Elimination rate constant k is related to clearance and volume of distribution by which formula?

• A. k = Vd / CL
• B. k = CL × Vd
• C. k = CL / Vd
• D. k = Dose / (Vd × CL)

Answer: (C)

In a one-compartment model with first-order elimination, the elimination rate constant k ties together how fast the body clears drug (clearance, CL) with how widely the drug distributes into the body’s apparent space (volume of distribution, Vd). The fundamental relation is CL = k × Vd, which makes sense because clearance is the volume of plasma cleared per unit time, and dividing that by the volume the drug distributes into yields a rate constant per time. Rearranging gives k = CL / Vd. This form also lines up with how half-life depends on k: a larger k means faster elimination and a shorter half-life.

The other proposed forms don’t fit dimensionally or causality. For example, k = CL × Vd would have inconsistent units (L/h × L = L^2/h) and isn’t how a rate constant behaves. Similarly, dose divided by (Vd × CL) mixes in dose and doesn’t produce a true rate constant.