Which plot yields a straight line for a first-order reaction?

• A. A vs time
• B. ln[A] vs time
• C. 1/[A] vs time
• D. [A]^2 vs time

Answer: (B)

First-order processes cause an exponential decay of the concentration with time. Starting from rate = -d[A]/dt = k[A], you can rearrange to d[A]/[A] = -k dt and integrate to get ln[A] = -kt + ln[A]0. This is a linear equation in time, so plotting ln[A] against time gives a straight line with slope -k and intercept ln[A]0. The other plots don’t produce a straight line for a first-order reaction: A vs time traces an exponential decay (not linear), 1/[A] vs time would be linear for a second-order reaction, and [A]^2 vs time does not produce a straight line. Therefore, the straight-line plot for a first-order reaction is ln[A] versus time.