What is the half-life expression for a zero-order reaction?

• A. t1/2 = 1/(k[A])
• B. t1/2 = [A]0/(2k)
• C. t1/2 = k[A]
• D. t1/2 = 1/(k[A]0)

Answer: (A)

In a zero-order reaction, the rate is a constant and does not depend on the concentration. That means the concentration decreases linearly over time: [A] = [A]0 − kt. For the half-life, you want the time when [A] drops to half of its initial value, so 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 the half-life depends on the initial amount and the rate constant: larger initial concentration or smaller k makes the half-life longer. It’s different from first-order behavior, where t1/2 is constant and does not depend on [A]0, and from second-order behavior, where t1/2 = 1/(k[A]0).