Chemistry - Chemical Kinetics Question with Solution | TestHub

Apply the Arrhenius equation.

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

Take natural logarithm on both sides.

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

$\mathrm{In}\mathrm{ }\frac{{\mathrm{k}}_1^{\mathrm{\prime }}}{\mathrm{k}}=\frac{\mathrm{Ea}}{\mathrm{R}}\left(\frac{1}{\mathrm{T}}-\frac{1}{{\mathrm{T}}^{\mathrm{\prime }}}\right)=\frac{\mathrm{Ea}}{\mathrm{R}}\times \frac{∆\mathrm{T}}{{\mathrm{TT}}^{\mathrm{\prime }}}$

$∆\mathrm{T}$ is positive, therefore greater the ${\mathrm{E}}_{\mathrm{a}}$ value, greater will be the value of $\frac{{\mathrm{k}}^{\mathrm{\prime }}}{\mathrm{k}}$

$\therefore \mathrm{ }\frac{{\mathrm{k}}_1^{\mathrm{\prime }}}{{\mathrm{k}}_1}>\frac{{\mathrm{k}}_2}{{\mathrm{k}}_2}$