A drug has a volume of distribution (Vd) of 150 L and a clearance of 3 L/hour. What is the elimination half-life?
- A 50 hours
- B 34.7 hours ✓
- C 17.3 hours
- D 100 hours
Correct answer: B. 34.7 hours
Explanation
Half-life (t½) = 0.693 × Vd / CL = 0.693 × 150 L / 3 L/hr = 0.693 × 50 = 34.65 hours, approximately 34.7 hours. The formula t½ = (0.693 × Vd) / CL is derived from first-order kinetics where CL = k × Vd and t½ = 0.693 / k. A large Vd prolongs half-life because more drug is distributed in tissues and takes longer to be delivered back to the clearing organs. A higher clearance shortens half-life by removing drug more rapidly from the central compartment.
Reference: KD Tripathi, Essentials of Medical Pharmacology, 8th ed.
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