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

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Solution

Q.
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. [2025]

1 6

2 12

3 2

4 3

Ans.
(1)

After every $t_{1 / 2}$ , concentration of reactants in a first order reaction becomes half.

$16 \frac{mg}{mL} \overset{6 months}{\to} 8 \frac{mg}{mL} \overset{6 months}{\to} 4 \frac{mg}{mL}$

So in 6 months, the drug becomes ineffective.

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