For the reaction $2 A + B \to$ Products, it is found that doubling the concentration of both reactants increases the rate by a factor of 8. But doubling the concentration of B alone, only doubles the rate. What is the order of the reaction w.r.t to A?

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Detailed Solution

$Rate = (R) = K {[A]}^{2} {[B]}^{1}$

$Rate = (R_{2}) = 8 R = K {[2 A]}^{2} 2 {[B]}^{1}$

$\Rightarrow \frac{8 R}{R} = \frac{K 2^{X} A^{x} \times 2 \times B}{{KA}^{X} B}$

$\Rightarrow 8 = 2^{X} . 2 \Rightarrow 2^{3} = 2^{x + 1}$

$\Rightarrow x + 1 = 3$

$∴ X = 2$

Since rate doubles when [B] only double, when both concentrations double. Rate increases by 8 times.

Then order of reaction with respect to ‘A’ is 2

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