Question

Mechanism of a hypothetical reaction $X _{2}+ Y _{2} \rightarrow 2 XY$ is given below: (i) $X_{2} \rightarrow X+X$ (fast) (ii) $X + Y _{2} \rightleftharpoons XY + Y$ ( slow ) (iii) $X + Y \rightarrow XY$ (fast) The overall order of the reaction will be

• A. 2
• B. 0
• C. 1.5
• D. 1

Answer 1

The Correct Option is C

The given mechanism for the hypothetical reaction X_{2}+ Y_{2} \rightarrow 2 XY is composed of three steps:

1. X_{2} \rightarrow X+X (fast)
2. X + Y_{2} \rightleftharpoons XY + Y (slow)
3. X + Y \rightarrow XY (fast)

To determine the overall order of the reaction, we need to analyze the rate-determining step, which is the slowest step in the mechanism. Here, the rate-determining step is step (ii): X + Y_{2} \rightleftharpoons XY + Y.

According to the rate law for elementary reactions, the rate of the slow step can be expressed as:

\text{Rate} = k [X] [Y_{2}]

We need an expression for the concentration of [X]. From step (i), since it is a fast and reversible equilibrium step, we can assume:

K = \frac{[X]^2}{[X_2]}

Where K is the equilibrium constant of step (i). Therefore, we rearrange to find [X]:

[X] = \sqrt{K [X_2]}

Substitute this expression into the rate law for the slow step:

\text{Rate} = k [Y_{2}] \sqrt{K [X_2]} = k' [Y_{2}] [X_2]^{1/2}

Here, k' = k \sqrt{K}, which encapsulates all constants. Thus, the overall order of the reaction is the sum of the powers in the rate law:

\text{Order of reaction} = 1 + \frac{1}{2} = 1.5

The correct answer is 1.5, which corresponds to choice: 1.5.