Consider the reaction : ${\text{Cl}}_{\text{2}}\left(\text{aq}\right){\text{\hspace{0.17em}+\hspace{0.17em}H}}_{\text{2}}\text{S}\left(\text{aq}\right)\to \text{S}\left(\text{s}\right){\text{\hspace{0.17em}+\hspace{0.17em}2H}}^{\text{+}}\left(\text{aq}\right){\text{\hspace{0.17em}+\hspace{0.17em}2Cl}}^{-}\left(\text{aq}\right)$              

 The rate equation for this reaction is $\text{rate\hspace{0.17em}=\hspace{0.17em}k}\left[{\text{Cl}}_{\text{2}}\right]\left[{\text{H}}_{\text{2}}\text{S}\right]$

Which of these mechanism is/are consistent with this rate equation ?

(A) ${\text{Cl}}_{\text{2}}{\text{\hspace{0.17em}+\hspace{0.17em}H}}_{\text{2}}\text{S\hspace{0.17em}}\to {\text{\hspace{0.17em}H}}^{\text{+}}{\text{\hspace{0.17em}+\hspace{0.17em}Cl}}^{-}{\text{\hspace{0.17em}+\hspace{0.17em}Cl}}^{\text{+}}{\text{\hspace{0.17em}HS}}^{-}\left(\text{slow}\right)$

${\text{Cl}}^{\text{+}}{\text{\hspace{0.17em}+\hspace{0.17em}HS}}^{-}\to {\text{\hspace{0.17em}H}}^{\text{+}}{\text{\hspace{0.17em}+\hspace{0.17em}Cl}}^{-}\text{\hspace{0.17em}+\hspace{0.17em}S}\left(\text{fast}\right)$           

 (B) ${\text{H}}_{\text{2}}\text{S\hspace{0.17em}}\rightleftharpoons {\text{\hspace{0.17em}H}}^{\text{+}}{\text{\hspace{0.17em}+\hspace{0.17em}HS}}^{-}\left(\text{fast\hspace{0.17em}equilibrium}\right)$   

  ${\text{Cl}}_{\text{2}}{\text{\hspace{0.17em}+\hspace{0.17em}HS}}^{-}\to {\text{\hspace{0.17em}2Cl}}^{-}{\text{\hspace{0.17em}+\hspace{0.17em}H}}^{\text{+}}\text{\hspace{0.17em}+\hspace{0.17em}S\hspace{0.17em}}\left(\text{Slow}\right)$

Since the slow step is the rate determining step hence if we consider option (A) we  find

 $\text{Rate\hspace{0.17em}=\hspace{0.17em}k\hspace{0.17em}}\left[{\text{Cl}}_{\text{2}}\right]\left[{\text{H}}_{\text{2}}\text{S}\right]$   Now if we consider option (B) we find            $\text{Rate\hspace{0.17em}=\hspace{0.17em}k}\left[{\text{Cl}}_{\text{2}}\right]\left[{\text{HS}}^{-}\right]\mathrm{...}\left(\text{i}\right)$

            $\text{For\hspace{0.17em}equation,}$

            ${\text{H}}_{\text{2}}\text{S\hspace{0.17em}}\rightleftharpoons {\text{\hspace{0.17em}H}}^{\text{+}}{\text{\hspace{0.17em}+\hspace{0.17em}HS}}^{-}$

            $\text{K\hspace{0.17em}=\hspace{0.17em}}\frac{\left[{\text{H}}^{\text{+}}\right]\left[{\text{HS}}^{-}\right]}{{\text{H}}_{\text{2}}\text{S}}$

            $\text{or\hspace{0.17em}}\left[{\text{HS}}^{-}\right]\text{\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}}\frac{\text{K}\left[{\text{H}}_{\text{2}}\text{S}\right]}{{\text{H}}^{\text{+}}}$

            Substituting this value in equation (i) we find

            $\text{Rate\hspace{0.17em}=\hspace{0.17em}k\hspace{0.17em}}\left[{\text{Cl}}_{\text{2}}\right]\text{K}\frac{\left[{\text{H}}_{\text{2}}\text{S}\right]}{{\text{H}}^{\text{+}}}\text{\hspace{0.17em}=\hspace{0.17em}k}\frac{\left[{\text{Cl}}_{\text{2}}\right]\left[{\text{H}}_{\text{2}}\text{S}\right]}{\left[{\text{H}}^{\text{+}}\right]}$

            Thus slow step should involve 1 molecule of ${\text{Cl}}_2$and 1 molecule of ${\text{H}}_{\text{2}}\text{S}$. Hence only,

            mechanism (A) is consistent with the given rate equation.