Question

The acid catalysed hydrolysis of an organic A at ${30}^{o}C$ has a half-life of 100 minutes when carried out in a buffer solution of $pH=5$ and 10 minutes when carried out at $pH=4$. Both the times the half-life are independent of the initial concentration of A. If the rate of reaction is given by $rate=K\left[A{]}^m\right[H^{+}{]}^n$, $m+n$ is ___________.

Answer 1

The half life period is independent of the initial concentration. This is characteristic of first order reaction. Thus, the reaction is first order w.r.t [A] and first order w.r.t $\left[H^{+}\right]$.
Hence, $rate=k\left[A{]}^1\right[H^{+}{]}^1$
Thus, $m=1,n=1$
$m+n=1+1=2$.