Question

The first order decomposition of $H_2{O}_2$ in an appropriate medium is characterised by a rate constant of $0.2303mi{n}^{-1}$. What is the time (in min) required to complete $9/10$ fraction of the reaction?

• A. $0.1$
• B. 10
• C. 100
• D. 0.01

Answer 1

Answer: (B)

Given, rate constant $(k)$ for

first order $=0.2303mi{n}^{-1}$.

For first order reaction,

Time $(t)=\frac{2.303}{k}\log \left[\frac{a}{a-x}\right]$

where, $a=$ initial concentration

$(a-x)=$ concentration at time $(t)$

$x=$ amount complete

Let, initial concentration $(a)=1$

$x=\frac{9}{10}$

then, $(a-x)=1-\frac{9}{10}=\frac{1}{10}$

From equation (i),

$t=\frac{2.303}{0.2303}\log \frac{1}{\left(\frac{1}{10}\right)}$

$t=10\log 10$

$t=10\times 1=10mi{n}^{-1}$