Page 177 - Thermodynamics of Biochemical Reactions

176 Chapter 10 Calorimetry of Biochemical Reactions

W 10.4 EFFECT OF TEMPERATURE

In Chapter 3 equations and Muthernuticu programs were given for calculating
AfGo and A,H" of species at temperatures other than 298.15 K on the basis of
the assumption that A,Ho at zero ionic strength is independent of temperature.
More accurate calculations are possible when CR values are known for species
and can be assumed to be independent of temperature. In this case,

AfHo(T) = A,H0(298.15 K) + A,C,O(T- 298.15 K) (10.4-1)
where AfC: is the difference between the standard molar heat capacity of the
species and the sum of the molar heat capacities of the elements making it up.
Therefore the standard enthalpy of a chemical reaction at temperature T is given
by
ArHo(T) = A,H0(298.15 K) + A,CF(T- 298.15 K) (10.4-2)
where

( 10.4-3)
j= 1 /= 1
CFmi is the standard heat capacity of species j at constant pressure, and N, is the
number of species in the chemical reaction. Note that the standard molar heat
capacities of the elements cancel in the summation. Equation 10.4-2 was given
earlier as equation 3.2-19, and it was used to show that the pK of acetic acid goes
through a maximum not far from room temperature. Equation 10.4-3 was given
earlier as equation 3.2-16.
When the pH is specified, the standard transformed molar heat capacity of a
species is given by (Alberty, 2001d)

where zj is the charge number for the ion and NH(j) is the number of hydrogen
atoms it contains. Values of the coefficient of the ionic strength term are given as
a function of temperature in Chapter 3. This equation is obtained by applying the
Gibbs-Helmholtz equation to the expression for ArH"( T).

'Table 10.1 Standard Molar Heat Capacities of
Species in Dilute Aqueous Solutions at 298.15 K

Species C,",/J K- ' mol- '
xylose 279 rt_ 20
ribose 276 20
arabinose 276 & 20
fructose 369 _+ 14
galactose 319 & 20
glucose 336 f 7
mannose 342 f 17
xylose 319 28
lyxose 285 & 20
ribose 5-phosphate2 10 * 45
glucose 6-phosphate2 48 f 17
mannose 6-phosphate' 57 _+ 19
fructose 6-phosphate2 - 89 f 17

Sozircc.: With permission from R. N. Goldberg and Y. Tewari,
d. Phjs. Chrrn Ref Datcr 18, 809 (1989). Copyright American
Institute of Physics.