40
which upon equating with equation (1-32) yields
(3T}p S
(1-39)
and
<|ยง) = V (1-40)
Equation (1-39) suggests an experimentally tractable
relationship between free energy (via K) and temperature,
when pressure is held constant. Moreover, we may extend
the relationship to include the changes in free energy as
a function of temperature for a process involving reactants
going to products. We may now equate (1-38) with equation
(1-32), rearrange, and solve for the partial differentials
to obtain
(9AG/9T)p = -AS
(1-41)
where AG = (G G , ) and S = (S ,
products reactants products
S reactants^ The entroPY term of equation (1-41) may be
eliminated by recalling that AS = (-AH + AG)/T and substi
tuting
(9G/9T)p = (-AH + AG)/T
(1-42)
Assume, henceforth, that the pressure will be held constant.
Rearranging (1-42) gives