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
\(3 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{Cr}_{2}
\mathrm{O}_{7}^{2-}(a q)+2 \mathrm{H}^{+}(a q) \longrightarrow\)
\(3 \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q)+4 \mathrm{Cr}^{3+}(a
q)+11 \mathrm{H}_{2} \mathrm{O}(l)\)
You analyze a breathalyzer test in which \(4.2 \mathrm{mg} \mathrm{K}_{2}
\mathrm{Cr}_{2} \mathrm{O}_{7}\) was reduced. Assuming the volume of the breath
was \(0.500 \mathrm{~L}\) at \(30 .{ }^{\circ} \mathrm{C}\) and \(750 . \mathrm{mm}
\mathrm{Hg}\), what was the mole percent alcohol of the breath?