Page 175 - Thermodynamics of Biochemical Reactions

174 Chapter 10 Calorimetry of Biochemical Reactions

effect due to the change in binding of magnesium ions. In the hydrolysis of ATP
to ADP and orthophosphate at 298.15 K, pH 7, pMg 4, and 0.25M ionic strength,
ArN, = - 0.62, ArNMg = - 0.49, and so
ArH'() = 177.74 - (-0.62)(0.41) - (-0.49)(465.36) = - 30.76 kJ mol-
(10.2-10)
Note that the effect of magnesium binding is larger than the first term and has
the opposite sign in this case (Alberty and Goldberg, 1993).

10.4 CALCULATION OF STANDARD TRANSFORMED
ENTROPIES OF BIOCHEMICAL REACTIONS

The determination of standard transformed enthalpies of biochemical reactions at
specified pH, either from temperature coefficients of apparent equilibrium con-
stants or by calorimetric measurements, makes it possible to calculate the
corresponding standard transformed entropy of reaction using
ArS" = ArH" - A,G"
T (10.3-1)

Substituting A,H" = C v:A,H:' and ArG" = C \>:AfG:' yieldc
(10.3-2)
where the standard transformed entropy of formation of pseudoisomer group i for
a particular set of conditions is given by
A~H;' - A,G;'
A,$' = (10.3-3)
T
Thus tables given earlier can be used to calculate standard transformed entropies
of formation. Standard transformed entropies of reactants have not been empha-
sized in previous chapters because the properties with the greatest practical
interest are AfGjo, which can be used to calculate K', and A,H)", which can be
used to calculate the temperature coefficient of K' and the heat effect of a
biochemical reaction. However, molar entropies Si(j) of species are sometimes
considered more interpretable than A,G? and A,H?. For example.
A,S"(298.15 K) = - 92.0 J K-' mol-' for the dissociation of acetic acid. whereas
the A,S" values for gas dissociation reactions are always positive, corresponding
with the increased degrees of freedom of the product gas molecules. The entropy
of dissociation of acetic acid indicates that hydrogen ion and the acetate ion have
fewer degrees of freedom than hydrated acetic acid molecules. The explanation of
this contradiction is that the ions are more hydrated than the neutral acetic acid
molecules because of the orienting effects of the electric fields in the neighborhood
of an ion. Thus the freedom of H,O molecules in an acetic acid solution is reduced
by the dissociation, and consequently the entropy of the products is lower than
the entropy of the acetic acid molecules. Therefore it is of interest to inquire more
deeply into the relation between the molar entropies of species and the standard
transformed entropy of formation of a pseudoisomer group at a specified pH.
The standard transformed enthalpy of formation of a pseudoisomer group is
given by equation 10.2-3. The standard transformed Gibbs energy of formation is
given by
N,,, NIX
A,G:" = c rjA,G)' + RT 2 r;ln 1'; (10.3-4)
j= 1 .; = 1
where Niso is the number of species in the pseudoisomer group. Substituting
equations 10.2-3 and 10.3-4 into equation 10.3-3 yields

(10.3-5)
j= 1 .j= 1