Two-component binary systems

However, as most experiments are carried out at atmospheric pressure, a planar diagram, using temperature and composition as variables, is usually 

In all of the binary phase diagrams discussed here, it is assumed that pressure is fixed at 1 atm. The sources of the experimental phase diagrams that have been adapted for this chapter are given in the Further Reading section. 

The simplest form of two-component phase diagram is exhibited by components that are very similar in chemical and physical properties. The nickel-copper 

At the bottom of the diagram, corresponding to the lowest temperatures, another homogeneous phase, a sohd, called the a phase, is found. Just as in the hquid phase, the copper and nickel atoms are distributed at random and, by analogy, such a material is called a sohd solution. Because the sohd solution exists from pure copper to pure nickel it is called a complete sohd solution. (The physical and chemical factors underlying sohd solution formation are described in Section 6.1.3.) 

Between the hquid and sohd phases, phase boundaries delineate a lens-shaped region. Within this area sohd (a) and hquid (L) coexist. The lower phase boundary, between the sohd and the 

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Follow the steps, once again, as explained above for two component (binary) system. 

This factor should be inputted if you have chosen the two-film method. Enter the value of the chosen light key component liquid phase mole fraction. This value should be obtained from an equilibrium curve, a two-component binary system, or a tray-to-tray computer program printout. The program uses this factor to calculate the slope of the equilibrium curve. Be sure to select the liquid light key mole fraction at the proper curve point or tray condition that corresponds to the K value used. 

The development of SCF processes involves a consideration of the phase behavior of the system under supercritical conditions. The influence of pressure and temperature on phase behavior in such systems is complex. For example, it is possible to have multiple phases, such as liquid-liquid-vapor or solid-liquid-vapor equilibria, present in the system. In many cases, the operation of an SCF process under multiphase conditions may be undesirable and so phase behavior should first be investigated. The limiting case of equilibrium between two components (binary systems) provides a convenient starting point in the understanding of multicomponent phase behavior. 

For a two-component (binary) system (C = 2), F becomes 4 — P with two solid phases existing in the presence of a gas phase, the system becomes monovariant, and the vapor pressure of each component is a function of temperature alone. If only one solid phase exists along with its vapor, F acquires the value of 2 (bivariant), and the system is not determined uniquely by the temperature but depends also on the composition of either phase. 

There are two types of VLE diagrams that are widely used to represent data for two-component (binary) systems. The first is a temperature versus x and y diagram (Txy). The X term represents the liquid composition, usually in terms of mole fraction. The y term represents the vapor composition. The second diagram is a plot of x versus y. 

The main emphasis will be upon stagewise, continuous feed distillation, schematically shown in figure 6.1. The column may contain trays or packing (as described later) to promote good vapour-liquid contact. The quantitative analysis is confined to two-component (binary) systems in trayed columns. 

In a gas fluidized bed where the bed particles are of different densities, it will be beneficial to know which component will sink (jetsam) and which will float (flotsam). In most cases, especially the two-component systems, the classification of flotsam and jetsam is obvious. In some isolated cases, whether the particular component will behave as a flotsam or a jetsam will have to be determined experimentally. This is especially true for a bed of multicomponent mixture with a wide size and density distribution. For a two-component binary system, Chiba et al. (1980) suggested the following general rules ... 

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

If a liquid system containing at least two components is not in thermodynamic equilibrium due to concentration inhomogenities, transport of matter occurs. This process is called mutual diffusion. Other synonyms are chemical diffusion, interdiffusion, transport diffusion, and, in the case of systems with two components, binary diffusion. 

In order for this concept to be applicable, the matrix and the reactant phase must be thermodynamically stable in contact with each other. One can evaluate this possibility if one has information about the relevant phase diagram — which typically involves a ternary system — as well as the titration curves of the component binary systems. In a ternary system, the two materials must lie at comers of the same constant-potential tie-triangle in the relevant isothermal ternary phase diagram in order to not interact. The potential of the tie-triangle determines the electrode reaction potential, of course. 

In 163—167 we have deduced some properties of systems of two components in two phases ( binary systems V) directly from the fundamental principles, and in 169—173 we have obtained quantitative relations in certain special cases. Here we shall j obtain some general equations relating to such systems with the i help of the thermodynamic potential (cf. 155)., ... 

In phase rule systems are categorized according to the number of components unary systems with only one component, binary systems with two components and (in this book) finally ternary systems with three components. The behaviour of the components in a system is determined by variables pressure, temperature and composition. 

