Q127 / 200 · MHT CET - Medical 2026 (25 April Shift 1) · Chemistry
A first order reaction takes 90 minutes for 75% decomposition. Calculate its rate constants.
- A$0.032\ \text{min}^{-1}$
- Correct answerB$0.015\ \text{min}^{-1}$
- C$0.039\ \text{min}^{-1}$
- D$0.045\ \text{min}^{-1}$
Solution
For a first order reaction, the time required for $75\%$ completion is equal to two half-lives.
$t_{75\%} = 2 \times t_{1/2}$
$90 = 2 \times t_{1/2}$
$t_{1/2} = 45\ \text{min}$
The rate constant $k$ is given by:
$k = \dfrac{0.693}{t_{1/2}}$
$k = \dfrac{0.693}{45}$
$k = 0.0154\ \text{min}^{-1}$
Rounding off, $k \approx 0.015\ \text{min}^{-1}$.
Answer: $0.015\ \text{min}^{-1}$
$t_{75\%} = 2 \times t_{1/2}$
$90 = 2 \times t_{1/2}$
$t_{1/2} = 45\ \text{min}$
The rate constant $k$ is given by:
$k = \dfrac{0.693}{t_{1/2}}$
$k = \dfrac{0.693}{45}$
$k = 0.0154\ \text{min}^{-1}$
Rounding off, $k \approx 0.015\ \text{min}^{-1}$.
Answer: $0.015\ \text{min}^{-1}$
Hence, the correct answer is option: 'B'.