Question

A drug is known to be ineffective after it has decomposed to the extent of 30%. The original concentration of a sample was 500 units/ml. when analysed 20 months later, the concentration was found to be 420 units/ml. Assuming that the decomposition is of first order, what will be the expiration time of the drug sample. What is the half-life of the drug?

• A. 0.00872 month, 41 month
• B. 0.00872 month, 79.49 month
• C. 41 month, 79.49 month
• D. 79.49 month, 41 month

Answer 1

Answer: (C)

41 month, 79.49 month

The initial concentration a is 500 units/ml.
After 20 months, the concentration is 420 units/ml.

$k=\frac{2.303}{t}log\frac{a}{a-x}=\frac{2.303}{200}log\frac{500}{420}=0.00872/month$

After 30% decomposition, $a-x=0.7\ast 500=350units/ml$

$t=\frac{2.303}{k}log\frac{a}{a-x}=\frac{2.303}{0.00872}log\frac{500}{350}=41month$

The half life period is given by the expression $t_{1/2}=\frac{0.693}{k}=\frac{0.693}{0.00872}=79.49month$