Lecture 32 : Theories Of Reaction Rates : Collision Theory
An experimental cross section data is shown in Fig 32.4.
Figure 32.4 Experimental ( ) for the reaction H + D 2 HD + D
To integrate eq (32.19) we need a functional form of ( ). Using an approximate form for ( ) vs for the above figure as follows,
( ) = 0 if < a
( ) = ( 1 - a / ) for > a
32.20)
The integral of eq ( 32.19 ) becomes
( ) d = ( 1- a / ) d
(32.21)
= ( k T / ) 1/ 2
(32.22)
We see that, while the exponent has the Arrhenius form, the preexponential is not a constant (as in the Arrhenius case) but a temperature dependent function. The additional temperature dependence of this factor is determined by the distribution function as well as the detailed form of the cross sections.
In Table 32.1, for the reaction in the last row, the reaction cross section was larger than the collision cross section. This can be understood through the harpoon mechanism as described below.
HD + D 
d 
