Physical Chemistry Third Edition

180 4 The Thermodynamics of Real Systems

Exercise 4.13

a.At 373.15 K and 1.000 atm, the Gibbs energy change of vaporization of water is equal to

zero, and the entropy change is equal to 109 J K−^1 mol−^1. Find the Gibbs energy change of

vaporization of superheated water at 378.15 K and 1.000 atm, using Eq. (4.4-18). What does

the sign of your answer mean?

b.Repeat the calculation of part a using Eq. (4.4-19). Assume that∆His constant and

equal to 40.67 kJ mol−^1. Comment on the comparison between your values for parts a

and b.

PROBLEMS

Section 4.4: Gibbs Energy Calculations

4.28 a.Find the value of∆Gfor 1.000 mol of an ideal gas
if it is isothermally pressurized from 1.000 atm to
3.000 atm at 298.15 K.
b.Find the value of∆Gfor 1.000 mol of an ideal gas
if it is isothermally pressurized from 2.000 atm to
4.000 atm at 298.15 K.
c.Explain in words why your answers for parts a and b
are not equal although the changes in pressure are
equal.

4.29 2.000 mol of helium gas (assume ideal) expands
isothermally and irreversibly at a constant external
pressure of 1.000 atm and a temperature of 298.15 K
from a volume of 10.00 L to a volume of 40.00 L.
a.Findq,w,∆U,∆S,∆Ssurr,∆H,∆A, and∆G.
b.Findq,w,∆U,∆S,∆Ssurr,∆H,∆A, and∆Gif
the process is carried out reversibly at the same
temperature.

4.30 a.Find the value of∆Gif 1.000 mol of liquid
water is pressurized at 0.00◦C from 1.000 atm to
50.000 atm. Assume that the liquid water has a fixed
volume.
b.Find the value of∆Gif 1.000 mol of solid water is
pressurized at 0.00◦C from 1.000 atm to 50.000 atm.
Assume that the solid water has a fixed volume.
c.Find the value of∆Gif 1.000 mol of solid water (ice)
melts at 0.00◦C and 1.000 atm.
d.Find the value of∆Gif 1.000 mol of solid water melts
at 0.00◦C and 50.000 atm. What does the sign of your
answer indicate?

4.31 a.Write an expression for∆Afor the isothermal

expansion of an ideal gas from volumeV 1 to

volumeV 2.

b. Find the value of∆Afor each of the processes in

parts a and b of Problem 4.28. Explain the relationship

of these values to the values of∆Gfor the same

processes.

4.32 a.At 273.15 K and 1.000 atm, the Gibbs energy change

of fusion of water is equal to zero, and the enthalpy

change is equal to 6008 J mol−^1. Find the Gibbs

energy change of fusion of water at 263.15 K and

1.000 atm, using Eq. (4.4-18). What does the sign of

your answer mean?

b. Repeat the calculation of part a using Eq. (4.4-20).

Comment on the comparison between your values for

parts a and b.

4.33 Consider a gas obeying the truncated virial equation

of state

PVm

RT

 1 +

B 2

Vm

+

B 3

Vm^2

a.Write an expression for∆Afor the isothermal

expansion from volumeV 1 to volumeV 2 fornmoles

of this gas.

b.Find the value of∆Afor the isothermal expansion of

1.000 mol of argon at 298.15 K from a volume of

10.000 L to a volume of 25.000 L, assuming that

B 3 ≈0. Compare with the result assuming argon to be

an ideal gas.

c.Manipulate the van der Waals equation of state into the

form of the virial equation of state and show that