1. Ideal and Dilute Solutions 2/21/2016

2. Master Thermodynamics Equations

5. Chemical Potential Diffusion from high to low potential. Chemical potential is a Partial Molar Quantity Sum of moles of components

6. Chemical Potential of a Binary (A & B) Mixture Chem. Potential applied to other variables:

7. Measures of Composition s = solute ; A = solvent; V = Tot. Vol. of solution. Weight %: Mole Fraction: Molarity: Molality: Different Composition Equations for different Laws

8. Other Partial Molar Quantities Partial Molar Volume: Partial Molar Enthalpy: Partial Molar Entropy:

9. Calculation for Partial Molar Volumes V = f(n A, n B ) @ constant P & T Integrate @ constant composition

11. Calculation for Partial Molar Volumes: 100 mL EtOH and 100 mL H 2 O EtOH (A): d = 0.785 g/mLM = 46.1 g/mol Water (B): d = 0.997 g/mLM = 18.0 g/mol Calculate moles of each component: Calculate mole fraction of A and use previous Partial Molar Volume curves to get partial molar volumes for both ethanol and water. Calculate Total Volume:

12. Raoult’s Law & Ideal Solutions Vapor Pressure (VP)  P i (escaping tendency   g) Gas Ideality => No Intermolecular forces Solution Ideality => Uniformity in Intermolecular forces. (Binary: A-A, B-B, A-B all the same) Dalton’s Law

15. Raoult’s Law & Ideal Solutions

16. Thermodynamics of Mixing for an Ideal Solution

17. TD’s of Mixing for an Ideal Binary (A-B) Solution See Mathcad plot

19. Finding Minimum of ΔG mix curve

21. Henry’s Law (Solubility of gases in liquids) In dilution solutions, each solute is surrounded by solvent molecules (uniform environment, relatively ‘ideal.’) Positive and Negative deviations from Raoult’s Law Endothermic Mixing versus Exothermic Mixing

24. Phase Diagrams

25. The Phase Diagrams of H 2 O and CO 2 Phase Diagrams

26. Phase Diagrams for Multi-components For 2 components: Need 3 variables ( T, P, composition ) P T Most common plots: VP vs.  @ constant T B. pt. vs.  @ constant P

27. Phase Diagrams for Multi-components Liquidus Curve: Vapour Curve:

29. Phase Diagrams for Multi-components Excel Vap-line

31. Boiling-Point Elevation Molal boiling-point-elevation constant, K b, expresses how much  T b changes with molality, m S : Decrease in freezing point (  T f ) is directly proportional to molality (K f is the molal freezing-point-depression constant): Colligative Properties

32. Figure 13.22

33. Solubility ( Conc’n vs. T ) Derivation starting with equilibrium thermodynamics, At equilibrium (constant P & T):

34. Freezing Point Depression ( T vs. conc’n ) K f = molal freezing point constant, all properties of the solvent A [ units = K kg mol -1 ] Similar equation for  T b

35. Osmosis movement of a solvent from low solute concentration to high solute concentration across a semipermeable membrane. Colligative Properties Figure 13.23

36. Osmosis Osmotic pressure, , is the pressure required to stop osmosis: Colligative Properties

37. Application to Polymeric Solutions

38. Ideal and Dilute Solutions