Page 54 - Thermodynamics of Biochemical Reactions

48 Chapter 3 Chemical Equilibrium in Aqueous Solutions

Table 3.1 Debye-Huckel Constant and Limiting Slopes of AfGc, AfH,, and C~,(I) as
Functions of Temperature

0 1.12938 2.56494 1.075 13.255
10 1.1471 7 2.70073 1.213 15.41
20 1.16598 2.841 96 1.3845 17.90
25 I. 17582 2.91482 1.4775 19.27
30 1.18599 2.98934 1.5775 20.725
40 1.20732 3.14349 1.800 23.885
Source: With permission from R. A. Alberty, J. Phys. Chem. B, 105, 7865 (2001). Copyright 2001
American Chemical Society.

coefficient 4, and so they used the Debye-Huckel limiting law in the form
lny = -3Am’’’, where m is the molality. The relation between these coefficients
and those needed here were first discussed by Goldberg and Tewari (1991).
Further discussion is to be found in Alberty (2001). The primary coefficients of
interest here are those for effects of ionic strength on In K, AfG , AfH . and CPn,.
These coefficients are a, RTa, RT2(da/?T),, and RT2(?a/2T), + T(i2x/?T2),],
respectively. The third coefficient is a consequence of the Gibbs-Helmholtz
equation. The fourth coefficient is a consequence of equation 2.5-25. The values
of these coefficients calculated from the tables of Clark and Glew (1980) are given
in Table 3.1.
In discussing the effect of temperature, it is more convenient to use the
molality because molality does not change with the temperature when there are
no reactions in the system. However, these values can be used In calculations
based on molarities.
The calculations of standard thermodynamic properties discussed in the rest
of this section are based on the assumption that the standard enthalpies of
formation of species are independent of temperature: in other words, the heat
capacities of species are assumed to be zero. In the future when more is known
about the molar heat capacities of species, more accurate calculations can be
based on the assumption that the molar heat capacities are independent of
temperature. When the heat capacities of species are equal to zero, the standard
entropies of formation are also independent of temperature. Under these condi-
tions the values of AfG: at other temperatures in the neighborhood of 298.15 K
can be calculated using

AfGP(T) = AfHY(298.15 K) - TAfS;(298.15 K) (3.7-1)

This equation can be written in terms of A,G:(298.15 K) and A,H,(298.15 K) by
substituting the expression for the entropy of formation of the species:
A,G,(T) = (&) A,G:(298.15 K) + ( - __ 29i:15) A,H,(298.15 K) (3.7-2)
1

In order to calculate values of AfGL: at other temperatures not too far from
298.15K, it is necessary to fit a to a power series in 7: The use of Fit in
Mathematica yields (see Problem 3.5)

a = 1.10708 - 1.54508 x lO-’T + 5.95584 x 10-6T2 (3.7-3)

Clarke and Glew (1980) give an equation with more parameters to yield values
of a from 0 to 150°C. When the quadratic fit is used, the coefficient RTx in the