Page 11 - Thermodynamics of Biochemical Reactions

4 Introduction to Apparent Equilibrium Constants

is referred to as a limiting law because it becomes more accurate as the ionic
strength approaches zero. At ionic strengths in the physiological range, 0.05 to
0.25 M, there are significant deviations from equation 1.2-1. Of the several ways
to extend this equation empirically to provide approximate activity coefficients in
the physiological range, the most widely used equation is

(1.2-2)

This is referred to as the extended Debye-Hiickel equation. It is an approximation
that gives a good fit of data at low ionic strengths (Goldberg and Tewari, 1991)
when B = 1.6 L”’ mol-’’’. Better fits can be obtained with more complicated
equations with more parameters, but these parameters are not known for
solutions involved in studying biochemical reactions. The way that ther-
modynamic properties vary with the ionic strength is discussed in more detail in
Section 3.6.
Since hydrogen ions and metal ions, like Mg”, are often reactants, it IS
convenient to define the pH, as -log[H+], where c refers to concentrations.
and pMg as -log[Mg2+]. However, a glass electrode measures pH, =
- log{y(H+)[H+]} where a refers to activity. Thus

PH, = -log{-?(H+)j + PH, (1.2-3)
Substituting the extended Debye-Hckel equation in this equation yields (Alberty,
2001d)
AI”~
PH, - PH, = (1.2-4)
1 + 1.61’12
The differences between the measured pH, and the pH, used in biochemical
thermodynamics are given as a function of ionic strength and temperature in
Table 1.1.
These are the adjustments to be subtracted from pH, obtained with a pH
meter to obtain pH,, which is used in the equations in this book. pH, is lower
than pH, because the ion atmosphere of H+ reduces its activity. In the rest of the
book, the subscript “c” on pH will be omitted so that pH = -log[H+].
In considering reactions in biochemical systems it is convenient to move the
activity coefficients into the equilibrium constants. For example, the equilibrium
constant expression for the dissociation of a weak acid can be written as follows:
HA = H+ +A- (1.2-5)

(1.2-6)

The acid dissociation constant K, is independent of ionic strength, but the acid
dissociation constant K, depends on the ionic strength, as indicated by equation
1.2-7. The equilibrium constant expression in equation 1.2-7 will be used in the
rest of the book, but the subscript “c” will be omitted. This will make it possible
for us to deal with concentrations of species, rather than activities.
The same considerations apply to the dissociations of complex ions. For
example, the equilibrium expression for the dissociation of a complex ion with a
magnesium ion can be written as follows:

MgA’ = Mg2+ + A- (1.2-8)

(1.2-9)