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Colligative Properties of Solutions Ken Rogers Miami Killian

Colligative Properties of Solutions Ken Rogers Miami Killian

Colligative Properties of Solutions Physical properties that depend on the # of solute particles Vapor pressure lowering Boiling point elevation Freezing point depression Osmotic pressure

1. Vapor Pressure Lowering (Raoult’s Law) Vapor pressure of solution Mole fraction of solvent Vapor pressure of solvent

Pure water at 20oC has a vapor pressure of 17.5 mm Hg For example suppose you had a solution that contained 3 moles of water and 1 mole sugar. Then the mole fraction of solvent would be 3 mole H2O 3 mole H2O + 1 mole sugar = 0.75 20oC Pure water at 20oC has a vapor pressure of 17.5 mm Hg 17.5 mm Hg

But adding a solute to the water blocks the ability of the solvent (water) to vaporize. 17.5 mm Hg ? mm Hg PA = ?

17.5 mm Hg 13 mm Hg

Another way of solving this problem is to realize the solution is 25% sugar. So the vapor pressure of the water is going to be lowered by 25% Change in vapor pressure of solution Mole fraction of solute Vapor pressure of solvent

Look at both ways together…. Change in vapor pressure of solution Mole fraction of solute Vapor pressure of solvent Vapor pressure of solution Mole fraction of solvent Vapor pressure of solvent

A solution is made by mixing 100g of H2O and 100g C2H5OH At 63.5oC vapor pressure of H2O is 175 torr vapor pressure of C2H5OH is 400 torr (more volatile) A solution is made by mixing 100g of H2O and 100g C2H5OH a) What is the mole fraction of ethanol? 100 g H2O = 5.56 mole 100 g C2H5OH = 2.17 mole

Total pressure of both vapors: Pethanol= 0.28 . 400 torr What is the ethanol vapor pressure? Pethanol= Xethanol Po Total pressure of both vapors: Pethanol= 0.28 . 400 torr Pethanol= 112 torr 112 torr +126 torr 238 torr c) What is the water vapor pressure? Pwater = Xwater Po Pwater = 0.72 . 175 torr Pwater = 126 torr

2. Boiling Point Elevation

Water Vapor Pressure Temperature (oC) Pressure (mm Hg) 0.0 4.6 5.0 6.5 10.0 9.2 15.0 12.8 20.0 17.5 25.0 23.8 30.0 31.8 35.0 42.2 40.0 55.3

Vapor pressure of 1m Solution Any liquid boils when its vapor pressure equals atmospheric pressure 760 mm Hg Vapor Pressure Adding a solute lowers the vapor pressure Vapor pressure of water Vapor pressure of 1m Solution 100oC Temperature

Vapor pressure of 1m Solution DT 760 mm Hg Vapor Pressure What’s the boiling point of the solution? Vapor pressure of water Vapor pressure of 1m Solution 100oC Temperature DT

The boiling point of a solution is always higher than the pure solvent. Dissolving anything in water raises the b. p. of the water (aqueous) solution. Dissolving anything in alcohol raises the b. p. of the alcohol solution. And the more concentrated the solution, the more the boiling point is raised.

Vapor pressure of 2m Solution DT 760 mm Hg Vapor Pressure Vapor pressure of 2m Solution DT 100oC Temperature

DTb = kb.m.i for water it’s 0.52oC/m # of ions produced by electrolyte molality of the solution the change in the boiling point of the solution molal boiling point constant for water it’s 0.52oC/m

A typical boiling point of solution question: What’s the b. p. of a 2.0m nonelectrolyte aqueous solution? DTb = kb . m . i =0.52oC/m . 2m . 1 =1.04oC Tb =100o + 1.04oC Tb =101.04oC

Vapor pressure of 2m Nonelectrolyte DT=1.04oC 760 mm Hg Vapor Pressure What’s the boiling point of the solution? Vapor pressure of water Vapor pressure of 2m Nonelectrolyte 100oC Temperature 101.04oC

DTb = kb. m . i What’s the b. p. of a 2.0m CaCl2 aqueous solution? If the solution was an electrolyte: What’s the b. p. of a 2.0m CaCl2 aqueous solution? CaCl2 a Ca+2 + 2Cl-1 i = 3 DTb = kb. m . i = 0.52oC/m . 2m . 3 =3.12o Tb =100o + 3.12o Tb =103.12oC

Vapor pressure of 2m CaCl2 3.12oC 760 mm Hg Vapor Pressure Vapor pressure of 2m CaCl2 100oC 103.12oC Temperature

