Which equation correctly relates the elimination rate constant k to clearance (Cl) and volume of distribution (Vd)?

• A. k = Cl / Vd
• B. k = Vd / Cl
• C. k = Cl × Vd
• D. k = 0.693 × Cl / Vd

Answer: (A)

In a one-compartment model with first-order elimination, the elimination rate constant k is determined by how quickly the body clears the drug relative to how much is distributed in the body. The rate of elimination is Cl multiplied by the concentration, and concentration relates to amount A by C = A / Vd. The rate of change of the amount is dA/dt = -k A. Setting the elimination rate equal to the clearance term gives k A = Cl × (A / Vd). Cancel A (assuming it’s not zero) and you get k = Cl / Vd. This means the units work out to 1/time (clearance in volume per time divided by volume). The alternative forms would misplace the units or tie k to the half-life with the factor 0.693, which belongs in t1/2 = 0.693 / k, not in k itself.