Ethanol, the alcohol in beer and wine, has the molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} .\) Calculate the mass percent of each element in ethanol.

We have the molecular formula of ethanol as \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\). To find the molar mass, we will sum the molar masses of all the elements in ethanol, using the atomic masses from the periodic table: Carbon (C): \(12.01 \: g/mol\) Hydrogen (H): \(1.01 \: g/mol\) Oxygen (O): \(16.00 \: g/mol\) Molar mass of Ethanol = 2 x molar mass of Carbon + 6 x molar mass of Hydrogen + 1 x molar mass of Oxygen = 2 x \(12.01 \: g/mol\) + 6 x \(1.01 \: g/mol\) + 1 x \(16.00 \: g/mol\)

Now, perform the calculations to obtain the molar mass of ethanol: = \(2\cdot(12.01)+6\cdot(1.01)+1\cdot(16.00)\) = \(24.02 + 6.06 + 16.00\) = \(46.08 \: g/mol\) The molar mass of ethanol is \(46.08 \, g/mol\).

Mass percentage of an element = (Mass of the element in one mole of ethanol / Molar mass of ethanol) * 100 Carbon in ethanol: Mass percentage of Carbon = ( Mass of carbon in ethanol / Molar mass of ethanol ) x 100 = \( \frac{(24.02)}{(46.08)}\times100 \) = \(52.14 \% \) Hydrogen in ethanol: Mass percentage of Hydrogen = ( Mass of Hydrogen in ethanol / Molar mass of ethanol ) x 100 = \( \frac{(6.06)}{(46.08)}\times100 \) = \(13.15 \% \) Oxygen in ethanol: Mass percentage of Oxygen = ( Mass of Oxygen in ethanol / Molar mass of ethanol ) x 100 = \( \frac{(16.00)}{(46.08)}\times100 \) = \(34.71 \% \) So, the mass percentages of the elements in ethanol are: Carbon: \(52.14 \% \) Hydrogen: \(13.15 \% \) Oxygen: \(34.71 \% \)