A plot of log concentration versus time that is linear indicates which type of kinetics?

A plot of log concentration versus time that is linear indicates which type of kinetics?

• A. Zero-order
• B. First-order
• C. Mixed-order
• D. Saturable kinetics

Answer: (B)

A straight line when you plot the natural or common logarithm of concentration against time indicates first-order kinetics. In first-order processes, the rate of decay is proportional to how much drug is left: dC/dt = -kC. Integrating this gives a relationship where ln C (or log10 C, with a simple scaling) decreases linearly with time: ln C = -kt + ln C0, or log10 C = -(k/2.303)t + log10 C0. The slope is negative and proportional to the rate constant, and the intercept equals the initial concentration. This linearity with log concentration does not occur for zero-order kinetics, where concentration declines linearly with time, nor for mixed or saturable kinetics, which show departures from a straight log-versus-time line.

A straight line when you plot the natural or common logarithm of concentration against time indicates first-order kinetics. In first-order processes, the rate of decay is proportional to how much drug is left: dC/dt = -kC. Integrating this gives a relationship where ln C (or log10 C, with a simple scaling) decreases linearly with time: ln C = -kt + ln C0, or log10 C = -(k/2.303)t + log10 C0. The slope is negative and proportional to the rate constant, and the intercept equals the initial concentration. This linearity with log concentration does not occur for zero-order kinetics, where concentration declines linearly with time, nor for mixed or saturable kinetics, which show departures from a straight log-versus-time line.