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Chapter 6 Exercise
Reaction Equilibrium in Ideal Gas
Mixtures
In Fig. 6.6a, draw the tangent line to the R ln K° curve at 1200 K and from the
P
slope of this line calculate H° . (Answer: 27 kcal/mol.)
1200

6.4 IDEAL-GAS EQUILIBRIUM CALCULATIONS

For an ideal-gas reaction, once we know the value of K° at a given temperature, we
P
can find the equilibrium composition of any given reaction mixture at that temperature
and a specified pressure or volume. K° can be determined by chemical analysis of a
P
single mixture that has reached equilibrium at the temperature of interest. However, it
is generally simpler to determine K° from G°, using G° RT ln K°. In Chapter 5,
P P
we showed how calorimetric measurements (heat capacities and heats of phase transi-
tions of pure substances, and heats of reaction) allow one to find G° values for a
f T
great many compounds. Once these values are known, we can calculate G° for any
T
chemical reaction between these compounds, and from G° we get K°.
P
Thus thermodynamics enables us to find K° for a reaction without making any mea-
P
surements on an equilibrium mixture. This knowledge is of obvious value in finding
the maximum possible yield of product in a chemical reaction. If G° is found to be
T
highly positive for a reaction, this reaction will not be useful for producing the desired
product. If G° is negative or only slightly positive, the reaction may be useful. Even
T
though the equilibrium position yields substantial amounts of products, we must still
consider the rate of the reaction (a subject outside the scope of thermodynamics).
Often, a reaction with a negative G° is found to proceed extremely slowly. Hence we
may have to search for a catalyst to speed up attainment of equilibrium. Often, several
different reactions can occur for a given set of reactants, and we must then consider
the rates and the equilibrium constants of several simultaneous reactions.
We now examine equilibrium calculations for ideal-gas reactions. We shall use K°
P
in all our calculations. K° could also have been used, but consistent use of K° avoids
c P
having to learn any formulas with K°. We shall assume the density is low enough to
c
allow the gas mixture to be treated as ideal.
The equilibrium composition of an ideal-gas reaction mixture is a function of T
and P (or T and V) and the initial composition (mole numbers) n , n , . . . of the
1,0 2,0
mixture. The equilibrium composition is related to the initial composition by a single
variable, the equilibrium extent of reaction j . We have [Eq. (4.95)] n n n
eq i i,eq i,0
n j . Thus our aim in an ideal-gas equilibrium calculation is to find j . We do this
i eq eq
by expressing the equilibrium partial pressures in K° in terms of the equilibrium mole
P
numbers n n n j, where, for simplicity, the eq subscripts have been omitted.
i i,0 i
The specific steps to find the equilibrium composition of an ideal-gas reaction
mixture are as follows.
1. Calculate G° of the reaction using G° n G° and a table of G°
T T i i f T,i f T
values.
2. Calculate K° using G° RT ln K°. [If G° data at the temperature T of the
P P f
reaction are unavailable, K° at T can be estimated using the form (6.39) of the
P
van’t Hoff equation, which assumes H° is constant.]
3. Use the stoichiometry of the reaction to express the equilibrium mole numbers n
i
in terms of the initial mole numbers n and the equilibrium extent of reaction j ,
i,0 eq
according to n n n j .
i i,0 i eq
4. (a) If the reaction is run at fixed T and P, use P x P (n / n )P and the ex-
i i i i i
pression for n from step 3 to express each equilibrium partial pressure P in terms
i i
of j .
eq