Question

Which of the statement is correct regarding the half-life of a first-order reaction?

• A. It depends on the initial concentration of reactants
• B. It is independent of the initial concentration of reactants
• C. It increases with increasing concentration of product
• D. It decreases with increasing initial concentration of reactants.

Hint:

For first order reactions, the half-life equals 0.693 divided by the rate constant.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For a first-order reaction, \(k = \dfrac{2.303}{t}\log\dfrac{[R]_0}{[R]}\).

Step 2: Half-life
Put \([R] = \dfrac{[R]_0}{2}\) and \(t = t_{1/2}\). This gives \(t_{1/2} = \dfrac{0.693}{k}\).

Step 3: Conclusion
The initial concentration \([R]_0\) does not appear, so the half-life is independent of the initial concentration.

Final Answer:
The half-life of a first-order reaction does not depend on the initial concentration. \[ \boxed{\text{(B) }\text{It is independent of the initial concentration of reactants}} \]