Editing Arrhenius equation (section)

=== Transition state theory ===
The [[Eyring equation]], another Arrhenius-like expression, appears in the "[[transition state theory]]" of chemical reactions, formulated by [[Eugene Wigner]], [[Henry Eyring (chemist)|Henry Eyring]], [[Michael Polanyi]] and [[Meredith Gwynne Evans|M. G. Evans]] in the 1930s. The Eyring equation can be written:
<math display="block">k = \frac{k_\text{B}T}{h} e^{-\frac{\Delta G^\ddagger}{RT}} = \frac{k_\text{B}T}{h} e^{\frac{\Delta S^\ddagger}{R}}e^{-\frac{\Delta H^\ddagger}{RT}},</math>
where <math>\Delta G^\ddagger</math> is the [[Gibbs free energy|Gibbs energy]] of activation, <math>\Delta S^\ddagger</math> is the [[entropy of activation]], <math>\Delta H^\ddagger</math> is the [[enthalpy]] of activation, <math>k_\text{B}</math> is the [[Boltzmann constant]], and <math>h</math> is the [[Planck constant]].<ref>{{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=378–83 |edition=1st}}</ref>

At first sight this looks like an exponential multiplied by a factor that is ''linear'' in temperature. However, free energy is itself a temperature dependent quantity. The free energy of activation <math>\Delta G^\ddagger = \Delta H^\ddagger - T\Delta S^\ddagger</math> is the difference of an enthalpy term and an entropy term multiplied by the absolute temperature. The pre-exponential factor depends primarily on the entropy of activation. The overall expression again takes the form of an Arrhenius exponential (of enthalpy rather than energy) multiplied by a slowly varying function of ''T''. The precise form of the temperature dependence depends upon the reaction, and can be calculated using formulas from [[statistical mechanics]] involving the [[Partition function (statistical mechanics)|partition functions]] of the reactants and of the activated complex.