# What does the Arrhenius equation calculate?

May 29, 2017

The Arrhenius equation is often written as:

$\ln \left({k}_{2} / {k}_{1}\right) = - {E}_{a} / R \left[\frac{1}{T} _ 2 - \frac{1}{T} _ 1\right]$ $\text{ "" } \boldsymbol{\left(1\right)}$

or

${\overbrace{\ln k}}^{y} = {\overbrace{- {E}_{a} / \left(R\right)}}^{m} {\overbrace{\frac{1}{T}}}^{x} + {\overbrace{\ln A}}^{b}$ $\text{ "" } \boldsymbol{\left(2\right)}$

for practical use, but tends to be introduced as

$k = A {e}^{- {E}_{a} \text{/} R T}$.$\text{ "" } \boldsymbol{\left(3\right)}$

Generally, the rate constant for multiple temperatures of the same reaction is plotted against $1 \text{/} T$ (as in $\left(2\right)$) to determine the activation energy from the slope. $\left(1\right)$ may be used for simple calculations between two temperatures.

The frequency factor $A$ can also be determined (how?). What is the expression to find ${E}_{a}$, if $\text{slope" = -E_a"/} R$?