Question

A drug was known to be effective after it has decomposed 30 %. The original concentration of a sample was 500 units/ml. When analyzed 20 months later, the concentration was found to be 420 units/ml. Assuming that decomposition is of Ist order, what will be the expiry time of the drug?

• A. 41 months
• B. 40 months
• C. 35 months
• D. 38 months

Answer 1

Answer: (A)

41 months

For a first order reaction expression for the specific rate constant is $k=\frac{2.303}{t}\log \frac{a}{(a-x)}$.
20 months later, the concentration was found to be 420 units/ml.
$k=\frac{2.303}{20}\log \frac{500}{\left(420\right)}$......(1)

For 30 % decomposition,
$k=\frac{2.303}{t}\log \frac{500}{(500-150)}$......(2)
From (1) and (2),

$\frac{2.303}{20}\log \frac{500}{\left(420\right)}=\frac{2.303}{t}\log \frac{500}{(500-150)}$

On calculation, we get-

$t=41months$