Physical Chemistry: Thermodynamics, Statistical Thermodynamics, and Kinetics, 4th Edition, by Thomas Engel and Philip Reid, 2019 Solutions

801 Pages·2019·13.114 MB·English

by  Thomas Engel, Philip Reid

INSTRUCTOR SOLUTIONS MANUAL

Physical Chemistry
FOURTH EDITION

Thomas Engel
University of Washington

Philip Reid
University of Washington
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ISBN-10: 0-13-481469-X
ISBN-13: 978-0-13-481469-8
Contents
Part One: Thermodynamics, Statistical Thermodynamics, and Kinetics T-1
Chapter 1 Fundamental Concepts of Thermodynamics ........................................................................................... T-3
Chapter 2 Heat, Work, Internal Energy, Enthalpy, and the First Law of Thermodynamics .................................. T-18
Chapter 3 The Importance of State Functions: Internal Energy and Enthalpy ....................................................... T-42
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Chapter 4 Thermochemistry ......................................................................................................................o............ T-57
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Chapter 5 Entropy and the Second and Third Laws o f Thermodynamics ..i............................................................ T-79
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Chapter 6 Chemical Equilibrium ..................1....................................................................................................... T-105
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Chapter 7 The Properties of Real Gases ..............................u.................................p............................................... T-134
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Chapter 8 Phase Diagrams an)d the Relative Stability of Solids, Liquids, and Gases .......................................... T-146
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Chapter 9 Ideal and R(eal Solutions ............. ................................ ......................................................................... T-172
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Chapter 10 Electrolyte Solutions ..........................................o................................................................................. T-193
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Chapter 11 Electrochemical Cells, Batteries, and Fueel Cells ................................................................................. T-213
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Chapter 12 Probability ..a.................................a........................................................................................................ T-229
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Chapter 13 The Boltzmann Distribution ................................................................................................................ T-246
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Chapter 14 Ensemble and Molecular Partition Functions ...................................................................................... T-263
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Chapter 15 Statistical Thermodynamics ................................................................................................................ T-293

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Chapter 16 Kinetic Theory of Gases ...................................................................................................................... T-332
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Chapter 17 Transport Phenomena .......................................................................................................................... T-357
Chapter 18 Elementary Chemical Kinetics ............................................................................................................ T-379
Chapter 19 Complex Reaction Mechanisms .......................................................................................................... T-417
Chapter 20 Macromolecules .................................................................................................................................. T-459
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Part Two: Quantum Chemistry and Spectroscopy Q-471
Chapter 1 From Classical to Quantum Mechanics .............................................................................................. Q-473
Chapter 2 The Schrödinger Equation .................................................................................................................. Q-484
Chapter 3 The Quantum-Mechanical Postulates ................................................................................................. Q-502
Chapter 4 Applying Quantum-Mechanical Principles to Simple Systems .......................................................... Q-511
Chapter 5 Applying the Particle in the Box Model to Real-World Topics ......................................................... Q-531
Chapter 6 Commuting and Noncommuting Operators and the Surprising Consequences
of Entanglement ........................................................................................................................... Q-548
Chapter 7 A Quantum-Mechanical Model for the Vibration and Rotation of Molecules ................................... Q-560
Chapter 8 Vibrational and Rotational Spectroscopy of Diatomic Molecules...................................................... Q-580
Chapter 9 The Hydrogen Atom ........................................................................................................................... Q-615
Chapter 10 Many-Electron Atoms ........................................................................................................................ Q-631
Chapter 11 Quantum States for Many-Electron Atoms and Atomic Spectroscopy .............................................. Q-649
Chapter 12 The Chemical Bond in Diatomic Molecules ...................................................................................... Q-666
Chapter 13 Molecular Structure and Energy Levels for Polyatomic Molecules ................................................... Q-691
Chapter 14 Electronic Spectroscopy ..................................................................................................................... Q-720
Chapter 15 Computational Chemistry .................................................................................................................. Q-734
Chapter 16 Molecular Symmetry and an Introduction to Group Theory .............................................................. Q-765
Chapter 17 Nuclear Magnetic Resonance Spectroscopy ....................................................................................... Q-784

