A drug has a volume of distribution of 70 L and a clearance of 7 L/hour. What is its elimination half-life?

• A 5 hours
• B 10 hours
• C 0.1 hours
• D 6.93 hours ✓

Explanation

Half-life = (0.693 × Vd) / CL = (0.693 × 70 L) / (7 L/hr) = 48.51 / 7 = 6.93 hours. This formula applies to first-order kinetics where elimination is proportional to concentration. The factor 0.693 is the natural logarithm of 2, reflecting the time for 50% of the drug to be eliminated. Five half-lives (approximately 34.65 hours) would be required to reach steady state or to eliminate ~97% of the drug.

Reference: KD Tripathi, Essentials of Medical Pharmacology, 8th ed.

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