Chemistry - Chemical Kinetics Question with Solution | TestHub

Question Explanation : Find the reactant fraction left.

Concept : First-order amount: $[A{]}_t/[A{]}_0=(1/2{)}^n$.

Solution :

For a first-order reaction, the fraction of reactant remaining after time $t$ is given by the formula: $\frac{[A{]}_t}{[A{]}_0}={\left(\frac{1}{2}\right)}^n$ where $n$ is the number of half-lives that have passed.

Given the total time of 40 minutes and the half-life of 20 minutes, we calculate $n$ as:

$$n=\frac{Totaltime}{Half-life}=\frac{40min}{20min}=2$$

Substituting this into the fraction formula yields:

$$\frac{[A{]}_t}{[A{]}_0}={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$$

This means that after two half-life periods, exactly one-quarter of the original concentration remains.

Final Answer: Option (A)