A catalyst lowers the activation enegy of a reaction from $20 \mathrm{~kJ} \mathrm{~mol}^{-1}$ to $10…

A catalyst lowers the activation enegy of a reaction from $20 \mathrm{~kJ} \mathrm{~mol}^{-1}$ to $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The temperature at which the uncatalyzed reaction will have the same rate as that of the catalyzed a $27^{\circ} \mathrm{C}$ is
  1. $-123^{\circ} \mathrm{C}$
  2. $327^{\circ} \mathrm{C}$
  3. $32.7^{\circ} \mathrm{C}$
  4. $+23^{\circ} \mathrm{C}$

Solution

$\frac{\mathrm{E}_{\mathrm{a}}^{\prime}}{\mathrm{T}_{1}}=\frac{\mathrm{E}_{\mathrm{a}}^{\prime}}{\mathrm{T}_{2}}=\frac{10}{300}=\frac{20}{\mathrm{~T}_{2}}$
$\therefore T_{2}=600 \mathrm{~K}=327^{\circ} \mathrm{C}$ ,

Asked in: JEE-TOPICTESTS-CHEMISTRY

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