Question

The half life of a first order reaction is 6.0 hours. How long will it take for the concentration of reactant to decrease from 0.4 M to 0.12 M?

• A. 30:36 h
• B. 10:42 h
• C. 4:25 h
• D. 9:51 h

Hint:

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

Answer 1

The Correct Option is B

Step 1: Understanding the first-order reaction.
For a first-order reaction, the half-life is independent of the initial concentration. The relationship between concentration and time is given by: \[ \ln \left( \frac{[A]_0}{[A]} \right) = kt \] Where \( [A]_0 \) is the initial concentration, \( [A] \) is the final concentration, \( k \) is the rate constant, and \( t \) is the time.

Step 2: Applying the formula.
Given that the half-life is 6.0 hours, we can use the equation for a first-order reaction to find the time required for the concentration to decrease from 0.4 M to 0.12 M. The time is found to be 10.42 hours.

Step 3: Conclusion.
The correct answer is (B) 10:42 h.