Question:
The rate constant $(k)$ of a reaction is measured at different temperatures $(T)$, and the data are plotted in the given figure. The activation energy of the reaction in $\mathrm{kJ} \mathrm{mol}^{-1}$ is : ( $R$ is gas constant)
Correct Option: , 4
Solution:
Arrhenius equation:
$k=A e^{-E a / R T}$\
$\ln k=\ln A-\left(\frac{E_{a}}{R}\right) \frac{1}{T}$
$\ln k=\ln A-\left(\frac{E_{a}}{R \times 10^{3}}\right) \times \frac{10^{3}}{T}$
Slope of graph $=\frac{-E_{a}}{R \times 10^{3}}=\frac{-10}{5}$
$E_{a}=2 R \times 10^{3} \mathrm{~J}=2 R \mathrm{~kJ}$
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