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For the reaction A+B $\to$ products, it is observed that:
(1) On doubling the initial concentration of A only, the rate of reaction is also doubled and
(2) On doubling the initial concentrations of both A and B, there is a change by a factor of 8 in the rate of the reaction. The rate of this reaction is given by:

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$rate = k [A] [B]^{2}$

$rate = k [A]^{2} [B]^{2}$

$rate = k [A] [B]$

$rate = k [A]^{2} [B]$

answer is A.

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Detailed Solution

When concentration of A is doubled, rate is doubled. Hence order with respect to A is one. When concentrations of both A and B are doubled, rate increases by 8 times hence order with respect to B is 2. $∴ rate = k [A]^{1} [B]^{2}$

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