Question

Half life period of a first order reaction is \(1386\) seconds. The rate constant of the reaction is

• A. \(5.5\times 10^{-2}\times s^{-1}\)
• B. \(0.5\times 10^{-3}\times s^{-1}\)
• C. \(5\times 10^{-2}\times s^{-1}\)
• D. \(5\times 10^{-3}\times s^{-1}\)

Hint:

For a first order reaction, k = 0.693 / t half.

Answer 1

The Correct Option is B

Step 1: Start from the first-order law:
At $t = t_{1/2}$, $[A] = [A]_0/2$, so $kt_{1/2} = \ln 2 = 0.693$.

Step 2: Rearrange:
$k = \dfrac{0.693}{1386}$. Note that $1386 = 2 \times 693$.

Step 3: Simplify:
$k = \dfrac{1}{2 \times 1000} = 5 \times 10^{-4}$ s$^{-1}$, which is $0.5 \times 10^{-3}$ s$^{-1}$, option B.

Final Answer:
Since 0.693 / 1386 = 5e-4, the rate constant is 0.5e-3 per second. \[ \boxed{\text{(B) }0.5 \times 10^{-3}\ \text{s}^{-1}} \]