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Phase Equilibria

Phase Equilibria. Evaporation-Condensation. Melting-Freezing. Sublimation-Condensation. Phase transition. S g >> S l > S s. The most stable phase is that with lowest chemical potential. Pressure Effect.

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Phase Equilibria

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

  2. Sg >> Sl > Ss The most stable phase is that with lowest chemical potential.

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

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

  5. Phase Diagram

  6. CO2

  7. Clapeyron Equation At Equilibrium Clapeyron Equation

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

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

  10. if pressure is changed by Dp, the melting point will change by DTm

  11. 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

  12. Determine the change in the freezing point of ice upon pressure increase from 1 atm to 2 atm. Vm(water)=18.02 cm3/mol and Vm(ice)=19.63 cm3/mol at 273.15 K. DHfus=6.009 kJ/mol. Benzene has a normal boiling point of 353.25 K. If benzene is to be boiled at 30oC, to what value must the pressure be lowered. DHvap=30.76 kJ/mol

  13. 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=0 F=1

  14. 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

  15. V V L L (pA)solvent > (pA)solution

  16. p-x phase diagram T=const.

  17. V L T const. A+B L V solve for xB

  18. Ex. Benzene and Toluene • Consider a mixture of benzene, C6H6, and toluene, C7H8, containing 1.0 mol benzene and 2.0 mol toluene. At 20 °C, the vapor pressures of the pure substances are:P°benzene = 75 torrP°toluene = 22 torr • Assuming the mixture obeys Raoult’s law, what is the total pressure above this solution?

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

  20. Distillation p=const.

  21. Colligative Properties

  22. Colligative Properties

  23. Kf and Kb

  24. Ex. Boiling Point Elevation A 2.00 g sample of a large biomolecule was dissolved in 15.0 g of CCl4. The boiling point of this solution was determined to be 77.85 °C. Calculate the molar mass of the biomolecule. For CCl4, the Kb = 5.07 °C/m and BPCCl4 = 76.50 °C.

  25. Ex. Freezing Point Depression Estimate the freezing point of a permanent type of antifreeze solution made up of 100.0 g ethylene glycol, C2H6O2, (MM = 62.07) and 100.0 g H2O (MM = 18.02).

  26. 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

  27. 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.

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

  29. Equation for Osmotic Pressure • Assumes dilute solutions p = i M R T • p = 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1K1

  30. 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? T(K)= 25°C + 273.15 p= MRT

  31. Using p 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 H2O 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.

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