Page 72 - Thermodynamics of Biochemical Reactions

4.4 Transformed Thermodynamic Properties of Biochemical Reactions 67

Application of the Gibbs-Helmholtz equation to equation 4.4-1 yields the stan-
dard transformed enthalpy of reaction

"
A,H'O = C VLA,H:O (4.4-3)
i=l
The standard transformed Gibbs energies of formation of reactants in a biochemi-
cal reaction at specified pH are very important because they can be used to
calculate the value of K' of the biochemical reaction at the specified pH. This
section and the next show how the standard transformed Gibbs energies of
formation of biochemical reactants at specified pH and ionic strength can be
calculated from the standard Gibbs energies of formation of the species they
contain. This section is concerned with the standard transformed Gibbs energies
of formation and standard transformed enthalpies of formation of species, and the
next section is concerned with the calculation of these properties for a reactant
that involves two or more species. These standard transformed properties can also
be calculated from experimental data using equations 4.4-2 and 4.4-3 in the
absence of information about the standard properties of the species involved.
The discussion of the standard transformed properties of a species starts with
the definition of the transformed chemical potential pi of the species given by
p'.=p.- N (' j)p(H+) (equation 4.1-4). This equation can be written in terms of
~
Gibbs energies of formation and transformed Gibbs energies of formation as
follou~s:
A,G> = AfGj - N,(j)A,G(H+) (4.4-4)
There is a corresponding equation for the transformed enthalpy of formation of
a species:
AfH> = AfHj - N,(j)A,H(H+) (4.4-5)
Instead of pj = py + RTln [Bj] (equation 4.1-11) we now use

AfGj = A,Gy + RTln[Bj] (4.4-6)
The corresponding relation for the enthalpy of formation of a species is
AfHj = A,HjO (4.4-7)
Using equation 4.4-6 in equation 4.4-4 yields
AfGi = AfGy + RTln[Bj] - NH(j){AfGo[H'] + RTln(lO-pH)}

= AfGF + RTln[Bj] (4.4-8)
where the standard transformed Gibbs energy of formation of species j is given by
AfG>' = AfGY - NH(j){A,Go[H'] + RTln(lO-pH)} (4.4-9)

As we have seen in the preceding chapter, the standard thermodynamic
properties of species in aqueous solutions are functions of ionic strength when
they have electric charges. Substituting equation 3.6-3 for species j and for H+ in
equation 4.4-9 yields the standard transformed Gibbs energy of formation of
species j as a function of pH and ionic strength at 298.15 K:
2.91482(2; - NH(j))1'I2
AfGSo = AfGy(Z = 0) + N,(j)RTln(lO)pH - (4.4-10)
1 + 1.61"'
It should be noted that Af Gio is a function of ionic strength for uncharged species
that contain hydrogen atoms, as well as charged species. There is an exception to
this statement when zj" - NH(j) = 0 for a species. The standard transformed
Gibbs energy of formation of a species is independent of ionic strength when
zj = 0 and NH(j) = 0. Equation 4.4-10 shows how the standard transformed
Gibbs energy of formation of a biochemical reactant consisting of a single species
can be calculated from the standard Gibbs energy of formation of the species at