Twenty milligrams of a drug is injected IV. One hour later the concentration is 0.4 mg/L. What is the volume of distribution for this drug?

• A. 0.8 L
• B. 8 L
• C. 20 L
• D. Unable to determine with the data provided

Answer: (D)

Volume of distribution connects how much drug is in the body to how much is in the plasma. For an IV bolus, the basic relation is C(t) = (Dose / Vd) × e^(−k t), where k is the elimination rate constant. This shows Vd is tied not only to the dose and the initial concentration but also to how quickly the drug is eliminated.

Here you know the dose (20 mg) and the concentration at one hour (0.4 mg/L), but you don’t know the concentration right after administration (C0) or the elimination rate constant (k). With only Dose and C at one time point, you have two unknowns (Vd and k) and only one equation, so there isn’t a unique solution. Different combinations of Vd and k could produce the same 1-hour concentration.

If you assumed no elimination (k = 0), you’d get Vd = Dose / C0 = 20 mg / 0.4 mg/L = 50 L, but that ignores real elimination. Without additional data (either C0 or k), Vd cannot be determined from the given information.