Question

In a first order reaction, the concentration of the reactant decreases from 800 mol $d{m}^{-3}in2\times {10}^{4}s.$ The rate constant of the reaction $in\left(s^{-1}\right)$ is

(IIT-JEE, 2003)

• A. $2\times {10}^4$
• B. $3.45\times {10}^{-5}$
• C. $1.386\times {10}^{-4}$
• D. $2\times {10}^{-4}$

Answer 1

The correct option is C $1.386\times {10}^{-4}$

$800\to 400\to 200\to 100\to 50$

There are four half lives involved.

Half life = $\frac{2\times {10}^4}{4}=5\times {10}^{3}s$

Rate constant, $k=\frac{0.693}{5\times {10}^3}=1.386\times {10}^{-4}{s}^{-1}$