How does the zero-order half-life depend on the concentration [A]?

How does the zero-order half-life depend on the concentration [A]?

• A. It increases with increasing [A]
• B. It remains constant
• C. It decreases with increasing [A]
• D. It becomes undefined

Answer: (C)

In zero-order kinetics, the rate is a constant k and does not depend on how much A is present. That means you’re removing a fixed amount of substance per unit time. If you start with [A]0, the concentration changes as [A] = [A]0 − kt. The time it takes to drop to half of the starting amount is when [A] = [A]0/2, giving t1/2 = [A]0/(2k). This shows the half-life grows linearly with the initial concentration: doubling [A]0 doubles the half-life. So the zero-order half-life increases as concentration increases. (If you think of the instantaneous half-life at a current concentration [A], that time is t = [A]/(2k), which also increases with [A].)

In zero-order kinetics, the rate is a constant k and does not depend on how much A is present. That means you’re removing a fixed amount of substance per unit time. If you start with [A]0, the concentration changes as [A] = [A]0 − kt. The time it takes to drop to half of the starting amount is when [A] = [A]0/2, giving t1/2 = [A]0/(2k). This shows the half-life grows linearly with the initial concentration: doubling [A]0 doubles the half-life. So the zero-order half-life increases as concentration increases. (If you think of the instantaneous half-life at a current concentration [A], that time is t = [A]/(2k), which also increases with [A].)