Question

A drug becomes ineffective after $30$% decomposition. The original concentration of a sample was $5mg/mL$, which becomes $4.2mg/mL$ during $20$ months. Assuming the decomposition of a first-order, calculate the expiry time of the drug in months. What is the half-life of the product?

Answer 1

$k=\frac{2.303}{t}{\log }_{10}\left(\frac{a}{a-x}\right)=\frac{2.303}{20}{\log }_{10}\left(\frac{5}{4.2}\right)$
$=0.00872{month}^{-1}$
Expiry time '$t$' may be calculated as:
$k=\frac{2.303}{t}{\log }_{10}\frac{a}{a-x}$
$0.00872=\frac{2.303}{t}{\log }_{10}\frac{100}{70}$
$t=40.9\approx 41$ month
$t_{1/2}=\frac{0.693}{0.00872}=79.4$ month