Drug X becomes ineffective after $50 \%$ decomposition. The original concentration of drug in a bottle was $16 \mathrm{mg} / \mathrm{mL}$ which becomes 4 $\mathrm{mg} / \mathrm{mL}$ in 12 months. The expiry time of the drug in months is ______ . Assume that the decomposition of the drug follows first order kinetics.

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Chemical Kinetics

Drug X becomes ineffective after

50%

decomposition. The original concentration of drug in a bottle was

16 mg / mL

which becomes 4

mg / mL

in 12 months. The expiry time of the drug in months is ______ .
Assume that the decomposition of the drug follows first order kinetics.

(A)12
(B)2
(C)3
(D)6✓ Correct

Answer: (D)

Solution

The drug's concentration drops from 16 mg/mL to 4 mg/mL over 12 months — a fourfold decrease, which for first-order kinetics corresponds to exactly two half-lives (

16 \to 8 \to 4

). Each half-life is therefore 6 months. The drug becomes ineffective once it has decomposed by 50%, i.e. after exactly one half-life, so the expiry time is 6 months.

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Single correct option

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