Pseudo-binary system

If the presence of the other components does not significantly affect the volatility of the key components, the keys can be treated as a pseudo-binary pair. The number of stages can then be calculated using a McCabe-Thiele diagram, or the other methods developed for binary systems. This simplification can often be made when the amount of the non-key components is small, or where the components form near-ideal mixtures. 

Where the concentration of the non-keys is small, say less than 10 per cent, they can be lumped in with the key components. For higher concentrations the method proposed by Hengstebeck (1946) can be used to reduce the system to an equivalent binary system. Hengstebeck s method is outlined below and illustrated in Example 11.5. Hengstebeck s book (1976) should be consulted for the derivation of the method and further examples of its application. 

For any component i the Lewis-Sorel material balance equations (Section 11.5) and equilibrium relationship can be written in terms of the individual component molar flow 

Estimates of the flows of the combined keys enable operating lines to be drawn for the equivalent binary system. The equilibrium line is drawn by assuming a constant relative volatility for the light key  

Hengstebeck shows how the method can be extended to deal with situations where the relative volatility cannot be taken as constant, and how to allow for variations in the liquid and vapour molar flow rates. He also gives a more rigorous graphical procedure based on the Lewis-Matheson method (see Section 11.8). 

i = the vapour flow rate of any component i from stage n, di = the flow rate of component i in the tops, bi = the flow rate of component i in the bottoms, 

U and are the limiting liquid and vapour rates of components lighter than the keys in the rectifying section, 

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Step 3. Calculate the weight average critical temperature and critical pressure for the remaining heavier components to form a pseudo binary system. (A shortcut approach good for most hydrocarbon systems is to calculate the weight average T only.)... 

The use of the K-factor charts represents pure components and pseudo binary systems of a light hydrocarbon plus a calculated pseudo heavy component in a mixture, when several components are present. It is necessary to determine the average molecular weight of the system on a methane-free basis, and then interpolate the K-value between the two binarys whose heavy component lies on either side of the pseudo-components. If nitrogen is present by more than 3-5 mol%, the accuracy becomes poor. See Reference 79 to obtain more detailed explanation and a more complete set of charts. 

Switendick was the first to apply modem electronic band theory to metal hydrides [5]. He compared the measured density of electronic states with theoretical results derived from energy band calculations in binary and pseudo-binary systems. Recently, the band structures of intermetallic hydrides including LaNi5Ht and FeTiH v have been summarized in a review article by Gupta and Schlapbach [6], All exhibit certain common features upon the absorption of hydrogen and formation of a distinct hydride phase. They are ... 

The sintering of boride-metal composites cannot be developed here, although it allows obtaining fully dense parts. For a review, limited to MB —M pseudo-binary systems containing more than SO vol% boride and excluding infiltrated borides, see ref. 1, 6.7.5.1.4. 

The mixture of the three additives was then dealt with as a pseudo-binary system to which the RST theory was applied. 

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

The adsorption plateaus on this solid, determined with each of the surfactants (Table II) and the individual CMC values, were used to calculate the adsorption constants input in the model. Figure 3 compares the total adsorption (sulfonate + NP 30 EO) of the pseudo-binary system investigated as a function of the initial sulfonate fraction of the mixtures under two types of conditions (1) on the powder solid, batch testing with a solid/liquid ratio, S/L = 0.25 g/cc (2) in the porous medium made from the same solid, for which this solid ratio is much higher (S/L = 4.0 g/cc). 

Glaser, F. W-, and W. Ivanick The pseudo-binary system ZrBs—TiBa. 

To our knowledge, direct experimental data on amphibole mixtures have been obtained only for the (pseudo)binary system actinolite-cummingtonite (Cameron, 1975) at Ptotai = -Phjo = 2 kbar and for the (pseudo)binary system tremolite-pargasite at Ptotai = PhjO = 1 kbar (Oba, 1980). In both cases, an extended miscibility gap (or solvus field in the second case), is evident at low T(i.e., 600 to 800 °C), which is indicative of strong positive interactions in the solid mixtures. Unmixing of other compositional terms is also evident in microprobe investigations (see Ghose, 1982 for an appropriate discussion). 

Figure 5.58 Phase stability relations in (pseudo) binary system NaAlSi308-KAlSi308 at various P and T conditions (Le = leucite Or = orthoclase Sa = sanidine L = liquid V = vapor). Here, orthoclase identifies simply an intermediate state of substitutional disorder.

