrons.) [4( 1 .007825 amu)] - [4.00260 amu - 2(0.000549 amu)] 0.027602 amu / � He

(

) [ )(

=

)[

)

0.027602 g I kg I mol He I mol H ( 1 .4525903 X 1 0 7 H atoms ) 2 3 3 mol He 4 mol H 6.022 x 1 0 H atoms 10 g 1 .6644967 x 10-22 kg (unrounded) Energy (�m)c 2 ( 1 .6644967 x 1 0-22 kg) (2.99792 X 1 0 8 mlS) 2 (J / (kgom2/s2 )) 1 .4959705 x 1 0-5 1 .4960 X 1 0-5 J d) Calculate the energy generated in part (b): 1 .7975048 x 1 0 1 7 J 1 kg 1 .0078 g H 1 mol H Energy 3 . 008 1 789 x 1 0- 10 J 3 1 mol H 1 kg H 6.022 x 1 0 2 3 atoms H 10 g Energy increase ( 1 .4959705 x 1 0-5 - 3 .008 1 789 x 1 0- 10 ) J 1 .4959404 x 1 0-5 1 .4959 X 1 0-5 J e) 3 : H � � He + 1 � P �m [3 ( 1 .007825 amu)] - [3.01 603 amu + 0.000549 amu] 0.006896 amu / � He 0.006896 g / mol � He �m

=

=

=

=

=

=

=

[

=

) [ )(

)[

)

=

=

=

=

(

) [ )(

=

=

)[

)

0.006896 g 1 kg 1 mol He I mol H ( 1 .4525903 x 1 07 H atoms ) 3 mol He 1 0 g 3 mol H 6.022 x 1 0 2 3 H atoms 5 .5447042 x 1 0-23 kg (unrounded) Energy (�m)c 2 (5.5447042 x 1 0-23 kg) (2.99792 X 1 0 8 mlS) 2 (J / (kgom2/s2 )) 4.983 3 1 64 x 1 0-6 4.983 X 1 0-6 J No, the Chief Engineer should advise the Captain to keep the current technology.

�m

=

=

=

=

=

=

343