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(B) The rate law for the reaction $A + 2B 	o C + D$ can be written as: $Rate = k[A]^x[B]^y$ Case $1$: When $[A]$ is increased $9$ times,the rate incr

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$\frac{3}{2}$

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(B) The rate law for the reaction $A + 2B 	o C + D$ can be written as: $Rate = k[A]^x[B]^y$ Case $1$: When $[A]$ is increased $9$ times,the rate increases $3$ times. $3 	imes Rate = k[9A]^x[B]^y$ Dividing by the original rate: $3 = (9)^x \implies 3^1 = (3^2)^x \implies 1 = 2x \implies x = \frac{1}{2}$ Case $2$: When $[B]$ is increased $2$ times,the rate increases $2$ times. $2 	imes Rate = k[A]^x[2B]^y$ Dividing by the original rate: $2 = (2)^y \implies y = 1$ The order of the reaction is the sum of the exponents: $n = x + y = \frac{1}{2} + 1 = \frac{3}{2}$.

For a chemical reaction,$A + 2B \to C + D,$ the rate of reaction increases $3$ times when the concentration of $A$ only is increased $9$ times. While when the concentration of $B$ only is increased $2$ times,the rate of reaction also increases $2$ times. The order of this reaction is:

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