Vapor-liquid equilibrium enthalpy-concentration

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

The figure-that follows for the ethanol + water sy.s-tem is an unusual one in that it shows both vapor-liquid equilibrium and the enthalpy concentration diagrams on a single plot. This is done as follows. The lower collection of heavy lines give the enthalpy concentration data for the liquid at various temperatures and the upper collection of lines is the enthalpy-concentration data for the vapor, each at two pressures, 0.1013 and 1 013 bar. (There are also enthalpy-concentration lines for several other temperatures.) The middle collection of lines connect the equilibrium compositions of liquid and vapor. For example, at a pressure of 1.013 bar, a saturated-vapor containing 71 wt % ethanol with an enthalpy of 1535 kJ/kg is in equilibrium with a liquid containing 29 wt % ethanol with an enthalpy of 315 kJ/kg at a temperature of 85°C. Note also that the azeotropes that form in the ethanol -f water system are indicated at each pressure. 

To achieve a reliable fitting of the required parameters over the entire range of concentration and temperature, a simultaneous fitting to all reliable thermodynamic data (vapor/liquid equilibrium, azeotropic data, excess enthalpy, actuivity coefficients, liquid/liquid equilibria) should be performed. 

The major difference between the McCabe-Thiele method and the Ponchon-Savarit method is that the liquid and vapor flow rates in the latter method are not assumed constant throughout the column. Because of this, the Ponchon-Savarit method is a more general and accurate method. Since the method is based on enthalpy values of fluid mixtures throughout the column, an enthalpy-concentration diagram is used in conjunction with a vapor-liquid equilibrium plot to determine the number of theoretical plates required for a specific separation. Units based on either moles (and mole fractions) or mass (and mass fractions) are acceptable as long as they are consistent. 

Enthalpy-concentration charts are particularly useful for two-component systems in which vapor and liquid phases are in equilibrium. The Gibbs phase rule (Equation 6.2-1) specifies that such a system has (2 -I- 2 - 2) = 2 degrees of freedom. If as before we fix the system pressure, then specifying only one more intensive variable—the system temperature, or the mass or mole fraction of either component in either phase—fixes the values of all other intensive variables in both phases. An H-x diagram for the ammonia-water system at 1 atm is shown in Figure 8.5-2. 

Schoonmaker and Porter ( ) analyzed the vapors in equilibrium with liquid CsOH and mixed KOH-CsOH condensed phases with a mass spectrometer and reported the presence of appreciable concentrations of dimer in the temperature range 650-700 K. By applying the method of relative equilibrium constants, these workers calculated the difference in the free energies of dimerization for KOH-CsOH. A 3rd law analysis of their free energy data for this pair leads to a difference in the enthalpies of dimerization of 4.9 kcal mol at 298.15 K for CsOH and KOH. Based upon the adopted value for KOH(g), AjH (dimerization, 298. 15 K) = -45.3 3.0 kcal mol" (2), we derive A H (dimerization, 298.15 K) -40.4 4.0 kcal mol" for 2 CsOH(g) = Cs2(0H)2(g). Combining this result with the enthalpy of formation for the gaseous monomer (3), that for the dimer is AjH (CS2(0H)2, g. 298.15 K) = -164.4+10.0 kcal mol" (-687.8+41.8 kJ mol" ). 

Figure 4.21 Enthalpy concentration chart for n-butane-n-heptane at 100 psia. Curve DFHC is the saturated vapor curve BEGA is the saturated liquid. The dashed lines are equilibrium tie lines connecting y and X at the same temperature.

