For a zero-order reaction, which statement about the half-life is correct?

For a zero-order reaction, which statement about the half-life is correct?

• A. It is constant regardless of initial concentration
• B. It increases as the reactant concentration decreases
• C. It decreases as the initial concentration increases
• D. It is proportional to the initial concentration

Answer: (D)

In a zero-order reaction, the rate is constant and does not depend on how much reactant is present. The integrated rate law is [A] = [A]0 − kt. To find the half-life, set [A] = [A]0/2 and solve for t: [A]0/2 = [A]0 − kt1/2 → kt1/2 = [A]0/2 → t1/2 = [A]0/(2k). This shows t1/2 is directly proportional to the initial concentration. So increasing the starting amount of reactant increases the time it takes to reach half of it, meaning half-life grows linearly with [A]0. For example, doubling [A]0 doubles t1/2 if k stays the same. The other possibilities don’t fit: a constant half-life would correspond to a first-order reaction, and a half-life that decreases with higher initial concentration would contradict t1/2 = [A]0/(2k).

In a zero-order reaction, the rate is constant and does not depend on how much reactant is present. The integrated rate law is [A] = [A]0 − kt. To find the half-life, set [A] = [A]0/2 and solve for t:

[A]0/2 = [A]0 − kt1/2 → kt1/2 = [A]0/2 → t1/2 = [A]0/(2k).

This shows t1/2 is directly proportional to the initial concentration. So increasing the starting amount of reactant increases the time it takes to reach half of it, meaning half-life grows linearly with [A]0. For example, doubling [A]0 doubles t1/2 if k stays the same.

The other possibilities don’t fit: a constant half-life would correspond to a first-order reaction, and a half-life that decreases with higher initial concentration would contradict t1/2 = [A]0/(2k).