Consider the reaction: $$\text{Cl}_2(\text{aq}) + \text{H}_2\text{S}(\text{aq}) \to \text{S}(\text{s}) + 2\text{H}^+(\text{aq}) + 2\text{Cl}^-(\text{aq})$$. The rate equation for this reaction is rate $$= k[\text{Cl}_2][\text{H}_2\text{S}]$$. Which of these mechanisms is/are consistent with this rate equation? (A) $$\text{Cl}_2 + \text{H}_2\text{S} \to \text{H}^+ + \text{Cl}^- + \text{Cl}^+ + \text{HS}^-$$ (slow); $$\text{Cl}^+ + \text{HS}^- \to \text{H}^+ + \text{Cl}^- + \text{S}$$ (fast). (B) $$\text{H}_2\text{S} \leftrightarrow \text{H}^+ + \text{HS}^-$$ (fast equilibrium); $$\text{Cl}_2 + \text{HS}^- \to 2\text{Cl}^- + \text{H}^+ + \text{S}$$ (slow).

The experimental rate law is given as
$$\text{rate}=k[\text{Cl}_2][\text{H}_2\text{S}]$$

To check any proposed mechanism, write the rate law predicted by that mechanism and compare it with the experimental one.

Case 1: Mechanism A
Slow (rate-determining) step: $$\text{Cl}_2+\text{H}_2\text{S}\;\longrightarrow\;\text{H}^++\text{Cl}^-+\text{Cl}^++\text{HS}^-$$

The rate is governed solely by this slow step:
$$\text{rate}=k_1[\text{Cl}_2][\text{H}_2\text{S}]$$

This is exactly the experimentally observed form. Hence mechanism A is consistent with the given rate law.

Case 2: Mechanism B
Step (i) fast equilibrium: $$\text{H}_2\text{S}\;\rightleftharpoons\;\text{H}^++\text{HS}^-$$
Step (ii) slow (rate-determining): $$\text{Cl}_2+\text{HS}^-\;\longrightarrow\;2\text{Cl}^-+\text{H}^++\text{S}$$

Rate predicted by the slow step:
$$\text{rate}=k_2[\text{Cl}_2][\text{HS}^-]$$

Because $$\text{HS}^-$$ is an intermediate, express it using the fast equilibrium. For equilibrium (i), let $$K=\dfrac{[\text{H}^+][\text{HS}^-]}{[\text{H}_2\text{S}]}$$, so
$$[\text{HS}^-]=\dfrac{K[\text{H}_2\text{S}]}{[\text{H}^+]}$$

Substituting:
$$\text{rate}=k_2K\frac{[\text{Cl}_2][\text{H}_2\text{S}]}{[\text{H}^+]}$$

This rate law contains an inverse dependence on $$[\text{H}^+]$$, which is absent in the experimentally observed law. Therefore mechanism B does not reproduce the correct rate expression (unless $$[\text{H}^+]$$ is kept strictly constant, which is not stated).

Thus, only mechanism A is compatible with the experimental kinetics.

Option D which is: A only