For a reaction A + B $\to$ product, the rate of the reaction was doubled when the concentration of A alone was reduced to half. Half life of reaction is doubled when concentration of B is reduced to half keeping concentration of A constant. Then order of reaction with respect to A and B are :

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2, 2

2, 3

$\frac{1}{2}, \frac{1}{2}$

$- 1, 2$

answer is D.

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Detailed Solution

$\begin{array}{l} A + B \to P \\ rate = K [A]^{x} {[B]}^{y} \end{array}$

Order of reaction w.r.t = -1

$t_{1 / 2} \propto \frac{1}{[A]^{n - 1}}$

$t_{\frac{1}{2}} = \frac{a_{0}}{2 K}$

1st $t_{1 / 2} = \frac{0.693}{k}$

2nd $t_{1 / 2} = \frac{1}{A_{0} \cdot K}$

$t_{\frac{1}{2}} = \frac{1}{A_{\frac{0}{2} K}} = \frac{2}{A_{0} k}$

$2 - t_{\frac{1}{2}}$

Order of reaction w.r.t B= 2

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