Question

The rate constant is given by Arrhenius equation:
$k=A{e}^{-E_a/RT}$
Calculate the ratio of the catalysed and uncatalysed rate constants at ${25}^{o}C$ if the energy of activation of a catalysed reaction is $162$ $kJ$ and for the uncatalysed reaction the value is $350$ $kJ$.

Answer 1

Let $k_{ca}$ and $k_{un}$ be the rate constants for catalysed and uncatalysed reactions.
$2.303{\log }_{10}{k}_{ca}=2.303{\log }_{10}A-\frac{162\times {10}^3}{RT}$ ...(i)
and $2.303{\log }_{10}{k}_{un}=2.303{\log }_{10}A-\frac{350\times {10}^3}{RT}$ ...(ii)
Subtracting equation (ii) from equation (i)
${\log }_{10}\frac{k_{ca}}{k_{un}}=\frac{{10}^3}{2.303RT}(350-162)$
$=\frac{188\times {10}^3}{2.303\times 8.314\times 298}=32.95$
$\frac{k_{ca}}{k_{un}}=8.88\times {10}^{32}$