Question

The concentration of grain alcohol (C₂H₅OH) in whisky is given in "degrees proof", which is twice the percent alcohol by volume (v/v). What are the mole fraction and molality of C₂H₅OH in 80.

Answer 1

An 80 degrees proof vodka means, 40% alcohol.

that is, it contains 40% alcohol + 60% water

Let us find the moles of alcohol and water.

moles = grams/molar mass

grams = density x volume

Density (given) for ethanol = 0.79 g/mL

Assuming the total volume of vodka is 1L = 0.4 L Ethanol + 0.6 L water

We have,

grams of ethanol = 0.79 g/mL x 400 mL = 316 g

density of water = 1 g/mL [standard value taken from literature]

Thus, grams of water = 1 g/mL x 600 mL = 600 g

Calculate moles of each component,

Molar mass of ethanol = 46.07 g/mol

molar mass of water = 18.02 g/mol

Thus,

moles of Ethanol = 316 / 46.07

                            = 6.86 moles

moles of water = 600 / 18.02

                         = 33.3 moles

Total moles = moles of ethanol + moles of water

                    = 6.86 + 33.3

                    = 40.16 moles

Mole fraction of ethanol = moles of ethanol / total moles

                                      = 6.86 / 40.16

                                      = 0.17

Molality of ethanol = moles of ethanol / kg of water

                              = 6.86 / 0.600

                              = 11.43 moles/kg

Therefore, the mole fraction of ethanol = 0.17 and molality is = 11.43 moles/kg