Professional Reference Shelf

Professional Reference Shelf

In Chapter 3 we presented a number of rate laws that depended on both concentration and temperature. For the elementary reaction

A + B  C + D

the elementary rate law is

We want to provide at least a qualitative understanding as to why the rate law takes this form. We will first develop the collision rate, using collision theory for hard spheres of cross section S_r, When all collisions occur with the same relative velocity, U_R the number of collisions between A and B molecules, , is

Next we will consider a distribution of relative velocities and only consider those collisions that have an energy of E_A or greater in order to react to show

where

with _AB = collision radius, k_B = Boltzmann’s constant, _AB = reduced mass, T = temperature and N_Avo = Avogadro’s number. To obtain an estimate of E_A, we use the Polyani Equation

Where H_Rx is the heat of reaction and and _P are the Polyani Parameters. With these equations for A and E_A we can make a first approximation to the rate law parameters without going to the lab.