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Part One :
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Thermodynamidcs, Stautistical
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Thermo(dynam ics, a nd Kinetics
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T-1
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1
Fundamental
Concepts of
Thermodynamics
Conceptual Problems
Q1.1 The location of the boundary between the system and the surroundings is a choice that must be made
by the thermodynamicist. Consider a beaker of boiling water in an airtight room. Is the system open or n

closed if you place the boundary just outside the liquid water? Is the system open or closed if you
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place the boundary just inside the walls of the room?
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If the system boundaries are just outside of the liquid water, the system is open because water cain escape
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from the top surface. The system is closed if the boundary is just insiide the walls, because the room is
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airtight. 8 t
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Q1.2 Real walls are never totally adiabatic. Order the following walls in increasing order with respect to
c
being diathermal: 1-cm-thick concrete, 1-cm-thick vacuum, 1-cm-thick copper, i1-cm-thick cork.
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1-cm-thick vacuum < 1-cm-thick cork < 1-cm-thick councrete < 1-cm-thick cpopper.
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Q1.3 Why is the possibility of exchange of matter or energy a necessary condition for equilibrium between
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two systems?
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Equilibrium is a dynamic process in which the rates of two opposing processes are equal. However, if the
rate in each directio(n is zero, no exchang e is possible, and ther efore the system cannot reach equilibrium.
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Q1.4 At sufficiently high temperaturoes, the van der Waals equation has the form P . Note that the
V b
m
attractive part of the potesntial has no influence in this expression. Justify this behavior using the
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potential energy diagram in Figure 1.9.
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At high temperaturaes, the energy of thea molecule is large, as indicated by the colored rectangular area
in the figure below.
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In this case, the well depth is a small fraction of the total energy. Therefore, the particle is unaffected
by the attractive part of the potential.
T-3
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T-4 Chapter 1 Fundamental Concepts of Thermodynamics
Q1.5 The parameter a in the van der Waals equation is greater for HO than for He. What does this say about the form
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of the potential function in Figure 1.9 for the two gases?
It says that the depth of the attractive potential is greater for HO than for He.
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Q1.6 Can temperature be measured directly? Explain your answer.
Temperature cannot be measured directly. It is measured indirectly by the effect of temperature on a property such
as the volume of a liquid, the pressure of a gas, the electrical resistance of a metal, or the voltage across the junc-
tion of two dissimilar metals (a thermocouple).
Q1.7 Give an example of two systems that are in equilibrium with respect to only one of two state variables.
The contents of a compressed gas cylinder are in thermal equilibrium with the surroundings, but the pressures are
different. A gas enclosed in an adiabatic piston and cylinder assembly can be in equilibrium with respect to pres-
sure, but not to temperature.
Q1.8 Explain how the ideal gas law can be deduced for the measurements shown in Figures 1.5 and 1.8.
Figure 1.5 shows that at constant volume, P increases linearly with T, so Pf(V)T.
Figure 1.5 shows that the product PV is a constant at constant T. Therefore PV T, where  and  are con-
stants to be determined from measurements and the units chosen for P, V, and T.
Q1.9 Give an example based on molecule–molecule interactions illustrating how the total pressure upon mixing two real
gases could be different from the sum of the partial pressures.
We define the partial pressure of a gas as the pressure that the gas would exert if it were the only gas in the vessel.
If HCl and NH were admitted to the vessel, a reaction would occur and the total pressure would be much less than
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the sum of the partial pressures.
Q1.10 Which of the following systems are open? (a) a dog, (b) an incandescent light bulb, (c) a tomato plant, (d) a can of
tomatoes. Explain your answers.
An open system can exchange matter with the surroundings. Using this criterion:
(a) A dog is an open system because matter can flow between it and the surroundings.
(b) The light bulb is a closed system because matter cannot flow between the interior and exterior of the bulb.
(c) A tomato plant is an open system because matter can flow between it and the surrounding.
(d) A can of tomatoes is a closed system because matter cannot flow between the interior and exterior of the can.
Q1.11 Which of the following systems are isolated? (a) a bottle of wine, (b) a tightly sealed, perfectly insulated thermos
bottle, (c) a closed tube of toothpaste, (d) our solar system. Explain your answers.
An isolated system cannot exchange matter or energy with the surroundings. Using this criterion:
(a) The bottle of wine is not an isolated system because it can exchange energy with the surroundings.
(b) The thermos bottle is an isolated system.
(c) A closed tube of toothpaste is not an isolated system because it can exchange energy with the surroundings.
(d) Our solar system is not an isolated system because it can exchange energy and mass with the rest of the
universe.
Q1.12 Why do the z and y components of the velocity vector not change in the collision depicted in Figure 1.2?
The z and y components of the velocity not change in the collision because there is no force acting on the particle
in those directions.
Q1.13 If the wall depicted in Figure 1.2 were a movable piston, under what conditions would it move as a result of the
molecular collisions?
It would move if the momentum transferred to it from the two sides was different. This is the case if there is a
pressure difference across the wall.
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Chapter 1 Fundamental Concepts of Thermodynamics T-5
Q1.14 The mass of a He atom is less than that of an Ar atom. Does that mean that because of its larger mass, Argon exerts a
higher pressure on the container walls than He at the same molar density, volume, and temperature? Explain your
answer.
The pressure exerted on the wall depends on the momentum transfer per unit time, which is proportional to
mv2 kT
the product of mass and speed in the form mv2. Because x  , the momentum transfer depends on the
x 2 2
temperature, but not on the mass of the atom striking the wall. An Ar atom has a larger mass than a He atom, but
its speed is less and the product mv2is the same for He and Ar at a given temperature.
x
Q1.15 Explain why attractive interactions between molecules in gas make the pressure less than that predicted by the
ideal gas equation of state.
The pressure exerted by a gas on the walls which contain it is determined by the force exerted on the wall by molecular
collisions. If the molecules nearest the wall experience an attractive interaction to the molecules near them, nthis will

