For the reaction $\mathrm{A}\to \mathrm{B},$the rate of reaction is quadrupled when the concentration of A is doubled. The rate of the reaction is $\mathrm{r}=\mathrm{k}{\left[\mathrm{A}\right]}^{\mathrm{n}}$ the value of n is

The reaction is $\mathrm{A}\to \mathrm{B},$

From the rate law, $\mathrm{rate},{\mathrm{r}}_1=\mathrm{k}{\left[\mathrm{A}\right]}^{\mathrm{n}}$

When the concentration of A is doubled,

$\mathrm{Rate},{\mathrm{r}}_2=\mathrm{K}{\left[2\mathrm{A}\right]}^2$

$\mathrm{Rate},{\mathrm{r}}_2=4\mathrm{K}{\left[\mathrm{A}\right]}^2$

if $\mathrm{n}=2,\mathrm{then} \mathrm{rate} {\mathrm{r}}_2=4{\mathrm{r}}_1$

Therefore, the order of reaction is 2(second order).