Consider the reaction,
`Cl_(2)(aq) + H_(2)S(aq) rarr S(s) + 2H^(+) (aq) + 2Cl^(-)(aq)`
The rate equation for this reaction is,
Rate `=k [Cl_(2)][H_(2)S]`
Which of these mechanisms is`//`are consistent with this rate equation ?
(I) `Cl_(2) + H_(2)S rarr H^(+) + Cl^(-) + Cl^(+) + HS^(-)` (slow)
`Cl^(+) + HS^(-) rarr H^(+) + Cl^(-) + S` (fast)
(II) `H_(2)S hArr H^(+) +HS^(-)` (fast equilibrium)
`Cl^(+) + HS^(-) rarr 2 Cl^(-) + H^(+) + S` (slow)

Options

A. B only
B. Both A and B
C. Neither A nor B
D. A only

Answer

D

Explanation

mechanism `(A)` has an intial slow step. Thus, we can write the rate law directly from this step:
Rate `=K[Cl_(2)][HST^(-)]`
To eliminate `HS^(-)` from the rate law we consder the first step, which is fast and reaches equilibrium. Writing the equilibrium constant we have
`K_(eq.)=([H^(+)][HS^(-)])/([H_(2)S])`
or `[HS^(-)]=K_(eq.)([H_(2)S])/([H^(+)])`
Substituting this expression into the rate law gives
Rate `=K_(2)K_(eq.)[Cl_(2)][H_(2)S]//[H^(+)]`
`=K'[Cl_(2)[H_(2)S]//[H^(+)]`
where `K'=K_(2)K_(eq.)`
Thus, only mechanism `(A)` is consistent with the given rate equation.