For any acid catalysed reaction $A\underset{ }{\overset{H^{+}}{\to }}B$

Half-life period is independent of concentration of A at given pH. At definite concentration of A half-life time is 10 min at pH = 2 and half-life time is 100 min at pH = 3. If the rate law expression of reaction is $r=k{\left[A\right]}^x{\left[H\right]}^{+}{]}^y$then calculate the value of $(x+y)$

Half life is independent of A

So it is first order reaction in A

Similarly when the pH changes from 2 to 3 the $\left[H^{+}\right]$changes from ${10}^{-2}to{10}^{-3}$Thus when the concentration is decreased by 10 times, the half life increases by 10 times from 10 to 100

 Thus the reaction is II order

Hence x = 1 and y = 2

Hence x + y = 3