$A$ reaction is first order in $A$ and second order in $B$.
$(i)$ Write the differential rate equation.
$(ii)$ How is the rate affected on increasing the concentration of $B$ three times?
$(iii)$ How is the rate affected when the concentrations of both $A$ and $B$ are doubled?

(N/A) $(i)$ The differential rate equation is $\text{Rate} = k[A][B]^2$.
$(ii)$ If the concentration of $B$ is increased $3$ times,the new rate is $\text{Rate}' = k[A][3B]^2 = 9k[A][B]^2 = 9 \times \text{Rate}$. Thus,the rate increases $9$ times.
$(iii)$ If the concentrations of both $A$ and $B$ are doubled,the new rate is $\text{Rate}'' = k[2A][2B]^2 = k[2A][4B^2] = 8k[A][B]^2 = 8 \times \text{Rate}$. Thus,the rate increases $8$ times.