Chapter 11, Problem 104QAP

In a first-order reaction, suppose that a quantity X of a reactant is added at regular intervals of time, Δt. At first the amount of reactant in the system builds up; eventually, however, it levels off at a saturation value given by the expression a saturation value

$\text{saturation}\text{value}=\frac{x}{1-{10}^{-a}}$ where $a=0.30\frac{\Delta t}{t_{1/2}}$This analysis applies to prescription drugs, of which you take a certain amount each day. Suppose that you take 0.100 g of a drug three times a day and that the half-life for elimination is 2.0 days. Using this equation, calculate the mass of the drug in the body at saturation. Suppose further that side effects show up when 0.500 g of the drug accumulates in the body. As a pharmacist, what is the maximum dosage you could assign to a patient for an 8-h period without causing side effects?