CBSE 2025, Set 3

Question

For the reaction A + B → Products, the following initial rates were obtained at various initial concentrations of reactants:

| Sl. No. | [A]/mol L$^{-1}$ | [B]/mol L$^{-1}$ | Initial rate/mol L$^{-1}$ s$^{-1}$ |
|---|---|---|---|
| 1 | 0.1 | 0.1 | 0.05 |
| 2 | 0.2 | 0.1 | 0.10 |
| 3 | 0.1 | 0.2 | 0.05 |

Determine the order of the reaction with respect to A and B and overall order of the reaction.

Edvaya · Accepted Answer

The correct answer is Subjective. Let Rate = $k[	ext{A}]^x[	ext{B}]^y$ **Finding order w.r.t. A (comparing Exp 1 and 2, [B] constant):** $$\frac{	ext{Rate}_2}{	ext{Rate}_1} = \frac{k(0.2)^x(0.1)^y}{k(0.1)^x(0.1)^y} = \left(\frac{0.2}{0.1}ight)^x = 2^x$$ $$\frac{0.10}{0.05} = 2 = 2^x \implies \boxed{x = 1}$$ **Finding order w.r.t. B (comparing Exp 1 and 3, [A] constant):** $$\frac{	ext{Rate}_3}{	ext{Rate}_1} = \frac{k(0.1)^x(0.2)^y}{k(0.1)^x(0.1)^y} = \left(\frac{0.2}{0.1}ight)^y = 2^y$$ $$\frac{0.05}{0.05} = 1 = 2^y \implies \boxed{y = 0}$$ **Rate law:** $	ext{Rate} = k[	ext{A}]^1[	ext{B}]^0 = k[	ext{A}]$ - Order w.r.t. A = **1** (first order) - Order w.r.t. B = **0** (zero order) - **Overall order = 1 + 0 = 1 (first order)**

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