9.21 Biochemical Reactions
401
written as
g = g
o
+ RT ln
i
[C i ]
ν i
.
(9.222)
The standard way to assign g o = g o
products −g o
reactants is to measure the difference
in the Gibbs free energy per mole of each of the molecules taking part in the reaction
at a concentration of one molar and standard temperature and pressure minus the
Gibbs free energy per mole of the atoms that make up the molecules, letting the
Gibbs free energy of widely separated atoms be zero. Tables of the Gibbs free energy
per mole can be found for most molecules of interest. 64 When we can neglect longrange interactions of the participating molecules in a chemical reaction, then we can
calculate g o by summing the tabulated g o for each of the molecules taking part
in the reaction.
Before equilibrium is reached, the concentration products in Eq. (9.222) we will
call K ne , while at equilibrium, we will call K. Evidently, when equilibrium is
reached (i.e. the left-hand side vanishes), we recover the equilibrium condition on
the concentrations, with an equilibrium constant
K =
i
[C i ]
ν i = exp (−g
o /RT ) .
(9.223)
Separating products from reactants, this becomes
K =
p [C p ] |νp|
r [C r ] |ν r | = exp (−g
o /RT ) ,
(9.224)
which we saw earlier as the ‘law of mass action’ (Eq. (9.220)). So, specifying the
equilibrium ‘constant’ is equivalent to giving the standard value for the change in
the Gibbs free energy per mole.
A common problem in dealing with chemical reactions is to find the equilibrium
concentrations after a reaction, given the initial concentrations and the equilibrium
‘constant’ K for a given temperature and pressure.
For example, consider the reaction of carbon monoxide with hydrogen to make
methyl alcohol. This reaction has an equilibrium constant of K = 14.5 per
square mole at 600 K. (A catalyst consisting of granules of copper, zinc oxide, and
aluminum oxide is used to speed the reaction, but its presence does not change the
final equilibrium concentrations.) If 1.0 molar concentrations of CO and of H 2 are
mixed, find the equilibrium concentration of alcohol. The stoichiometric-balanced
reaction is
64 See, for example, Robert A. Alberty, Calculating apparent equilibrium constants of enzyme
catalyzed reactions at pH 7, Biochemical Education 28, 12–17 (2000).
401
written as
g = g
o
+ RT ln
i
[C i ]
ν i
.
(9.222)
The standard way to assign g o = g o
products −g o
reactants is to measure the difference
in the Gibbs free energy per mole of each of the molecules taking part in the reaction
at a concentration of one molar and standard temperature and pressure minus the
Gibbs free energy per mole of the atoms that make up the molecules, letting the
Gibbs free energy of widely separated atoms be zero. Tables of the Gibbs free energy
per mole can be found for most molecules of interest. 64 When we can neglect longrange interactions of the participating molecules in a chemical reaction, then we can
calculate g o by summing the tabulated g o for each of the molecules taking part
in the reaction.
Before equilibrium is reached, the concentration products in Eq. (9.222) we will
call K ne , while at equilibrium, we will call K. Evidently, when equilibrium is
reached (i.e. the left-hand side vanishes), we recover the equilibrium condition on
the concentrations, with an equilibrium constant
K =
i
[C i ]
ν i = exp (−g
o /RT ) .
(9.223)
Separating products from reactants, this becomes
K =
p [C p ] |νp|
r [C r ] |ν r | = exp (−g
o /RT ) ,
(9.224)
which we saw earlier as the ‘law of mass action’ (Eq. (9.220)). So, specifying the
equilibrium ‘constant’ is equivalent to giving the standard value for the change in
the Gibbs free energy per mole.
A common problem in dealing with chemical reactions is to find the equilibrium
concentrations after a reaction, given the initial concentrations and the equilibrium
‘constant’ K for a given temperature and pressure.
For example, consider the reaction of carbon monoxide with hydrogen to make
methyl alcohol. This reaction has an equilibrium constant of K = 14.5 per
square mole at 600 K. (A catalyst consisting of granules of copper, zinc oxide, and
aluminum oxide is used to speed the reaction, but its presence does not change the
final equilibrium concentrations.) If 1.0 molar concentrations of CO and of H 2 are
mixed, find the equilibrium concentration of alcohol. The stoichiometric-balanced
reaction is
64 See, for example, Robert A. Alberty, Calculating apparent equilibrium constants of enzyme
catalyzed reactions at pH 7, Biochemical Education 28, 12–17 (2000).