Consider the reaction :
`Cl_(2)(aq)+H_(2)S(aq) to S(s)+2H^(+)(aq)+2Cl^(-)(aq)`
the rate equation for this reaction is rate=`k[Cl_(2)][H_(2)S]`
Which of these mechanism is/ are consistent with this rate equation?
A. `Cl_(2)+H_(2)S to H^(+)+Cl^(-)+HS^(-)` (Slow)
`Cl^(+)+HS^(-) to H^(+)+Cl^(-)+S` (fast)
B. `H_(2)S harr H^(+)+HS^(-)` (fast equilibirium)
`Cl_(2)+HS^(-) to 2Cl^(-)+H^(+)+S` (Slow)

Options

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

Answer

D

Explanation

Since the slow step is the rate determining step hence if we consider option (A) we find
Rate`=k[Cl_(2)][H_(2)S]`
Now, it we consider option (B) we find
Rate`=k[Cl_(2)][HS^(-)]` …(i)
For equationn
`H_(2)S harrH^(+)+HS^(-)`
`K=([H^(+)][HS^(-)])/([H_(2)S]) or, [HS^(-)]=(K[H_(2)S])/([H^(+)])`
Substituting this value in equation (i) we find
Rate`=k[Cl_(2)]k([H_(2)S])/([H^(+)])=(k[Cl_(2)][H_(2)S])/([H^(+)])` Thus slow step should involve 1 molecues of `Cl_(2)` and 1 molecule of `H_(2)S`
Hence only, mechanism (A) is consistent with the given rate equation