For the reaction, A+B arrow products, it is observed that (1) On...

For the reaction, $\mathrm{A}+\mathrm{B} \longrightarrow$ Products On doubling the initial concentration of A only, the rate of reaction is also doubled, therefore \text{ Rate } \propto[\mathrm{A}]^1 Let initially rate law is $\text{ Rate }=$k[A][B]^y If concentration of and both are doubled, the rate gets changed by a factor of 8 . $$\begin{array}{r}8 \times \text{ Rate }=\mathrm{k}[2 \mathrm{~A}][2 \mathrm{~B}]^{\mathrm{y}} \quad \ldots(\text{ iii) }\\ {\left[\because \text{ Rate } \propto[\mathrm{A}]^1\right]} \end{array}$$ Dividing Eq. (iii) by Eq. (ii), $$\begin{aligned}& 8=2 \times2^y \\ & 4=2^y \\ & \therefore \quad \mathrm{y}=2 \\ & \end{aligned}$$Hence, rate law is, rate $=\mathrm{k}[\mathrm{A}][\mathrm{B}]^2