Question

The half life of a chemical reaction is 1386 seconds. The specific rate constant for the reaction is:

• A. $0.5 \times 10^{-2} s^{-1}$
• B. $0.5 \times 10^{-3} s^{-1}$
• C. $0.5 \times 10^{-4} s^{-1}$
• D. $0.5 \times 10^{-5} s^{-1}$

Hint:

In competitive exams, numbers like 693 and 1386 are common because $1386 = 2 \times 693$, making division simple.

Answer 1

The Correct Option is B

Step 1: Concept
The relationship between half-life ($t_{1/2}$) and the rate constant ($k$) for a first-order reaction is $k = \frac{0.693}{t_{1/2}}$.

Step 2: Calculation
Given $t_{1/2} = 1386$ s:
$k = \frac{0.693}{1386} = \frac{6.93 \times 10^{-1}}{1386}$

Step 3: Simplification
Note that $1386$ is exactly $2 \times 693$.
$k = \frac{0.693}{1386} = 0.0005 = 0.5 \times 10^{-3} s^{-1}$.

Step 4: Conclusion
The rate constant is $0.5 \times 10^{-3} s^{-1}$. Final Answer: (B)