Liquid-phase properties from VLE data Fugacity –For 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 P i sat for pure species i
Fig. 12.1Table 12.1 The first three columns are P-x 1 -y 1 data. Columns 4 and 5 are: Column 6 is:
Fig 12.2 Henry’s constant, the limiting slope of the curve at x i = 0. Henry’s law expresses:, it is approximate valid for small values of x i Fig 12.3
Henry’s law Gibbs/Duhem equation Lewis/Randall rule Gibbs/Duhem equation for binary mixture at const. T and P: Division by dx 1 limit when x 1 = 1, The Lewis/Randall rule, x 1 → 0 x 2 → 1
Excess Gibbs energy Table 12.2 –Column 6:
Fig Positive deviation from Raoult’s law behavior: The dimensionless excess Gibbs energy: The value of G E /RT is zero at both x 1 = 0 and x 1 =1
From Fig 12.5(b), linear relation: Similarly,The Margules equations Limiting conditions:
VLE data for diethyl ketone (1) / n-hexane (2) at 65°C are given in the first three columns of Table Reduce the data. Table 12.4 Fig 12.7 Fig 12.7(b) for (G E /x 1 x 2 RT) fitting: The solid lines. Not consistency! Omit Barker’s method
Models for the excess Gibbs energy G E /RT = f (T, P, composition) –At constant T: weak The Margules equation The Redlich/Kister expansion The van Laar equation Data fitting, convenient, but only for binary system
Local composition models Can be applied to multi-component systems The Wilson equation: The NRTL(Non-Random-Two-Liquid) equation: The UNIQUAC equation and the UNIFAC method: –App. H.
Property changes of mixing Excess properties The M change of mixing Because of their direct measurability, V and H are the property changes of mixing of major interest.
The 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 x i. The partial properties:
Fig 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.
Heat 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 solution –based on 1 mol of solute dissolve in liquids:
Calculate the heat of formation of LiCl in 12 mol of H 2 O at 25°C. Fig 12.14
A 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°C 2 kg/s 15% LiCl Q 1.25 kg superheated steam at 132°C and 1 atm 0.75 kg 40% LiCl at 132°C The energy balance: the total enthalpy of the product streams minus the total enthalpy of the feed stream separation of 2 kg of a 15% LiCl solution into its pure constituents at 25°C mixing of 0.45 kg of water with 0.30 kg of LiCl (s) to form a 40% solution at 25°C 0.75 kg of 40% LiCl solution is heated to 132°C liquid water is vaporized and heated to 132°C
Enthalpy/concentration diagrams The enthalpy/concentration (Hx) diagram Fig 12.17
Solid NaOH at 70°F is mixed with H 2 O 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 H 2 O. Fig 12.19, x 1 = 0: Fig 12.19, x 1 = 45%: