Physical Chemistry - Phase Diagrams 2024-1.pptx

Physical Chemistry

1. P HYSICAL C HEMISTRY (CHM311) 202 4 Binary Phase Systems Lecturer Prof Fanelwa Ngece - Ajayi Contact Details: Office : 4.25 Chemical Sciences Building Chemistry Department Consultations: By appointments

2. Introduction We encountered one- component phase diagrams previously. The phase equilibria of binary systems are more complex because composition is an additional variable.

3. DEFINITIONS A binary phase diagram shows the phases formed in differing mixtures of two elements over a range of temperatures. Compositions run from 100% Element A on the left of the diagram, through all possible mixtures, to 100% Element B on the right. Partial vapor pressure is the vapor pressure that a single component in a mixture contributes to the total pressure in the system. Partial pressure is the pressure exerted by the individual gas in the mixture of different gases at the same temperature.

4. An ideal solution is a mixture in which the molecules of different species are distinguishable, the molecules exert forces on one another. When those forces are the same for all molecules independent of species then a solution is said to be ideal. Mole fraction is given as the number of moles of a given solute in the solution to the total number of moles in the solution. DEFINITIONS

5. Vapour Pressure Diagrams The partial vapour pressures of the components of an ideal solution of two volatile liquids are related to the composition of the liquid mixture by Raoult’s law pA = xA p*A pB = xB p*B (1) where p*A is the vapour pressure of pure A and p*B that of pure B and x is the mole fraction. The total vapour pressure p of the mixture is therefore p = pA + pB = xA p*A + xB p*B (2) A law stating that the vapor pressure of an ideal solution is proportional to the mole fraction of solvent.

6. FIG URE: 5.29 This expression shows that the total vapour pressure (at some fixed temperature) changes linearly with the composition from p*B to p*A as xA changes from to 1 (Fig. 5.29).

7. (a) The composition of the vapour The compositions of the liquid and vapour that are in mutual equilibrium are not necessarily the same. Common sense suggests that the should be richer in the more vapour volatile component. This expectation can be confirmed as follows;

8. It follows from Dalton’s law that the mole fractions in the gas, yA and yB , are yA = P A /P yB = P B /P (3) (a) The composition of the vapour A law stating that the pressure exerted by a mixture of gases in a fixed volume is equal to the sum of the pressures that would be exerted by each gas alone in the same volume.

9. FIG URE 5.32 The dependence of the total vapour pressure of an ideal solution on the mole fraction of A in the entire system. A point between the two lines corresponds to both liquid and vapour being present; outside that region there is only one phase present. The mole fraction of A is denoted Za .

10. Point a indicates the vapour pressure of a mixture of composition xA . P oint b indicates the composition of the vapour that is in equilibrium with the liquid at that pressure. T he horizontal axis is showing the overall composition, zA, of the system. A ll the points down to the solid diagonal line in the graph correspond to a system that is under such high pressure that it contains only a liquid phase . T he applied pressure is higher than the vapour pressure), so zA = xA, the composition of the liquid . FIGURE 5.32

11. All the points below the lower curve correspond to a system that is under such low pressure that it contains only a vapour phase . T he applied pressure is lower than the vapour pressure), so zA = yA. Points between the two lines correspond to a system in which there are two phases present, one a liquid and the other a vapour. To see this interpretation, consider the effect of lowering the pressure on a liquid mixture of overall composition a in Fig. 5.33. FIGURE 5.32

12. FIG URE 5.33 The changes to the system do not affect the overall composition . T he state of the system moves down the vertical line that passes through a. This vertical line is called an isopleth. U ntil the point a1 is reached, when pressure us p1, the sample is a single phase, the liquid phase.

