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CHAPTER
11 Reaction Equilibrium

in Nonideal Systems

CHAPTER OUTLINE

11.1 The Equilibrium Constant

11.2 Reaction Equilibrium in
Nonelectrolyte Solutions As noted at the start of Chapter 6, reaction equilibrium calculations have important
industrial, environmental, biochemical, and geochemical applications. Chapter 6 dealt
11.3 Reaction Equilibrium in with equilibrium in ideal-gas reactions and Sec. 9.8 mentioned equilibrium in ideally
Electrolyte Solutions
dilute solutions. Equilibria in aqueous solutions commonly involve ionic species, for
11.4 Reaction Equilibria Involving which the ideally dilute solution approximation is poor. Some key industrial gas-phase
Pure Solids or Pure Liquids reactions are run at high pressures, where the gases are far from ideal. It is therefore
essential to know how to compute equilibrium compositions in nonideal systems,
11.5 Reaction Equilibrium in which is what Chapter 11 is about.
Nonideal Gas Mixtures
11.6 Computer Programs for 11.1 THE EQUILIBRIUM CONSTANT
Equilibrium Calculations
For the chemical reaction 0 ∆ n A with stoichiometric numbers n , the reaction
i
i
i
i
11.7 Temperature and Pressure equilibrium condition is n m i,eq 0 [Eq. (4.98)], where m i,eq is the equilibrium value
i
i
Dependences of the of the chemical potential (partial molar Gibbs energy) of the ith species.
Equilibrium Constant To obtain a convenient expression for m , we choose a standard state for each
i
species i and define the activity a of i in the reaction mixture by
i
11.8 Summary of Standard States
a e 1m i m° i 2>RT (11.1)
i
11.9 Gibbs Energy Change for a
i
i
Reaction where m is the chemical potential of i in the reaction mixture and m° is its standard-
state chemical potential. The activity a depends on the choice of standard state and is
i
11.10 Coupled Reactions meaningless unless the standard state has been specified. From (11.1), a depends on
i
the same variables as m . The activity a is a dimensionless intensive property.
i
i
11.11 Summary Comparison of (11.1) with (10.3) and (10.94) shows that a in (11.1) is what we pre-
i
viously defined to be the activity of a species in a solid, liquid, or gaseous mixture.
Table 11.1 in Sec. 11.8 summarizes the choices of standard states. Taking logs of
(11.1), we get
m m° RT ln a i (11.2)*
i
i
Substitution of (11.2) into the equilibrium condition n m i,eq 0 gives
i
i
a n m° RT a n ln a i,eq 0 (11.3)
i
i
i
i i
where a i,eq is the equilibrium value of the activity a . The first sum in this equation is
i
defined to be G°, the standard Gibbs energy change for the reaction (reactants and
n
n
products each in standard states). We have n ln a i,eq ln (a ) i ln ß (a ) i
i
i
i,eq
i,eq
i
i
[Eqs. (1.70) and (1.69)], so (11.3) becomes
¢G° RT ln q 1a i,eq 2 0
n i
i