COLLIGATIVE PROPERTIES:

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1 COLLIGATIVE PROPERTIES: A colligative property is a property that depends only on the number of solute particles present, not their identity. The properties we will look at are: lowering of vapor pressure; the elevation of boiling point, the depression of freezing point, and the osmotic pressure arising from the presence of a solute. Only applicable to dilute solutions.

2 COLLIGATIVE PROPERTIES: All the colligative properties stem from the reduction of the chemical potential of the liquid solvent as a result of the presence of solute. A * A RT ln x A

3 VAPOR PRESSURE LOWERING: As solute molecules are added to a solution, the solvent become less volatile (=decreased vapor pressure). Solute-solvent interactions contribute to this effect.

4 VAPOR PRESSURE LOWERING: Therefore, the vapor pressure of a solution is lower than that of the pure solvent.

5 VAPOR PRESSURE LOWERING: RAOULT S LAW where P A = x A P A X A is the mole fraction of compound A P A is the normal vapor pressure of A at that temperature NOTE: This is one of those times when you want to make sure you have the vapor pressure of the solvent.

6 SAMPLE PROBLEM: Glycerin (C 3 H 8 O 3 ) is a nonvolatile nonelectrolyte with a density of 1.26 g/ml at 25 o C. Calculate the vapor pressure at 25 o C of a solution made by adding 50.0 ml of glycerin to ml of water. The vapor pressure of pure water at 25 C is 23.8 torr. PRACTICE EXERCISE The vapor pressure of pure water at 110 o C is 1070 torr. A solution of ethylene glycol and water has a vapor pressure of 1.00 atm at 110 C. Assuming that Raoult s law is obeyed, what is the mole fraction of ethylene glycol in the solution?

7

8 BOILING POINT ELEVATION: How do we figure out where the new boiling point is when a solute is present? Look for the temperature at which at 1 atm,, the vapor of pure solvent vapor has the same chemical potential as the solvent in the solution.

9 BOILING POINT ELEVATION: Let s s denote solvent A and solute B. Equilibrium is established when: A ( g ) A * ( g ) RT ln x A A * ( l) RT ln x A T Kx B K RT *2 vap H

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11 BOILING POINT ELEVATION: T Kx B K RT *2 vap H T T makes no reference to the identity of the solute, only to its mole fraction. So the elevation of boiling point is a colligative property.

12 BOILING POINT ELEVATION: T Kx B For practical purposes : T K b m K b boiling point constant; m molality

13

14 FREEZING POINT DEPRESSION: Let s s denote solvent A and solute B. Equilibrium is established when: A ( s) * A ( l) RT ln x A Same calculation as before (Justification 5.1) T K x B K RT *2 fus H

15 FREEZING POINT DEPRESSION: T Kx B For practical purposes : T K f m K f freezing point constant; m molality

16

17 SAMPLE PROBLEM: What will be the freezing point and boiling point of an aqueous solution containing 55.0 g of glycerol, C 3 H 5 (OH) 3, and 250 g of water? K b (H 2 O) = 0.51 o C/m and K f = 1.86 o C/m.

18 SAMPLE PROBLEM: A solution is prepared from 25.0 g of benzene, C6H6, and 2.50 g of an unknown compound. The freezing point of this solution is 4.3oC. The normal freezing point of benzene is 5.5 oc and the freezing point depression constant for benzene is 5.12 oc/m. Determine the molar mass of the compound.

19 Cryoscopy T K f b K f freezing point constant; b molality b n 1 kg solvent m M 1 kg solvent

20 Solubility Although solubility is not strictly a colligative property (because solubility varies with the identity of the solute), it may be estimated using the same techniques. When a solid solute is left in contact with a solvent, it dissolves until the solution is saturated with the dissolved solute.

21

22 Solubility B ( s) B * ( l) RT ln x B See Justification 5.2 ln x B fus H R 1 T f 1 T

23 OSMOSIS: Osmosis refers to the spontaneous passage of a pure solvent into a solution separated from it by a semi-permeable membrane. In this case, the membrane is permeable to the solvent but not to the solute.

24

25 OSMOSIS: The osmotic pressure, is the pressure that must be applied to the solution to stop the influx of solvent. Examples of osmosis includes the transport of fluids across cell membranes and dialysis.

26 OSMOSIS: c 2 is the is the M 2 osmotic is the M is molarity concentrat molar pressure c 2 MRT of or ion the RT M 2 of the mass of of the solution solute the solution in solute g/l

27 SAMPLE PROBLEM: An aspartic acid solution will produce an osmotic pressure of 1.80 atm measured against pure water at 18.5 C. How many g of Aspartic Acid(C 4 H 7 NO 4, M=133.1 g/mol) must be dissolved in a liter of water to produce an isotonic solution?

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