Question

A medicine containing rate constant k = 4.215 x 10⁻³ per month becomes uneffective after 40% dissociation. Assume that its dissociation follow first order. Calculate the expiry date in months for this medicine-

• A. 119
• B. 122
• C. 244
• D. 238

Answer 1

Answer: (B)

122 months

Answer 2

For a first‐order reaction, the relation is

$$\ln\left(\frac{[A]_0}{[A]}\right)=kt.$$

After 40% dissociation, remaining fraction $=0.6$ so that

$$\ln\left(\frac{1}{0.6}\right)=\ln(1.667)=0.5108.$$

Thus,

$$t=\frac{0.5108}{4.215\times10^{-3}} \approx121.17 \; \text{months}\approx122\; \text{months}.$$