Which plot indicates a first-order reaction when analyzing concentration-time data?

• A. [A] vs t
• B. 1/[A] vs t
• C. ln[A] vs t
• D. ln[A] vs 1/t

Answer: (C)

For a first-order reaction, the concentration decays exponentially with time, following d[A]/dt = -k[A]. Integrating gives ln[A] = -kt + ln[A]0, which means a plot of ln[A] versus time is a straight line with slope -k. That linear relationship is the telltale sign of first-order kinetics, because the natural log of concentration removes the exponential decay and reveals a constant rate in time.

If you plotted [A] versus time, you’d see a curved, exponential decline rather than a straight line, which is not characteristic of first-order behavior. A plot of 1/[A] versus time would be linear only for a second-order process, since that integrates to 1/[A] = kt + 1/[A]0. A plot of ln[A] versus 1/t doesn’t align with the standard integrated forms for simple reaction orders, so it wouldn’t produce a straight line for first-order kinetics.

So the ln[A] versus time plot is the one that best indicates a first-order reaction.