The slope of Arrhenius Plot lnk v/s 1 T of first order reaction is - 5 × 10 3 K . The value of E a of the…

Arrhenius equation is $\mathrm{k}={\mathrm{Ae}}^{-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{RT}}}$

So, $\mathrm{lnk}=\mathrm{lnA}-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{RT}}$

This is a straight-line equation of form $\mathrm{y}=\mathrm{mx}+\mathrm{c}$

where $\mathrm{y}=\mathrm{lnk},\mathrm{x}=\frac{1}{\mathrm{T}},\mathrm{m}=-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}$ and $\mathrm{c}=\ln \mathrm{A}$

$\mathrm{m}=-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}$

$-5\times {10}^3\mathrm{K}=-\frac{{\mathrm{E}}_{\mathrm{a}}}{8.314}$

${\mathrm{E}}_{\mathrm{a}}=8.314\times 5\times {10}^3 {\mathrm{Jmol}}^{-1}=41.5 \mathrm{kJ}{ \mathrm{mol}}^{-1}$