Question

The value of rate constant for a first order reaction is $2.303\times {10}^{-2}se{c}^{-1}$. What will be the time required to reduce the concentration to $\frac{1}{10}th$ of its initial concentration ?

• A. 100 s
• B. 10 s
• C. 2303 s
• D. 230.2 s

Answer 1

The correct option is A 100 s

Given, rate constant for first order reaction:
$k=2.303\times {10}^{-2}{s}^{-1}$

Let, initial concentration be a.

Then, final concentration $(a-x)=\frac{1}{10}$ of an $\frac{a}{10}$

Integrated rate law expression for first order reaction is:

$k=\frac{2.303}{t}log\frac{a}{(a-x)}$

or $t=\frac{2.303}{k}log\frac{a}{(a-x)}$

On substituting values, we get:

$t=\frac{2.303}{2.303\times {10}^{-2}}log\frac{a}{\frac{a}{10}}$

$={10}^{2}log10$

$={10}^2=100s$