Page 73 - Thermodynamics of Biochemical Reactions

68 Chapter 4 Thermodynamics of Biochemical Reactions at Specified pH

zero ionic strength. Note that the coefficient of the ionic strength term is a
function of temperature, as discussed in Section 3.7. The calculation of the
standard transformed properties of species is discussed by Alberty ( 1999).
Equation 4.4-5 leads to the corresponding equation for the standard trans-
formed enthalpy of formation of a species:
At Hi' = A,HY - NH(j)Af H'(H') (4.4-1 1)

Substituting equation 3.6-3 yields the standard transformed enthalpy of formation
of species j as a function of pH and ionic strength at 298.15 K:
AfHio = A,H,O(Z = 0) + 1.4775(z: - NH(j))I'lZ (4.4- 1 2)
1 + 1.611'2
Thus the availability of A,Hg(Z = 0) for a species makes it possible to calculate
ArH;', and vice versa. Note that the standard transformed enthalpy of a species
is independent of pH, even when it contains hydrogen atoms. At temperatures
other than 298.15 K the numerical coefficient of the ionic strength term has
different values, as discussed in Section 3.7.

4.5 THERMODYNAMICS OF PSEUDOISOMER
GROUPS AT SPECIFIED pH

When there are two or more species in a pseudoisomer group, the standard
transformed Gibbs energy of formation Af G:' and standard transformed enthalpy
of formation AfHio of the pseudoisomer group have to be calculated using isomer
group thermodynamics (Section 3.5). The isomer group equations were introduc-
ed in equations 3.5-1 1 to 3.5-14. At a specified pH, the various forms of a reactant
have the same A[G; at chemical equilibrium, and so the standard transformed
Gibbs energy of formation of the pseuodisomer group can be calculated using

(4.5-1)

where Niso is the number of species in the pseudoisomer group. The equilibrium
mole fraction vj of the jth pseudoisomer in the pseudoisomer group is given by
vi = exp {Af G;oR-TA, Gi0
(4.5-2)

The standard transformed enthalpy of formation of the pseudoisomer group is a
mole fraction weighted average and is given by

(4.5-3)

Note that although AfHiO values for species are independent of pH, this is not
true for AfHio values of reactants consisting of two or more species because the
ri are functions of pH. The pseudoisomer group has a corresponding standard
transformed entropy of formation given by
A,H;' - A,G;'
to
AfSi = (4.5-4)
T
The standard transformed heat capacity at constant pressure of a reactant is
discussed later in Chapter 10 on calorimetry. The calculation of A,H" using
equation 4.5-3 looks simple, but note that the standard transformed Gibbs
energies of formation of all of the species are involved in the calculation. These
equations were applied to the ATP series by Alberty and Goldberg (1992).
Equation 4.5-1 for A,G;' can also be written (Alberty, 1999) in terms of the
binding polynomial (partition function) P (see Section 1.3). Equation 4.5-1 can be