Question

Which from following is correct regarding \(t_{1/2}\) of reaction if we double the initial concentration of a reactant in first order reaction?

• A. \(t_{1/2}\) will increase by two times
• B. \(t_{1/2}\) will decrease by four times
• C. \(t_{1/2}\) remains the same
• D. \(t_{1/2}\) will decrease by two times

Hint:

Only first-order reactions have constant half-life.

Answer 1

The Correct Option is C

Concept:
For a first-order reaction: \[ t_{1/2} = \frac{0.693}{k} \] Step 1: Observe formula. Half-life depends only on rate constant \(k\), not on concentration.
Step 2: Effect of doubling concentration. If initial concentration is doubled: \[ [A]_0 \rightarrow 2[A]_0 \] But since \(t_{1/2}\) does not contain \([A]_0\), it remains unchanged.
Step 3: Conclusion. \[ t_{1/2} \text{ remains constant} \]