•• A A colligativecolligative property is a property that depends property is a property that depends only on the number of solute particles present, only on the number of solute particles present, not their identity.not their identity.

•• The properties we will look at are: lowering of The properties we will look at are: lowering of vapor pressure; the elevation of boiling point, the vapor pressure; the elevation of boiling point, the depression of freezing point, and the osmotic depression of freezing point, and the osmotic pressure arising from the presence of a solute.pressure arising from the presence of a solute.

•• Only applicable to dilute solutions.Only applicable to dilute solutions.

COLLIGATIVE PROPERTIES:

•• All the All the colligativecolligative properties stem from the properties stem from the reduction of the chemical potential of the liquid reduction of the chemical potential of the liquid solvent as a result of the presence of solute.solvent as a result of the presence of solute.

A*AA xlnRT

COLLIGATIVE PROPERTIES:

As solute molecules are added to a solution, the solvent become less volatile (=decreased vapor pressure).

Solute-solvent interactions contribute to this effect.

VAPOR PRESSURE LOWERING:

Therefore, the vapor pressure of a solution is lower than that of the pure solvent.

VAPOR PRESSURE LOWERING:

PA = xA PAwhere• XA is the mole fraction of compound A• PA 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.

VAPOR PRESSURE LOWERING: RAOULT’S LAW

Glycerin (C3 H8 O3 ) is a nonvolatile nonelectrolyte with a density of 1.26 g/mL at 25oC. Calculate the vapor pressure at 25oC of a solution made by adding 50.0 mL of glycerin to 500.0 mL of water. The vapor pressure of pure water at 25°C is 23.8 torr.

PRACTICE EXERCISEThe vapor pressure of pure water at 110oC 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?

SAMPLE PROBLEM:

•• How do we figure out where the new boiling point How do we figure out where the new boiling point is when a solute is present?is when a solute is present?

•• Look for the temperature at which at 1 Look for the temperature at which at 1 atmatm, the , the vapor of pure solvent vapor has the same vapor of pure solvent vapor has the same chemical potential as the solvent in the solution.chemical potential as the solvent in the solution.

BOILING POINT ELEVATION:

•• LetLet’’s denote solvent A and solute B.s denote solvent A and solute B.•• Equilibrium is established when: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

BOILING POINT ELEVATION:

T makes no reference to the identity of the T makes no reference to the identity of the solute, only to its mole fraction.solute, only to its mole fraction.

So the elevation of boiling point is a So the elevation of boiling point is a colligativecolligative

property.property.

T Kx B K RT * 2

vap H

BOILING POINT ELEVATION:

molality m constant; point boiling K mKT:purposes practical For

KxT

bb

B

BOILING POINT ELEVATION:

•• LetLet’’s denote solvent A and solute B.s denote solvent A and solute B.•• Equilibrium is established when:Equilibrium is established when:

A ( s) A* ( l ) RT ln x A

Same calculation as before (Justification 5.1)Same calculation as before (Justification 5.1)

T K x B K RT * 2

fus H

FREEZING POINT DEPRESSION:

molality m constant; point freezing K mKT:purposes practical For

xKT

ff

B

FREEZING POINT DEPRESSION:

What will be the freezing point and boiling point of an aqueous solution containing 55.0 g of glycerol, C3 H5 (OH)3 , and 250 g of water? Kb (H2 O) = 0.51oC/m and Kf = 1.86o C/m.

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.

SAMPLE PROBLEM:

CryoscopyCryoscopy

T K f b K f freezing point constant; b molality

b n

1 kg solvent

m M1 kg solvent

SolubilitySolubility•• Although solubility is not strictly a Although solubility is not strictly a colligativecolligative

property (because solubility varies with the property (because solubility varies with the identity of the solute), it may be estimated using identity of the solute), it may be estimated using the same techniques.the same techniques.

•• When a solid solute is left in contact with a When a solid solute is left in contact with a solvent, it dissolves until the solution is saturated solvent, it dissolves until the solution is saturated with the dissolved solute.with the dissolved solute.

SolubilitySolubility

•• See Justification 5.2See Justification 5.2

B ( s) B* ( l ) RT ln x B

ln x B fus H

R1

T f

1T

•• Osmosis refers to the spontaneous passage of a Osmosis refers to the spontaneous passage of a pure solvent into a solution separated from it by a pure solvent into a solution separated from it by a semisemi--permeable membrane.permeable membrane.

•• In this case, the membrane is permeable to the In this case, the membrane is permeable to the solvent but not to the solute.solvent but not to the solute.

OSMOSIS:

•• The osmotic pressure, The osmotic pressure,

is the pressure that is the pressure that must be applied to the solution to stop the influx must be applied to the solution to stop the influx of solvent.of solvent.

•• Examples of osmosis includes the transport of Examples of osmosis includes the transport of fluids across cell membranes and dialysis.fluids across cell membranes and dialysis.

OSMOSIS:

OSMOSIS:

solute the ofmass molar theis Mg/L in solute the of ionconcentrat theis c

MRT

c

orsolution the of molarityis M

solution the of pressure osmotic theis MRT

2

2

22

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(C4 H7 NO4 , M=133.1 g/mol) must be dissolved in a liter of water to produce an isotonic solution?

SAMPLE PROBLEM: