Question

The decomposition of $H_2{O}_2$ is studied by volumetric measurement of the concentration of $H_2{O}_2$ by $KMn{O}_4$ solution at different intervals of time.
$(H_2{O}_2\to H_{2}O+\frac{1}{2}{O}_2)$
If 5 ml of $H_2{O}_2$ required 10 mL of 0.1 N $KM{n}_4$ at the start of the reaction and after 10 min, 5 mL of $H_2{O}_2$ required 5 Ml of 0.1 $KMn{O}_4$. The rate constant k of $-\frac{d\left[H_2{O}_2\right]}{dt}=k\left[H_2{O}_2\right]$ is_________. ($inmi{n}^{-1}$)

Answer 1

$-\frac{d\left[H_2{O}_2\right]}{dt}=k\left[H_2{O}_2\right]\Rightarrow$ decomposition is first order so,
kt = 2.303 log$\frac{c_0}{c_t}=\frac{0.2}{0.1}$
k = $\frac{2.303}{t}log\frac{V_0}{V_t}(for{H}_2{O}_2\to O_2+H_{2}O)$

Time	t = 0	10 min
Vol $KMn{O}_4$	10 mL	5 mL

$\Rightarrow \frac{V_0}{V_t}=\frac{10}{5}=2$
$\Rightarrow k=\frac{2303}{10}log2=0.0693mi{n}^{-1}$