Question

A first-order reaction has a half-life of 20 minutes. The time required for \(87.5%\) completion of the reaction is:

• A. \(40\) min
• B. \(60\) min
• C. \(80\) min
• D. \(100\) min

Hint:

For first-order reactions, memorize: \(50%\) completion = 1 half-life, \(75%\) completion = 2 half-lives, \(87.5%\) completion = 3 half-lives, \(93.75%\) completion = 4 half-lives.

Answer 1

The Correct Option is B

Concept: For a first-order reaction: \[ t_{1/2}=\frac{0.693}{k} \] A characteristic feature of first-order kinetics is that the half-life remains constant throughout the reaction.

Step 1: Determine fraction remaining. Completion: \[ 87.5% \] Therefore reactant remaining: \[ 100-87.5=12.5% \] \[ 12.5%=\frac18 \] Hence: \[ \frac{[A]}{[A]_0}=\frac18 \]

Step 2: Express in terms of half-lives. After one half-life: \[ \frac12 \] After two half-lives: \[ \frac14 \] After three half-lives: \[ \frac18 \] Therefore three half-lives are required.

Step 3: Calculate total time. \[ t=3\times20 \] \[ t=60\text{ min} \] Hence option (B) is correct.