Physical Chemistry Third Edition

4.4 Gibbs Energy Calculations 181

B 3 b^2. 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.

Compare with the result assuming argon to be an

ideal gas.

4.34Assume that argon obeys the truncated pressure virial
equation of state

PVmRT+A 2 P

withA 2 − 15 .8cm^3 mol−^1.

a.Find the value ofGm−G◦mfor argon gas at 298.15 K

and 1.000 atm.

b. Repeat the calculation for 298.15 K and 20.00 atm.

4.35 a.Find an expression for∆Afor the isothermal expansion
of a gas obeying the van der Waals equation of state
from volumeV 1 to volumeV 2.
b.Find the value of∆Afor the isothermal expansion of
1.000 mol of argon gas at 298.15 K from a volume of
10.000 L to a volume of 25.000 L. Compare with the
result assuming argon to be an ideal gas, and with the
result of Problem 4.33.

4.36 Calculate∆Gfor each of the following processes. If∆G
cannot be calculated, write “no numerical calculation
possible.”
a.1.000 mol of ice is melted at 0.00◦C and 1.000 atm.
b. 1.000 mol of water is heated at a constant pressure of
1.000 atm from 20.00◦C to 80.00◦C.
c.2.500 mol of an ideal gas is compressed isothermally at
a temperature of 400.0 K from 1.000 bar to
5.35 bar.
d.1.000 mol of solid water (ice) is pressurized
isothermally from 1.000 atm to 50.00 atm.

4.37 a.Calculate∆H◦,∆S◦,∆H◦−T∆S◦, and∆G◦for the
reaction at 298.15 K:
CH 4 (g)+2O 2 (g)−→CO 2 (g)+2H 2 O(g).
b.Calculate∆H◦,∆S◦, and∆G◦for the same reaction
at 498.15 K. Assume that the heat capacities are
constant.
c.If 2.000 mol of methane is burned at constant pressure
and a temperature of 498.15 K and 80.0% of the heat
produced is put into a steam engine with an efficiency
that is 75.0% as great as that of a Carnot engine
operating between 200.0◦C and 100.0◦C, find the

amount of work in joules that can be done on the

surroundings.

4.38 If∆Gcan be defined for the process, calculate∆Gfor

each of the following processes:

a. 1.000 mol of water is vaporized at 100.0◦C and

1.000 atm.

b. 1.000 mol of an ideal gas is heated at a constant

pressure of 1.000 atm from 20.00◦C to 80.00◦C.

c.1.000 mol of diamond is converted isothermally into

graphite at 298.15 K and 1.000 bar.

4.39Assume that a gas can be described adequately by either of

the following equations of state:

PVm

RT

 1 +

B 2

Vm

or

PVmRT+A 2 P

where it can be shown thatA 2 B 2.

a.Find a formula for∆Gfor an isothermal pressure

change of such a gas.

b.Find a formula for∆Afor an isothermal volume

change of a such a gas.

c.Find∆Gfor the isothermal expansion at 50.0◦Cof

2.000 mol of CO 2 from a pressure of 5.000 atm to a

pressure of 1.000 atm. For CO 2 at 50.0◦C,

B 2 − 1. 03 × 10 −^4 m^3 mol−^1.

4.40Assume that a gas can equally well be described by the two

equations of state:

PVm

RT

 1 +

B 2

Vm

and

PVmRT+A 2 P

where it can be shown thatA 2 B 2.

a. Find an expression for∆Gand∆Afor isothermally

changing the volume of 1.000 mol of the gas from a

molar volumeVm1to a molar volumeVm2.

b. Find the value of∆Gand∆Afor compressing

1.000 mol of argon from 25.00 L to 5.00 L at a constant

temperature of 298.15 K. The value of B 2 for argon at

this temperature is− 15 .8cm^3 mol−^1.