4.4 Gibbs Energy Calculations
181
B 3 b 2 . Find the value of ∆A for 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.
4.34 Assume that argon obeys the truncated pressure virial
equation of state
PV m RT + A 2 P
with A 2 −15.8 cm 3 mol −1 .
a. Find the value of G m − G ◦
m for 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 ∆A for the isothermal expansion
of a gas obeying the van der Waals equation of state
from volume V 1 to volume V 2 .
b. Find the value of ∆A for 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 ∆G for 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 ∆G can be defined for the process, calculate ∆G for
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.
4.39 Assume that a gas can be described adequately by either of
the following equations of state:
PV m
RT
1 +
B 2
V m
or
PV m RT + A 2 P
where it can be shown that A 2 B 2 .
a. Find a formula for ∆G for an isothermal pressure
change of such a gas.
b. Find a formula for ∆A for an isothermal volume
change of a such a gas.
c. Find ∆G for the isothermal expansion at 50.0 ◦ C of
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 .
4.40 Assume that a gas can equally well be described by the two
equations of state:
PV m
RT
1 +
B 2
V m
and
PV m RT + A 2 P
where it can be shown that A 2 B 2 .
a. Find an expression for ∆G and ∆A for isothermally
changing the volume of 1.000 mol of the gas from a
molar volume V m1 to a molar volume V m2 .
b. Find the value of ∆G and ∆A for 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 −15.8 cm 3 mol −1 .
181
B 3 b 2 . Find the value of ∆A for 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.
4.34 Assume that argon obeys the truncated pressure virial
equation of state
PV m RT + A 2 P
with A 2 −15.8 cm 3 mol −1 .
a. Find the value of G m − G ◦
m for 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 ∆A for the isothermal expansion
of a gas obeying the van der Waals equation of state
from volume V 1 to volume V 2 .
b. Find the value of ∆A for 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 ∆G for 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 ∆G can be defined for the process, calculate ∆G for
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.
4.39 Assume that a gas can be described adequately by either of
the following equations of state:
PV m
RT
1 +
B 2
V m
or
PV m RT + A 2 P
where it can be shown that A 2 B 2 .
a. Find a formula for ∆G for an isothermal pressure
change of such a gas.
b. Find a formula for ∆A for an isothermal volume
change of a such a gas.
c. Find ∆G for the isothermal expansion at 50.0 ◦ C of
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 .
4.40 Assume that a gas can equally well be described by the two
equations of state:
PV m
RT
1 +
B 2
V m
and
PV m RT + A 2 P
where it can be shown that A 2 B 2 .
a. Find an expression for ∆G and ∆A for isothermally
changing the volume of 1.000 mol of the gas from a
molar volume V m1 to a molar volume V m2 .
b. Find the value of ∆G and ∆A for 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 −15.8 cm 3 mol −1 .