Which formula correctly expresses the elimination half-life in terms of Vd and Cl?

• A. t1/2 = 0.693 × Vd / Cl
• B. t1/2 = 0.693 × Cl / Vd
• C. t1/2 = Vd / (0.693 × Cl)
• D. t1/2 = Cl / (0.693 × Vd)

Answer: (A)

In first-order kinetics, the half-life reflects how fast the drug is cleared relative to how much is distributed in the body. The rate constant for elimination is k = Cl / Vd, since clearance removes drug per unit time from a volume of distribution Vd. The half-life is the time it takes for the concentration to fall to half, which gives t1/2 = ln(2) / k = 0.693 / (Cl / Vd) = 0.693 × Vd / Cl.

This shows why the correct form makes sense: increasing the volume of distribution (Vd) spreads the drug into more tissues and lengthens the half-life, while increasing clearance (Cl) removes drug faster and shortens the half-life. For a quick check, plug in numbers: higher Vd with the same Cl yields a longer t1/2; higher Cl with the same Vd yields a shorter t1/2. The other expressions would give incorrect relationships or incorrect units, so they don’t match the fundamental link t1/2 = 0.693 × Vd / Cl.