Question

The rate of the reaction is given by rate, $ r=k\,[H^{+}]^{n} $ If the rate becomes $100$ times when the pH changes from $2$ to $1$ the order of the reaction is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

$r=k\left[H^{+}\right]^{n} $
Exp .(l) $ r_{1}=k\left[10^{-2}\right]^{n}$
(If $p H=2$ then $\left[H^{+}\right]=10^{-2}$ )
Exp. (II) $100 r_{1}=k\left[10^{-1}\right]^{n}$
(If $p H=1$ then $\left[H^{+}\right]=10^{-1}$ )
$\frac{\text{Exp} .(I I)}{\text{Exp} .(I I)}=\frac{100 r_{1}}{r_{1}}$
$=\frac{k[0.1]^{n}}{k[0.01]^{n}}=\frac{100}{1}$
$=\left[\frac{10}{1}\right]^{n}$ or $n=2$
Order of reaction is $2$ .