Liquid equilibria involving

The potential-pH diagram for the system tellurium-water at 25 °C is given in Fig. 2.4. It was constructed by using the following homogeneous and heterogeneous (solid/liquid, gas/liquid) equilibria, involving redox and non-redox processes, in which all of the above-referred dissolved substances of tellurium, as well as the solid ones, participate ... 

The characteristic features of phase equilibria in polymer-solvent mixtures will be examined in the present section, the discussion being confined to systems having both phases completely liquid. Equilibria involving a polymer-rich phase in which the polymer is semicrystalline will be the subject of the following section. 

Heat economies by combined extraction-distillation processes, in comparison to direct distillation, will result depending upon the respective vapor-liquid equilibria involved. Meissner, et al. (Ill, 112) in turn have proposed the dehydration of concentrated aqueous solutions of certain organic liquids by extraction of the water by means of strong solutions of salts. 

Calculations of vapor-liquid equilibrium involving a gas dissolved in a liquid are performed using the Lewis-Randall rule for the fugacity of the liquid phase and Henry s law for the vapor phase. Using the subscript s for the solvent, and i for the gas, the equilibrium criterion for the two components is. 

Membrane distillation is one of the membrane processes in which the membrane is not directly involved in separation. The only function of the membrane is to act as a barrier between the two phases. Selectivity is completely determined by the vapour-liquid equilibrium involved. This means that the component with the highest partial pressure will show the highest permeation rate. Thus, in the case of an etbanol/water mixture where the membrane is not wetted at low ethanol concentrations, both components will be transported through the membrane but the permeation rate of ethanol will always be relatively higher. With salt solutions, for example NaCl in water, only water has a vapour pressure, i.e. the vapour pressure of NaCl can be neglected, which means that only water will permeate through the membrane and consequently very high selectivities are obtained. 

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

It is clear that pure" anhydrous sulfuric acid, far from being a single substance in the bulk liquid phase, comprises a dynamic equilibrium involving at least seven well-defined species. The... 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

This is an equilibrium involving three species in the liquid phase, H20, H+(aq), and OH (aq). The equilibrium law can be written... 

There is one other three-phase equilibrium involving clathrates which is of considerable practical importance, namely that between a solution of Q, the clathrate, and gaseous A. For this equilibrium the previous formulas and many of the following conclusions also hold when replacing fiQa by fiQL, the chemical potential of Q in the liquid phase. But a complication then arises since yqL and the difference are not only... 

Unfortunately, the analysis of chemical absorption is far more complex than physical absorption. The vapor-liquid equilibrium behavior cannot be approximated by Henry s Law or any of the methods described in Chapter 4. Also, different chemical compounds in the gas mixture can become involved in competing reactions. This means that simple methods like the Kremser equation no longer apply and complex simulation software is required to model chemical absorption systems such as the absorption of H2S and C02 in monoethanolamine. This is outside the scope of this text. 

In the sealed container of liquid water, I would expect to find droplets of water on the inside of the container where the water vapor condensed. The equilibrium involved in this case is ... 

Solvent extraction, sometimes called liquid-liquid extraction, involves the selective transfer of a substance from one liquid phase to another. Usually, an aqueous solution of the sample is extracted with an immiscible organic solvent. For example, if an aqueous solution of iodine and sodium chloride is shaken with carbon tetrachloride, and the liquids allowed to separate, most of the iodine will be transferred to the carbon tetrachloride layer, whilst the sodium chloride will remain in the aqueous layer. The extraction of a solute in this manner is governed by the Nernstpartition or distribution law which states that at equilibrium, a given solute will always be distributed between two essentially immiscible liquids in the same proportions. Thus, for solute A distributing between an aqueous and an organic solvent,... 

The relative amount of the different phases present at a given equilibrium is given by the lever rule. When the equilibrium involves only two phases, the calculation is the same as for a binary system, as considered earlier. Let us apply the lever rule to a situation where we have started out with a liquid with composition P and the crystallization has taken place until the liquid has reached the composition 2 in Figure 4.17(a). The liquid with composition 2 is here in equilibrium with a with composition 2. The relative amount of liquid is then given by... 

The worst deviations from the Clapeyron equation occur when one of the phases is a gas. This occurs because the volume of a gas depends strongly on temperature, whereas the volume of a liquid or solid does not. Accordingly, the value of A Vm is not independent of temperature when the equilibrium involves a gas. 

The purpose of this chapter is to outline the simplest methods of arriving at a description of the distribution of species in mixtures of liquids, gases and solids. Homogeneous equilibrium deals with single phase systems, such as electrolyte solutions (e.g., seawater) or gas mixtures (e.g., a volcanic gas). Heterogeneous equilibrium involves coexisting gaseous, liquid and solid phases. 

