For a first order reaction $\text{A}\to \text{Products}$, the concentration of $\text{A}$ decreases from $0.8\text{ M}$ to $0.2\text{ M}$ in $20\text{ minutes}$. The rate constant of the reaction in ${\text{min}}^{-1}$ is:

Solution

1. The integrated rate law for a first order reaction is $k=\frac{2.303}{t}\log \frac{[\text{A}{]}_0}{[\text{A}{]}_t}$.
2. Substitute the given values: $k=\frac{2.303}{20}\log \frac{0.8}{0.2}$.
3. Simplify the expression: $$\begin{array}{rl}k& =\frac{2.303}{20}\log 4\\ & =\frac{2.303\times 0.602}{20}\end{array}$$.
4. Calculate the value: $k=0.0693{\text{ min}}^{-1}$.
5. Hence the answer is (A).