Blood alcohol content (BAC) is often reported in weight–volume percent (w/v%). For example, a BAC of 0.10% corresponds to 0.10 g CH₃CH₂OH per 100 mL of blood. Estimates of BAC can be obtained from breath samples by using a number of commercially available instruments, including the Breathalyzer for which a patent was issued to R. F. Borkenstein in 1958. The chemistry behind the Breathalyzer is described by the oxidation-reduction reaction below, which occurs in acidic solution:

A Breathalyzer instrument contains two ampules, each of which contains 0.75 mg K₂Cr₂O₇ dissolved in 3 mL of 9 M H₂SO₄(aq). One of the ampules is used as reference. When a person exhales into the tube of the Breathalyzer, the breath is directed into one of the ampules, and ethyl alcohol in the breath converts Cr₂O₇^2- into Cr³⁺. The instrument compares the colors of the solutions in the two ampules to determine the breath alcohol content (BrAC), and then converts this into an estimate of BAC. The conversion of BrAC into BAC rests on the assumption that 2100 mL of air exhaled from the lungs contains the same amount of alcohol as 1 mL of blood. With the theory and assumptions described in this problem, calculate the molarity of K₂Cr₂O₇ in the ampules before and after a breath test in which a person with a BAC of 0.05% exhales 0.500 L of his breath into a Breathalyzer instrument.

Transcribed Image Text:

CH3CH₂OH(g) + Cr₂O7² (aq) ethyl alcohol (yellow-orange) CH₂COOH(aq) + Cr³+ (aq) (not balanced) (green)