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?
rate = k[A]²[B]
rate = k[A][B]
rate = k[A]²[B]²
rate = k[A][B]²
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 .
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 (). Since rate , . The reaction is first order w.r.t. A.
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 (). Since rate , . The reaction is second order w.r.t. B.
Conclusion: The rate law is Rate = k[A][B]².
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