JEE MAIN - Chemistry (2010 - No. 19)
Consider the reaction :
Cl2(aq) + H2S(aq) → S(s) + 2H+ (aq) + 2Cl– (aq)
The rate equation for this reaction is rate = k [Cl2] [H2S]
Which of these mechanisms is/are consistent with this rate equation?
(A) Cl2 + H2S $$\to$$ H+ + Cl– + Cl+ + HS– (slow)
Cl+ + HS– $$\to$$ H+ + Cl– + S (fast)
(B) H2S $$ \Leftrightarrow $$ H+ + HS– (fast equilibrium)
Cl2 + HS– $$\to$$ 2Cl– + H+ + S (slow)
B only
Both A and B
Neither A nor B
A only
Explanation
Since the slow step is the rate determining step hence-
if we consider option $$(1)$$ we find
Rate $$ = k\left[ {C{l_2}} \right]\left[ {{H_2}S} \right]$$
Now if we consider option $$(2)$$ we find
Rate $$ = k\left[ {C{l_2}} \right]\left[ {H{S^ - }} \right]\,\,\,\,\,...\left( 1 \right)$$
From equation $$(i)$$
$$k = {{\left[ {{H^ + }} \right]\left[ {H{S^ - }} \right]} \over {{H_2}S}}$$ $$\,\,\,\,\,$$ or
$$\left[ {H{S^ - }} \right] = {{k\left[ {{H_2}S} \right]} \over {{H^ + }}}$$
Substituting this value in equation $$(1)$$ we find
Rate $$ = k\left[ {C{l_2}} \right]K{{\left[ {{H_2}S} \right]} \over {{H^ + }}}$$
$$ = k'{{\left[ {C{l_2}} \right]\left[ {{H_2}S} \right]} \over {\left[ {{H^ + }} \right]}}$$
hence only, mechanism $$(1)$$ is consistent with the given rate equation.
if we consider option $$(1)$$ we find
Rate $$ = k\left[ {C{l_2}} \right]\left[ {{H_2}S} \right]$$
Now if we consider option $$(2)$$ we find
Rate $$ = k\left[ {C{l_2}} \right]\left[ {H{S^ - }} \right]\,\,\,\,\,...\left( 1 \right)$$
From equation $$(i)$$
$$k = {{\left[ {{H^ + }} \right]\left[ {H{S^ - }} \right]} \over {{H_2}S}}$$ $$\,\,\,\,\,$$ or
$$\left[ {H{S^ - }} \right] = {{k\left[ {{H_2}S} \right]} \over {{H^ + }}}$$
Substituting this value in equation $$(1)$$ we find
Rate $$ = k\left[ {C{l_2}} \right]K{{\left[ {{H_2}S} \right]} \over {{H^ + }}}$$
$$ = k'{{\left[ {C{l_2}} \right]\left[ {{H_2}S} \right]} \over {\left[ {{H^ + }} \right]}}$$
hence only, mechanism $$(1)$$ is consistent with the given rate equation.
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