A new drug has a volume of distribution of 3.5 L/kg and a clearance of 1.75 L/hr/kg. In a 70-kg patient, what is the elimination half-life? [Vd = 3.5 L/kg × 70 kg = 245 L; CL = 1.75 L/hr/kg × 70 kg = 122.5 L/hr; t½ = 0.693 × Vd/CL]
- A 0.98 hours
- B 2.8 hours
- C 1.39 hours ✓
- D 4.2 hours
Correct answer: C. 1.39 hours
Explanation
Using t½ = 0.693 × Vd/CL: Vd = 3.5 × 70 = 245 L; CL = 1.75 × 70 = 122.5 L/hr; t½ = 0.693 × 245/122.5 = 0.693 × 2.0 = 1.386 ≈ 1.39 hours. This is the standard formula for first-order elimination half-life. The half-life depends on both volume of distribution (how widely the drug distributes) and clearance (how efficiently it is eliminated); a larger Vd prolongs half-life, while higher CL shortens it.
Reference: KD Tripathi, Essentials of Medical Pharmacology, 8th ed.
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