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

Options

A. 79.4 months
B. 36.2 months
C. 59.4 months
D. 41.0 months

Answer

D

Explanation

`k=(2.303)/(t )log_(10)(a)/(a-x)=(2.303)/(20)log_(10)(a)/(a-x)=(2.303)/(20)log_(10)(5)/(4.2)=0.000872 month^(-1)`
`0.00872 =(2.3030)/(t)log_(10)(100)/(70)`,t=40.9 = 41 month