Chapter 22, Problem 157CP

A chemical “breathalyzer” test works because ethanol in the breath is oxidized by the dichromate ion (orange) to form acetic acid and chromium(III) ion (green). The balanced reaction is

${\text{3C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH}\left(aq\right)+2{\text{Cr}}_{\text{2}}{\text{O}}_7^{2-}\left(aq\right)+{\text{2H}}^{\text{+}}\left(aq\right)\to 3{\text{HC}}_2{\text{H}}_3{\text{O}}_2\left(aq\right)+4{\text{Cr}}^{\text{3+}}\left(aq\right)+{\text{ 11H}}_2\text{O}\left(l\right)$You analyze a breathalyzer test in which 4.2 mg K₂Cr₂O₇ was reduced. Assuming the volume of the breath was 0.500 L at 30.°C and 750. mm Hg, what was the mole percent alcohol of the breath?