Vapor-liquid equilibria distribution coefficients

Eew multicomponent systems exist for which completely generalized equilibrium data are available. The most widely available data are those for vapor-liquid systems, and these are frequently referred to as vapor-liquid equilibrium distribution coefficients or K value. The K values vary with temperature and pressure, and a selectivity that is equal to the ratio of the K values is used. Eor vapor-liquid systems, this is referred to as the relative volatility and is expressed for a binary system as... 

Vapor-liquid equilibrium distribution coefficients, or /<-valucs, may be calculated with varying degrees of accuracy. For a propylene-isobutane mixture at 50°C, where the two components are equimolar in the vapor phase, compare the /f-values at 860,1380, and 1900 kPa using each of the following methods ... 

K Vapor-liquid equilibrium distribution coefficient Lj Liquid molar flow rate leaving tray j Lji Component i molar flow rate in liquid leaving tray j N Number of equilibrium stages in a column... 

D Distillate or overhead stream designation or molar flow rate F Feed stream designation or molar flow rate K Vapor-liquid equilibrium distribution coefficient... 

Vapor-liquid equilibrium distribution coefficient for component i on tray /... 

Table 14.138 Vapor-Liquid Equilibrium Distribution Coefficients for Sulfur Compounds and Carbon Dioxide in... 

Table 14.146 Vapor-LIquId Equilibrium Distribution Coefficients for DIoiefins in Anhydrous M-Pyrol Solvent (49)...

K Vapor-liquid equilibrium distribution coefficient L Liquid molar flow rate L Liquid molar flow rate on a solute-free basis P Stage or column pressure Component vapor pressure... 

Vapor-liquid equilibrium distribution coefficient Liquid molar flow rate in the column Side product... 

Vapor-liquid or liquid-liquid equilibrium distribution coefficient... 

Selection of Solubility Data Solubility values determine the liquid rate necessaiy for complete or economic solute recoveiy and so are essential to design. Equihbrium data generally will be found in one of three forms (1) solubility data expressed either as solubility in weight or mole percent or as Heniy s-law coefficients, (2) pure-component vapor pressures, or (3) equilibrium distribution coefficients (iC values). Data for specific systems may be found in Sec. 2 additional references to sources of data are presented in this section. 

Whenever data are available for a given system under similar conditions of temperature, pressure, and composition, equilibrium distribution coefficients (iC = y/x) provide a much more rehable tool for predicting vapor-liquid distributions. A detailed discussion of equilibrium iC vahies is presented in Sec. 13. 

The papers in the second section deal primarily with the liquid phase itself rather than with its equilibrium vapor. They cover effects of electrolytes on mixed solvents with respect to solubilities, solvation and liquid structure, distribution coefficients, chemical potentials, activity coefficients, work functions, heat capacities, heats of solution, volumes of transfer, free energies of transfer, electrical potentials, conductances, ionization constants, electrostatic theory, osmotic coefficients, acidity functions, viscosities, and related properties and behavior. 

Material balance calculations on separation processes follow the same procedures used in Chapters 4 and 5. If the product streams leaving a unit include two phases in equilibrium, an equilibrium relationship for each species distributed between the phases should be counted in the degree-of-freedom analysis and included in the calculations. If a species is distributed between gas and liquid phases (as in distillation, absorption, and condensation), use tabulated vapor-liquid equilibrium data, Raoult s law, or Henry s law. If a solid solute is in equilibrium with a liquid solution, use tabulated solubility data. If a solute is distributed between two immiscible liquid phases, use a tabulated distribution coefficient or equilibrium data. If an adsorbate is distributed between a solid surface and a gas phase, use an adsorption isotherm. 

For a system consisting of C components, the phase rule indicates that, in the two-phase region, there are F=C-2 + 2 = C degrees of freedom. That is, it takes C independent variables to define the thermodynamic state of the system. The independent variables may be selected from a total of 2C intensive variables (i.e., variables that do not relate to the size of the system) that characterize the system the temperature, pressure, C - 1 vapor-component mole fractions, and C - 1 liquid-component mole fractions. The number of degrees of freedom is the number of intensive variables minus the number of equations that relate them to each other. These are the C vapor-liquid equilibrium relations, Yj = K,X, i=l,. .., C. The equilibrium distribution coefficients, AT, are themselves functions of the temperature, pressure, and vapor and liquid compositions. The number of degrees of freedom is, thus, 2C - C = C, which is the same as that determined by the phase rule. 

It is convenient to define an equilibrium ratio as the ratio of mole fractions of a species in two phases in equilibrium. For the vapor-liquid case, the constant is referred to as the K-value or vapor-liquid equilibrium ratio as defined by (1-3) as Ki s yjxi- For the liquid-liquid case, the constant is frequently referred to as the distribution coefficient or liquid-liquid equilibrium ratio as defined by (1-6) as Kd, x ilx i. ... 

This method therefore would indicate that the distribution coefficient and hence the mole fraction of water in the vapor phase would not be influenced by the addition of an inert gas. Consider a mixture of chlorine and water in vapor-liquid equilibrium in a closed container. By that assumption, addition of nitrogen pressure to the container would cause further vaporization of the water in order to maintain the same vapor-phase mole fraction. What happens in fact is that the vapor-phase activities of chlorine and water remain nearly unchanged. That statement properly ignores any absorption of nitrogen into the liquid and is practically equivalent to saying that, while the mole fraction of chlorine in the vapor phase decreases, its partial pressure is not affected. The equations developed here correspond to that situation. 

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