Page 173 - Thermodynamics of Biochemical Reactions

172 Chapter 10 Calorimetry of Biochemical Reactions

The transformed enthalpy of a biochemical reaction is a function of tempera-
ture, pH, and ionic strength. Knowledge of AfGo, AfHo, and Cjm for all the species
in a biochemical reaction makes it possible to calculate A,G", A,H", Arc:, and
K' for the biochemical reaction at the desired 7: pH, and ionic strength. Note that
when ions are involved there is an electrostatic contribution that varies with
temperature (see Section 3.7).

10.1 CALORIMETRIC DETERMINATION OF THE
STANDARD TRANSFORMED ENTHALPY OF
REACTION

When a biochemical reaction that is affected by pH and pMg is carried out in a
calorimeter in a buffer, the hydrogen ions and magnesium ions that are produced
or consumed react with the buffer to produce a heat effect that is characteristic of
the buffer, rather than the reaction being studied. Therefore this contribution
should be calculated and should be used to correct the calorimetric heat effect to
obtain the standard transformed enthalpy of the biochemical reaction A,H".
The analysis by Alberty and Goldberg (1993) shows that the enthalpy change in
the calorimetric experiment A,H(cal) is given by
A,H(cal) = ArWo + ATNHArHo(Buf) + A,N,,A,H'(MgBuff) (10.1-1)
where the enthalpy of dissociation of hydrogen ions from the acidic form of the
buffer is given by
A,Ho(Buff) = AfHo(H+) + A,Ho(Buff-) - A,H"(HBuf) (10.1-2)

and the enthalpy of dissociation of magnesium ions from a complex ion is given
by
A,HO(MgBuff) = AfH0(Mg2+) + A,H"(Buff-) - A,HO(MgBuffl) (10.1-3)

Thus, if hydrogen ions or metal ions are produced or consumed, it is
neccssary to know all of the pK's and dissociation constants of magnesium
complexes of the all of the species of all of the reactant in order to calculate ArNH
and A,N,,. However, there is an experimental method for determining ArN,{ and
A,N,, that can be used with complicated reactants where it is not possible to
determine all of the pK's and dissociation constants of magnesium complexes.
This is based on determining the apparent equilibrium constant K' for the
biochemical reaction as a function of pH and pMg. The changes in binding are
calculated using

(10.1-4)

(10.1-5)

as shown in Section 4.5. The change in the binding of hydrogen ions ArNH can
also be determined by use of a pHstat.

H 10.2 CALCULATION OF STANDARD TRANSFORMED
ENTHALPIES OF REACTIONS FROM THE
STANDARD ENTHALPIES OF FORMATION OF
SPECIES

If the enthalpies of formation of all the species involved are known, the standard
transformed enthalpy of a biochemical reaction A,H'" at a specific 7; P, pH, etc.,