Q27 / 150 · MHT CET 2026 (11 April Shift 2) · Chemistry
Half life period of a first order reaction is $1386$ seconds. The rate constant of the reaction is
- A$5.5 \times 10^{-2} \times s^{-1}$
- Correct answerB$0.5 \times 10^{-3} \times s^{-1}$
- C$5 \times 10^{-2} \times s^{-1}$
- D$5 \times 10^{-3} \times s^{-1}$
Solution
For a first order reaction, the rate constant $k$ is related to the half life period $t_{1/2}$ by the formula:
$k = \dfrac{0.693}{t_{1/2}}$
Given $t_{1/2} = 1386 \text{ s}$, substituting this value:
$k = \dfrac{0.693}{1386}$
$k = \dfrac{693 \times 10^{-3}}{2 \times 693}$
$k = 0.5 \times 10^{-3} \text{ s}^{-1}$
Answer: $0.5 \times 10^{-3} \times s^{-1}$
$k = \dfrac{0.693}{t_{1/2}}$
Given $t_{1/2} = 1386 \text{ s}$, substituting this value:
$k = \dfrac{0.693}{1386}$
$k = \dfrac{693 \times 10^{-3}}{2 \times 693}$
$k = 0.5 \times 10^{-3} \text{ s}^{-1}$
Answer: $0.5 \times 10^{-3} \times s^{-1}$
Hence, the correct answer is option: 'B'.