Physical Chemistry Third Edition

304 7 Chemical Equilibrium

7.1 Gibbs Energy Changes and the

Equilibrium Constant

In a general chemistry course a quotient of concentrations and/or partial pressures is set

equal to an equilibrium constant. We now use thermodynamics to derive an equilibrium

constant expression in terms of activities that will apply to all cases. Equation (2.7-7)

is a generic chemical equation that can stand for any chemical reaction:

0 

∑c

i 1

viFi (7.1-1)

where the chemical formula of substance numberiis abbreviated byFiand its

stoichiometric coefficient is denoted byνi. The stoichiometric coefficients of prod-

ucts are positive, and those of reactants are negative. The arrow or double arrow that

we ordinarily use is replaced by an equals sign, and all substances’ formulas are on the

right side of the equation. For example, the equation for the gas-phase decomposition

of N 2 O 4 is written as

N 2 O 4 (g)
2NO 2 (g) (7.1-2a)

or

0 2NO 2 (g)−N 2 O 4 (g) (7.1-2b)

so that

ν(NO 2 ) 2

ν(N 2 O 4 )− 1

The inconvenience of writing chemical equations in this unfamiliar way is outweighed

by the resulting ability to write compact thermodynamic equations that apply to any

chemical reaction.

Consider a one-phase closed system maintained at constant pressure and tempera-

ture in which a single chemical reaction can occur. We assume that the system is in

a metastable state as equilibrium is approached so that the Gibbs energy and other

thermodynamic variables of the system have well-defined values. From Chapter 4,

we know that the Gibbs energy of the system must decrease until it reaches a stable

minimum value at equilibrium.

The Gibbs energy of the system is a function ofT,P,n 1 ,n 2 ,...,nc, wherecis the

number of substances in the system. If an infinitesimal amount of reaction takes place

at constantTandP, it changes the amounts of the substances and the change in the

Gibbs energy is given by Eq. (4.5-3):

dG

∑c

i 1

μidni (constantTandP) (7.1-3)

Since the system is closed then’s can change only by the progress of the reaction. To

expressdGin terms of the amount of reaction that takes place, we define theextent of