Page 10 - Thermodynamics of Biochemical Reactions

1.2 Acid Dissociation Constants and Dissociation Constants of Complex Ions 3

of ATP in such a table and made a suggestion as to how to handle it. In 1977
Thauer, Jungermann, and Decker published a table of standard Gibbs energies of
formation of many species of biochemical interest, and showed how to adjust
standard Gibbs energies of reaction to pH 7 by adding mAfGo(H+), where m is
the net number of protons in the reaction.
During the 1960s and 1970s, new nomenclature for treating the ther-
modynamics of biochemical reactions was developed, including the use of K' for
the apparent equilibrium constant written in terms of sums of species, but
omitting [H']. These changes led to the publication of Recommendations ,for
Measurement and Presentation of Biochemical Equilibrium Data by an IUPAC-
IUB Committee (Wadso, Gutfreund, Privalov, Edsall, Jencks, Armstrong, and
Biltonen, 1976).
Goldberg and Tewari published an evaluation of thermodynamic and trans-
port properties of carbohydrates and their monophosphates in 1989 and of the
ATP series in 1991. Miller and Smith-Magowan published on the ther-
modynamics of the Krebs cycle and related compounds in 1990.
Alberty (1992a, b) pointed out that when the pH or the free concentration of
a metal ion is specified, the Gibbs energy C does not provide the criterion for
spontaneous change and equilibrium. When intensive variables in addition to the
temperature and pressure are held constant, it is necessary to define a transformed
Gibbs energy G' by use of a Legendre transform, as discussed in Chapters 2 and
4. This leads to a complete set of transformed thermodynamic properties at
specified pH, that is, a transformed entropy S', transformed enthalpy H', and a
transformed heat capacity at constant pressure Cim. These changes led to the
publication of Recommendations for Nonienclature and Tables in Biochemical
Thermodynamics by an IUPAC-IUBMB Committee (Alberty, Cornish-Bowden,
Gibson, Goldberg, Hammes, Jencks, Tipton, Veech, Westerhoff, and Webb, 1994).
This introductory chapter describes the thermodynamics of biochemical
reactions in terms of equilibrium constants and apparent equilibrium constants
and avoids references to other thermodynamic properties, which are introduced
later.

W 1.2 ACID DISSOCIATION CONSTANTS AND
DISSOCIATION CONSTANTS OF COMPLEX IONS

Strictly speaking, equilibrium constant expressions for chemical reactions involv-
ing ions in aqueous solutions should be written in terms of activities a, of species,
rather than concentrations. The activity of species i is given by ai = yici, where yi
is the activity coefficient, which is a function of ionic strength. Activity coefficients
of neutral molecules are close to unity in dilute aqueous solutions, but the activity
coefficients of ions may deviate significantly from unity, depending on their
electric charges and the ionic strength. The ionic strength of a solution is defined
by I = ($zzci, where zi is the charge on ion i and c, is its concentration on the
molar scale. When dilute aqueous solutions are studied, the ionic strength is under
the control of the investigator and is essentially constant when the composition
changes during a reaction. Thus it is convenient to take equilibrium constants and
other thermodynamic properties to be functions of the ionic strength so that
equilibrium constant expressions can be written in terms of concentrations. The
exception to this statement is H,O. In dilute aqueous solutions the convention in
thermodynamics is to omit [HzO] in the expression for the equilibrium constant
because its activity remains essentially at unity.
In 1923 Debye and Hckel showed that the activity coefficient yi of an ion
decreases with increasing ionic strength, according to
2 1/2
logyi = -Az, I (1.2-1)
where A = 0.510651 L-'" mol'i2 at 298.15 K in water at a pressure of 1 bar. This