During the kinetic study of the reaction, 2A + B → C + D, following results were obtained:

| Run | [A] / mol

Question

During the kinetic study of the reaction, 2A + B → C + D, following results were obtained:

| Run | [A] / mol L⁻¹ | [B] / mol L⁻¹ | Initial rate of formation of D / mol L⁻¹ min⁻¹ |
| :--- | :--- | :--- | :--- |
| I | 0.1 | 0.1 | 6.0 × 10⁻³ |
| II | 0.3 | 0.2 | 7.2 × 10⁻² |
| III | 0.3 | 0.4 | 2.88 × 10⁻¹ |
| IV | 0.4 | 0.1 | 2.40 × 10⁻² |

Based on the above data which one of the following is correct?

Accepted Answer

To determine the rate law, we compare the initial rates from different experiments where the concentration of one reactant changes while the other remains constant .

1.  **Determine order with respect to A:** Compare Run I and Run IV.
    *   [B] is constant (0.1 M).
    *   [A] increases by a factor of 4 (0.1 → 0.4).
    *   Rate increases by a factor of 4 ($2.40 	imes 10^{-2} / 6.0 	imes 10^{-3} = 4$).
    *   Since rate $\propto [A]^x$, $4 = 4^x \Rightarrow x = 1$. The reaction is **first order** w.r.t. A.

2.  **Determine order with respect to B:** Compare Run II and Run III.
    *   [A] is constant (0.3 M).
    *   [B] increases by a factor of 2 (0.2 → 0.4).
    *   Rate increases by a factor of 4 ($2.88 	imes 10^{-1} / 7.2 	imes 10^{-2} = 4$).
    *   Since rate $\propto [B]^y$, $4 = 2^y \Rightarrow y = 2$. The reaction is **second order** w.r.t. B.

**Conclusion:** The rate law is **Rate = k[A][B]²**.

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