Page 70 - Thermodynamics of Biochemical Reactions

4.3 Transformed Thermodynamic Properties of Species and Reactants 65

where ArS' is the transformed reaction entropy. The second Maxwell equation is

The change in binding of hydrogen ions in the biochemical reaction is given by

(4.2-1 3)

This second Maxwell equation will be discussed in Section 4.7.
The transformed reaction entropy is of interest in its own right, but it also
leads to a noncalorimetric method for determining the transformed reaction
enthalpy.
Note that since H' = G' + TS'.

ArH' = ArG' + TA,S' (4.2-14)
Substituting equation 4.2-1 1 in this equation yields the Gibbs-Helmholtz equation
at a specified pH:
ArH'= -T2 ( dT ) (4.2- 15)
d(A G'/ T)
P,pH,I"

4.3 TRANSFORMED THERMODYNAMIC PROPERTIES
OF SPECIES AND REACTANTS

In order to learn more about the transformed chemical potential of a reactant,
we consider the fundamental equation for G' (equation 4.1-18) for a system
containing a single reactant
dG' = -S'dT+ VdP + p'dn' + RTln(lO)n,(H)dpH (4.3-1)

This indicates that p' is given by

(4.3-2)

Integration of equation 4.3-1 at constant 7; P, and pH yields

G' = p'n' (4.3-3)
so that the transformed chemical potential of a reactant is equal to its molar
transformed Gibbs energy. An expression for p' for reactant B that contains two
species, which differ by one hydrogen atom, can be obtained by starting with

p' = p" + RTln[B] (4.3-4)

The concentration of the reactant is [B] = [Bl] + [BJ, where [B,] and [BJ are
the concentrations of the species at the given pH. The standard transformed
Gibbs energy of the reactant when the acid dissociation is at equilibrium can be
calculated using

(4.3-5)
RT
or, alternatively,

p" = rlpio + r,pLo + RT(r, lnr, + rzlnrz) (4.3-6)