For a reaction $\mathrm{A}+\mathrm{B}\to \mathrm{P},$ the rate is given by

$\mathrm{Rate}=\mathrm{k}\left[\mathrm{A}\right]{\left[\mathrm{B}\right]}^2$

(a) How is the rate of reaction affected , if the concentration of B is quadrupled?

(b) What is the overall order of the reaction , if A is present in large excess? 

(a)

(i) For a reaction, $\mathrm{A}+\mathrm{B}\to \mathrm{P}$

      ${\mathrm{R}}_1=\mathrm{k}\left[\mathrm{A}\right]{\left[\mathrm{B}\right]}^2 ...\left(\mathrm{I}\right)$

If the concentration of B is doubled,

      ${\mathrm{R}}_2=\mathrm{k}\left[\mathrm{A}\right]{\left[2 \mathrm{B}\right]}^2 ....\left(\mathrm{ii}\right)$

On dividing (i) and (ii)

$$\begin{gathered} \frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}=\frac{\mathrm{k}\left[\mathrm{A}\right]{\left[\mathrm{B}\right]}^2}{\mathrm{k}\left[\mathrm{A}\right]{\left[2 \mathrm{B}\right]}^2} \\ \frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}=\frac{{\mathrm{B}}^2}{4{\mathrm{B}}^2} \\ {\mathrm{R}}_2=4{\mathrm{R}}_1 \end{gathered}$$

The rate of reaction will be four times the initial rate.

(b) If A is present in large excess, then the rate of the reaction will be independent of A and will  depend only on the concentration of B. The overall rate of the reaction will be 2.