Editing Arrhenius equation (section)

=== Collision theory ===
{{main|Collision theory}}
One approach is the [[collision theory]] of chemical reactions, developed by [[Max Trautz]] and [[William Lewis (physical chemist)|William Lewis]] in the years 1916–18. In this theory, molecules are supposed to react if they collide with a relative [[kinetic energy]] along their line of centers that exceeds ''E''<sub>a</sub>. The number of binary collisions between two unlike molecules per second per unit volume is found to be<ref name=LM>{{cite book |last1=Laidler |first1=Keith J. |last2=Meiser |first2=John H. |title=Physical Chemistry |date=1982 |publisher=Benjamin/Cummings |isbn=0-8053-5682-7 |pages=376–78 |edition=1st}}</ref>
<math display="block"> z_{AB} = N_\text{A} N_\text{B} d_{AB}^2 \sqrt\frac{8 \pi k_\text{B}T}{ \mu_{AB}} ,</math>
where ''N<sub>A</sub>'' and ''N<sub>A</sub>'' are the number densities of ''A'' and ''B'', ''d<sub>AB</sub>'' is the average diameter of ''A'' and ''B'', ''T'' is the temperature which is multiplied by the [[Boltzmann constant]] ''k''<sub>B</sub> to convert to energy, and ''μ<sub>AB</sub>'' is the [[reduced mass]] of ''A'' and ''B''.

The rate constant is then calculated as {{tmath|1= k = z_{AB}e^\frac{-E_\text{a} }{RT} }}, so that the collision theory predicts that the pre-exponential factor is equal to the collision number ''z<sub>AB</sub>''. However for many reactions this agrees poorly with experiment, so the rate constant is written instead as {{tmath|1= k = \rho z_{AB}e^\frac{-E_\text{a} }{RT} }}. Here ''<math>\rho</math>'' is an empirical [[steric factor]], often much less than 1.00, which is interpreted as the fraction of sufficiently energetic collisions in which the two molecules have the correct mutual orientation to react.<ref name=LM/>