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.

Solution

Chemistry ma’am · 3 steps

16 to 4 is two halvings, so 12 months is two half-lives and one half-life is the expiry.

1. Count half-lives. In first order kinetics the half-life does not depend on concentration. So 16 → 8 and 8 → 4 each take the same time, one half-life each.

   2 t_(1/2) = 12 months ⇒ t_(1/2) = 6 months

2. Expiry condition. The drug stops working at 50% decomposition, that is, when 16 mg/mL falls to 8 mg/mL. That is exactly one half-life.
3. So. The expiry time is t_(1/2) = 6 months, option (c).

The idea to keep. For first order decay, the fraction left after n half-lives is (1/2)ⁿ. When the drop is a clean power of 2, count the halvings instead of using logs.

Answer from the NTA final answer key. Solution by PrepWiser.