Multicomponent systems liquid/solid solutions

Unfortunately, the study of phase equilibria in solution, e.g., liquid-solid adsorption, is not a highly popular area of research. Gas-solid adsorption and vapor-solution equilibria have been studied in far more detail, although most of the information available concerns the fate of single components in a diphasic system. Liquid-solid adsorption has benefited mainly from the extension of the concepts developed for gas phase properties to the case of dilute solutions. Multicomponent systems and the competition for interaction with the stationary phase are research areas that have barely been scratched. The problems are difficult. The development of preparative chromatography and its applications are changing this situation. 

Despite these apparent weaknesses, within the context of a general purpose system for predicting the vapor-liquid-solid equilibria of multicomponent aqueous solutions, GCES as a tool succeeds remarkably well as will be seen in a few illustrations after the following description of the software structure and use. 

The thermodynamic equations for the Gibbs energy, enthalpy, entropy, and chemical potential of pure liquids and solids, and for liquid and solid solutions, are developed in this chapter. The methods used and the equations developed are identical for both pure liquids and solids, and for liquid and solid solutions therefore, no distinction between these two states of aggregation is made. The basic concepts are the same as those for gases, but somewhat different methods are used between no single or common equation of state that is applicable to most liquids and solids has so far been developed. The thermodynamic relations for both single-component and multicomponent systems are developed. 

Here, we only present the simplest thermodynamic expressions used in the CALPHAD method for the major phase classes observed in multicomponent systems namely, disordered miscible and immiscible phases and ordered sublattice phases. The reader is referred to specialized textbooks for further discussion. The Gibbs energies for disordered two-component solid and liquid solution phases are most easily represented by the regular solution model (Eq. 2.10) or one of its variants ... 

As a molecule approaches the solid surface, a balance is established between the intermolecular attractive and repulsive forces. If other molecules are already adsorbed, both adsorbent-adsorbate and adsorbate-adsorbate interactions come into play. It is at once evident that assessment of the adsorption energy is likely to become exceedingly complicated in the case of a multicomponent system - especially if the adsorption is taking place from solution at a liquid-solid interface. For this reason, in the numerous attempts made to calculate energies of adsorption, most attention has been given to the adsorption of a single component at the gas-solid interface. 

The chromatographic method of analysis makes it possible to investigate the adsorption from multicomponent systems. For study of adsorption from solutions of volatile compounds gas chromatography can be used and for the investigation of solid compound or non-volatile substances liquid chromatography is used. In this cases chromatography is applied as method of determination of components concentration in equilibrium solution over the adsorbent [3-5]. 

However, in normal phase adsorption systems (or liquid-solid chromatography) the interaction of the mobile phase solvent with the solute is often less Important than the competing Interactions of the mobile phase solvent and the solute with the stationary phase adsorption sites. Solute retention is based upon a displacement mechanism. Multicomponent mobile phases and their combination to optimize separations in liquid-solid chromatography have been studied in detail (31-35). Here, solvents are classified as to their interaction with the adsorption surface (Reference 32, in particular) ... 

Physical Properties of Multicomponent Systems (Solution Behaviour, Liquid/Liquid-, Liquid/Solid-, LiquidA apour-Systems, etc.). 

Air is a multiphase and multicomponent system or, in other words, a mixture of gases and particles. The latter we distinguish into liquid droplets and solids. Solid particles are also often mixtures and always contain water to different extents, i. e. they are humid. Within the troposphere, droplets are exclusively aqueous solutions (hydrometeors) but in the stratosphere, droplets can be formed from sulfuric and nitric acid. 

For multicomponent systems the composition of the equilibrium solid phase can be determined indirectly by the so-called wet-residues method, first proposed by Schreinemakers (1893), in which the need for solid-liquid separation before analysis is avoided. In practice, the equilibrium system is allowed to settle and then most of the saturated supernatant solution is decanted off the sedimented solids. A sample of the wet solids is then scooped out and quickly weighed in a closed weighing bottle, to avoid solvent loss, and subsequently analysed by the most convenient analytical technique. 

The equilibrium = f(c ) or the partition between an ionic component in the solid or resin phase and in the fluid phase of multicomponent systems depends on many material properties and the temperature and has to be measured. Things are easier for binary systems in which the ionic species a is exchanged. With the concentration q and the mass fraction in the solid or resin phase and the concentration C3 and the mass fraction in the liquid or solution phase the equilibrium =/(Ca) or a = f (y ) cau be described by the mass actiou equilibriiun Constant or selectivity coefficient (see (9.3-3)) ... 

We take up the topic of multicomponent equilibria by drawing a distinction between systems in which several or all components are present in the two equilibrated phases, and those in which only one component plays a key role by distributing itself in significant amounts between the phases in question. Vapor-liquid equilibria of mixtures and other similar multicomponent systems involving the appearance of several solutes in each phase are the prime example of the former, while distributions of a single component occur in a number of different contexts, which we take up in turn below. They include the equilibrium of a single gas with a liquid solvent, or a solid (gas... 

For a multicomponent system Eqs. (1.2) and (1.3) can be primary extended by a term describing the composition influence of the participated components xa,b,c,...-The thermodynamic activity of any component (e. g. A) is expressed by the chemical potential gA = ftA + T-T In Xa i corresponds to solid or liquid or vapor. The chemical potential can be understood in terms of the Gibbs free energy per mole of substance, and it demonstrates the decreasing influence of a pure element or a compound in a diluted system. If any pure component is diluted then the term R- T In Xa will always take values lower than zero (note, that only an ideal solution behavior is considered by the mole fraction Xa- Eor real cases the so-called activity... 

These three approaches have found widespread application to a large variety of systems and equilibria types ranging from vapor-liquid equilibria for binary and multicomponent polymer solutions, blends, and copolymers, liquid-liquid equilibria for polymer solutions and blends, solid-liquid-liquid equilibria, and solubility of gases in polymers, to mention only a few. In some cases, the results are purely predictive in others interaction parameters are required and the models are capable of correlating (describing) the experimental information. In Section 16.7, we attempt to summarize and comparatively discuss the performance of these three approaches. We attempt there, for reasons of completion, to discuss the performance of a few other (mostly) predictive models such as the group-contribution lattice fluid and the group-contribution Flory equations of state, which are not extensively discussed separately. 

Although the liquid explosives are multicomponent mixture systems, they have good component uniformity and density consistency. And the solution-type liquid explosive is an intermolecular mixed explosive with the uniformity of pure solution. Although another liquid explosive with suspended solid particles has not uniformity as the former does, it also has relatively good uniformity in components and density, and physical stability of the system. 

In a multicomponent, multiphase system at equilibrium, ji, is the same in every phase, but in most cases /i° and therefore fi, — fi° is different for solids, liquids, gases, and solutes (we know this without knowing the numerical value of either term). Thermodynamic properties are determined and tabulated for substances in these various standard states, and how they relate to one another in chemical reactions can be seen when we consider the equilibrium constant (Chapter 9). 

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