Question

The following results were obtained in the decomposition of $H_2{O}_2$ in presence of $I^{-}$ ions at 298 K.

t/min	3.0	6.0	9.0	$\infty$
Volume of $O_2$ evolved/$c{m}^3$	6.2	11.8	16.8	60.6

Show that the reaction, $H_2{O}_2\left(g\right)\stackrel{I^{-}}{\to }{H}_{2}O\left(l\right)+1/2O_2\left(g\right)$ is a first reaction. What is the rate constant?

Answer 1

(i) For first order reaction:-

$K=\frac{2.303}{t}\log \frac{V_{\infty }}{V_{\infty }-V_t}$, $V_{\infty }=60.6$

(ii) Value of $K$ [rate constant] at different times are:-

Time (min)	$V_{\infty }-V_t$	$\frac{2.303}{t}\log \frac{V_{\infty }}{V_{\infty }-V_t}$
$3.0$	$60.6-6.2=54.4$	$\frac{2.303}{3}\log \frac{60.6}{54.4}=0.03mi{n}^{-1}$
$6.0$	$60.6-11.8=48.8$	$\frac{2.303}{6}\log \frac{60.6}{48.8}=0.03mi{n}^{-1}$
$9.0$	$60.6-16.8=43.8$	$\frac{2.303}{9}\log \frac{60.6}{43.8}=0.03mi{n}^{-1}$

A constant value of $K$ shows that the reaction is of the first order.