Page 67 - Thermodynamics of Biochemical Reactions

62 Chapter 4 Thermodynamics of Biochemical Reactions at Specified pH

where the subscripts have been omitted since they are complicated. Comparison
of equations 4.1-18 and 4.1-20 shows that

(4.1-2 1)

(4.1-22)

(4.1-23)

(4.1-24)

where {nl} is the set of amounts of reactants. Equation 4.1-21 shows how the
transformed entropy S’ of the system can be obtained from measurements of the
transformed Gibbs energy G‘. Substituting equation 4.1-19 in equation 4.1-21
yields
S‘ = c (4.1-25)
Nt

i= 1
where the molar transformed entropy of a reactant is given by

(4.1-26)

The transformed enthalpy of the system at specified pH is given by H‘ = G’ + TS’
(equation 4.1-16), and substituting equation 4.1-21 yields

This is the Gibbs-Helmholtz equation for the system at specified pH. Substituting
equation 4.1-19 in equation 4.1-27 yields

N,
H‘ = n:Hki (4.1-28)
i= 1
where the molar transformed enthalpy of a reactant is given by the Gibbs-
Helmholtz equation in the form

(4.1-29)

If there is one reactant, equation 4.1-18 leads to D(D - 1)/2 = 4 x 3/2 = 6
Maxwell equations. One of these is discussed in Section 4.7 on the calculation of
the average binding of hydrogen ions by a reactant.
At specified pH, equation 4.1-18 can be written
”
(dc’),,, = -S’dT+ VdP + 1 pidnl (4.1-30)
i= 1
This equation has the same form as equation 4.1-5, which applies to a cheniical
reaction described in terms of species. It shows why the world of biochemical
thermodynamics at specified pH looks so much like the world of chemical
thermodynamics that is described by equation 4.1-5. An important difference
between these equations is that the terms in the summation on the right side of
equation 4.1-30 deal with pseudoisomer groups, like ATP, rather than species.