What is the rate law for a first-order reaction?

• A. rate = k
• B. rate = k[A]^2
• C. rate = k/t
• D. rate = k[A]

Answer: (D)

For a first-order reaction, the rate depends directly on the concentration of the reactant to the first power. That means the rate law is rate = k[A]. If you double the amount of A, the rate doubles, reflecting a direct, linear dependence on [A]. The other forms don’t match first-order behavior: rate = k is a zero-order form where the rate is independent of [A]; rate = k[A]^2 would be second-order, with rate growing with the square of [A]; rate = k/t isn’t a standard rate law. In practical terms, first-order reactions show a natural log plot of [A] versus time that’s a straight line with slope -k, and the half-life remains constant regardless of starting concentration, both of which align with the rate being proportional to [A].