Question

For any acid catalysed reaction, $A\underset{}{\overset{H^{+}}{\to }}B$.
The half-life period is independent of concentration of $A$ at given $pH$. At same concentration of $A$, the 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 $(x+y)$.

Answer 1

At a given pH, the half-life period is independent of the concentration of A.
This indicates, the reaction is first order in A.

Similarly when the pH changes from 2 to 3, the hydrogen ion concentration changes from ${10}^{-2}$ to ${10}^{-3}$.
Thus, when the concentration is decreased by 10 times, the half-life period increases by 10 times from 10 to 100.
Thus, the reaction is of second order in hydrogen ion concentration.

Hence, $x=1$ and $y=2$.

Hence, $x+y=1+2=3$.