Question

In a first order reaction the concentration of reactant decreases from $800{\text{mol/dm}}^3$ to $50{\text{mol/dm}}^3$ in $2\times {10}^4\text{sec}$. The rate constant of the reaction in ${\text{sec}}^{-1}$ is:

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

Answer 1

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

For first order reaction,
$k=\frac{2.303}{t}log\frac{[A{]}_0}{[A{]}_t}$
Substituting the values, we have,
$k=\frac{2.303}{2\times {10}^4\text{sec}}log\frac{800}{50}=1.386\times {10}^{-4}{\text{sec}}^{-1}$