Chemistry - Chemical Kinetics Question with Solution | TestHub

Over all reaction will be
${\text{A}}_2+2\text{B}\to \text{2P}$
here 'A' is intermediate
${\text{A}}_2\stackrel{{\text{K}}_{\text{eq}}}{\rightleftharpoons }2\text{A}\left(\text{fast}\right)$
${\mathrm{K}}_{\mathrm{e}\mathrm{q}}=[\mathrm{A}{]}^2/[{\mathrm{A}}_2]$
$\left[\mathrm{A}\right]=\sqrt{{\mathrm{K}}_{\mathrm{e}\mathrm{q}}\left[{\mathrm{A}}_2\right]}$
$\mathrm{A}+\mathrm{B}\stackrel{{\mathrm{k}}_1}{\to }\left(\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{w}\right)\to \mathrm{R}\mathrm{D}\mathrm{S}$
$\mathrm{R}\mathrm{a}\mathrm{t}{\mathrm{e}}_{\mathrm{R}\mathrm{D}\mathrm{S}}={\mathrm{k}}_1\left[\mathrm{A}\right]\left[\mathrm{B}\right]$
$={\mathrm{k}}_1\sqrt{{\mathrm{K}}_{\mathrm{e}\mathrm{q}}}\sqrt{\left[{\mathrm{A}}_2\right]}.\left[\mathrm{B}\right]$
Note: Overall reaction is${\mathrm{A}}_2+2\mathrm{B}\to 2\mathrm{P}$.