Question

Calculate the time in seconds required to reduce the concentration of reactant to half of initial concentration for first order reaction if rate constant is \(1.386 \times 10^{-3} \mathrm{~s}^{-1}\).

• A. 140 s
• B. 290 s
• C. 390 s
• D. 500 s

Hint:

For a first order reaction, the time to reach half concentration is 0.693 divided by the rate constant.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a first order reaction \(t_{1/2}=\dfrac{0.693}{k}\).

Step 2: Substitute
\(k=1.386\times10^{-3}\text{ s}^{-1}\).

Step 3: Calculation
\(t_{1/2}=\dfrac{0.693}{1.386\times10^{-3}}=0.5\times10^{3}\text{ s}\).

Step 4: Result
\(t_{1/2}=500\text{ s}\).

Final Answer:
The time required is 500 s. \[ \boxed{\text{(D) }\text{500 s}} \]