Question

A first-order reaction is 50% completed in 16 minutes. The percentage of reactant that will react in 32 minutes is

• A. 100%
• B. 12.5%
• C. 25%
• D. 75%

Hint:

For a first-order reaction, after one half-life, 50% of the reactant has reacted, and after two half-lives, 75% of the reactant will have reacted.

Answer 1

The Correct Option is D

Step 1: Understanding the first-order reaction.
For a first-order reaction, the fraction of reactant remaining at any time is given by: \[ \frac{[A]_t}{[A]_0} = e^{-kt} \] Where \([A]_t\) is the concentration at time \(t\), \([A]_0\) is the initial concentration, and \(k\) is the rate constant.
Step 2: Using the given information.
We are told that the reaction is 50% completed in 16 minutes, which means half of the reactant has reacted. For a first-order reaction, this corresponds to one half-life. After 32 minutes, two half-lives have passed, so 75% of the reactant will have reacted.
Step 3: Conclusion.
The correct answer is (D) 75% because after 32 minutes, two half-lives have passed and 75% of the reactant is consumed.