Page 174 - Thermodynamics of Biochemical Reactions

10.2 Calculation of Standard Transformed Enthalpjes of Reactions 173

can be calculated. The basic relation is (see equation 4.4-3)
"
A,H'O = 1 I(A,H;O (10.2-1)
i= 1
where the 1); are the apparent stoichiometric numbers of the N' reactants (sums
of species) in the biochemical reaction and the AfHio are the standard transformed
enthalpies of formation of the reactants under the desired conditions. In the
following treatment it is assumed that Mg2+ is bound as well as H'. In order to
calculate AfHio for a reactant, it is necessary to calculate the AfHio for each
species of the reactant at the desired conditions. For example, if species j contains
NH(j) hydrogen atoms and NM,(j) magnesium atoms, this adjustment is made
with
A,HSo = A,HY - NH(j)AfHo(H+) - N,,(j)AfH0(Mg2+) (10.2-2)
where A,HY is the standard enthalpy or formation of species j, AfHo(Hf) is the
standard enthalpy of the hydrogen ion, and AfHo(Mg2+) is the standard enthalpy
of the magnesium ion, all three of these quantities having been calculated at the
desired ionic strength. When a reactant consists of two or more species, the
standard transformed enthalpy of formation for the reactant is the mole fraction-
weighted average of the standard transformed enthalpies of the Niso species in the
pseudoisomer group (see equation 4.5-3):

NiSO
A,H;O = C rj~f~;o (10.2-3)
j= 1
where rj is the equilibrium mole fraction of speciesj, calculated using the standard
transformed Gibbs energies of formation of the species under the desired condi-
tions (see equation 4.3-7). Substituting equation 10.2-2 shows that the standard
transformed enthalpy of formation of a reactant is made up of three contributions:
AfH:O = (A,Hy) - mH(i)AfHO(Hf) - mMg(i)A,H0(Mg2+) (10.2-4)

where (AfHY) is the mole fraction-weighted enthalpy of formation of the species
in the pseudoisomer group. The average numbers of hydrogen atoms and
magnesium atoms bound are given by
Ni,,,
( 10.2-5)

and

(10.2-6)

The convention is that NH(j) is the total number of hydrogen atoms in species j
and NMg(j) is the number of magnesium atoms in the species.
Substituting equation 10.2-4 for each reactant in equation 10.2-1 yields
"
A,H" = vi(A,H:) - ArNHA,Ho(H+) - ArNMgAfH0(MgZf) (10.2-7)
i= 1
where the changes in the binding of H+ and Mg2+ in the reaction are given by
"
ArNl, = 1 v;N13(i) (10.2-8)
i=l
N'
ArNMg = 1 v;NMg(i) (10.2-9)
i= 1
Equation 10.2-7 shows that there are three contributions to the transformed
enthalpy of reaction in this case: the effects of the standard enthalpies of formation
of the species, the effect due to the change in binding of hydrogen ions: and the