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Colligative Properties

• Changes in colligative properties depend only on the number of solute particles present, not on the identity of the solute particles.

• Among colligative properties are– Vapor pressure lowering – Boiling point elevation– Melting point depression– Osmotic pressure

Colligative Properties:

•Vapor Pressure•Freezing Point Depression•Boiling Point Elevation•Osmotic Pressure

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Vapor Pressure

Because of solute-solvent intermolecular attraction, higher concentrations of nonvolatile solutes make it harder for solvent to escape to the vapor phase.

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Raoult’s Law

PA = XAPA

where– XA is the mole fraction of compound A, and

– 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:

• Raoult’s Law: Psolution = XsolventPoH2O

12g Sucrose (C12H22O11)is dissolved in 250.0g water at 90 °C.

What is the vapor pressure of water over this solution?

(PoH2O = 525.8 mmHg- from data table)

• Ans. 524 mmHg

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Boiling Point Elevation and Freezing Point Depression

Nonvolatile solute-solvent interactions also cause solutions to have higher boiling points and lower freezing points than the pure solvent.

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Boiling Point Elevation• The change in boiling point

is proportional to the molality of the solution:

Tb = Kb m

where Kb is the molal boiling point elevation constant, a property of the solvent.

Tb is added to the normal boiling point of the solvent.

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Boiling Point Elevation• The change in freezing

point can be found similarly:

Tf = Kf m

• Here Kf is the molal freezing point depression constant of the solvent.

Tf is subtracted from the normal boiling point of the solvent.

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Boiling Point Elevation and Freezing Point Depression

Note that in both equations, T does not depend on what the solute is, but only on how many particles are dissolved.

Tb = Kb m

Tf = Kf m

Freezing Point Depression:

• Freezing Point Depression: ΔTfp = Kfpmsolution

• A solution is prepared by adding 0.50g of caffeine (C8H10O2N4) to 100g of benzene (C6H6).

• Calculate the freezing point of this solution.

• The freezing point of pure benzene is 5.50°C• Kfp for benzene = 5.23 °C/m)

Ans.: 0.132 ° CTfreezing= 5.37C

Boiling Point Elevation:

• Boiling point elevation: ΔTbp = Kbpmsolute

• A glycerol solution (C3H8O3) in water is prepared by dissolving glycerol is 500g water. The boiling point of the solution is 100.42°C at 760mmHg. What mass of glycerol was dissolved to make this solution?

• Kbp = 0.5121 °C/m

Ans: 38 g glycerol

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Colligative Properties of Electrolytes

Since these properties depend on the number of particles dissolved, solutions of electrolytes (which dissociate in solution) should show greater changes than those of nonelectrolytes.

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van’t Hoff Factor

• We modify the previous equations by multiplying by the van’t Hoff factor, i.

Tf = Kf m i

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van’t Hoff Factor

• Reassociation is more likely at higher concentration.

• Therefore, the number of particles present is concentration-dependent.

Role of Electrolytes on Colligative Properties:

• Van’t Hoff Factor: ΔTfp = Kfpmsolutei

• A 0.0711m aqueous solution of Sodium sulfate freezes at -0.32C. What is the actual value (i) of the van’t Hoff factor? Kfp = 1.86 °C/m

Ans: i = 2.42

Rank for following:

• Increasing boiling point (ΔTb)– 0.25 m C6H12O11

– 0.40 m NaCl– 0.15 m MgCl2

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Osmosis

In osmosis, there is net movement of solvent from the area of higher solvent concentration (lower solute concentration) to the are of lower solvent concentration (higher solute concentration).

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Osmotic Pressure

The pressure required to stop osmosis, known as osmotic pressure, , is

nV

= ( )RT = MRT

where M is the molarity of the solution.

If the osmotic pressure is the same on both sides of a membrane (i.e., the concentrations are the same), the solutions are isotonic.

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Osmosis in Blood Cells

• If the solute concentration outside the cell is greater than that inside the cell, the solution is hypertonic.

• Water will flow out of the cell, and crenation results.

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Osmosis in Cells

• If the solute concentration outside the cell is less than that inside the cell, the solution is hypotonic.

• Water will flow into the cell, and hemolysis results.

Osmotic Pressure

• Osmotic Pressure: π= MRT

• What is the osmotic pressure of a 0.1M solution of sucrose at 25C?

(remember: R= .08206 L-atm/mol-K)

Ans: 2.45 atm

Another Osmotic pressure problem.

• 100. mg of a protein are dissolved in enough water to make 10.0 mL of a solution.

• If this solution has an osmotic pressure of 13.3 mmHg at 25°C, what is the molar mass of the protein?

Ans: 1.4 x 104 g/mole

VP problem

• How would you prepare 1.00L of an aqueous oxalic acid, H2C2O4, solution (d= 1.05 g/mL) with a vapor pressure of 21.97 mmHg at 24°C (H20 vp = 22.38 mmHg)?

Ans. Dissolve 89g in 1.0 L solution