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. I only
B. II only
C. Both I and II
D. Neither I and II

Answer

A

Explanation

Rate determining step is the slowest step
`:.` In case of (I), rate law is given as
rate `=k[Cl_(2)][H_(2)S]`
But in case of (II) the rate law is given as
rate `= k[Cl_(2)][HS^(-)]`
For the first reactions,
`K=([H^(+)][HS^(-)])/([H_(2)S])`
`:. [HS^(-)]=(K[H_(2)S])/([H^(+)])`
`:.` rate `= ([Cl_(2)]K[H_(2)S])/([H^(+)])=(k'[Cl_(2)][H_(2)S])/([H^(+)])`
`:.` mechanism (I) is consistent with the given rate law.