If the activation energy of a reaction is 80.9 text kJ mol ^ -1 , the fraction of molecules at 700 K having sufficient energy to react is e^ -x . Find the value of x (nearest integer). [Use R = 8.31 text J K ^ -1 text mol ^ -1 ]

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JEE MAIN Chemistry QUESTION #5537

Question 1

If the activation energy of a reaction is $80.9\ \text{kJ mol}^{-1}$, the fraction of molecules at 700 K having sufficient energy to react is $e^{-x}$. Find the value of $x$ (nearest integer). [Use $R = 8.31\ \text{J K}^{-1}\text{mol}^{-1}$]

14✔️
13
12
11

Correct Answer Explanation

The fraction of molecules with energy $\geq E_a$ is given by $f = e^{-E_a/RT}$. So $x = \frac{E_a}{RT} = \frac{80900}{8.31\times700} = \frac{80900}{5817} \approx 13.9 \approx 14$.

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