Multiple-Phase Systems

1. Multiple-PhaseSystems Ch E 201Material and Energy Balances

2. Phase-change Operations phase-change operations employed on mixtures to separate components or purify a product phase-change phenomena and operations freezing melting evaporation condensation leaching distillation adsorption/scrubbing crystallization

3. Phase Equilibrium When a species transfers from one phase to another, the rate of transfer generally decreases with time until the second phase is saturated with the species, holding as much as it can hold at the prevailing process conditions. When concentrations of all species in each phase cease to change, the phases are said to be at phase equilibrium.

4. Phase Diagrams At most temperatures/pressures, a pure substance exists in a single phase: solid, liquid, or gas. At some conditions, two or three phases may coexist. A phase diagram of a pure substance is a plot system variables that shows the conditions at which the substance exists in various phases.

5. Phase Diagrams

6. Phase Diagrams vapor pressure of pure substance at T boiling point temperature normal boiling point melting/freezing point at P sublimation point T at P triple point critical temperature critical pressure

7. Vapor Pressure The volatility of a species is the degree to which the species tends to transfer from the liquid phase to the vapor phase. The vapor pressure of a species is a measure of its volatility. Estimation of vapor pressure can be performed by empirical correlation p*(T). Reid, Prausnitz, and Poling summarize such methods.

8. Vapor Pressure Estimation Clapeyron Equation relates p* to T at reasonable pressures, Vg >> Vl and Vg = RT/p* Therefore, one can plot ln(p*) vs 1/T to obtain a straight line with a slope that permits determination of the latent heat of vaporization.

9. Vapor Pressure Estimation If the latent heat of vaporization is assumed to be independent of temperature in the range of temperature for which p* is available, the Clapeyron can be reduced to the Clausius-Clapeyron equation, where B is a constant unique to each substance. A plot of ln p* vs. 1/T should be a straight line with slope and intercept as seen.

10. Vapor Pressure Estimation Antoine Equation where A, B, and C are empirical constants unique to each compound.

11. Phase Equilibrium When two phases are brought into contact, a redistribution of the components of each phase occurs through evaporation, condensation, dissolution, and/or precipitation until a state of equilibrium is reached in which the temperatures and pressures of both phases are the same, and the compositions of each phase no longer change with time.

12. Gibbs Phase Rule Intensive variables do not depend upon the size of the system; extensive variables are size dependent. intensive variables temperature pressure density specific volume mass/mole fraction extensive variables mass volume

13. Gibbs Phase Rule The number of intensive variables that can be specified independently for a system at equilibrium in which no chemical reactions are occuring is called the degree of freedom (DF) of the system, and is related to the number of components (c) and the number of phases (?) present in the system. If r independent reactions occur,

14. Application of Gibbs Phase Rule Consider pure liquid water 2 intensive variables may be specified, after which other intensive variables may be determined.

15. Application of Gibbs Phase Rule Consider the triple point of water no intensive variables may be specified, all intensive variables are fixed by the given information.

16. Application of Gibbs Phase Rule Consider a 2-phase liq/vapor system of water 1 intensive variable may be specified.

17. Application of Gibbs Phase Rule Consider a vapor/liquid mixture of acetone and methyl ethyl ketone 2 intensive variables may be specified.

18. Gas-Liquid Systems: 1 condensable Systems of multiple components of which only 1 may condense at process conditions are common. evaporation, drying, humidification involve the transfer of a species from the liquid to the gas phase. condensation, dehumidification involve the transfer of a species from the gas to the liquid phase.

19. Gas-Liquid Systems: 1 condensable Consider a container of dry air into which water is introduced. Water evaporates into the air, resulting in an increase in yH2O and pH2O in the gas phase. Evaporation continues until the air is a saturated vapor (i.e., can hold no additional water) at T and P of the system. From Gibbs Phase Rule,it follows that only two ofT, P, and yH2O can be independently specified.

20. Gas-Liquid Systems: 1 condensable If a gas at T and P contains a saturated vapor at concentration yi, and if this vapor is the only species that would condense if the temperature were slightly lowered, then the partial pressure of the vapor in the gas equals the pure component vapor pressure pi*(T) at the system T. Raoult�s Law (limiting case fora single condensable species)

21. Use of Raoult�s law Air and water are contained at equilibrium in a closed container at 75�C and 760 mm Hg. Calculate the molar composition of the gas phase. Gas/liq are in equilibrium, so air must be saturated with water vapor. Thus, Raoult�s law may be used.

