Professional Reference Shelf

Recalling Equation (19) and substituting for S_r

Which is similar to the equation for hard sphere collisions except for the term

This equation gives the correct Arrhenius dependence and the correct order of magnitude for A.

We now will manipulate and plot the distribution function to obtain a qualitative understanding of how temperature increases the number of reacting molecules. Figure PRS.3A-8 shows a plot the distribution function given by Equation (17) after it has been converted to an energy distribution.

in terms of energy by letting to obtain

where f(,T) d is the fraction of molecules with kinetic energies between  and (+d). We could further multiply and divide by k_BT

Recalling

By letting , we could have put the distribution in dimensionless form

f(X,T) dX is the fraction of molecules that have energy ratios between and

Fraction of collisions that have E_A or above

This integral is shown by the shaded area on Figure PRS.3A-8