Page 158 - Thermodynamics of Biochemical Reactions

9.1 Basic Equations 157

at equilibrium at a specified pH is given by (Silbey and Alberty, 2001)

(9.1-4)

This is usually referred to as the Nernst equation (see equations 8.3-10 and
8.4-14). It is assumed that the salt bridge contributes a negligible junction
potential. This equation can be written as

Where the two terms correspond with half-reactions 9.1-2 and 9.1-3.
When the pH is specified, the change in the transformed Gibbs energy G’ in
a biochemical redox reaction like equation 9.1-1 is given by
Ar G‘ = A, Gk - Ar GI, (9.1-6)

where Arc; and are the transformed Gibbs energies for half-reactions 9.1-2
and 9.1-3. Equation 9.1-6 can be written as

(9.1-7)
A,Gko + RTln ~ lRedl) - (A, GLo + R T In ~
[Ox1
When the reactants are at their standard concentrations (1 M) or standard
pressures (1 bar), the logarithmic terms disappear and this equation becomes
A, G‘O = Ar G: - Ar GF (9.1-8)

Comparison of equations 9.1-5 and 9.1-7 shows that the standard apparent
reduction potentials for the half-reactions at specified pH are givcn by

(9.1-9)

(9.1-10)

where vl is the stoichiometric number of reactant i. The prime is needed to
distinguish these stoichiometric numbers from the stoichiometric numbers of the
underlying chemical reactions. The Af GIo are the standard transformed Gibbs
energies of formation of reactants (sums of species). In calculating the standard
transformed Gibbs energies for half-reactions, we take the standard transformed
Gibbs energies of the formal electrons in equation 9.1-2 and 9.1-3 to be zero.
Substituting equation 9.1-9 and 9.1-10 in equation 9.1-8 yields

Arc’’ = - Iv,IFEKO + Iv,/FE;P = Iv,/FE’O (9.1-1 1)

Note that when two half-reactions are added, their A,G“ values add but their E’O
values do not.
The apparent equilibrium constant for a biochemical reaction (like equation
9.1-1) at specified pH can be calculated using
[ RT ] [-‘TI
- A, G’O
V;~f~;o
K’= exp _____ = exp (9.1 - 1 2)
Equations 9.1-8 to 9.1-10 show that the apparent equilibrium constant can also
be calculated using

(9.1 - 1 3)