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

2 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. Things to be Covered in This Chapter

3  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. Homogeneous and Heterogeneous Phases

4  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. Phase Distinctions in the Water Systems

5  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 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 1. Compare slopes. 2. Points of intersection of the curves of the three phases. 3. iG m for pure phases. Example Entropy of the three phases.

12 Phase Equilibria of One-Component System, Water as an Example Interesting mathematics link: 5. Heat capacity dependence. 6. Effect of decrease of pressure. 7. Effect of increase of pressure. 8. Triple point. 9. Sublimation

13 Effect of Pressure Decrease

14 Phase Equilibria of One-Component System, Water as an Example Interesting mathematics link: 5. Heat capacity dependence. 6. Effect of decrease of pressure. 7. Effect of increase of pressure. 8. Triple point. 9. Sublimation

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 pressure is 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 pressure is 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 Liquid or solid Increasing T

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 Solution is any homogeneous phase that contains more than one component. These components can’t be physically differentiated.  A Solvent is the component with the larger proportion or quantity in the solution. A Solute is 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.  C 2 H 5 Cl – C 2 H 5 Br.  CHCl 3 – HClC=CCl 2.

35 Application of Raoult’s Law Problem 5.21: Benzene and toluene form nearly ideal solutions. If at 300 K, P*(toluene) = kPa and P*(benzene) = 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 deviation occurs 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:  CCl 4 – C 2 H 5 OH system.  n-C 6 H 14 – C 2 H 5 OH system

37 Deviations from Raoult’s Law For a binary system made of A and B molecules.  Negative deviation occurs 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:  CCl 4 – CH 3 CHO system.  H 2 O – CH 3 CHO 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 (m 2 ) dissolved by a given volume of solvent at constant T is proportional to the pressure of the gas (P 2 ) above and in equilibrium with the solution. m 2 = k 2 P 2 where k 2 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: P 2 = k’ x 2 P 2 = k” c 2

41 Henry’s Law  The vapor pressure of a solute, P 2, in a solution in which the solute has a mole fraction of x 2 is given by: P 2 = x 2 P 2 * where P 2 * 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, n 1, n 2, n 3, …).

44  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 H 2 O molecules added is dependent on the nature of surrounding molecules. Partial Molar Volume water V = V w ethanol V = V eth V*(H 2 O) = 18 mL V tot = V w + 18 mLV tot = V w + 14 mL

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 are cm 3 /mol and cm 3 /mol, respectively. What is the volume of a solution of a mass kg?

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

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

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)

51 Chemical Potential dG = (μ i β – μ i α ) dn i In a spontaneous processes, dG < 0 at constant T and P. dn i moves from phase α to phase β to have negative change in free energy. The spontaneous transfer of a substance takes place from a region with a higher μ i to a lower μ i. The process continues to equilibrium where dG = 0, and μ i and μ i become equal. Phase β Phase α

52 Chemical Potential dG is negative Phase β Phase α Phase γ dG = 0 Phase β Phase α Phase γ dn i α dn j α dn i β dn j β dn i γ dn j γ

53 Thermodynamic of an Ideal Solution

54 Colligative Properties

55 Colligative Properties

56 Colligative Properties

57 Colligative Properties

58 Colligative Properties

59 Colligative Properties

60 Colligative Properties

61 Colligative Properties

62 Colligative Properties