Temperature-Dependent Term of a Rate Equation

For many reactions, and particularly elementary reactions, the rate expression can be written as a product of a temperature-dependent term and a composition-dependent term, or 

For such reactions the temperature-dependent term, the reaction rate constant, has been found in practically all cases to be well represented by Arrhenius law  

At the same concentration, but at two different temperatures, Arrhenius law indicates that 

But what moles are we referring to in the units of E This is unclear. However, since E and R always appear together, and since they both refer to the same number of moles, this bypasses the problem. This whole question can be avoided by using the ratio E/R throughout. 

This shows that Arrhenius law is a good approximation to the temperature dependency of both collision and transition-state theories. 

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