Question

Catalyst A reduces the activation energy for a reaction by $10{\text{kJ mol}}^{-1}$ at $300K$. The ratio of rate constants, $\frac{{}^{k}T,\text{Catalysed}}{{}^k\text{T, Uncatalysed}}$ is $e^x$. Calculate the value of $x$ (nearest integer).
[Assume that the pre - exponential factor is same in both the cases. and take value of $R=8.31J{K}^{-1}{\text{mol}}^{-1}]$

Answer 1

We know that Arhenius equation is $k=A{e}^{\frac{-Ea}{RT}}$
Let's say that $k_{catalysed}=A{e}^{\frac{-E_{a,catalysed}}{RT}}$
$k_{uncatalysed}=A{e}^{\frac{-E_{a,uncatalysed}}{RT}}$
$\frac{k_{catalysed}}{k_{uncatalysed}}=e^{\frac{E_{a,uncatalysed}-E_{a,catalysed}}{RT}}=e^{\frac{10\times 1000}{8.31\times 300}}=e^{4.009}=e^x$
Thus, $x=4$