13. At a 1 the liquid can exist in equilibrium with its vapour. As we have seen, the composition of the vapour phase is given by point a ′ 1 . A line joining two points representing phases in equilibrium is called a tie line. Now consider the effect of lowering the pressure to p 2 , so taking the system to a pressure and overall composition represented by the point a″ 2 . FIGURE 5.33

14. This new pressure is below the vapour pressure of the original liquid, so it vaporizes until the vapour pressure of the remaining liquid falls to p 2 . Now we know that the composition of such a liquid must be a 2 . Moreover, the composition of vapour in equilibrium with the liquid must be given by the point a′ 2 at the other end of the tie line . FIGURE 5.33

15. If the pressure is reduced to p 3 , a similar readjustment in composition takes place, and now the compositions of the liquid and vapour are represented by the points a 3 and a′ 3 , respectively. The latter point corresponds to a system in which the composition of the vapour is the same as the overall composition, so we have to conclude that the amount of liquid present is now virtually zero, but the tiny amount of liquid present has the composition a 3 . A further decrease in pressure takes the system to the point a 4 ; at this stage, only vapour is present and its composition is the same as the initial overall composition of the system (the composition of the original liquid).

16. (c) The lever rule A point in the two- phase region of a phase diagram indicates not only qualitatively that both liquid and vapour are present, but represents quantitatively the relative amounts of each. To find the relative amounts of two phases α and β that are in equilibrium, we measure the distances lα and lβ along the horizontal tie line, and then use the lever rule (Fig. 5.35): nαlα = nβlβ Here nα is the amount of phase α and nβ the amount of phase β.

17. (c) The lever rule In the case illustrated in Fig. 5.35, because lβ ≈ 2lα, the amount of phase α is about twice the amount of phase β.

18. (c) The lever rule In t he lever distances lα r ule , t he and lβ are u sed to find the proportions o f the phases amounts α (such as liquid) and β (for example, vapour) present at equilibrium. The lever rule is so called because a similar rule relates the masses at two ends of a lever to their distances from a pivot ( mαlα = mβlβ for balance).

19. Temperature–composition diagrams To discuss distillation we need a temperature–composition diagram , a phase diagram in which the boundaries show the composition of the phases that are in equilibrium at various temperatures (and a given pressure , typically 1 atm). An example is shown in Fig. 5.36. Note that the liquid phase now lies in the lower part of the diagram.

20. Consider what happens when a liquid of composition a 1 in Fig. 5.36 is heated. It boils when the temperature reaches T 2 . Then the liquid has composition a 2 (the same as a 1 ) and the vapour (which is present only as a trace) has composition a′ 2 . The vapour is richer in the more volatile component A (the component with the lower boiling point). From the location of a 2 , we can state the vapour’s composition at the boiling point, and from the location of the tie line joining a 2 and a′ 2 we can read off the boiling temperature (T 2 ) of the original liquid mixture .

21. In a simple distillation, the vapour is withdrawn and condensed. This technique is used to separate a volatile liquid from a non- volatile solute or solid. In fractional distillation, the boiling and condensation cycle is repeated successively. This technique is used to separate volatile liquids. We can follow the changes that occur by seeing what happens when the first condensate of composition a3 is reheated. The phase diagram shows that this mixture boils at T3 and yields a vapour of composition a′3 , which is even richer in the more volatile component. That vapour is drawn off, and the first drop condenses to a liquid of composition a4.

22. The cycle can then be repeated until in due course almost pure A is obtained in the vapour and pure B remains in the liquid. The efficiency of a fractionating column is expressed in terms of the number of theoretical plates, the number of effective vaporization and condensation steps that are required to achieve a condensate of given composition from a given distillate. Thus, to achieve the degree of separation shown in Fig. 5.37a, the fractionating column must correspond to three theoretical plates. To achieve the same separation for the system shown in Fig. 5.37b, in which the components have more fractionating similar column partial pressures, the must be designed to correspond to five theoretical plates.

23. F IG 5.37 The number of theoretical plates is the number of steps needed to bring about a specified degree of separation of two components in a mixture. The two systems shown correspond to (a) 3, (b) 5 theoretical plates.

