Consider the reaction:
$C l_{2} (a q) + H_{2} S (a q) \to S (s) + 2 H^{+} (a q) + 2 C l^{-} (a q)$
The rate equation for this reaction is rate $= k [C l_{2}] [H_{2} S]$
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) $H_{2} S ⇌ H^{+} + H S^{-}$ (fast equilibrium)
$C l_{2} + H S^{-} \to 2 C l^{-} + H^{+} + S$ (slow)

Question

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Answer 1

Consider the reaction:
$C l_{2} (a q) + H_{2} S (a q) \to S (s) + 2 H^{+} (a q) + 2 C l^{-} (a q)$

The rate equation for this reaction is rate $= k [C l_{2}] [H_{2} S]$ .
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) $H_{2} S ⇌ H^{+} + H S^{-}$ (fast equilibrium)

$C l_{2} + H S^{-} \to 2 C l^{-} + H^{+} + S$ (slow)
Based on mechanism (B), the rate equation will be rate $= k [C l_{2}] [H_{2} S]^{1 / 2}$ and not rate $= k [C l_{2}] [H_{2} S]$ .
From slow step , rate $= k^{'} [C l_{2}] [H S^{-}]$ ......(1)
From fast equilibrium step,
$K = \frac{[ H ^{+} ] [ H S ^{-} ]}{[ H _{2} S ]} = \frac{[ H S ^{-} ] ^{2}}{[ H _{2} S ]} (∵ [H^{+}] ≃ [H S^{-}])$
$[H S^{-}] = (K [H_{2} S])^{1 / 2}$ ......(2)
Substitute (2) in (1)

rate $= k^{'} [C l_{2}] [H S^{-}]$
rate $= k^{'} [C l_{2}] (K [H_{2} S])^{1 / 2}$
rate $= k [C l_{2}] [H_{2} S]^{1 / 2}$

Answer 2

Consider the reaction:

C l_{2} (a q) + H_{2} S (a q) \to S (s) + 2 H^{+} (a q) + 2 C l^{-} (a q)

The rate equation for this reaction is rate

= k [C l_{2}] [H_{2} S]

.

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 ⇌ H^{+} + H S^{-}

(fast equilibrium)

C l_{2} + H S^{-} \to 2 C l^{-} + H^{+} + S

(slow)

Based on mechanism (B), the rate equation will be rate

= k [C l_{2}] [H_{2} S]^{1 / 2}

and not rate

= k [C l_{2}] [H_{2} S]

.

From slow step , rate

= k^{'} [C l_{2}] [H S^{-}]

......(1)

From fast equilibrium step,

K = \frac{[ H ^{+} ] [ H S ^{-} ]}{[ H _{2} S ]} = \frac{[ H S ^{-} ] ^{2}}{[ H _{2} S ]} (∵ [H^{+}] ≃ [H S^{-}])

[H S^{-}] = (K [H_{2} S])^{1 / 2}

......(2)

Substitute (2) in (1)

rate

= k^{'} [C l_{2}] [H S^{-}]

rate

= k^{'} [C l_{2}] (K [H_{2} S])^{1 / 2}

rate

= k [C l_{2}] [H_{2} S]^{1 / 2}

B only

Both A and B

Neither A nor B

A only

The mechanism of the reaction $2 N O + O_{2} \to 2 N O_{2}$ is:

$N O + N O k_{- 1} ⇌ k_{1} N_{2} O_{2}$ (fast) ------ 1

$N_{2} O_{2} + O_{2} \to k_{2} 2 N O_{2}$ (slow) -----2

The rate constant of the reaction is:

In the following reaction, how is the rate of appearance of the underlined product related to the rate of disappearance of the underlined reactant?
$B r O_{3 (a q)}^{-} + \underline{5 B r^{-}}_{(a q)} + 6 H_{(a q)}^{+} \to \underline{3 B r_{2 (1)}} + 3 H_{2} O_{(1)}$

The reaction $N_{2} O_{5}$ (in $C C l_{4}$ ) $\to 2 N O_{2} + 1 / 2 O_{2} (g)$ is first order in $N_{2} O_{5}$ with rate constant $6.2 \times 10^{- 4}$ . What is the value of rate of reaction when $[N_{2} O_{5}] = 1.25 m o l e$ $L^{- 1}$

The rate equation for the reaction $2 A + B \to C$ is found to be:
Rate $= k [A] [B]$ .

Revise with Concepts

Rate Law, Rate Expression and Rate Constant

Order and Molecularity of a Reaction.

B only

Both A and B

Neither A nor B

A only

The mechanism of the reaction 2NO+O2​→2NO2​ is: NO+NOk−1​⇌​k1​​N2​O2​(fast) ------ 1 N2​O2​+O2​→k2​2NO2​(slow) -----2 The rate constant of the reaction is:

In the following reaction, how is the rate of appearance of the underlined product related to the rate of disappearance of the underlined reactant? BrO3(aq)−​+5Br−​(aq)​+6H(aq)+​→3Br2(1)​​+3H2​O(1)​

The reaction N2​O5​ (in CCl4​)→2NO2​+1/2O2​(g) is first order in N2​O5​ with rate constant 6.2×10−4. What is the value of rate of reaction when [N2​O5​]=1.25mole L−1

The rate equation for the reaction 2A+B→C is found to be: Rate =k[A][B].

Revise with Concepts

Rate Law, Rate Expression and Rate Constant

Order and Molecularity of a Reaction.

The mechanism of the reaction $2 N O + O_{2} \to 2 N O_{2}$ is:

$N O + N O k_{- 1} ⇌ k_{1} N_{2} O_{2}$ (fast) ------ 1

$N_{2} O_{2} + O_{2} \to k_{2} 2 N O_{2}$ (slow) -----2

The rate constant of the reaction is:

In the following reaction, how is the rate of appearance of the underlined product related to the rate of disappearance of the underlined reactant?
$B r O_{3 (a q)}^{-} + \underline{5 B r^{-}}_{(a q)} + 6 H_{(a q)}^{+} \to \underline{3 B r_{2 (1)}} + 3 H_{2} O_{(1)}$

The reaction $N_{2} O_{5}$ (in $C C l_{4}$ ) $\to 2 N O_{2} + 1 / 2 O_{2} (g)$ is first order in $N_{2} O_{5}$ with rate constant $6.2 \times 10^{- 4}$ . What is the value of rate of reaction when $[N_{2} O_{5}] = 1.25 m o l e$ $L^{- 1}$

The rate equation for the reaction $2 A + B \to C$ is found to be:
Rate $= k [A] [B]$ .