## DT RT2779

and on integrating we get the form of the Arrhenius equation that was first obtained based on experiment kf = A°e-Ef/RT, (7.80)

where A° is the integration constant. More generally, in the Arrhenius expression, A° can be weakly dependent on temperature. We can see this from simple collision theory. The probability that two molecules A and B collide with a combined energy of at least Ef is given by the exponential term in the above equation. This is equal to the fraction of effective collisions, where the total number of colliding molecules per cm3 per s is given by ZonAnB. The rate of change in the number density of molecules A is equal to the number of effective collisions between the two types of molecules and so can be written as

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