Question

In hypothetical reaction $X_2 + Y_2 \rightarrow 2XY$

Follows the mechanism as given below $X_2 \rightleftharpoons X + X$ (fast reaction) $X + Y_2 \rightarrow XY + Y$ (slow reaction) $X + Y \rightarrow XY$ (fast reaction) The correct statement(s) is/are

• A. Order of reaction is 3/2
• B. Order of reaction w.r.t. $Y_2$ is 1.
• C. R = k $[X]^5 [Y_2]$
• D. Both molecularity and order = 3

Answer 1

Answer: (A), (B)

A, B

Answer 2

The reaction mechanism is given as:

1. $X_2 \rightleftharpoons X + X$ (fast reaction)
2. $X + Y_2 \rightarrow XY + Y$ (slow reaction)
3. $X + Y \rightarrow XY$ (fast reaction)

Step 1: Determine the rate law from the slow step.

The rate of a reaction is determined by its slowest step (rate-determining step). From the slow reaction (Step 2): Rate (R) = $k_{slow} [X] [Y_2]$

Step 2: Express the concentration of the intermediate in terms of reactants.

In the rate law, $[X]$ is an intermediate species. Its concentration needs to be expressed in terms of the reactant $X_2$. We use the fast equilibrium step (Step 1) for this. For the equilibrium $X_2 \rightleftharpoons X + X$: The equilibrium constant $K_{eq}$ is given by: $K_{eq} = \frac{[X][X]}{[X_2]} = \frac{[X]^2}{[X_2]}$

Solving for $[X]$: $[X]^2 = K_{eq} [X_2]$ $[X] = (K_{eq} [X_2])^{1/2} = K_{eq}^{1/2} [X_2]^{1/2}$

Step 3: Substitute the intermediate concentration into the rate law.

Substitute the expression for $[X]$ into the rate law from Step 1: R = $k_{slow} (K_{eq}^{1/2} [X_2]^{1/2}) [Y_2]^1$ R = $(k_{slow} K_{eq}^{1/2}) [X_2]^{1/2} [Y_2]^1$

Let the new overall rate constant $k = k_{slow} K_{eq}^{1/2}$. So, the final rate law is: R = $k [X_2]^{1/2} [Y_2]^1$

Step 4: Determine the order of the reaction and evaluate the statements.

• Order with respect to $X_2$: From the rate law, the exponent of $[X_2]$ is $1/2$.
• Order with respect to $Y_2$: From the rate law, the exponent of $[Y_2]$ is $1$.
• Overall order of reaction: Sum of the individual orders = $1/2 + 1 = 3/2$.

Now let's evaluate each statement:

(A) Order of reaction is 3/2 This statement is correct, as the overall order calculated is 3/2.

(B) Order of reaction w.r.t. $Y_2$ is 1. This statement is correct, as the order with respect to $Y_2$ is 1.

(C) R = k $[X]^5 [Y_2]$ This statement is incorrect. The rate law should be in terms of reactants ($X_2$ and $Y_2$), not an intermediate ($X$), and the exponents are incorrect.

(D) Both molecularity and order = 3 Molecularity is defined for elementary steps, not for the overall complex reaction. For the slow step ($X + Y_2 \rightarrow XY + Y$), the molecularity is 2. The overall order is 3/2, not 3. Therefore, this statement is incorrect.

Based on the analysis, statements (A) and (B) are correct.