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The slope of Arrhenius Plot ($\ln k$ v/s $1/T$) of first order reaction is $-5\times10^3$ K. The value of $E_a$ of the reaction is. Choose the correct option for your answer. [Given $R=8.314\ JK^{-1}\ mol^{-1}$]
A
$83.0\ kJ\ mol^{-1}$
B
$166\ kJ\ mol^{-1}$
C
$-83\ kJ\ mol^{-1}$
D
$41.5\ kJ\ mol^{-1}$
Detailed Solution
$\ln k = \ln A - \frac{E_a}{R}\left(\frac{1}{T}\right)$, so the slope of $\ln k$ vs $\frac{1}{T}$ is $-\frac{E_a}{R}$
$-5 \times 10^3 = -\frac{E_a}{8.314}$
$E_a = 5 \times 10^3 \times 8.314 = 41570$ J $mol^{-1} \approx 41.5$ kJ $mol^{-1}$