24. (b) Azeotropes Although many liquids have temperature– composition phase diagrams resembling the ideal version in Fig. 5.36, in a number of important cases there are marked deviations. A maximum in the phase diagram (Fig. 5.38) may occur when the favourable interactions between A and B molecules reduce the vapour pressure of the mixture below the ideal value: in effect, the A–B interactions stabilize the liquid. In such cases the excess Gibbs energy, G E (Section 5.4), is negative (more favourable to mixing than ideal). Examples of this behaviour include trichloromethane/propanone and nitric acid/water mixtures.

25. (b) Azeotropes Phase diagrams showing a minimum (Fig. 5.39) indicate that the mixture is destabilized relative to the ideal solution, the A–B interactions then being unfavourable. G E For such mixtures is positive (less favourable to mixing than ideal), and there may be contributions from both enthalpy and entropy effects. Examples include dioxane/water and ethanol/water mixtures.

26. F IG 5.38 Consider a liquid of composition a on the right of the maximum in Fig. 5.38. The vapour (at a′2) of the boiling mixture (at a2) is richer in A. If that vapour is removed (and condensed elsewhere), then the remaining liquid will move to a composition that is richer in B, such as that represented by a3, and the vapour in equilibrium with this mixture will have composition a′3. A high- boiling azeotrope. When the liquid of composition a is distilled, the composition of the remaining liquid changes towards b but no further.

27. F IG 5.38 As that vapour is removed, composition of the the boiling liquid shifts to a point such as a4, and the composition of the vapour shifts to a′4 . Hence, as proceeds, evaporation the composition of the remaining liquid shifts towards B as A is drawn off. The boiling point of the liquid rises, and the vapour becomes richer in B.

28. F IG 5.38 When so much A has been evaporated that the liquid has reached the composition b, the vapour has the same composition as the liquid. Evaporation then occurs without change of composition. The mixture is said to form an azeotrope When the azeotropic composition has been reached, distillation cannot separate the two liquids because the condensate has the same composition as the azeotropic liquid. One example of azeotrope formation is hydrochloric acid/water, which is azeotropic at 80 per cent by mass of water and boils unchanged at 108.6°C.

29. F IG 5.39 The system shown in Fig. 5.39 is also azeotropic, but shows its azeotropy in a different way. Suppose we start with a mixture of composition a1, and follow the changes in the composition of the vapour that rises through a fractionating column (essentially a vertical glass tube packed with glass rings to give a large surface area). The mixture boils at a2 to give a vapour of composition a′2. A low-boiling azeotrope. When the mixture at a is fractionally distilled, the vapour in equilibrium in the fractionating column moves towards b and then remains unchanged.

30. This vapour condenses in the column to a liquid of the same composition (now marked a3). That liquid reaches equilibrium with its vapour at a′3, which condenses higher up the tube to give a liquid of the same composition, which we now call a4. The fractionation therefore shifts the vapour towards the azeotropic composition at b, but not beyond, and the azeotropic vapour emerges from the top of the column. An example is ethanol/water, which boils unchanged when the water content is 4 per cent by mass and the temperature is 78°C.

31. Liquid- Liquid Phase diagrams Phase separation of partially miscible liquids may occur when the temperature is below the upper critical solution temperature or above the lower critical solution temperature; the process may be discussed in terms of the model of a regular solution. The upper critical solution temperature is the highest temperature at which phase separation occurs. temperature below which components mix in The lower critical solution temperature is the all proportions and above which they form two phases. The outcome of a distillation of a low- boiling azeotrope depends on whether the liquids become fully miscible before they boil or boiling occurs before mixing is complete.

