Page 53 - Thermodynamics of Biochemical Reactions

3.7 Effect of Temperature on Thermodynamic Properties 47

to provide activity coefficients in the physiological range by introducing an
empirical term to form the extended Debye-Huckel equation.

cx.; Ill2
lny, = - (3.6-1)
1 + BPI~
where B is 1.6 L1'2 mol-'". This equation works quite well in the 0.05 to 0.25 M
range of ionic strengths for a number of electrolytes for which activity coefficients
have been determined accurately. It is evident from this equation that the effect
of ionic strength on the thermodynamic properties of ionic species of biochemical
interest are significant in the 0.05 to 0.25 M range. The effects are especially
significant when ions have charges of 2, 3, or 4. The treatments of the ther-
modynamics of electrolyte solutions at higher concentrations require more
complicated equations with more empirical parameters (Pitzer, 1991, 1995).
However, there is insufficient data on the specific effects of various ions in
biochemical buffers to go beyond equation 3.6-1 at present.
Thus the standard enthalpy of formation AfHY(I) and standard Gibbs energy
of formation AfG:(I) of an ionic species at 298.15 K in kJ mol- ' can be calculated
using (Clark and Glew, 1980; Goldberg and Tewari, 1991)
A,HP(I) = A,HP(I = 0) + 1.4775~?1"~ (3.6-2)
1 + BP

2.91482221 'I2
A, GP(I) = A, Gp(Z = 0) - (3.6-3)
1 + BP
These equations will be very useful in the next chapter.
The standard thermodynamic properties of ions are given in tables of
standard thermodynamic properties at I = 0. The effect of ionic strength on Arc"
for a chemical reaction is obtained by substituting equation 3.6-3 in equation
3.1- 12:
2.91482I1I2 E viz;
A,G"(I) = A,G"(I = 0) - (3.6-4)
1 + BI'I~
where E:viz? is the change in z; in the reaction. The effect of ionic strength on
ArH'(I) for a chemical reaction is obtained by using the Gibbs-Helmholtz
equation (2.5-18 and 3.2-12):
A,HP(I) = A,Hp(I = 0) + 1.47751'/2Evi~f (3.6-5)
1 + BI"~
The effect of ionic strength on the equilibrium constant for a chemical reaction at
25"C is obtained by substituting equation 3.6-4 in equation 3.1-2:
In K(I) = In K(I = 0) + 1.1 75821112Cviz2 (3.6-6)
1 + BI'I2

3.7 EFFECT OF TEMPERATURE ON
THERMODYNAMIC PROPERTIES

In order to discuss thermodynamic properties in dilute aqueous solutions at
temperatures other than 298.15 K, it is necessary to have the standard enthalpies
of the species involved. Over narrow ranges of temperature, calculations can be
based on the assumption that A,HP values are independent of temperature, but
more accurate calculations can be made when C&i) values are known. It is also
necessary to take into account the temperature dependencies of the numerical
coefficients in equations 3.6-4 to 3.6-6. Clarke and Glew (1980) calculated the
Debye-Huckel slopes for water between 0 and 150'C. They were primarily
concerned with electrostatic deviations from ideality of the solvent osmotic