CHEM 212

1. CHEM 212 Chapter 5 Phases and Solutions Dr. A. Al-Saadi

2. Things to be Covered in This Chapter • Substances can exist in more than one phase. • Introduction to phases, phase recognitions and equilibrium between phases. • Clapeyron equation and Clausius-Clapeyron equation for phase changes. • Trouton’s Rule (relationship between enthlapy and entropy of vaporization). • Gibbs equation (variation of vapor pressure with external pressure). • First-order and second-order phase transitions. • Raoult’s and Henry’s Laws for ideal solutions. • Gibbs-Duhem equation (relationship between volumes and concentrations). • The chemical potential. • Thermodynamics of solutions. • The colligative properties.

3. Homogeneous and Heterogeneous Phases • Phase can be defined as a state of aggregation. • Homogeneous phase is uniform throughout in its chemical composition and physical state. (no distinction or boundaries) • Water, ice, water vapor, sugar dissolved in water, gases in general, etc. • Heterogeneous phase is composed of more than one phase These phases are distinguished from each other by boundaries. • A cube of ice in water. (same chemical compositions but different physical states) • Oil-water mixture. • The two phases are said to be coexistent.

4. Phase Distinctions in the Water Systems • Phase diagram shows the phase equilibria with respect to pressure and temperature. • Pure states. • Coexistence of two phases at equilibrium. • Metastable state “not the thermodynamically most stable state”. • Water phase diagram is not that representative because of the –ve slope.

5. Phase Distinctions in the Water Systems • Polymorphism takes place at an extremely high pressure (order of 2000 bar) at which different crystalline forms of ice may exist. • Triple point: is where all the three phases coexist. It is also known as the invariant point.

6. Phase of Liquid Crystals • Liquid crystal is an intermediate phase between solid and liquid and has some properties of both phases. • Mesogens are the building units of liquid crystals. They are long, cylinder-shaped in their structure and fairly rigid. • The liquid-like properties come from the fact that they can flow easily one past another. • The solid-like properties come from the fact that during flow they don’t disturb their structure.

7. Phase of Liquid Crystals

8. Phase of Liquid Crystals Texture of LC in the nematic phase when is put under microscope. It shows the optical properties of such a phase.

9. Phase Equilibria of One-Component System, Water as an Example

10. Phase Equilibria of One-Component System, Water as an Example

11. Phase Equilibria of One-Component System, Water as an Example Compare slopes. Points of intersection of the curves of the three phases. iGm for pure phases. Example 5.1 Entropy of the three phases.

12. Phase Equilibria of One-Component System, Water as an Example Heat capacity dependence. Effect of decrease of pressure. Effect of increase of pressure. Triple point. Sublimation Interesting mathematics link: http://www-rohan.sdsu.edu/~jmahaffy/courses/s00a/math121/lectures/graph_deriv/diffgraph.html

13. Effect of Pressure Decrease

14. Phase Equilibria of One-Component System, Water as an Example Heat capacity dependence. Effect of decrease of pressure. Effect of increase of pressure. Triple point. Sublimation Interesting mathematics link: http://www-rohan.sdsu.edu/~jmahaffy/courses/s00a/math121/lectures/graph_deriv/diffgraph.html

15. Thermodynamics of Vapor Pressure • Two phases of a pure substance can coexist if ΔG = 0 at a given T and P. • If we are at one of the phase-equilibrium lines and either P or T has been varied, one phase will disappear, and ΔG ≠ 0. • How can we maintain the equilibrium while P or T is changing.

16. Clapeyron Equation

17. Clausius-Clapeyron Equation

18. Clausius-Clapeyron Equation

19. Trouton’s Rule

20. Trouton’s Rule

21. Trouton’s Rule

22. The Vapor Pressure of a Liquid Vapor pressureis the pressure of a vapor in equilibrium with its non-vapor phases. All liquids and solids have a tendency to evaporate (escape) to a gaseous form, and all gases have a tendency to condense back into their original form (either liquid or solid). At any given temperature, for a particular substance, there is a pressure at which the gas of that substance is in dynamic equilibrium with its liquid or solid forms. This is the vapor pressure of that substance at that temperature. Vapor pressure Liquid or solid

23. The Vapor Pressure of a Liquid Vapor pressureis the pressure of a vapor in equilibrium with its non-vapor phases. All liquids and solids have a tendency to evaporate (escape) to a gaseous form, and all gases have a tendency to condense back into their original form (either liquid or solid). At any given temperature, for a particular substance, there is a pressure at which the gas of that substance is in dynamic equilibrium with its liquid or solid forms. This is the vapor pressure of that substance at that temperature.

24. The Vapor Pressure of a Liquid Vapor pressure Increasing T Liquid or solid

25. Effect of Nonvolatile Solutes on Vapor Pressure

26. Effect of External Pressure on Vapor Pressure External pressure may be applied either by: • compressing the condensed phase, or by • mixing the vapor with inert gas. In both cases the vapor pressure of the condensed phase increases.

