THE BINARY SYSTEM

In a binary system the composition of the mixture can be varied and plotted on a horizontal line, usually as a mole fraction x or mass fraction w. At the ends of this line two vertical axes are drawn on which the temperature is represented most of the time. We shall now have a closer look at three kinds of binary systems. 

The binary system which is easiest to describe is the so-called ideal binary system . As you can tell from the inverted commas, such a system does not really exist, but there are systems which come very close. In an ideal system the components in the S and L phase are completely miscible. In order to be so in the S phase, the substances need to be isomorphous, i.e. possess the same crystal structure. This is often accompanied by an analogous chemical structure. Some examples of these systems are silver (Ag) / gold (Au) and sodium nitrate (NaN03) / calcium carbonate (CaC03). 

In figure 6.7 you can see the T, x diagram of the ideal binary system with the components A and B (the binary system A / B) for the L and S phases at one specific pressure. 

The bottom line of the diagram is called the liquidus curve. This line represents a collection of the melting points of all mixtures and of the pure components A and B. The top line is called the solidus curve and is a collection of all the solidification points of all mixtures and the pure substances A and B. In the L field one liquid phase and in the S field one solid phase occur. In the L + S field a solid and a liquid phase are present. How should such a diagram be read First of all it is important to realise that every point in the diagram represents a system which is characterized by a temperature, com- 

Between the temperatures T (l) and T 2) the system possesses an L and an S phase. The compostion of these two phases can be read from the diagram. For instance system Q has a temperature T Q), a solid phase with the composition x(Q)S and a liquid phase with composition x(Q)L. When the temperature of the system drops to T 2), the last drop of the L phase will disappear and further cooling will result in the presence of only one S phase. Now work out for yourself that heating an S mixture with composition x(P) and T(2) will result in the formation of the first L droplet with a composition close to value 0. 

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Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

An adequate prediction of multicomponent vapor-liquid equilibria requires an accurate description of the phase equilibria for the binary systems. We have reduced a large body of binary data including a variety of systems containing, for example, alcohols, ethers, ketones, organic acids, water, and hydrocarbons with the UNIQUAC equation. Experience has shown it to do as well as any of the other common models. V7hen all types of mixtures are considered, including partially miscible systems, the... 

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... 

Eutectics melting at about —30, —47, and —40° C are formed in the binary systems, cesium—sodium at about 9% sodium, cesium—potassium at about 25% potassium, and cesium—mbidium at about 14% mbidium (34). A ternary eutectic with a melting point of about —72°C has the composition 73% cesium, 24% potassium, and 3% sodium. Cesium and lithium are essentially completely immiscible in all proportions. 

Landolt-Bornstein Physikalische-chemische TabeUen, Eg. I, p. 303, 1927. Phase-equilibrium data for the binary system NH3-H2O are given by Clifford and Hunter,y. Fhys. Chem., 37, 101 (1933). 

Enthalpy and phase-equilibrium data for the binary system HCI-H2O are given by Van Nuys, Trans. Am. Inst. Chem. Engts., 39, 663 (1943). 

Table 13-1, based on the binary-system activity-coefficient-eqnation forms given in Table 13-3. Consistent Antoine vapor-pressure constants and liquid molar volumes are listed in Table 13-4. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanol-hexane system, whose activity coefficients are snown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may...

The photo-induced process of modification of cellulose and its derivatives was reported by Geacintov and coworkers [67,68]. Thus, acrylonitrile, vinyl acetate, styrene, MMA, and the binary system of styrene and AN were grafted onto cellulose and cellulose derivatives. In... 

The continuous CVM can also be applied to an fee alloy. We use the pair approximation of continuous CVM within the NN pair approximation in the fee binary alloys. For the binary system, we use the chemical potential to control the composition as was done in the 2-D case. For convenience, we choose... 

The composition of these alloys extends beyond the binary system and they may be categorised as the Duralumin type H15 and the complex types H12 and H16. 

Figure 3 gives the P-T-x diagram for the binary system hydroquinone-argon and shows that at ordinary temperatures the three-... 

In most cases the critical temperature of the solute is above room temperature. As can be seen in the binary system H2S-H20 drawn in Fig. 6, the three-phase line HL2G is then intersected by the three-phase line HL G. The point of intersection represents the four-phase equilibrium HLXL2G and indicates the temperature... 

Fig. 8. The system CHCla-HaS-HaO. The univariant equilibria of the single-component systems have been indicated by dotted lines, those of the binary systems by thin lines, and those of the ternary system by heavy lines. The latter are approximate only, except for the lower half of the four-phase line HnLxL%G measured by von Stackelberg and Friihbuss.4 ...

Figure 8 represents the system CHC13-H2S-H20, where hydrates occur in the binary systems H2S-H20 and CHC13-H20, both of which are known.41 48 It is assumed that the binary system H2S-CHC13 does not show demixing in the liquid phase so that Lx represents a nonaqueous liquid which changes continuously from pure H2S to pure CHC13. All binary equilibria have been drawn with thin lines in Fig. 8. 

It is known that the three-phase line H G in the binary system H2S-H20 lies below the liquid vapor line (LG) of pure H2S. Likewise, after addition of CHC13 the four-phase line lies... 

Figure 9 represents the system CC14-H2S-H20, where no hydrates occur in the binary system CC14-H20. In the ternary system von Stackelberg and Fruhbuss again determined the lower half of the four-phase line As the binary quadruple point... 

FIG. 4 Phase diagram of the binary system water/C12 a-ester sulfonate. (From Ref. 58.)... 

The binary system lead-thallium shows an unusual type of phase diagram. Fig. 1, taken from Hansen (1936), represents in the main the results obtained by Kumakow Pushin (1907) and by Lewkonja (1907). The liquidus curve in the wide solid-solution region has a maximum at about 63 atomic percent thallium. The nature of this maximum has not previously been made clear. 

The error in variables method can be simplified to weighted least squares estimation if the independent variables are assumed to be known precisely or if they have a negligible error variance compared to those of the dependent variables. In practice however, the VLE behavior of the binary system dictates the choice of the pairs (T,x) or (T,P) as independent variables. In systems with a... 

Fig. 3 Detail of the O- - I interaction in the binary system associating the 4-amino-2,2,6,6-tetramethyl(piperidin-l-yloxyl) radical 7 with pTFDIB... 

J. G. WOJTASINSKI. J. Chem. Eng. Data, 1963 (July), pp. 381-385. Measurement of total pressures for determining liquid-vapour equilibrium relations of the binary system isobutyraldehyde-n-butyraldehyde. 

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