Question

$H_2{O}_2$ undergoes self decomposition according to first-order reaction. The volume strength of $H_2{O}_2$ solution change from 40 V to 10 V in 200 min. Half-life period of decomposition of $H_2{O}_2$ is :

• A. 50 min
• B. 100 min
• C. 150 min
• D. 200 min

Answer 1

The correct option is B 100 min

Given:

Volume Initial=$40V$

Volume Final=$10V$

Time=$200min$

$t_{1/2}=?$

For first order reaction:

$k=\frac{2.303}{t}Log\frac{Initialconc}{finalconc}$

$k=\frac{2.303}{200}Log\frac{40}{10}$

$k=\frac{2.303}{200}2\times Log2$

Log$2=0.3010$

$k=\frac{0.693}{200}\times 2$

$k=\frac{0.693}{100}$------------------------------(1)

$t_{1/2}=\frac{0.693}{k}$

on putting the value of $k$ from eq--$1$ we will get

$t_{1/2}=\frac{0.693}{0.693}\times 100$

$t_{1/2}=100minutes$

Option B is correct.