22. Things to consider A gas in equilibrium with a liquid must be saturated with the volatile components of the liquid. The partial pressure of a vapor at equilibrium in a gas mixture containing a single condensable component cannot exceed the vapor pressure of the pure component at the system temperature. If pi = pi*, the vapor is saturated. Any attempt to increase pi will result in condensation occurring.

23. Superheated Vapor A vapor present in a gas in less than its saturation amount is referred to as a superheated vapor. For such a vapor, pi = yiP < pi*(T). If a gas containing a single superheated vapor is cooled at constant P, the temperature at which the vapor becomes saturated is referred to as the dew point. From Raoult�s law, pi = yiP = pi*(Tdp). Difference (T � Tdp) is called degrees of superheat.

24. Condenser Material Balances From given, calculate dew point and degrees of superheat of the air; % of vapor that condenses and the final composition of the gas phase if the air is cooled to 80�C at constant P; % condensation and final gas-phase composition if the air is instead compressed isothermally to 8500 mm Hg.

25. Condenser Material Balances

26. Condenser Material Balances From given, calculate dew point and degrees of superheat of the air; % of vapor that condenses and the final composition of the gas phase if the air is cooled to 80�C at constant P; % condensation and final gas-phase composition if the air is instead compressed isothermally to 8500 mm Hg.

27. Condenser Material Balances

28. Condenser Material Balances nDF = 3 unknowns (n1, n2, y) � 2 independent species balances � 1 saturation condition (Raoult�s law) = 0

29. Condenser Material Balances Raoult�s law dry air balance total mole balance

30. Condenser Material Balances From given, calculate dew point and degrees of superheat of the air; % of vapor that condenses and the final composition of the gas phase if the air is cooled to 80�C at constant P; % condensation and final gas-phase composition if the air is instead compressed isothermally to 8500 mm Hg.

31. Condenser Material Balances Initially, Saturation occurs when P becomes sufficiently large that this relation becomes an equality.

32. Condenser Material Balances Raoult�s law at process conditions

33. Condenser Material Balances Raoult�s law atprocess conditions dry airbalance total molebalance

34. Other means of expressing saturation relative saturation (relative humidity) molal saturation(molal humidity) absolute saturation(absolute humidity) percent saturation(percent humidity) see Example 6.3-3

35. Multicomponent Gas-Liquid Systems Many processes by which the various components of a system are seperated typically involves equilibrium of gas and liquid phases. Evaluation of multiple-component gas-liquid systems requires the use of vapor-liquid equilibrium data (i.e., equilibrium compositions of the various components in each phase).

36. Multicomponent Gas-Liquid Systems A gas stream consisting of 100 lb-mol/h of an SO2-air mixture containing 45 mol% SO2 is contacted with liquid water in a continous absorber at 30�C, 1 atm to produce a liquid containing 2 mass% SO2. Calculate the fraction of the entering SO2 absorbed in the water and the required water feed rate.

37. Multicomponent Gas-Liquid Systems Look up vapor pressures of H2O and SO2 over SO2 solution of indicated composition. Calculate vapor composition: ndf = 3 unknowns � 3 ind. species balances = 0

38. Multicomponent Gas-Liquid Systems air balance: effluent liquid compostion

39. Multicomponent Gas-Liquid Systems SO2 balance:

40. Multicomponent Gas-Liquid Systems H2O balance:

41. Multicomponent Gas-Liquid Systems SO2 absorbed: SO2 fed: fraction SO2 absorbed = 1756/2880 = 0.610

42. Phase-equilibrium Thermodynamics Phase-equilibrium thermodynamics deals with the relationships that govern the distribution of a substance between gas and liquid phases. In Ch E 201, we will cover some of the simple relationships that provide reasonably accurate predictions over a wide range of conditions. These relations form the bases of more precise methods to be learned in thermodynamics courses.

43. Gas-Liquid Equilibria Raoult�s Law approximation generally valid when xA~1 (i.e., liquid nearly pure A) or when the components are similar in structure. Henry�s Law approximation generally valid when xA~0 (dilute solution of A) provided A does not dissociate, ionize, or react in the liquid phase. In an ideal solution, the gas-liquid behavior of every volatile component can be described by Raoult�s or Henry�s Law.

44. Use of Henry�s Law A gas containing 1.00 mol% of ethane is contacted with water at 20.0�C and 20.0 atm. Estimate the mole fraction of dissolved ethane. hydrocarbons are relatively insoluble in water, so the solution of ethane is likely to be very dilute. We should therefore assume Henry�s law applies, and look up a Henry�s constant for ethane in water.

