Catalyst A reduces the activation energy for a reaction by 1

Question

Catalyst A reduces the activation energy for a reaction by 10 kJ mol^{$-$ 1} at 300 K. The ratio of rate constants, ${{{}^kT,\,Catalysed} \over {{}^kT,\,Uncatalysed}}$ is e^x. The value of x is ___________. [nearest integer]

[Assume that the pre-exponential factor is same in both the cases. Given R = 8.31 J K^{$-$ 1} mol^{$-$ 1}]

DivineJEE · Accepted Answer

Activation Energy : It is the minimum amount of energy required to activate the molecules/ atoms so that they can undergo the chemical reaction.

A catalyst increases the rate of a reaction by lowering the activation energy so that more reactant molecules collide with enough energy to surmount the smaller energy barrier.

In the Question,

Given :

\mathrm{E}_{\text {cat }}-\mathrm{E}_{\text {uncat }}=10 \mathrm{~kJ} / \mathrm{mol}

\mathrm{T}=300 \mathrm{~K}

According to Arrhenius Equation,

\begin{aligned} & \mathrm{K}=A \mathrm{e}^{-\mathrm{Ea} / \mathrm{RT}} \\\\ & \frac{\mathrm{E}_{\text {cat }}}{\mathrm{E}_{\text {uncat }}}=e^{\frac{E a-E_a^1}{R T}} \end{aligned}

\begin{aligned} & =e^{\frac{10 \times 10^3}{8.21 \times 300}} \\\\ & =e^4 \\\\ & =4 \end{aligned}

Explanation

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