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Ken Rogers

2. Colligative
Properties
of Solutions
Ken Rogers
Miami Killian

3. Colligative
Properties
of Solutions
Ken Rogers
Miami Killian

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

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

6. 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

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

8. 17.5 mm Hg
13 mm Hg

9. 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

10. 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

11. 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 g C2H5OH = 2.17 mole

12. 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= torr
Pethanol= 112 torr
112 torr +126 torr 238 torr
c) What is the water vapor pressure?
Pwater = Xwater Po
Pwater = torr
Pwater = 126 torr

13. 2. Boiling Point Elevation

14. Water Vapor Pressure
Temperature (oC)
Pressure (mm Hg)

15. 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

16. Vapor pressure of 1m SolutionDT
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

17. 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.

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

19. 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

20. 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 oC
Tb =101.04oC

21. 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

22. 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 o
Tb =103.12oC

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

24. 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

25. 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

26. 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

27. 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 o
Tb =82.63oC

28. 3. Freezing Point Depression

29. 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.

30. 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

31. 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

32. DTf = kf . m . i What’s the f. p. of a 2.0m CaCl2 aqueous solution?
For that same solution that boiled at oC:
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 oC
Tf = oC

33. 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 = oC

34. 4. Osmotic Pressure

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

36. Osmotic pressure is the pressure needed to stop osmosis.

37. 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 =

38. 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