Concise Physical Chemistry

c07 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

102 EQUILIBRIUM

Although the Gibbs chemical potential applies to the many-component nonideal case

as well as the ideal case, it is mathematically rigorous and it is a thermodynamic

function.

From these definitions of the Gibbs chemical potentials, it follows that

μA=μ◦A+RTlnfA

and

μB=μ◦B+RTlnfB

In the general case, Gibbs chemical potentials are

μi=μ◦i+RTlnfi

for an indefinite number of fugacities.

Analogous definitions for the general case lead to

μi=μ◦i+RTlnai

for activitiesai, with

Q=

[C]c[D]d...

[A]a[B]b...

=

∏

i

[X]i

∏

j

[X]j

where the[X]iand[X]jare relative concentration variables, pressure fractions, mole

fractions, mass fractions, and so on, symbolized by eitherforaand taken to the

appropriate stoichiometric coefficient.

7.8 FREE ENERGY AND EQUILIBRIA IN BIOCHEMICAL SYSTEMS

Reactions of biochemical interest do not normally occur in the gas phase. Rather

they occur in solution, usually saline solution. Therefore the correct expression

of the free energy changes of reaction and the equilibrium constant is in terms

of the corresponding activities and changes in chemical potential. Determination of

activities and activity coefficients over a concentration range on nonideal solutions is

not a simple matter, nor is it necessary forin vitrostudies of biochemical reactions.

Instead, concentrations are used with the stipulation that the “background” condi-

tions must be constant over the course of the study and must be reproduced from one

study to the next. For example, energy studies on dephosphorylation of adenosine