32. Now we consider temperature– composition diagrams for systems that consist of pairs of partially miscible liquids, which are liquids that do not mix in all proportions at all temperatures. An example is hexane and nitrobenzene. The same principles of interpretation apply as to liquid–vapour diagrams. Liquid- Liquid Phase diagrams

33. Liquid- Liquid Phase diagrams Fig. 5.41 The temperature–composition diagram for hexane and nitrobenzene at 1 atm. The region below the curve corresponds to the compositions and temperatures at which the liquids are partially miscible. The upper critical temperature, Tuc, is the temperature above which the two liquids are miscible in all proportions.

34. (a) Phase separation Suppose a small amount of a liquid B is added to a sample of another liquid A at a temperature T′. Liquid B dissolves completely, and the binary system remains a single phase. As more B is added, a stage comes at which no more dissolves. The sample now consists of two phases in equilibrium with each other, the most abundant one consisting of A saturated with B, the minor one a trace of B saturated with A .

35. (a) Phase separation In the temperature–composition diagram drawn in Fig. 5.41, the composition of the former is represented by the point a′ and that of the latter by the point a″. The relative abundances of the two phases are given by the lever rule. When more B is added, A dissolves in it slightly. The compositions of phases in equilibrium and a″. the two remain a′ A stage is reached when so much B is present that it can dissolve all the A, and the system reverts to a single phase. The addition of more B now simply dilutes the solution, and from then on a single phase remains.

36. (a) Phase separation The composition of the two phases at equilibrium varies with the temperature. For hexane and nitrobenzene, raising the temperature increases their miscibility. The two- phase region therefore covers a narrower range of composition because each phase in equilibrium is richer in its minor component: the A- rich phase is richer in B and the B- rich phase is richer in A. We can construct the entire phase diagram by repeating the observations at different temperatures and drawing the envelope of the two- phase region.

37. (b) Critical solution temperatures The upper critical solution temperature, Tuc (or upper consolute temperature), is the which highest phase temperature at separation occurs. Above the upper critical temperature the two components are fully miscible. This temperature exists because the greater thermal motion overcomes any potential energy advantage in molecules of one type being close together. One example is the nitrobenzene/hexane system shown in Fig. 5.41. An example of a solid solution is the palladium/hydrogen system, which shows two phases, one a solid solution hydrogen in palladium and the other a palladium hydride, up to 300°C but forms a single phase at higher temperatures (Fig. 5.43). Fig. 5.43 The phase diagram for palladium of and palladium hydride, which has an upper critical temperature at 300°C.

38. (b) Critical solution temperatures Some systems show a lower critical solution temperature, Tlc (or lower consolute temperature), below which they mix in all proportions and above which they form two phases. An example is water and triethylamine (Fig. 5.46). In this case, at low temperatures the two components are more miscible because they form a weak complex; at higher temperatures the complexes break up and the two components are less miscible. Fig. 5.46 The temperature–composition diagram for water and triethylamine. This system shows a lower critical temperature at 292 K. The labels indicate the interpretation of the boundaries.

39. (b) Critical solution temperatures Some systems have both upper and lower critical solution temperatures. They occur because, after the weak complexes have been disrupted, leading to partial miscibility, the thermal motion at higher temperatures homogenizes the mixture again, just as in the case of ordinary partially miscible liquids. The most famous example is nicotine and water, which are partially miscible between 61°C and 210 °C (Fig. 5.47). Fig. 5.47 The temperature–composition diagram for water and nicotine, which has both upper and lower critical temperatures. Note the high temperatures for the liquid (especially the water): the diagram corresponds to a sample under pressure.

40. (c) The distillation of partially miscible LIQUIDS Consider a pair of liquids that are partially miscible and form a low- boiling azeotrope. This combination is quite common because both properties reflect the tendency of the two kinds of molecule to avoid each other. There are two possibilities: one in which the liquids become fully miscible before they boil; the other in which boiling occurs before mixing is complete.

