Which statement below regarding the half-life of a zeroth-order reaction is true?

• A. The half-life of a zeroth-order reaction increases as the rate constant increases.
• B. The half-life of a zeroth-order reaction is independent of the initial concentration.
• C. The half-life of a zeroth-order reaction decreases as the initial concentration decreases.
• D. The half-life of a zeroth-order reaction is directly proportional to the initial concentration.

Answer: (D)

Verified step by step guidance

1. Recall the integrated rate law for a zeroth-order reaction: \([A] = [A]_0 - k t\), where \([A]_0\) is the initial concentration, \(k\) is the rate constant, and \(t\) is time.
2. Define the half-life (\(t_{1/2}\)) as the time required for the concentration to decrease to half its initial value, so \([A] = \frac{[A]_0}{2}\) at \(t = t_{1/2}\).
3. Substitute \([A] = \frac{[A]_0}{2}\) into the integrated rate law: \(\frac{[A]_0}{2} = [A]_0 - k t_{1/2}\).
4. Rearrange the equation to solve for \(t_{1/2}\): \(k t_{1/2} = [A]_0 - \frac{[A]_0}{2} = \frac{[A]_0}{2}\), so \(t_{1/2} = \frac{[A]_0}{2k}\).
5. From this expression, conclude that the half-life of a zeroth-order reaction is directly proportional to the initial concentration \([A]_0\) and inversely proportional to the rate constant \(k\).