lessen the force that they exert on the wall. Therefore, the pressure will be less.
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Q1.16 State whether the following are intensive or extensive variables: (a) temperature, (b) pressure, (c) mass. Explain
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your answer. i
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(a) Temperature is an intensive variable becaus e if a system is dividied into two parts, thae temperature of each
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part is unchanged. a
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(b) Pressure is an intensive variable bec1ause if a system is divided into two parts, the pressure of each part is
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(c) Mass is an extensive variable because if a system is udivided into two partsp, the mass of each part is changed.
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Q1.17 State whether the following are intensive or extensived variables. (a) densityu (b) mean square speed v2 (c) volume.
) x
Explain your answers. c E D
(a) Density is an intensive variable because if a system is divided into two parts, the density of each part is
unchanged. (
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(b) The mean square speed is an intensive variable because if a system is divided into two parts, the mean
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square speed of each part iso unchanged.
(c) Volume is an extensive variable because if a system is divided into two parts, the volume of each part is
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Numerical Problems a a
Section 1.2 e S
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P1.1 Devise a temperature scale, abbr eviated G, for which the magnitude of the ideal gas constant is 7.41JG1mol1.
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Let T and Trepresent the Koelvin and G scales, and R and Rrepresent the gas constant in each of these scales. Then
PV nRT nRT
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R 8.314
T T  T 1.12T
t R 7.41
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The temperature on the G scale is the value in K multiplied by 1.12.
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P1.2 Suppose that you measured the product PV of 1 mol of a dilute gas and found that PV 23.60Latm at 0.00°C
and 32.35 L atm at 100.°C. Assume that the ideal gas law is valid, with T t(C)a, and that the values of R and
a are not known. Determine R and a from the measurements provided.
Expressing the ideal gas law in the form PV R(ta)m(ta),
PV (32.3523.60)latmmol1
m  0.0875L atmmol1 C1R
t 100.0C

PV 32.35 latmmol1
a t 100.C270.C
R 0.0875atmmol1 C1
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