Question

In a first-order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is:

• A. 7.5 minutes
• B. 15 minutes
• C. 30 minutes
• D. 60 minutes

Hint:

For a first-order reaction, the half-life is independent of the initial concentration.

Answer 1

The Correct Option is C

Step 1: Understanding Half-Life in First-Order Reactions
For a first-order reaction, the half-life (\( t_{1/2} \)) is constant and given by: \[ t_{1/2} = \frac{0.693}{k} \] From the given data, the concentration falls from \( 0.8 M \) to \( 0.4 M \) in 15 minutes.
Since \( t_{1/2} \) is constant, another half-life will reduce it from 0.4 M to 0.2 M in another 15 minutes.
Another half-life will further reduce it from 0.1 M to 0.025 M, which takes another 15 minutes.
Step 2: Total Time Required
Two half-lives are needed to reduce \( 0.1 M \) to \( 0.025 M \).
\( 2 \times 15 = 30 \) minutes.
Final Answer: 30 minutes.