1. Phase Equilibria Melting-Freezing Evaporation-Condensation Sublimation-Condensation Phase transition

2. S g >> S l > S s The most stable phase is that with lowest chemical potential.

4. Pressure Effect  -T curve of gases much more largely affected by pressure change than liquids or solids

5. Pressure increase: - Boiling point elevation - Freezing point elevation/depression

6. Phase Diagram

7. CO 2

8. Clapeyron Equation At Equilibrium Clapeyron Equation

9. Solid-Liquid Equilibrium Slope of pT-curve  Usually positive  ~ 40 atm/K  40 atm are needed to change the melting point by 1 K

10. Upon pressure increase Melting point elevation Melting point depression water Ice skating

11. if pressure is changed by  p, the melting point will change by  T m

12. Liquid-Gas Equilibrium Slope of pT-curve  always positive  ~ 0.04 atm/K  Boiling point increases by 25 K upon increasing the pressure by 1 atm. Clausius-Clapeyron Equation applies also to s-g equilibrium

14. Benzene has a normal boiling point of 353.25 K. If benzene is to be boiled at 30 o C, to what value must the pressure be lowered.  H vap =30.76 kJ/mol Determine the change in the freezing point of ice upon pressure increase from 1 atm to 2 atm. V m (water)=18.02 cm 3 /mol and V m (ice)=19.63 cm 3 /mol at 273.15 K.  H fus =6.009 kJ/mol.

17. Phase Rule  F: Number of degrees of freedom Number of independent variables that can be changed without changing the number of phases  C: number of independent components  P: number of coexisting phases F=1 F=2 F=1 F=0

19. Liquid-Gas Equilibrium of a binary mixture Ideal solution: Energy of interaction AA,BB = A-B Intramolecular forces AA,BB = A-B Ideal solutions obey Raoults Law

20. L V L V (p A ) solvent > (p A ) solution

21. p-x phase diagram T=const.

22. A+BA+B L V solve for x B L V T const.

23. Ex. Benzene and Toluene Consider a mixture of benzene, C 6 H 6, and toluene, C 7 H 8, containing 1.0 mol benzene and 2.0 mol toluene. At 20 °C, the vapor pressures of the pure substances are: P° benzene = 75 torr P° toluene = 22 torr Assuming the mixture obeys Raoult’s law, what is the total pressure above this solution? 23

24. T-x phase diagram p=const. Lever Rule

25. Distillation p=const.

29. Colligative Properties

31. K f and K b 31

32. Ex. Boiling Point Elevation A 2.00 g sample of a large biomolecule was dissolved in 15.0 g of CCl 4. The boiling point of this solution was determined to be 77.85 °C. Calculate the molar mass of the biomolecule. For CCl 4, the K b = 5.07 °C/m and BP CCl4 = 76.50 °C.

33. Ex. Freezing Point Depression Estimate the freezing point of a permanent type of antifreeze solution made up of 100.0 g ethylene glycol, C 2 H 6 O 2, (MM = 62.07) and 100.0 g H 2 O (MM = 18.02). 33

34. Membranes and Permeability Membranes – Separators – Example: Cell walls – Keep mixtures organized and separated Permeability – Ability to pass substances through membrane Semipermeable Membrane – Some substances pass, others don’t. – Selective

35. Osmosis and Osmotic Pressure A.Initially, Soln B separated from pure water, A, by osmotic membrane (permeable to water). No osmosis occurred yet B.After a while, volume of fluid in tube higher. Osmosis has occurred. 35

36. Flow of water molecules Net flow Column rises Pressure increases Increase of flow from right to left Finally: Equilibrium established Flow of water molecules Net flow = 0 Osmotic pressure (  ): Pressure needed to stop the flow.

37. Equation for Osmotic Pressure Assumes dilute solutions  = i M R T –  = osmotic pressure – i = number of ions per formula unit = 1 for molecules – M = molarity of solution Molality, m, would be better, but M simplifies Especially for dilute solutions, where m  M – T = Kelvin Temperature – R = Ideal Gas constant = 0.082057 L·atm·mol  1 K  1 37

38. Eye drops must be at the same osmotic pressure as the human eye to prevent water from moving into or out of the eye. A commercial eye drop solution is 0.327 M in electrolyte particles. What is the osmotic pressure in the human eye at 25°C?  = MRT T(K) = 25°C + 273.15

39. Using  to determine MM The osmotic pressure of an aqueous solution of certain protein was measured to determine its molar mass. The solution contained 3.50 mg of protein in sufficient H 2 O to form 5.00 mL of solution. The measured osmotic pressure of this solution was 1.54 torr at 25 °C. Calculate the molar mass of the protein.