Lecture 29 : Temperature Dependence of Reaction Rates
Similarly, or A – A(0) + PV, or
(29.61)
For an ideal gas, PV = nRT,
(29.62)
Substituting these values in (29.61), we get
where N = number of molecules = number of moles Avogadro number, i.e. . Defining the molar partition as in units of mol -1, we have the final expression.
(29.63)
This is a very central expression which is useful for the calculation of equilibrium constants in terms of partition functions.
Consider the reaction
(29.64)
To obtain the equilibrium constant K, we need , the standard free energy change for the reaction, which is given by
(29.65)
Where
(29.66)
is the standard molar free energy of A (subscript m refers to molar and superscript 0 refers to the standard state of 1 bar pressure). We can write similar relations for and and equation (29.65) becomes
(29.66)
We know that at T = 0, U(0) = H(0) = A(0) = G(0) and the first three terms of eq (29.65) can be combined to give
(29.67)
The last three terms of eq (29.66) can be combined and using (29.67) and ,
(29.68)
This is an expression for the equilibrium constant for reaction (29.64) in terms of the partition functions of reactants and products and the reference values of their energies U0. This can be very easily generalized to reaction of all stoichiometry.
or A – A(0) + PV, or 
Avogadro number, i.e. 
. Defining the molar partition as 
in units of mol -1, we have the final expression.
, the standard free energy change for the reaction, which is given by
is the standard molar free energy of A (subscript m refers to molar and superscript 0 refers to the standard state of 1 bar pressure). We can write similar relations for 
and 
and equation (29.65) becomes
,
