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Chapter 6 increase in P at 900 K will decrease the equilibrium amount of water vapor. (Note,
Reaction Equilibrium in Ideal Gas however, from Fig. 6.11a that an isothermal increase in P always decreases n .)
Mixtures tot
One finds (Prob. 6.52) that an increase in P from 10 bar to 30 bar at 900 K shifts re-
action (1) to the left and shifts reaction (2) to the right, the side with the greater number
of moles of gas. What about the reasoning in the Isothermal Pressure Change subsec-
tion, which predicted a shift to the side with the smaller number of moles? The answer
is that that reasoning assumed the system had only one reaction. When two reactions
with species in common are present, the two reactions influence each other and the sit-
uation is complex and not easily analyzed by simply looking at the stoichiometry of
the reactions. (See also Prob. 6.46, where it is shown that the extent of one reaction
depends on the choice of the second reaction.) However, it can be proved that no mat-
ter how many reactions occur in the ideal-gas system, an isothermal pressure increase
will always produce a shift toward smaller n and smaller V.
tot
Other bizarre shifts in systems with several reactions (for example, dilution lead-
ing to precipitation) are discussed in the references given in I. Nagypál et al., Pure
Appl. Chem., 70, 583 (1998).

6.7 SUMMARY
The chemical potential of gas i at partial pressure P in an ideal gas mixture is m
i
i
m°(T) RT ln (P /P°), where m°(T), the standard-state chemical potential of i, equals
i
i
i
G° (T), the molar Gibbs energy of pure gas i at P° 1 bar and T.
m,i
For the ideal-gas reaction 0 ∆ n A , use of this expression for m in the equi-
i
i
i
i
librium condition n m 0 leads to G° RT ln K°, where G° n m°and
i
i
i
i i i
P
n
the standard equilibrium constant K° (P /P°) i is a function of T only. The tem-
i,eq
i
P
perature dependence of the standard equilibrium constant is given by d ln K° /dT
P
2
H°/RT .
The equilibrium composition of an ideal-gas mixture at a given T with a known
value of K° is found by using the relation n n j (where j is the unknown extent
i
i
P
of reaction at equilibrium) to relate the equilibrium numbers of moles to the initial
numbers of moles, and using either P x P (n /n )P if P is known or P n RT/V
i
i
i
i
tot
i
if V is known to express the partial pressures in terms of the moles; then the expres-
sions for the partial pressures (which contain only the single unknown j) are substi-
tuted into the K° expression.
P
When a change is made in a system in reaction equilibrium, the direction of the
shift needed to restore equilibrium is found by comparing the values of Q° and K°. If
P
P
Q° K°, then the equilibrium will shift to the left; if Q° K°, the equilibrium will
P
P
P
P
shift to the right.
Important kinds of ideal-gas equilibrium calculations dealt with in this chapter
include:
• Calculation of K° and G° from the observed equilibrium composition.
P
• Calculation of K° from G° using G° RT ln K°.
P
P
• Calculation of the equilibrium composition from K° and the initial composition
P
for constant-T-and-P or constant-T-and-V conditions.
2
• Calculation of K° at T from K° at T using d ln K°/dT H°/RT .
P
2
P
1
P
• Calculation of H°, G°, and S° for a reaction from K° versus T data using
P
G° RT ln K° to get G°, d ln K°/dT H°/RT to get H°, and G°
2
P
P
H° T S° to get S°.
FURTHER READING
Denbigh, chap. 4; Zemansky and Dittman, chap. 15; de Heer, chaps. 19 and 20.