Page 71 - Thermodynamics of Biochemical Reactions

66 Chapter 4 Thermodynamics of Biochemical Reactions at Specified pH

where the equilibrium mole fractions of the species within the pseudoisomer
group are given by

rl =exp[ $0 Rli';ol -
(4.3-7)

r2 = exp/" 'O RT - P2 'O]
(4.3-8)

The standard transformed chemical potentials of the species at zero ionic
strength are given by

p',' = ,uy - N,,RTln(lO)pH (4.3-9)

,u; = pi - N,,RTln(lO)pH (4.3-10)
where NHl is the number of hydrogen atoms in species 1. This derivation has been
made at zero ionic strength as a simplification, but the effects of ionic strength are
taken into account fully in the next section. Substituting these two equations in
equation 4.3-6 yields
p" = rlpy + r2p: + RT(r, lnr, + r21nr2) - N,RTln(lO)pH' (4.3-11)

where the average number of hydrogen ions bound by the reactant is given by

(4.3-1 2)
NH = 'INHI + rZ"H2
Substituting equation 4.3-1 1 in equation 4.3-4 yields

p' = r,py + r,p; + RT(r, lnr, + r21nr2) - N,RTln(lO)pH + RTln[B]
(4.3-13)

so that the transformed chemical potential of a reactant is equal to the mole
fraction average of the chemical potentials of the species, plus the Gibbs energy
of mixing, minus an adjustment for the pH that is proportional to the average
binding of hydrogen ions, plus RTln[B].

4.4 TRANSFORMED THERMODYNAMIC PROPERTIES
OF BIOCHEMICAL REACTIONS

In the preceding three sections, pl has been used for a species and has been used
for a pseudoisomer group, but in treating experimental data Gibbs energies of
formation A, G, and transformed Gibbs energies of formation, we use AfGl instead
because it is not possible to determine absolute values of chemical potentials. The
Gibbs energies of formation of species are relative to reference states of the
elements or to conventions, like A,Go(Ht) = 0 at zero ionic strength at each
temperature. These reference states cancel when differences are taken in discussing
reactions or phase distributions.
Thus, in making calculations, we rewrite equation 4.2-4 for a biochemical
reaction as

N'
A,G' = C V;A,GI (4.4-1)
i= 1
and the standard transformed Gibbs energy of reaction is given by

N'
A,G0 = 1 vIAfGIo = -RTlnK' (4.4-2)
i= 1