Question

1. the rate - equation for the reaction: $cl_{2(aq)}+h_{2}s_{(aq)}\to s_{(s)} + 2hcl_{(aq)}$ was found to be rate = $kcl_{2}h_{2}s$. which of the following mechanisms are consistent with this rate law?

(a) $cl_{2}\to 2cl$ (slow)
$cl + h_{2}s\to hcl+hs$ (fast)
$cl + hs\to hcl + s$ (fast)
overall $cl_{2}+h_{2}s\to s + 2hcl$
(b) $cl_{2}\to 2cl$ (fast)
$cl + h_{2}s\to hcl+hs$ (fast)
$cl + hs\to hcl + s$ (slow)
overall $cl_{2}+h_{2}s\to s + 2hcl$
(c) $cl_{2}+h_{2}s\to cl+hs + hcl$ (slow)
$cl + hs\to hcl + s$ (fast)
overall $cl_{2}+h_{2}s\to s + 2hcl$

Explanation:

Step1: Recall rate - determining step concept

The rate - law of a reaction is determined by the slowest step (rate - determining step) in the reaction mechanism. The rate law for the overall reaction $\text{Cl}_{2(aq)}+\text{H}_{2}\text{S}_{(aq)}
ightarrow\text{S}_{(s)} + 2\text{HCl}_{(aq)}$ is rate = $k[\text{Cl}_{2}][\text{H}_{2}\text{S}]$.

Step2: Analyze mechanism (a)

In mechanism (a), the slow step is $\text{Cl}_{2}
ightarrow2\text{Cl}$. The rate law for this slow step is rate = $k[\text{Cl}_{2}]$, which does not match the given rate law rate = $k[\text{Cl}_{2}][\text{H}_{2}\text{S}]$.

Step3: Analyze mechanism (b)

In mechanism (b), the slow step is $\text{Cl}+\text{HS}
ightarrow\text{HCl}+\text{S}$. The rate law for this slow step is rate = $k[\text{Cl}][\text{HS}]$. Since $\text{Cl}$ and $\text{HS}$ are intermediates, we need to express them in terms of reactants. From the first - step $\text{Cl}_{2}
ightleftharpoons2\text{Cl}$ (fast equilibrium), $[\text{Cl}]=K_{1}[\text{Cl}_{2}]^{\frac{1}{2}}$, and from the second - step $\text{Cl}+\text{H}_{2}\text{S}
ightleftharpoons\text{HCl}+\text{HS}$ (fast equilibrium), $[\text{HS}]$ is related to reactants in a complex way. The overall rate law will not be rate = $k[\text{Cl}_{2}][\text{H}_{2}\text{S}]$.

Step4: Analyze mechanism (c)

In mechanism (c), the slow step is $\text{Cl}_{2}+\text{H}_{2}\text{S}
ightarrow\text{Cl}+\text{HS}+\text{HCl}$. The rate law for this slow step is rate = $k[\text{Cl}_{2}][\text{H}_{2}\text{S}]$, which matches the given rate law.

Answer:

(c)