The activation energy of a reaction is $94.14$ kj/mole, and the value of rate constant at $313$K is $1.8\times 10^{-1}se{c}^{-1}$. Calculate the frequency factor A.

By using arrhenius equation,
$⟹\log k=\frac{-E_a}{2.303RT}+\log A$

We get
$⟹\log A=\log (1.8\times 10^{-5})+\frac{94140}{2.303\times 8.314\times 313}$
$⟹(\log 1.8)-5+15.7082)$
$⟹0.2553-5+15.7082=10.9635$

$\therefore \log A=(10.9634)=9.914\times 10^{10}$