2Liquid-phase properties from VLE data FugacityFor species i in the vapor mixture:Vapor/liquid equilibrium:The vapor phase is assumed an ideal gas:Therefore:The fugacity of species i (in both the liquid and vapor phases) is equal to the partial pressure of species i in the vapor phase.Its value increases from zero to Pisat for pure species i
3Fig. 12.1Table 12.1The first three columns are P-x1-y1 data.Columns 4 and 5 are:Column 6 is:
4Fig 12.3Fig 12.2Henry’s constant, the limiting slope of thecurve at xi = 0.Henry’s law expresses: , it is approximate valid for small values of xi
5Henry’s law Lewis/Randall rule Gibbs/Duhem equation x1 → 0 x2 → 1 Gibbs/Duhem equation for binary mixture at const. T and P:The Lewis/Randall rule,Division by dx1when x1 = 1,limit
7Fig. 12.5Positive deviation from Raoult’s law behavior:The dimensionless excess Gibbs energy:The value of GE/RT is zero at both x1= 0 and x1 =1
8From Fig 12.5(b), linear relation: Similarly,The Margules equationsLimiting conditions:
9VLE data for diethyl ketone (1) / n-hexane (2) at 65°C are given in the first three columns of Table Reduce the data.Table 12.4Fig 12.7The solid lines.Not consistency!Omit Barker’s methodFig 12.7(b) for (GE/x1x2RT) fitting:
10Models for the excess Gibbs energy weakGE/RT = f (T, P, composition)At constant T:Data fitting, convenient, but only for binary systemThe Redlich/Kister expansionThe Margules equationThe van Laar equation
11Local composition models Can be applied to multi-component systemsThe Wilson equation:The NRTL(Non-Random-Two-Liquid) equation:The UNIQUAC equation and the UNIFAC method:App. H.
12Property changes of mixing Excess propertiesThe M change of mixingBecause of their direct measurability, V and H are the property changes of mixing of major interest.
14The excess enthalpy (heat of mixing) for liquid mixture of species 1 and 2 at fixed T and P is represented by the equation:Determine expressions for and as functions of xi.The partial properties:
15Fig 12.131. Each ΔM is zero for a pure species.2. The Gibbs energy change of mixing ΔG is always positive.3. The entropy change of mixing ΔS is positive.
16Heat effects of mixing processes Heat of mixing:For binary systems:When a mixture is formed, a similar energy change occurs because interactions between the force fields of like and unlike molecules are different.Heat of solutionbased on 1 mol of solute dissolve in liquids:
17Calculate the heat of formation of LiCl in 12 mol of H2O at 25°C. Fig 12.14
18A single-effect evaporator operating at atmospheric pressure concentrates a 15% (by weight) LiCl solution to 40%. The feed enters the evaporator at the rate of 2 kg/s at 25°C. The normal boiling point of a 40% LiCl solution is about 132°C, and its specific heat is estimated as 2.72 kJ/kg °C. What is the heat transfer rate in the evaporator?Feed at 25°C2 kg/s 15% LiCl1.25 kg superheated steam at 132°C and 1 atm0.75 kg 40% LiCl at 132°CQThe energy balance:the total enthalpy of the product streams minus the total enthalpy of the feed streamliquid water is vaporized and heated to 132°C0.75 kg of 40% LiCl solution is heated to 132°Cmixing of 0.45 kg of water with 0.30 kg of LiCl(s) to form a 40% solution at 25°Cseparation of 2 kg of a 15% LiCl solution into its pure constituents at 25°C
19Enthalpy/concentration diagrams The enthalpy/concentration (Hx) diagramFig 12.17
20Solid NaOH at 70°F is mixed with H2O at 70°F to produce a solution containing 45% NaOH at 70°F. How much heat must be transferred per pound mass of solution formed?Energy balance:45% NaOH: on the basis of 1 (lbm):0.45(lbm) of solid NaOH dissolved in 0.55 (lbm) of H2O.Fig 12.19, x1 = 0:Fig 12.19, x1 = 45%: