Question

What is half life of a first order reaction if time required to decrease concentration of reactant from 0.4 M to 0.1 M is $x$ hour?

• A. $x$ hour
• B. $2x$ hour
• C. $\frac{x}{2}$ hour
• D. $\frac{3x}{2}$ hour

Hint:

For first-order reactions, each half-life reduces the concentration by exactly $50%$, regardless of the starting amount.

Answer 1

The Correct Option is C

Step 1: Analysis
The concentration decreases from $0.4\text{ M} \rightarrow 0.2\text{ M}$ (1st half-life) and then $0.2\text{ M} \rightarrow 0.1\text{ M}$ (2nd half-life).

Step 2: Relation
Total time $x$ corresponds to two half-lives ($2 \times t_{1/2}$).

Step 3: Calculation
$2 \cdot t_{1/2} = x \implies t_{1/2} = \frac{x}{2}$.

Step 4: Conclusion
The half-life is $\frac{x}{2}$ hour.
Final Answer: (C)