Physical Chemistry Third Edition

158 4 The Thermodynamics of Real Systems

PROBLEMS

Section 4.1: Criteria for Spontaneous Processes
and for Equilibrium: The Gibbs and Helmholtz
Energies

4.1If a simple system is somehow maintained at constant

SandP, show that its enthalpy cannot increase.

4.2 a.Calculate∆S◦and∆H◦for the vaporization of

1.000 mol of water at 298.15 K from the data in

Table A.8 in the appendix.

b. Calculate∆G◦for the vaporization of 1.000 mol of

water at 298.15 K.

c.Assume that both∆S◦and∆H◦for the vaporization of

water are temperature-independent. Find the temperature

at which∆G◦∆H◦−T∆S◦vanishes. If your

assumption were correct, this should be the temperature

at which liquid water and water vapor are at equilibrium

if the pressure is 1.000 bar.

d.Assume thatCP, mis temperature-independent

for both the solid and the liquid and find the

temperature at which∆G◦∆H◦−T∆S◦

vanishes.

4.3Consider the reaction at 298.15 K:

2H 2 (g)+O 2 (g)−→2H 2 O(l)

a.Calculate the value of∆H◦for this reaction.

b.Assume that∆H◦is temperature-independent. If the

heat from this reaction is used to power a steam turbine

with an efficiency that is 60.0% as great as that of a

Carnot engine operating between 200.0◦C and

400.0◦C, find the maximum amount of work that

can be done by the combustion of 2.000 mol of

hydrogen gas.

c.Calculate∆G◦for this reaction at 298.15 K from∆H◦

and∆S◦.

d.This reaction is carried out in fuel cells in spacecraft.

Calculate the maximum amount of net work that can be

done on the surroundings by the reaction of 2.000 mol of

hydrogen gas at 298.15 K. Calculate the total amount of

work that can be done on the surroundings. Comment

on the comparison between your results from parts b

and d.

4.2 Fundamental Relations for Closed Simple Systems

Thermodynamics includes a number of useful relations that allow one variable to be

replaced by another to which it is equal but which can be more easily evaluated. In this

section we obtain several such relations based on expressions for the differentials of

state functions. For a closed simple system and for reversible processes the first law of

thermodynamics is

dUdqrev−PdV (closed simple system) (4.2-1)

and the second law is

dS

dqrev

T

(closed simple system) (4.2-2)

Combination of these equations using the fact thatTcannot be negative gives an

important relation fordUfor reversible processes in a simple closed system:

dUTdS−PdV

(simple closed system;

reversible processes)

(4.2-3)

This equation is restricted to reversible changes of state becausedqrevwas used in its

derivation and becausePP(transmitted) was assumed.