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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
i1
v i F i
(7.1-1)
where the chemical formula of substance number i is abbreviated by F i and its
stoichiometric coefficient is denoted by ν i . The stoichiometric coefficients of products 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 temperature 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 of T , P, n 1 , n 2 , . . . , n c , where c is the
number of substances in the system. If an infinitesimal amount of reaction takes place
at constant T and P, it changes the amounts of the substances and the change in the
Gibbs energy is given by Eq. (4.5-3):
dG
c
i1
µ i dn i (constant T and P)
(7.1-3)
Since the system is closed the n’s can change only by the progress of the reaction. To
express dG in terms of the amount of reaction that takes place, we define the extent of
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
i1
v i F i
(7.1-1)
where the chemical formula of substance number i is abbreviated by F i and its
stoichiometric coefficient is denoted by ν i . The stoichiometric coefficients of products 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 temperature 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 of T , P, n 1 , n 2 , . . . , n c , where c is the
number of substances in the system. If an infinitesimal amount of reaction takes place
at constant T and P, it changes the amounts of the substances and the change in the
Gibbs energy is given by Eq. (4.5-3):
dG
c
i1
µ i dn i (constant T and P)
(7.1-3)
Since the system is closed the n’s can change only by the progress of the reaction. To
express dG in terms of the amount of reaction that takes place, we define the extent of