A first order reaction is $50 \%$ completed in 20 minutes at $27^{\circ} \mathrm{C}$ and in 5 minutes at $47^{\circ} \mathrm{C}$. The energy of activation of the reaction is :

Question

Aicharya · Accepted Answer

$\mathrm{k}_{1(300)}=\frac{0.693}{20} ; \mathrm{k}_{2(320)}=\frac{0.693}{5}$
$\operatorname{In} \frac{\mathrm{k}_{2}(320)}{\mathrm{k}_{1(300)}}=\frac{\mathrm{E}_{\mathrm{a}}}{\mathrm{R}}\left[\frac{1}{\mathrm{~T}_{1}}-\frac{1}{\mathrm{~T}_{2}}ight]$
$\mathrm{E}_{\mathrm{a}}=\frac{2.303 \mathrm{RT}_{1} \mathrm{~T}_{2}}{\left(\mathrm{~T}_{2}-\mathrm{T}_{1}ight)} \log \frac{\mathrm{k}_{2}}{\mathrm{k}_{1}}$
$=\frac{2.303 \times 8.314}{20 \times 1000} \times 300 \times 320 \log 4$
$=55.14 \mathrm{~kJ} / \mathrm{mol}$

A first order reaction is $50 \%$ completed in 20 minutes at $27^{\circ} \mathrm{C}$ and in 5 minutes at…

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