Question

A drug becomes ineffective after 30% decomposition. The original concentration of a sample was 5 mg/ml which becomes 4.2 mg/ml in 20 months. The expiry time of the drug in months assuming the first order decomposition is:

• A. 41 months
• B. 79 months
• C. 20 months
• D. 60 months

Answer 1

The correct option is A 41 months

$k=\frac{2.303}{t}\log \left[\frac{a}{a-x}\right]$

$=\frac{2.303}{20}{\log }_{10}\frac{5}{4.2}$

$=0.00872mont{h}^{-1}$

Expiry time t can be calculated as:

$k=\frac{2.303}{t}{\log }_{10}\left[\frac{a}{a-x}\right]$

$0.00872=\frac{2.303}{t}\log \left[\frac{100}{70}\right]$

$t=40.9=41$ months