Question

In a first order reaction, 87.5% of reactant is converted into product in 15 minutes. The rate constant for the reaction is given by

• A. \(\dfrac{0.693}{5}\ \text{min}^{-1}\)
• B. \(\dfrac{0.693}{15}\ \text{min}^{-1}\)
• C. \(\dfrac{5}{0.693}\ \text{min}^{-1}\)
• D. \(0.693 \times 5\ \text{min}^{-1}\)

Hint:

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

Answer 1

The Correct Option is A

Step 1: Determine fraction of reactant remaining.
If 87.5% reacts, then remaining reactant \(= 12.5% = \frac{1}{8}\).

Step 2: Relate to half-life.
For a first order reaction: \[ \left(\frac{1}{2}\right)^n = \frac{1}{8} \Rightarrow n = 3 \] Thus, 3 half-lives have elapsed in 15 minutes.

Step 3: Calculate half-life.
\[ t_{1/2} = \frac{15}{3} = 5\ \text{min} \]

Step 4: Calculate rate constant.
For first order reaction: \[ k = \frac{0.693}{t_{1/2}} = \frac{0.693}{5}\ \text{min}^{-1} \]

Step 5: Conclusion.
The rate constant is \(\dfrac{0.693}{5}\ \text{min}^{-1}\).