The ratio [Sc(Cp )2Ph] / [Sc(Cp )2H] was obtained from relative heights of H nuclear magnetic resonance (NMR) peaks, and [C6H6] was calculated from the density of benzene. The determination of [H2] was more complicated because this substance is also involved in a gas-liquid equilibrium. The procedure used by the authors is as follows. 

In general, the formulation of the problem of vapor-liquid equilibria in these systems is not difficult. One has the mass balances, dissociation equilibria in the solution, the equation of electroneutrality and the expressions for the vapor-liquid equilibrium of each molecular species (equality of activities). The result is a system of non-linear equations which must be solved. The main thermodynamic problem is the relation of the activities of the species to be measurable properties, such as pressure and composition. In order to do this a model is needed and the parameters in the model are usually obtained from experimental data on the mixtures involved. Calculations of this type are well-known in geological systems O) where the vapor-liquid equilibria are usually neglected. 

Since the vast majority of chemical engineering systems involve liquid and vapor phases, many vapor-liquid equilibrium relationships are used. They range from the very simple to the very complex. Some of the most commonly used relationships are listed below. More detailed treatments are presented in many thermodynamics texts. Some of the basic concepts are introduced by Luyben aM... 

In Fig. 1.2, phase transformations are pnt into their context of physical processes used for separation of mixtures of chemical compounds. However, the figure has been drawn asymmetrically in that two Uqnids (I and II) are indicated. Most people are familiar with several organic Uqnids, Uke kerosene, ether, benzene, etc., that are only partially miscible with water. This lack of miscibility allows an equilibrium between two liquids that are separated from each other by a common phase boundary. Thus the conventional physical system of three phases (gas, liquid, and solid, counting all solid phases as one), which ordinarily are available to all chemists, is expanded to four phases when two immiscible liquids are involved. This can be of great advantage, as will be seen when reading this book. 

Gas-liquid relationships, in the geochemical sense, should be considered liquid-solid-gas interactions in the subsurface. The subsurface gas phase is composed of a mixture of gases with various properties, usually found in the free pore spaces of the solid phase. Processes involved in the gas-liquid and gas-solid interface interactions are controlled by factors such as vapor pressure-volatilization, adsorption, solubility, pressure, and temperature. The solubility of a pure gas in a closed system containing water reaches an equilibrium concentration at a constant pressure and temperature. A gas-liquid equilibrium may be described by a partition coefficient, relative volatilization and Henry s law. 

Separation processes which involve non-volatile salts arise in two situations. First, as an alternative to extractive or azeotropic distillation, salts may be added to a system to alter the vapor-liquid equilibrium behavior. Second, there are cases where a salt is generated in the process before final product purification. For example, product streams from processes involving esterification, etherification, or neutralization contain salts and are often fed to separation units such as distillation or stripping columns. 

The performance of a given column or the equipment requirements for a given separation are established by solution of certain mathematical relations. These relations comprise, at every tray, heat and material balances, vapor-liquid equilibrium relations, and mol fraction constraints. In a later section, these equations will be stated in detail. For now, it can be said that for a separation of C components in a column of n trays, there still remain a number, C + 6, of variables besides those involved in the dted equations. These must be fixed in order to define the separation problem completely. Several different combinations of these C + 6 variables may be feasible, but the ones commonly fixed in column operation are the following ... 

In applying equation 33, Cpsl (the constant-pressure molar heat capacity of the stoichiometric liquid) is usually extrapolated from high-temperature measurements or assumed to be equal to Cpij of the compound, whereas the activity product, afXTjafXT), is estimated by interjection of a solution model with the parameters estimated from phase-equilibrium data involving the liquid phase (e.g., solid-liquid or vapor-liquid equilibrium systems). To relate equation 33 to an available data base, the activity product is expressed... 

An additional problem arises when the stability of the critical phase involving the gas-liquid equilibrium in a binary system is studied. The conditions of stability of a homogenous system at constant pressure are d2A/dV2)T x> 0 and d25/dx )T P > 0 from Equations (5.136) and (5.141), respectively. The question arises of which of the two conditions becomes zero first as the boundary between stable and unstable phases is approached. 

When a solute is distributed between two immiscible liquids, different species, formed from the solute, may exist in the two liquids. Thus, when an organic liquid such as benzene or carbon tetrachloride and water are used as the two liquids, a weak acid may dimerize in the organic phase and partially ionize in the aqueous phase. The condition of equilibrium is the equality of the chemical potential of the monomeric, nonionized species in the two phases. If the dimerization is complete, the condition of equilibrium involves half of the chemical potential of the dimer in the organic phase. 

The concept of melting point may be put on a more quantitative basis. The process of melting is a thermal one and is characterized by the collapse of molecular units in a crystal to a disordered array. Energy is required to rupture the crystal lattice so that the heat of fusion, A/7fus, is positive. In addition, the solid-liquid transition involves an increase of randomness and the entropy of fusion, ASfts, is also positive. Melting point is the temperature of fusion (7 ) at which solid and liquid phases are in equilibrium. Therefore,... 

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