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
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).
The vapor pressure of a solution containing 38.7 g glycerin (C3H8O3) in 146.2 g ethanol (C2H5OH)...
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