In 1989, a teenager in Ohio was poisoned by breathing vapors from spilled mercury. The mercury level in his urine, which is proportional to its concentration in his body, was found to be 1.54 mg · L^–1. Suppose you are working in a toxicology laboratory. You need to know from a urine analysis how much mercury a person has ingested and decide to use this case as a standard. Mercury(II) is eliminated from the body by a first-order process and has a half-life in the body of 6 days (6.0 d). What would be the concentration of mercury(II) in the urine of the teenager in milligrams per liter after 30. d if therapeutic measures are not taken?

ANTICIPATE Thirty days is five half-lives, so you should expect that most of the mercury will have been eliminated.

PLAN The level of mercury(II) in the urine can be predicted by using the integrated firstorder rate law, Eq. 1b. To use this equation, you need the rate constant. Therefore, start by calculating the rate constant from the half-life (Eq. 3) and substitute the result into Eq. 1b.

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t1/2 In 2 k₂ (3)