Question

The vapor pressure of a solution containing 38.7 g glycerin (C3H8O3) in 146.2 g ethanol (C2H5OH) is 40.4 torr and 20 degrees C. Calculate the vapor pressure of pure ethanol at 20 degrees C assuming that glycerin is a nonvolatile, nonelectrolyte solute in ethanol.

Vapor pressure = _________ torr

Answer 1

Mass of glycerin, C₃H₈O₃ = 38.7 g.

Mass of ethanol, C₂H₅OH = 146.2 g.

The atomic masses are

C: 12.011 g/mol

H: 1.008 g/mol

O: 15.999 g/mol

Molar mass of C₃H₈O₃ = (3*12.011 + 8*1.008 + 3*15.999) g/mol = 92.094 g/mol.

Molar mass of C₂H₅OH = (2*12.011 + 6*1.008 + 1*15.999) g/mol = 46.069 g/mol.

Mol(s) glycerin corresponding to 38.7 g = (38.7 g)/(92.094 g/mol) = 0.4202 mol.

Mol(s) ethanol corresponding to 146.2 g = (146.2 g)/(46.069 g/mol) = 3.1735 mol.

Mole fraction of ethanol in the mixture, χ =

(number of moles of ethanol)/(total number of moles in the mixture)

= (3.1735 mole)/(3.1735 mole + 0.4202 mole)

= (3.1735 mole)/(3.5937 mole)

= 0.8831

The vapor pressure of ethanol in the mixture of the compounds is given by Raoult’s law as

P = χ*P⁰

where P⁰ is the vapor pressure of pure ethanol in the mixture.

Plug in values and get

40.4 torr = (0.8831)*P⁰

======> P⁰ = (40.4 torr)/(0.8831)

======> P⁰ = 45.7479 torr ≈ 45.7 torr (correct to 3 sig.figs)

The vapor pressure of pure ethanol is 45.7 torr (ans).