27. Effect of External Pressure on Vapor Pressure

28. First-Order and Second-Order Phase Transitions

29. Lambda () Phase Transitions

30. Ideal Solutions • A Solutionis any homogeneous phase that contains more than one component. These components can’t be physically differentiated. • A Solventis the component with the larger proportion or quantity in the solution. A Soluteis the component with the smaller proportion or quantity in the solution. • The idea of Ideal Solutions is used to simplify the study of the phase equilibrium for solution. The solution is considered to be ideal when: • its components are assumed to have similar structures and sizes, and when • it represents complete uniformity of molecular forces (basically attraction forces).

31. Ideal Solutions When considering a binary system, we are often interested to study the behavior of that system in terms of the variables P, T and n.

32. Raoult’s Law Recall that the vapor pressure is a measure of the tendency of the substance to escape from the liquid. For an ideal solution composed of two components (binary systems) , Raoult’s law relates between the vapor pressure of each component in its pure state (P*) to the partial vapor pressure of that component when it is in the ideal solution (P).

33. Raoult’s Law To know what partial vapor pressure a component in a solution has is important. This is because it gives you information about the cohesive forces in the system.

34. Raoult’s Law • If the solution has partial vapor pressures that follow: then the system is said to obey Raoult’s law and to be ideal, taken into consideration T is fixed for the solvent and solution. • Examples include: • Benzene – toluene. • C2H5Cl – C2H5Br. • CHCl3 – HClC=CCl2.

35. Application of Raoult’s Law Problem 5.21: Benzene and toluene form nearly ideal solutions. If at 300 K, P*(toluene) = 3.572 kPa and P*(benzene) = 9.657 kPa, compute the vapor pressure of a solution containing 0.60 mole fraction of toluene. What is the mole fraction of toluene in the vapor over this liquid?

36. Deviations from Raoult’s Law Deviations from Raoult’s law occur for nonideal solutions. Consider a binary system made of A and B molecules. • Positive deviationoccurs when the attraction forces between A-A and B-B pairs are stronger than between A-B. As a result, both A and B will have more tendency to escape to the vapor phase. • Examples: • CCl4 – C2H5OH system. • n-C6H14 – C2H5OH system

37. Deviations from Raoult’s Law For a binary system made of A and B molecules. • Negative deviationoccurs when the attraction force between A-B pairs is stronger than between A-A and B-B pairs. As a result, both A and B will have less tendency to escape to the vapor phase. • Examples: • CCl4 – CH3CHO system. • H2O – CH3CHO system

38. Deviations from Raoult’s Law Another important observation is that at the limits of infinite dilution, the vapor pressure of the solvent obeys Raoult’s law.

39. Henry’s Law • The mass of a gas (m2) dissolved by a given volume of solvent at constant T is proportional to the pressure of the gas (P2) above and in equilibrium with the solution. m2 = k2 P2 where k2 is the Henry’s law constant.

40. Henry’s Law • For a mixture of gases dissolved in a solution. Henry’s law can be applied for each gas independently. • The more commonly used forms of Henry’s law are: P2 = k’ x2 P2 = k” c2

41. Henry’s Law • The vapor pressure of a solute, P2, in a solution in which the solute has a mole fraction of x2 is given by: P2 = x2 P2* where P2* is the vapor pressure of the solute in a pure liquefied state. • It is also found that at the limits of infinite dilution, the vapor pressure of the solute obeys Henry’s law.

42. Application of Henry’s Law

43. Partial Molar Quantities • The method using partial molar quantities enables us to treat nonideal solutions. In this method we consider the changes in the properties of the system as its compositions change by adding or subtracting. • The thermodynamic quantities, such as U, H, and G, are extensive functions, i.e. they depend on the amounts of the components in the system. Also they depend on the P and T. For example, G = G(P, T, n1, n2, n3, …).

44. water V = Vw Partial Molar Volume • In this treatment, the volume is used as starting point to lead to the thermodynamic functions in terms of partial molar quantities. • The volume occupied by H2O molecules added is dependent on the nature of surrounding molecules. V*(H2O) = 18 mL Vtot = Vw + 18 mL Vtot = Vw + 14 mL ethanol V = Veth

45. Partial Molar Quantities • Partial molar volume is defined as:

46. Partial Molar Quantities

47. Partial Molar Volumes Exercise: The partial molar volumes of acetone and chloroform in a solution mixture in which mole fraction of chloroform is 0.4693 are 74.166 cm3/mol and 80.235 cm3/mol, respectively. What is the volume of a solution of a mass 1.000 kg?

48. Chemical Potential • The chemical potential (μi) of a thermodynamic system is the amount by which the energy of the system would change if an additional particle (dni) were introduced. • If a system contains more than one species of particles, there is a separate chemical potential associated with each species (μi , μj , …).

49. Chemical Potential • The chemical potential (μi) of a thermodynamic system is the amount by which the energy of the system would change if an additional particle (dni) were introduced. • If a system contains more than one species of particles, there is a separate chemical potential associated with each species (μi , μj , …).

50. Chemical Potential In spontaneous processes at constant T and P, system moves towards a state of minimum Gibbs energy. (dG < 0) In the condition of equilibrium at constant T and P, there is no change in Gibbs energy (dG = 0)