Consider the reaction: \(\mathrm{Cl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{~S}(\mathrm{aq}) \rightarrow \mathrm{S}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})\) The rate equation for this reaction is rate \(=\mathrm{k}\left[\mathrm{Cl}_{2}\right]\left[\mathrm{H}_{2} \mathrm{~S}\right]\) Which of these mechanisms is/are consistent with this rate equation? (A) \(\mathrm{Cl}_{2}+\mathrm{H}_{2} \rightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{Cl}^{+}+\mathrm{HS}^{-}\)(slow) \(\mathrm{Cl}^{+}+\mathrm{HS}^{-} \rightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{S}\) (fast) (B) \(\mathrm{H}_{2} \mathrm{~S} \Leftrightarrow \mathrm{H}^{+}+\mathrm{HS}^{-}\)(fast equilibrium) \(\mathrm{Cl}_{2}+\mathrm{HS}^{-} \rightarrow 2 \mathrm{Cl}^{-}+\mathrm{H}^{+}+\mathrm{S}\) (slow)

JEE Main · 2010 · 11 Apr 2010 · Offline · Chemical Kinetics

Consider the reaction:

Cl_{2} (aq) + H_{2} S (aq) \to S (s) + 2 H^{+} (aq) + 2 Cl^{-} (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?
(A)

Cl_{2} + H_{2} \to H^{+} + Cl^{-} + Cl^{+} + HS^{-}

(slow)

Cl^{+} + HS^{-} \to H^{+} + Cl^{-} + S

(fast)
(B)

H_{2} S \Leftrightarrow H^{+} + HS^{-}

(fast equilibrium)

Cl_{2} + HS^{-} \to 2 Cl^{-} + H^{+} + S

(slow)

Answer: (D)

The rate law is set by the slow step. In the first scheme the slow step is the direct reaction of

C l_{2}

with

H_{2} S

, giving rate

= k [C l_{2}] [H_{2} S]

, exactly the observed law. In the second scheme the slow step consumes

H S^{-}

, whose concentration is fixed by the fast equilibrium

H_{2} S ⇌ H^{+} + H S^{-}

; substituting that equilibrium places

[H^{+}]

in the denominator, so the predicted law is

k [C l_{2}] [H_{2} S] / [H^{+}]

, which does not match. Only the first mechanism is consistent with the data.

JEE Main · 2010 · 11 Apr 2010 · Offline · Single correct option