Question

How do you calculate the pre-exponential factor from the Arrhenius equation?

Answer 1

The Arrhenius equation is
$k=A{e}^{-E_n/RT}$
where:

$\bullet k$ is the rate constant, in units of $\frac{1}{M^{1-m-n}\dot{}s}$, where $m$ and $n$ are the order of reactant $A$ and $B$ in the reaction, respectively.
$\bullet A$ is the pre-exponential factors, correlating with the number of properly-priented collisions.
$\bullet E_a$ is the activation energy in, say, $J$.
$\bullet R$ is the universal gas constant $8.314472J/mol.K$
$\bullet T$ is the temperature in $K$.

So by taking the natural log, we can solve for $A$.

$\ln k=\ln A{e}^{-\frac{E_a}{RT}}$

$=\ln A-\frac{E_a}{RT}$

Thus, we have

$\stackrel{y}{\stackrel{ˆ}{\ln k}}=\stackrel{m}{\widehat{-\frac{E_a}{R}}}\stackrel{x}{\stackrel{ˆ}{\frac{1}{T}}}+\stackrel{b}{\stackrel{ˆ}{\ln A}}$

So this way plotting $\ln k$ vs $\frac{1}{T}$ makes it experimentally possible to determine $A$.

Another way is :

$A=\frac{k}{e^{-E_a/RT}}$