Which plot would be linear for a zero-order reaction?

Which plot would be linear for a zero-order reaction?

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

Answer: (A)

For a zero-order reaction, the rate is constant, so the concentration changes at a steady rate over time. Mathematically, d[A]/dt = -k, which integrates to [A] = [A]0 - kt. This makes a plot of [A] versus time a straight line with slope -k and intercept [A]0. The other plots won’t be linear for a zero-order process: ln[A] versus time would follow ln([A]0 - kt), which is not a straight line; 1/[A] versus time corresponds to the second-order relation 1/[A] = 1/[A]0 + kt and isn’t linear for zero-order; and plotting log[A] versus time gives log([A]0 - kt), also not linear. So only the [A] versus t plot is linear for a zero-order reaction.

For a zero-order reaction, the rate is constant, so the concentration changes at a steady rate over time. Mathematically, d[A]/dt = -k, which integrates to [A] = [A]0 - kt. This makes a plot of [A] versus time a straight line with slope -k and intercept [A]0. The other plots won’t be linear for a zero-order process: ln[A] versus time would follow ln([A]0 - kt), which is not a straight line; 1/[A] versus time corresponds to the second-order relation 1/[A] = 1/[A]0 + kt and isn’t linear for zero-order; and plotting log[A] versus time gives log([A]0 - kt), also not linear. So only the [A] versus t plot is linear for a zero-order reaction.