Carbon tetrachloride, CCl4 solvent Normal B.P. Kb (oC/m) Normal F.P. Kf Water, H2O 100oC 0.52 0oC 1.86 Benzene, C6H6 80.1oC 2.53 5.5oC 5.12 Ethanol, C2H5OH 78.4oC 1.22 -114.6oC 1.99 Carbon tetrachloride, CCl4 76.8oC 5.02 -22.3oC 29.8 Chloroform, CHCl3 61.2oC 3.63 -63.5oC 4.68

Carbon tetrachloride, CCl4 solvent Normal B.P. Kb (oC/m) Normal F.P. Kf Water, H2O 100oC 0.52 0oC 1.86 Benzene, C6H6 80.1oC 2.53 5.5oC 5.12 Ethanol, C2H5OH 78.4oC 1.22 -114.6oC 1.99 Carbon tetrachloride, CCl4 76.8oC 5.02 -22.3oC 29.8 Chloroform, CHCl3 61.2oC 3.63 -63.5oC 4.68

Carbon tetrachloride, CCl4 solvent Normal B.P. Kb (oC/m) Normal F.P. Kf Water, H2O 100oC 0.52 0oC 1.86 Benzene, C6H6 80.1oC 2.53 5.5oC 5.12 Ethanol, C2H5OH 78.4oC 1.22 -114.6oC 1.99 Carbon tetrachloride, CCl4 76.8oC 5.02 -22.3oC 29.8 Chloroform, CHCl3 61.2oC 3.63 -63.5oC 4.68

DTb = kb. m . i = 2.53oC/m =2.53o Tb =80.1o + 2.53o Tb =82.63oC solvent Normal B.P. Kb (oC/m) Normal F.P. Kf Benzene, C6H6 80.1oC 2.53 5.5oC 5.12 Boiling point of a 1m nonelectrolyte solution with benzene as the solvent? DTb = kb. m . i = 2.53oC/m . 1m . 1 =2.53o Tb =80.1o + 2.53o Tb =82.63oC

3. Freezing Point Depression

As in the boiling point elevation, the freezing point also changes when a solute is added to a solvent. The solute particles interfere with the ability of the solvent to freeze. The solution has a lower freezing point. In the case of water, which normally freezes at 0oC, an aqueous solution will freeze below 0oC. We’re talking negative numbers here.

DTf = kf . m . i for water, 1.86oC/m The more concentrated the solution, the lower the freezing point. So the equation is similar to the boiling point elevation equation. # of ions produced by electrolyte DTf = kf . m . i molality of the solution the change in the freezing point of the solution molal freezing point constant for water, 1.86oC/m

Carbon tetrachloride, CCl4 solvent Normal B.P. Kb (oC/m) Normal F.P. Kf Water, H2O 100oC 0.52 0oC 1.86 Benzene, C6H6 80.1oC 2.53 5.5oC 5.12 Ethanol, C2H5OH 78.4oC 1.22 -114.6oC 1.99 Carbon tetrachloride, CCl4 76.8oC 5.02 -22.3oC 29.8 Chloroform, CHCl3 61.2oC 3.63 -63.5oC 4.68

DTf = kf . m . i What’s the f. p. of a 2.0m CaCl2 aqueous solution? For that same solution that boiled at 103.12oC: What’s the f. p. of a 2.0m CaCl2 aqueous solution? CaCl2 a Ca+2 + 2Cl-1 i = 3 DTf = kf . m . i =1.86oC/m . 2m . 3 = 11.16oC Tf = 0oC - 11.16oC Tf = -11.16oC

DTf = kf. m . i = 4.68oC/m =4.68o Tb = -63.5o – 4.68o Tb = -68.18oC solvent Normal B.P. Kb (oC/m) Normal F.P. Kf Chloroform, CHCl3 61.2oC 3.63 -63.5oC 4.68 Freezing point of a 1m nonelectrolyte solution with chloroform as the solvent? DTf = kf. m . i = 4.68oC/m . 1m . 1 =4.68o Tb = -63.5o – 4.68o Tb = -68.18oC

4. Osmotic Pressure

glass tube pure solvent Osmosis is the spontaneous process of water diffusing through a membrane to the more concentrated solution. concentrated solution semipermeable membrane

Osmotic pressure is the pressure needed to stop osmosis.

p=MRTi P = RTi V n P=MRTi = osmotic pressure The equation to calculate the pressure needed to stop osmosis (osmotic pressure) is derived from the ideal gas law. moles/liters = molarity Kelvin P = RTi V n 0.082 L.atm/mol.K P=MRTi p=MRTi osmotic pressure =

p=MRTi CaCl2 a Ca+2 + 2Cl-1 i = 3 What’s the osmotic pressure of a 2.0M CaCl2 solution at 25oC? CaCl2 a Ca+2 + 2Cl-1 i = 3 p=MRTi = (2.0 M) . (0.082 L.atm/mol.K) . (298K) . 3 = 147 atm