1. © 2009, Prentice-Hall, Inc. 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

2. Colligative Properties: Vapor Pressure Freezing Point Depression Boiling Point Elevation Osmotic Pressure

3. © 2009, Prentice-Hall, Inc. Vapor Pressure Because of solute- solvent intermolecular attraction, higher concentrations of nonvolatile solutes make it harder for solvent to escape to the vapor phase.

4. © 2009, Prentice-Hall, Inc. Raoult’s Law P A = X A P  A where – X A is the mole fraction of compound A, and – 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.

5. Vapor Pressure: Raoult’s Law: P solution = X solvent P o H2O 12g Sucrose (C 12 H 22 O 11 )is dissolved in 250.0g water at 90 °C. What is the vapor pressure of water over this solution? (P o H2O = 525.8 mmHg- from data table) Ans. 524 mmHg

6. © 2009, Prentice-Hall, Inc. 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.

7. © 2009, Prentice-Hall, Inc. Boiling Point Elevation The change in boiling point is proportional to the molality of the solution:  T b = K b  m where K b is the molal boiling point elevation constant, a property of the solvent.  T b is added to the normal boiling point of the solvent.

8. © 2009, Prentice-Hall, Inc. Boiling Point Elevation The change in freezing point can be found similarly:  T f = K f  m Here K f is the molal freezing point depression constant of the solvent.  T f is subtracted from the normal boiling point of the solvent.

9. © 2009, Prentice-Hall, Inc. 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.  T b = K b  m  T f = K f  m

10. Freezing Point Depression: Freezing Point Depression: ΔT fp = K fp m solution A solution is prepared by adding 0.50g of caffeine (C 8 H 10 O 2 N 4 ) to 100g of benzene (C 6 H 6 ). Calculate the freezing point of this solution. The freezing point of pure benzene is 5.50°C K fp for benzene = 5.23 °C/m) Ans.: 0.132 ° C T freezing = 5.37C

11. Boiling Point Elevation: Boiling point elevation: ΔT bp = K bp m solute A glycerol solution (C 3 H 8 O 3 ) 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? K bp = 0.5121 °C/m Ans: 38 g glycerol

12. © 2009, Prentice-Hall, Inc. 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.

13. © 2009, Prentice-Hall, Inc. van’t Hoff Factor We modify the previous equations by multiplying by the van’t Hoff factor, i.  T f = K f  m  i

14. © 2009, Prentice-Hall, Inc. van’t Hoff Factor Reassociation is more likely at higher concentration. Therefore, the number of particles present is concentration- dependent.

15. Role of Electrolytes on Colligative Properties: Van’t Hoff Factor: ΔT fp = K fp m solute i A 0.0711m aqueous solution of Sodium sulfate freezes at -0.32C. What is the actual value (i) of the van’t Hoff factor? K fp = 1.86 °C/m Ans: i = 2.42

16. Rank for following: Increasing boiling point (ΔTb) – 0.25 m C 6 H 12 O 11 – 0.40 m NaCl – 0.15 m MgCl 2

17. © 2009, Prentice-Hall, Inc. 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).

18. © 2009, Prentice-Hall, Inc. Osmotic Pressure The pressure required to stop osmosis, known as osmotic pressure, , is nVnV  = ( ) 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.

19. © 2009, Prentice-Hall, Inc. 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.

20. © 2009, Prentice-Hall, Inc. 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.

21. 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

22. 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 10 4 g/mole

23. VP problem How would you prepare 1.00L of an aqueous oxalic acid, H 2 C 2 O 4, solution (d= 1.05 g/mL) with a vapor pressure of 21.97 mmHg at 24°C (H 2 0 vp = 22.38 mmHg)? Ans. Dissolve 89g in 1.0 L solution