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A solution is made by mixing 33.0 ml of ethanol, C2H6O and 67.0 ml of water. Assuming ideal behavior, what is the vapor pressure of the solution at 20 degree C? Ethanol= .789 g/ml 43.9 torr. water= .998 g/ml 17.5 torr

Verified Answer :

MissPhiladelphia

Grams ethanol = 33 ml times .789 gms/ml = 26.037 gms 

Moles ethanol = 26.037 gms / 46 gms/mole = .57 moles 

Moles water = 67 ml or 67 grams/18 gms/mole = 3.22 moles 

total moles = .57 + 3.72 = 4.29 moles 

Mole fraction ethanol = .57 moles ethanol / 4.29 moles total = 0.13

Moles fraction water = 3.72 moles water / 4.29 moles total = 0.87

Partial pressure of ethanol = mole fraction ethanol (.13) _ times VP ethanol 43.9 torr) = 5.707 torr 

partial pressure water = mole fraction water .87) times VP water (l7.5 torr) = 15.23 torr 

Total vapor pressure over solution = 5.71 torr + 15.23 torr = 20.94 torr

The vapor pressure of the solution is 20.757 torr.

According to Raoult's law, the vapor pressure can be given by:

Vapor pressure = Mole fraction \(\times\) Partial pressure

Density = \(\rm \dfrac{Mass}{Volume}\)

Mass = Density \(\times\) Volume

Mass of ethanol = 0.789 g/ml \(\times\) 33 ml

Mass of ethanol = 26.037 grams

Mass of water = 0.998 g/ml \(\times\) 67

Mass of water = 66.866 grams

Moles = \(\rm \dfrac{weight}{molecular\;weight}\)

Moles of ethanol = \(\rm \dfrac{26.037}{46}\)

Moles of ethanol = 0.566 mol

Moles of Water = \(\rm \dfrac{66.866}{18}\)

Moles of water = 3.714 mol

Total moles of solution = Moles of water + Moles of ethanol

Total moles of solution = 3.714 mol + 0.566 mol

Total moles of solution = 4.28 mol

Mole fraction = \(\rm \dfrac{moles\;of\;solute}{moles\;of\;solution}\)

Mole fraction of ethanol = \(\rm \dfrac{0.566}{4.28}\)

Mole fraction of ethanol = 0.13

Mole fraction of water = \(\rm \dfrac{3.714}{4.28}\)

Mole fraction of water = 0.86

Vapor pressure of ethanol = 0.13 \(\times\) 43.9

Vapor pressure of ethanol = 5.707 torr

Vapor pressure of water = 0.86 \(\times\) 17.5

Vapor pressure of water = 15.05 torr

The vapor pressure of solution = Vapor pressure of ethanol + Vapor pressure of water

The vapor pressure of solution = 5.707 + 15.05 torr

The vapor pressure of solution = 20.757 torr.

The vapor pressure of the solution is 20.757 torr.

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