Pharmacokinetics concerns the ingestion, distribution, reaction, and elimination reaction of drugs in the body. Consider the application of pharmacokinetics to one of the major problems we have in the United States, drinking and driving. Here, we shall model how long one must wait to drive after having a tall martini. In most states, the legal intoxication limit is 0.8 g of ethanol per liter of body fluid. The ingestion of ethanol into the bloodstream and its subsequent elimination can be modeled as a series reaction. The rate of absorption from the gastrointestinal tract into the bloodstream and body is a first-order reaction with a specific reaction-rate constant of 10 h^–1. The rate at which ethanol is broken down in the bloodstream is limited by regeneration of a coenzyme. Consequently, the process may be modeled as a zero-order reaction with a specific reaction rate of 0.192 g/h · L of body fluid. Suppose you immediately drank two tall martinis after arriving at a party. How long would you have to wait before your blood alcohol concentration is below the legal limit in order to drive

(a) In the United States,

(b) In Sweden,

(c) In Russia? How would your answer change if

(d) the drinks were taken ½ h apart

(e) If the two drinks were consumed at a uniform rate during the first hour?

(f) Suppose that one went to a party, had two tall martinis right away, and then received a phone call saying an emergency had come up and the person needed to drive home immediately. How many minutes would the individual have to reach home before he/she became legally intoxicated, assuming that the person had nothing further to drink?

(g) How would a plot of blood alcohol concentration-time curve change in part
(h) if you continuously drank Bud Light at a rate of one, 1 oz. swallow per minute for 2 h?

(i) How would your answers be different for a thin person? A heavy person?

Additional information:

For a more complete description of alcohol metabolism and pharmacokinetics, see PRS on the Web site for