Page 51 - The engineering of chemical reactions

Reaction Rates Near Equilibrium 35

at chemical equilibrium. In this expression aj is the activity of species j, which is a measure
of the amount of a species defined such that aj = 1 in the standard state where pj = ~7.
For gases the standard state is usually defined as the ideal-gas state at 1 bar (1 bar=1.023
atm), while for liquids it may be either the pure material or the material in a solution at a
concentration of unity. The definitions of standard state and activity are somewhat arbitrary,
but they are uniquely related by the definition of unit activity in the standard state. Once
the standard state is defined, the situation is well defined.
Next, dividing the preceding equation by RT and taking exponentials on both sides,
we obtain

Since we define C vjp; = AGjj, the Gibbs free energy change of the reaction in the
standard state, we obtain

%a; = exp (-z) = Ke,
where K,, is the equilibrium constant as defined by this equation. [We note in passing
that this notation is misleading in that the “equilibrium constant” is constant only for
fixed temperature, and it usually varies strongly with temperature. To be consistent with
our definition of the “rate coefficient,” we should use “equilibrium coefficient” for the
equilibrium constant, but the former designation has become the accepted one.]
We define the standard state of a liquid as aj = 1 and for gases as an ideal gas pressure
of 1 bar, Pj = 1. For ideal liquid solutions (activity coefficients of unity), we write aj = Cj;
so at chemical equilibrium

and for gases

where the difference between these Keqs is that they are defined from wjs at Cj = 1 and
Pj = 1, respectively. In these expressions K,, is dimensionless, while Pj has dimensions;
this equation is still correct because we implicitly write each partial pressure as Pj / 1 and
Cj / 1, which are dimensionless.