Question

In a first order reaction, concentration of reactant is reduced to (1/8)th of concentration in 23.03 minutes. What is half-life period of reaction?

• A. 25 min
• B. 7.7 min
• C. 15 min
• D. 30 min

Hint:

For first-order reactions, recognizing powers of $\frac{1}{2}$ saves you from doing complex logarithmic calculations! $\frac{1}{2}$ is 1 half-life, $\frac{1}{4}$ is 2 half-lives, $\frac{1}{8}$ is 3 half-lives, $\frac{1}{16}$ is 4 half-lives, and so on.

Answer 1

The Correct Option is B

Step 1: Count the halvings.
Dropping to one eighth means halving three times, since $\tfrac{1}{8} = \left(\tfrac{1}{2}\right)^3$. So 3 half-lives have passed.

Step 2: Link time and half-life.
Total time $= 3 \times t_{1/2}$, and the total time given is $23.03$ min.

Step 3: Solve.
$$t_{1/2} = \frac{23.03}{3} \approx 7.7\ \text{min}$$
\[ \boxed{7.7\ \text{min}} \]