Question

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

• A. Neither $A$ nor $B$
• B. $A$ only
• C. $B$ only
• D. Both $A$ and $B$

Answer 1

Answer: (B)

$A$ only

For mechanism B, rate =$k\left[C{l}_2\right]\left[H{S}^{-}\right]$

Further if $k_{eq}=\frac{\left[H^{+}\right]\left[H{S}^{-}\right]}{\left[H_{2}S\right]}$

then rate= $k\left[C{l}_2\right].\frac{k_{eq}\left[H_{2}S\right]}{\left[H^{+}\right]}=K^{\prime }\frac{\left[C{l}_2\right]\left[H_{2}S\right]}{\left[H^{+}\right]}$

This is not in accordance with the given rate.

For mechanism A,

rate=$k\left[C{l}_2\right]\left[H_{2}S\right]$....[from slow reaction]

This is consistent with the given rate.