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

Since the slow step is the rate determining step hence if we consider option (1) we find
 `"Rate" = k[Cl_(2)][H_(2)S]`
 Now if we consider option (2) we find
`"Rate"= k[Cl_(2)][HS^(-1)]`
 From equation (i)
`k=([H^(+)][HS^(-)])/(H_(2)S)`
Substituting this value in equation (1) we find
`"Rate" = k[Cl_(2)K]([H_(2)S])/(H^(+))=k.([Cl_(2)][H_(2)S])/([H^(+)])`
hence only, mechanism (i) is consistent with the given rate equation.