FIG. 2-7 Enthalpy-concentration diagram for aqueous ammonia. From Thermodynamic and Physical Properties NH3-H20, Int Inst. Refrigeration, Paris, France, 1994 (88 pp.). Reproduced by permission. In order to determine equilibrium compositions, draw a vertical from any liquid composition on any boiling line (the lowest plots) to intersect the appropriate auxiliary curve (the intermediate curves). A horizontal then drawn from this point to the appropriate dew line (the upper curves) will establish the vapor composition. The Int. Inst. Refrigeration publication also gives extensive P-v-xtah es from —50 to 316°C. Other sources include Park, Y. M. and Sonntag, R. E., ASHRAE Trans., 96,1 (1990) 150-159 x, h, s, tables, 360 to 640 K) Ibrahim, O. M. and S. A. Klein, ASH E Trans., 99, 1 (1993) 1495-1502 (Eqs., 0.2 to 110 bar, 293 to 413 K) Smolen, T. M., D. B. Manley, et al.,/. Chem. Eng. Data, 36 (1991) 202-208 p-x correlation, 0.9 to 450 psia, 293-413 K)i Ruiter, J. P, 7nf. J. R rig., 13 (1990) 223-236 gives ten subroutines for computer calculations. 

FIG. 2-10 Enthalpy -concentration diagram for aqueous ethyl alcohol. Reference states Enthalpies of liquid water and ethyl alcohol at 0 °C are zero. NOTE In order to interpolate equilibrium compositions, a vertical may be erected from any liquid composition on the boiling line and its intersection with the auxiliary line determined. A horizontal from this intersection will establish the equilibrium vapor composition on the dew line. Bosnjakovic, Technische Thermodynamik, T. Steinkopjf, Leipzig, 1935.)... 

The MESH equations constitute a nonlinear and strongly coupled system of algebraic equations since the equilibrium ratios Ki j and the enthalpies and are complex functions of temperature and concentrations. The system (5.2-71) is numerically solved by the iterative Newton-Raphson algorithm. Commercial software packages (e.g., ASPEN, HYSYS, CHEMCAD) contain both the mathematical solver and the required system properties, such as vapor liquid equilibria and enthalpies. 

The Ponchon-Savarit method is summarized in Fig. 5.3-8. The method involves an enthalpy-concentration diagram, and the enthalpies of the saturated liquid and vapor are first plotted on the diagram. Next, the equilibrium tie lines are added, based on phase equilibria. Compositions of feed, distillate, and bottoms are then located on the diagram (in the example shown the feed is mixed vapor-liquid and the distillate and bottoms are saturated liquids). A reflux ratio is chosen, and the enthalpy of the reflux is located as the top difference point, Ag- (The reflux ratio is equal numerically to the vertical distance from the difference poim to the value of y/v> divided by the vertical distance from y to Xg.)... 

Some properties of the enthalpy-concentration plot are as follows. The region in between the saturated vapor line and the saturated liquid line is the two-phase liquid-vapor region. From Table 11.1-1 for = 0.411, the vapor in equilibrium is y = 0.632. These two points are plotted in Fig. 11.6-1 and this tie line represents the... 

Condensation theory is based on thermodynamic equilibrium. More than a century s worth of experiments have yielded thermodynamic data (entropy and enthalpy of formation, plus heat capacity) for elements and compounds. Equations of state describing the stabilities of different compounds under various conditions can be calculated from these data, as briefly described in Box 7.1. Because liquids are not normally stable at the low pressures appropriate for space, the compounds in condensation calculations are generally solid minerals, but liquids can exist at higher pressures (achievable if areas of the nebula with enhanced dust concentrations relative to gas were vaporized). 

Classical Adiabatic Design Method The classical adiabatic design method assumes that the heat of solution serves only to heat up the liquid stream and there is no vaporization of the solvent. This assumption makes it feasible to relate increases in the liquid-phase temperature to the solute concentration x by a simple enthalpy balance. The equilibrium curve can then be adjusted to account for the corresponding temperature rise on an xy diagram. The adjusted equilibrium curve will be concave upward as the concentration increases, tending to decrease the driving forces near the bottom of the tower, as illustrated in Fig. 14-10 in Example 6. 

An open kettle contains 50 kmol of a dilute aqueous solution of methanol (2 mol% of methanol), at the bubble point, into which steam is continuously sparged. The entering steam agitates the kettle contents so that they are always of uniform composition, and the vapor produced, always in equilibrium with the liquid, is led away. Operation is adiabatic. For the concentrations encountered it may be assumed that the enthalpy of the steam and evolved vapor are the same, the enthalpy of of the liquid in the kettle is essentially constant, and the relative volatility is constant at 7.6. 

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