Page 47 - Thermodynamics of Biochemical Reactions

3.3 Importance of Components 41

GkJ mol-'

-:/mol
0.2 0.4 0.6 0.8 I
Fig. 3.2 Acid dissociation constant for acetic acid as a function of temperature (see
Problem 3.4).

If A,Ho is independent of temperature, integration of this equation from TI to T2
yields

(3.2-1 8)

If Ci,(i) does not change significantly in the experimental temperature range,
the enthalpy of reaction will change linearly with T and the entropy of reaction
will change logarithmically:
A,Ho(T) = A,H0(298.15 K) + A,C:(T- 298.15K) (3.2- 19)

m
1
ArSo(T) = A,S0(298.15 K) + A,C:ln (3.2-20)
298.15 K
Substituting these relations in A,Go = - RTlnK = A,Ho(T) - TA,So(T) yields
A,H0(298.15) A,S0(298. 15) A, Cg 298.15 K - In

lnK= - RT + R --(I- R T 298.15 K
(3.2-21)

The plot in Fig. 3.2 of the acid dissociation constant for acetic acid was calculated
using equation 3.2-21 and the values of standard thermodynamic properties
tabulated by Edsall and Wyman (1958). When equation 3.2-21 is not satisfactory,
empirical functions representing Arc: as a function of temperature can be used.
Clark and Glew (1966) used Taylor series expansions of the enthalpy and the heat
capacity to show the form that extensions of equation 3.2-21 should take up to
terms in d3A,C:/dT3.

3.3 IMPORTANCE OF COMPONENTS

The role of components in reaction systems is discussed in Beattie and Oppen-
heim (1979) and Smith and Missen (1982). An elementary introduction to
components has been provided by Alberty (1995~). In chemical reactions the
atoms of each element and electric charges are conserved, but these conservation
equations may not all be independent. It is only a set of independent conservation
equations that provides a constraint on the equilibrium composition. The
conservation equations for a chemical reaction system can also be written in terms
of groups of atoms that occur in molecules. This is discussed in detail in the