# How do you solve the Arrhenius equation?

Apr 7, 2016

The Arrhenius equation is:

$\setminus m a t h b f \left(k = A {e}^{- {E}_{a} \text{/} R T}\right)$

where:

• $k$ is the rate constant, in units that depend on the rate law. For instance, if $r \left(t\right) = k {\left[A\right]}^{2}$, then $k$ has units of "M"/"s" * 1/"M"^2 = 1/("M"cdot"s").
• $A$ is the "pre-exponential factor", which is merely an experimentally-determined constant correlating with the frequency of properly oriented collisions.
• ${E}_{a}$ is the activation energy in units of, say, $\text{J}$.
• $R$ is the universal gas constant. Using $\text{J}$, $R = \text{8.314472 J/mol"cdot"K}$.
• $T$ is temperature in $\text{K}$.

People can determine the temperature themselves when they experimentally figure out the rate constant, so you can assume that you know $T$ and $k$. The only values in the Arrhenius equation not known are generally $A$ and ${E}_{a}$, the pre-exponential factor and activation energies.

I go into how to calculate those here.