In a linear plot of first-order kinetics (log C vs time), what does the y-intercept represent?

In a linear plot of first-order kinetics (log C vs time), what does the y-intercept represent?

• A. Rate constant K
• B. Initial concentration of drug at time zero
• C. Final concentration
• D. Amount eliminated per hour

Answer: (B)

In a first-order plot of log concentration versus time, the y-intercept is the log of the concentration at time zero. This follows from the equation log C = log C0 − (k/2.303) t (for base-10 logs); when time t = 0, log C equals log C0, so the intercept directly represents the initial concentration. The slope, not the intercept, encodes the rate constant. Final concentration and amount eliminated per hour aren’t read from the intercept. If you used natural logs, the same idea holds: ln C = ln C0 − k t, with the intercept ln C0.

In a first-order plot of log concentration versus time, the y-intercept is the log of the concentration at time zero. This follows from the equation log C = log C0 − (k/2.303) t (for base-10 logs); when time t = 0, log C equals log C0, so the intercept directly represents the initial concentration. The slope, not the intercept, encodes the rate constant. Final concentration and amount eliminated per hour aren’t read from the intercept. If you used natural logs, the same idea holds: ln C = ln C0 − k t, with the intercept ln C0.