41. (c) The distillation of partially MISCIBLE LIQUIDS phase diagram for Figure 5.48 shows the two components that become fully miscible before they boil. Distillation of a mixture of composition a1 leads to a vapour of composition b1, which condenses to the miscible solution at completely single-phase b2. Phase separation occurs only when this distillate is cooled to a point in the two- phase liquid region, such as b3. Fig. 5.48 The temperature–composition diagram for a binary system in which the upper critical temperature is less than the boiling point at all compositions. The mixture forms a low- boiling azeotrope.

42. (c) The distillation of partially miscible liquids This description applies only to the first drop of distillate. If distillation continues, the composition of the remaining liquid changes. whole sample evaporated In the end, when the has and condensed, the composition is back to a1.

43. (c) The distillation of partially miscible liquids Figure 5.49 shows the second possibility, in which there is no upper solution critical temperature. The distillate obtained from a liquid initially of composition a1 has composition b3 and is a two- phase mixture. One phase has composition b′3 and the other has composition b3″. Fig. 5.49 The temperature–composition diagram for a binary system in which boiling occurs before the two liquids are fully miscible.

44. (c) The distillation of partially miscible liquids The behaviour of a system of composition represented by the isopleth e in Fig. 5.49 is interesting. A system at e1 forms two phases, which persist (but with changing proportions) up to the boiling point at e2. The vapour of this mixture has the same composition as the liquid (the liquid is an azeotrope). Similarly, condensing a vapour of composition e3 gives a two-phase liquid of the same overall composition. At a fixed temperature, the mixture vaporizes and condenses like a single substance.

45. Liquid–solid phase diagrams Knowledge of the temperature–composition diagrams for solid mixtures guides the design of manufacture of liquid crystal displays important industrial processes, such as the and semiconductors. In this section, we shall consider systems where solid and liquid phases may both be present at temperatures below the boiling point. Consider the two- component liquid of composition a1 in Fig. 5.51. The changes that occur as the system is cooled may be expressed as follows .

46. Eutectics 1. a1→a2. enters the The system two- phase region labelled ‘Liquid + B’. Pure solid B begins to come out of solution and the remaining liquid becomes richer in A. 2. a2 → a3. More of the solid B forms, and the relative amounts of the solid and liquid (which are in equilibrium) are given by the lever rule. At this stage there are roughly equal amounts of each.

47. F IG 5.51 The liquid phase is richer in A than before (its composition is given by b3) because some B has been deposited. 3. a3→a4. At the end of this step, there is less liquid than at a3, and its composition is given by e2. This freezes to liquid now give a two- phase system of pure B and pure A.

48. to the The isopleth at e2 in Fig. 5.51 corresponds eutectic composition, the mixture with the lowest melting point.3 A liquid with the eutectic composition freezes at a single temperature, without previously depositing solid A or B. A solid with the composition melts, eutectic without of composition, at the temperature of any change lowest mixture. Solutions of composition to the right of e2 deposit B as they cool, and solutions to the left deposit A: only the eutectic mixture (apart from pure A or pure B) solidifies at a single definite temperature without gradually unloading one or other of the components from the liquid.

49. F IG 5.52 Thermal analysis is a very useful practical way of detecting eutectics. We can see how it is used by considering the rate of cooling down the isopleth through a1 in Fig. 5.51. The liquid cools steadily until it reaches a2, when B begins to be deposited (Fig. 5.52). Cooling is now slower because the solidification of B is exothermic and retards the cooling.

50. When the remaining liquid reaches the eutectic composition, the temperature remains constant until the whole sample has solidified: this region of constant temperature is the eutectic halt. If the liquid has the eutectic composition e initially, the liquid cools steadily down to the freezing temperature of the eutectic, when there is a long eutectic halt as the entire sample solidifies (like the freezing of a pure liquid). Monitoring the cooling curves at different overall compositions gives a clear indication of the structure of the phase diagram. The solid–liquid boundary is given by the points at which the rate of cooling changes. The longest eutectic halt gives the location of the eutectic composition and its melting temperature .