Question

The half-life of a first-order reaction depends on:

• A. Initial concentration
• B. Temperature only
• C. Rate constant
• D. Both (a) and (c)

Hint:

For first-order reactions, the half-life is constant regardless of how much material you start with. If it takes 10 minutes for 100g to become 50g, it will also take 10 minutes for 2g to become 1g.

Answer 1

The Correct Option is C

Concept:
The half-life (\( t_{1/2} \)) is the time required for the concentration of a reactant to decrease to half of its initial value.

Step 1: Recall the formula for the half-life of a first-order reaction.
For a first-order reaction, the integrated rate law leads to the expression: $$ t_{1/2} = \frac{\ln 2}{k} \approx \frac{0.693}{k} $$ where \( k \) is the rate constant.

Step 2: Analyze dependencies.
From the formula, it is clear that \( t_{1/2} \) is inversely proportional to the rate constant \( k \). Notably, the initial concentration \( [A]_0 \) does not appear in the equation, meaning the half-life is independent of the starting amount.