As in any two phase binary system, considering the monomer and dimer as the two components, rjm + rjd — 1 and em + ed — 1, will allow Equation 4 and the pure component form of Equation 3 to be reduced to... 

The process is also known as chemical diffusion, interdiffusion, transport diffusion, and in the case of systems with two components, binary diffusion. 

The relationship between G, H, and S of ideal solutions is shown in Figure 15.1. This uses the binary (or two-component) olivine system as an example. This system is relatively ideal, so the three ideal curves of Figure 15.1a should approximate reality in this case. 

The constants a, b, and m in eqn [3] depend on the solute and on the chromatographic system. b = (ka) " , where ka is the retention factor in a pure nonpolar solvent. Equation [2] or [3] can be used as the basis of optimization of the composition of two-component (binary) mobile phases in NPLC, using a common window diagram or overlapping resolution mapping approach, as illustrated in an example in Figure 3. 

Apart from the difference in the form of the equilibrium relationships there is complete formal similarity between the single-component adiabatic system and the general two-component isothermal system which was considered previously. However, for an adiabatic system, the c - T (or q - T) characteristics are generally nonlinear so the simplicity of the ideal binary Langmuir... 

In Section 1.1, we briefly Illustrate the meaning of separation between two regions for a system of two components in a closed vessel. Section 1.2 extends this to a multicomponent system. In Section 1.3, various definitions of compositions and concentrations are given for a two-component system. In Section 1.4, we are concerned with describing the various indices of separation and their interrelationships for a two-region, two-component separation system. A number of such indices are compared with regard to their capacity to describe separation in Section 1.5 for a binary system. Next, Section 1.6 briefly considers the definitions of compositions and indices of separation for the description of separation in a multicomponent system between two regions in a closed vessel. Finally, Section 1.7 briefly describes some terms that are frequently encountered. 

In fact, one can go a step further by identifying the benzene extract phase as region 1 and the water raffinate phase as region 2 and working only with the concentrations of the two acids in each region. We then, in effect, have a binary system of benzoic acid and picric acid between two regions, 1 (benzene layer), and 2 (water layer), and one could proceed with the description in the manner of Section 1.1. Thus the description of a four-component separation system may he reduced to that of a two-component separation system provided each of the immiscihle phases is made up of essentially one species... 

Under the heading of solution growth also the analytical description of the phase diagram of a two-component ideal system can be treated. If we do not start the solidification from a binary hquid solution with a 1 1 composition, the term solution growth appears to be justifiable. 

The solvent components usually have a low mutual solubility and are present in reasonably large mole fractions in the system. If solvents are not so designated, we take as the "solvent components" those two components, present in significant mole fraction in the system, that have the lowest binary solubilities. ... 

The principal point of interest to be discussed in this section is the manner in which the surface tension of a binary system varies with composition. The effects of other variables such as pressure and temperature are similar to those for pure substances, and the more elaborate treatment for two-component systems is not considered here. Also, the case of immiscible liquids is taken up in Section IV-2. 

Though the solution procedure sounds straightforward, if tedious, practice difficulty is encountered immediately because of the implicit nature of the available flux models. As we saw in Chapter 5 even the si lest of these, the dusty gas model, has solutions which are too cumbersc to be written down for more than three components, while the ternary sol tion itself is already very complicated. It is only for binary mixtures therefore, that the explicit formulation and solution of equations (11. Is practicable. In systems with more than two components, we rely on... 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

The Class I binary diagram is the simplest case (see Fig. 6a). The P—T diagram consists of a vapor—pressure curve (soHd line) for each pure component, ending at the pure component critical point. The loci of critical points for the binary mixtures (shown by the dashed curve) are continuous from the critical point of component one, C , to the critical point of component two,Cp . Additional binary mixtures that exhibit Class I behavior are CO2—/ -hexane and CO2—benzene. More compHcated behavior exists for other classes, including the appearance of upper critical solution temperature (UCST) lines, two-phase (Hquid—Hquid) immiscihility lines, and even three-phase (Hquid—Hquid—gas) immiscihility lines. More complete discussions are available (1,4,22). Additional simple binary system examples for Class III include CO2—hexadecane and CO2—H2O Class IV, CO2—nitrobenzene Class V, ethane—/ -propanol and Class VI, H2O—/ -butanol. 

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