A. Collision Theory
Overview – Collision Theory
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 Sr, When all collisions occur with the same relative velocity, UR the number of collisions between A and B molecules, , is
{collisions/s/molecule]
Next we will consider a distribution of relative velocities and only consider those collisions that have an energy of EA or greater in order to react to show
where
with AB = collision radius, kB = Boltzmann’s constant, AB = reduced mass, T = temperature and NAvo = Avogadro’s number. To obtain an estimate of EA, we use the Polyani Equation
Where HRx is the heat of reaction and and P are the Polyani Parameters. With these equations for A and EA we can make a first approximation to the rate law parameters without going to the lab.
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