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Question: Consider the reaction \(\text{C}\text{l}_{2}\ (\text{aq})\text{ + }\text{H}_{2}S(\text{aq})\ \overs...

Consider the reaction

Cl2 (aq) + H2S(aq) → S(s) + 2H+ (aq) + 2Cl− (aq)\text{C}\text{l}_{2}\ (\text{aq})\text{ + }\text{H}_{2}S(\text{aq})\ \overset{\quad\quad}{\rightarrow}\text{ S}(s)\text{ + 2}\text{H}^{+}\ (\text{aq})\text{ + 2C}\text{l}^{-}\ (\text{aq}) The rate equation for this reaction is, rate = k [Cl2][H2S]

Which of these mechanisms is/are consistent with this rate equation?

A.$Cl_{2} + H_{2}S\overset{\quad\quad}{\rightarrow}H^{+} + Cl^{-} + Cl^{+} + HS^{-}(slow);

}{Cl_{2} + HS\overset{\quad\quad}{\rightarrow}2Cl^{-} + H^{+} + S(slow)}$$
A

B only

B

Both A and B

C

Neither A nor B

D

A only

Answer

A only

Explanation

Solution

Mechanism (1)

rate = K [Cl2] [H2S]\text{K }\lbrack\text{C}\text{l}_{2}\rbrack\ \lbrack H_{2}S\rbrack

Mechanism (2)

rate = K1 [Cl2] [HS−]K_{1}\ \lbrack\text{C}\text{l}_{2}\rbrack\ \lbrack\text{H}\text{S}^{-}\rbrack

Keq=[H+][HS−][H2S]K_{eq} = \frac{\left\lbrack H^{+} \right\rbrack\left\lbrack HS^{-} \right\rbrack}{\left\lbrack H_{2}S \right\rbrack}

[HS−]=Keq[H2S][H+]\left\lbrack HS^{-} \right\rbrack = \frac{K_{eq}\left\lbrack H_{2}S \right\rbrack}{\left\lbrack H^{+} \right\rbrack}

=K1Keq[Cl2][H2S][H+]= K_{1}K_{eq}\frac{\left\lbrack Cl_{2} \right\rbrack\left\lbrack H_{2}S \right\rbrack}{\left\lbrack H^{+} \right\rbrack}

∴\therefore Mechanism (1) is consistent with this rate equation.