45. Use of Raoult�s Law An equimolar liquid mixture of benzene and toluene is in equilibrium with its vapor at 30.0�C. What is the system pressure and the composition of the vapor? structurally similar, thus assume Raoult�s law applies.

46. VLE of Ideal Solutions If heat is added to a mixture of components, liquid temperature rises until a bubble of vapor is formed. In most cases, the composition of this vapor bubble differs from that of the liquid from which it formed. As vaporization proceeds, the composition of the remaining liquid continously changes, and hence so does its vaporization temperature. An analogous process occurs when condensing a vapor comprised of a number of components.

47. VLE of Ideal Solutions When a liquid is heated slowly at constant pressure, the temperature at which the first vapor bubble forms is called the bubble-point temperature. When a vapor is colled slowly at constant pressure, the temperature at which the first liquid droplet forms is the dew-point temperature. For mixtures that behave as ideal solutions (Raoult�s and Henry�s laws apply), and the gas phase can be considered ideal, calculation of these temperatures is relatively simple.

48. Graphical Representation of VLE

49. Bubble-Point Calculation Calculate the temperature and composition of a vapor in equilibrium with a liquid that is 40.0 mol% benzene and 60.0 mol% toluene at 1 atm. total system pressure can be related to the vapor pressures of each species using Raoult�s law identify Tbp that makes this equality true

50. Bubble-Point Calculation Calculate the temperature and composition of a vapor in equilibrium with a liquid that is 40.0 mol% benzene and 60.0 mol% toluene at 1 atm.

51. Bubble-Point Calculation Calculate the temperature and composition of a vapor in equilibrium with a liquid that is 40.0 mol% benzene and 60.0 mol% toluene at 1 atm.

52. Dew-Point Calculation Calculate the temperature and composition of a liquid in equilibrium with a gas mixture containing 10.0 mol% benzene, 10.0 mol% toluene, and balance nitrogen (considered noncondensable) at 1 atm.

53. Liquid/Solid Systems The solubility of a solid in a liquid is the maximum amount of that substance that can be dissolved in a specified amount of the liquid at equilibrium. A solution that contains this maximum of solute is said to be saturated with that species. If a saturated solution is cooled, the solubility decreases. Since the crystallization process can be slow, the solution can be in a meta-stable state for which the dissolve amount of solute exceeds the maximum solubility, a state called supersaturation. This is NOT an equilibrium state.

54. Solid Solubilities Gibbs Phase Rule shows that specifying temperature and pressure for a two-component system at equilibrium containing a solid solute in a liquid solution fixes the values of all other intensive variables. Because the properties of liquids and solids are only slightly affected by pressure, a single plot of solubility vs. temperature can be applicable over a wide range of pressure.

55. Hydrated Salts Solid crystals formed from aqueous solution can contain water molecules in the crystalline structure. These solids are called hydrated salts, and the water molecules are referred to as waters of hydration. A water-free crystal is called an anhydrous salt.

56. Colligative Solution Properties Colligative solution properties are those properties of a solution that differ from those of the pure solvent, and depend solely on the concentration of solute in the solution. Colligative properties of interest in this course: vapor pressure boiling point freezing point

57. Liquid/Liquid Equilibrium If water and methyl isobutyl ketone (MIBK) are mixed at 25�C, one phase results if the mixture contains > 98% water or > 97.7% MIBK by mass. Otherwise, the mixture separates into two liquid phases: 98% H2O/2% MIBK in one, and 97.7% MIBK/2.3% H2O in the other. Water and MIBK are said to be partially miscible. If the seperating phases contained negligible amounts of the other species, the phases are said to be immiscible.

58. Liquid/Liquid Equilibrium If a 3rd component is added to a 2-phase liquid mixture, this component distributes between the 2 liquid phases. This phenomenon is exploited to achieve a separation by liquid extraction processes. Suppose A and S are two nearly immiscible liquids, and B is a solute distributed between the phases of an A-S mixture. The distribution coefficient K(partition ratio) of component B is the ratio of mass fraction of B in the S phase to that in A phase.

59. Ternary Phase Diagrams

60. Adsorption on Solid Surfaces The attraction of chemical species from the gas or liquid phase to a solid surface is the basis for a class of separation processes referred to as adsorption. The solid is called the adsorbent, while the component attracted to the surface is the adsorbate. The equilibrium data between amount adsorbed vs. concentration in the bulk phase is called an adsorption isotherm.