Since in an extractive distillation process based on this ternary system the extractive agent is nonvolatile and remains in the liquid phase, and since because of the similarity of the molar latent heats of nitric acid and water there is substantially constant molar liquid overflow, the mole fraction of magnesium nitrate remains almost constant throughout the process. It is appropriate to represent the equilibrium situation as a pseudo-binary system for each magnesium nitrate concentration, and Figure 7 shows vapor-liquid equilibria on a nitric acid-water basis at a series of magnesium nitrate concentrations from zero to 0.25 mole fraction in the liquid phase. 

Smith, P. Pennings, A. J., "Eutectic Crystallization of Pseudo Binary Systems of Polyethylene and High Melting Diluents," Polymer, 15, 413 (1974). 

Therefore, measurements carried out over a range of concentrations Ci and C2 with pure binary solutions, allow the determination of fci, Ai,mi,fc2, A2 and m2. From the retention times measured with pseudo-binary systems, i.e., for pulses of component 1 over concentration plateaus of solutions of component 2 alone (Cl = 0) and for pulses of component 2 over plateaus of solutions of component 1 alone (C2 = 0), one can derive from Eq. 4.96 ... 

Therefore, by measuring the retention times of pulses in pseudo-binary systems of various concentrations, the parameters B12, M12, B21, and H2i can also be determined. 

It depends thus on the composition of the mixture in which both the ternary eutectic points of the system will solidify. The boundary line etj-et2 falls down from its summit S towards both the eutectic points. This summit is simultaneously the eutectic point of the pseudo-binary system AX-BY. 

The application of the Gibbs equation to ternary systems can be made only in cross-sections with a constant ratio of the amounts of substances, e.g. in the system A—B—C the pseudo-binary system A/B—C. The Gibbs equation in the ternary system is... 

Again, it is mentioned that the binary mass flux definitions given above are commonly used also for pseudo-binary systems. In these particular cases the above relationships are only approximate. 

Zhang-Presse, M., Oppermann, H., Thermochemical investigation of RE203-Se02 Systems. III. Yttrium selenium oxides in the pseudo-binary system, J. Therm. Anal. Calorim., 69, (2002), 301-316. Cited on pages 356,585. 

A number of facts lead to the view that in the case of phosphorus as in the case of sulphur, a condition of dynamic allotropy exists (Cohen and Olie, Z. pkysikaL Chem., 1910, 71, I Stock and Stamm, Ber., 1913, 46, 3497 Smits and Bokhorst, Z, pkysikaL Chem, 1916, 91, 249). The equilibrium relations would therefore be those of a pseudo-binary system or of a system of perhaps even higher order. For a discussion of the phosphorus systems from this point of view, see Smits, FersL K, Akad. Wetensch, Amsterdam, 1912, 21, 753 1914, 22, 1145 Smits and Bokhorst, Z, physikal. Chem., 1916, 91, 249,... 

But there are not a few systems in which the number of molecular species is greater than the number of components that is, substances which have the same chemical composition (but which may be isomeric forms) may give rise to different molecular species, between which, in the liquid or vapour state, a condition of equilibrium can exist. This fact may alter very markedly the behaviour of a system. Although, therefore, a system may appear to be unary, so far as chemical composition is concerned, it may, as a matter of fact, behave in some respects as a binary system. It forms a pseudo-binary system. The behaviour of these systems, as we shall see, depends largely on the rate at which the internal equilibrium between the different molecular species in the liquid or vapour phase is established. In the present chapter some of the more important aspects of these pseudobinary systems will be considered. 

As a result of the recent investigations of the pseudo-binary systems of the substance sulphur we obtain the diagram shown in Fig. 67. Here, the points A, D, and G represent the ideal freezing-points of monoclinic, rhombic, and nacreous sulphur respectively, or the temperatures at which these three crystalline forms are in equilibrium with pure molten Sa. The curve HEB represents the dynamic equilibrium curve for Sa, S i, and S,r in molten sulphur and the points B, E, and H, where this equilibrium curve cuts the freezing-point curves, represent the natural freezing-points of the three modifications of sulphur. 

Phosphorus as Pseudo-binary System.—For the purpose of illustrating the behaviour of a one-component system as interpreted by means of the theory of allotropy put forward by Smits, a brief discussion of the behaviour of phosphorus may be given. ... 

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