Question

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

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

Answer 1

Answer: (B)

Consider the reaction:
$C{l}_2\left(aq\right)+H_{2}S\left(aq\right)\to S\left(s\right)+2H^{+}\left(aq\right)+2C{l}^{-}\left(aq\right)$

The rate equation for this reaction is rate $=k\left[C{l}_2\right]\left[H_{2}S\right]$.

The rate equation indicates that the reaction is first order in chlorine and first order in hydrogen sulphide.

The mechanism (A) is consistent with this rate equation.
(A) $C{l}_2+H_{2}S\to H^{+}+C{l}^{-}+C{l}^{+}+H{S}^{-}$ (slow)

$C{l}^{+}+H{S}^{-}\to H^{+}+C{l}^{-}+S$ (fast)

The mechanism (A) is not consistent with this rate equation.

(B) $H_{2}S\rightleftharpoons H^{+}+H{S}^{-}$ (fast equilibrium)

$C{l}_2+H{S}^{-}\to 2C{l}^{-}+H^{+}+S$ (slow)

Based on mechanism (B), the rate equation will be rate $=k\left[C{l}_2\right][H_{2}S{]}^{1/2}$ and not rate $=k\left[C{l}_2\right]\left[H_{2}S\right]$.

From slow step , rate $=k^{\prime }\left[C{l}_2\right]\left[H{S}^{-}\right]$......(1)

From fast equilibrium step,

$K=\frac{\left[H^{+}\right]\left[H{S}^{-}\right]}{\left[H_{2}S\right]}=\frac{[H{S}^{-}{]}^2}{\left[H_{2}S\right]}(\because [H^{+}]\simeq [H{S}^{-}\left]\right)$

$\left[H{S}^{-}\right]=\left(K\right[H_{2}S]{)}^{1/2}$......(2)

Substitute (2) in (1)

rate $=k^{\prime }\left[C{l}_2\right]\left[H{S}^{-}\right]$

rate $=k^{\prime }\left[C{l}_2\right]\left(K\right[H_{2}S]{)}^{1/2}$

rate $=k\left[C{l}_2\right][H_{2}S{]}^{1/2}$