Drug $X$ becomes ineffective after $50 \%$ decomposition. The original concentration of drug in a bottle was…

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.
  1. 2
  2. 6
  3. 12
  4. 3

Solution

Drug $\mathrm{X} \xrightarrow{\text { 1st order }}$ Product
Initial concentration of drug $=16 \mathrm{mg} / \mathrm{mL}$
Concentration of drug after 12 months $=4 \mathrm{mg} / \mathrm{mL}$
Half life of drug = 6 months
Drug become ineffective after 50\% decomposition. The expiry time of drug $=6$ months

Asked in: JEE Main 2025 (29 Jan Shift 2)

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