Lecture 29 : Temperature Dependence of Reaction Rates
29.1
Introduction
Temperature dependence of physical and chemical parameters is of great interests to chemists and predicting correct temperature dependence is a test as well as a challenge for framing suitable theories. In thermodynamics, temperature dependence of heat capacities and enthalpies was used in calculating equilibrium constants at different temperatures. The departure of real gas behaviour from the ideal gas behaviour is expressed through the temperature dependent viral coefficients.
In chemical kinetics, it was observed that for many reactions, increasing the temperature by 10oC, doubled the rates. In rate processes, the temperature dependence is quite striking. In this lecture, we will consider preliminary attempts at explaining this temperature dependence and take up the detailed explanations in later lectures. A knowledge of the distribution of molecular speeds at a given temperature and the population of energy levels is essential in understanding the temperature dependent rate processes and these aspects will also be outlined here.
The most common analysis of temperature dependence of reaction rates over a small temperature range of a few tens of degrees Celsius has been through the Arrhenius equation given below.
k = A e - Ea / RT
(29.1)
Where A is the pre exponential factor (commonly referred to as the frequency factor) and
Ea is the energy of activation. The absolute temperature is denoted by T and R is the gas constant. The rationalization of the Arrhenius equation was given by Van't Hoff, who noted that the equilibrium constant Kc for a reaction like
A + B
C + D
(29.2)
depends on temperature according to the Gibbs Helmholtz equation (lecture 21)
(
ln Kc / T )p =
U0 / R T 2
(29.3)
Where U0 is the standard internal energy change for the reaction. Since
C + D 
ln Kc / 
U0 / R T 2 
