Binary System Example

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. 

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... 

Phase transitions in binary systems, nomially measured at constant pressure and composition, usually do not take place entirely at a single temperature, but rather extend over a finite but nonzero temperature range. Figure A2.5.3 shows a temperature-mole fraction T, x) phase diagram for one of the simplest of such examples, vaporization of an ideal liquid mixture to an ideal gas mixture, all at a fixed pressure, (e.g. 1 atm). Because there is an additional composition variable, the sample path shown in tlie figure is not only at constant pressure, but also at a constant total mole fraction, here chosen to be v = 1/2. 

Examples of ideal binary systems ate ben2ene—toluene and ethylben2ene—styrene the molecules ate similar and within the same chemical families. Thermodynamics texts should be consulted before making the assumption that a chosen binary or multicomponent system is ideal. When pressures ate low and temperatures ate at ambient or above, but the solutions ate not ideal, ie, there ate dissimilat molecules, corrections to equations 4 and 5 may be made ... 

McCabe-Thie/e Example. Assume a binary system E—H that has ideal vapor—Hquid equiHbria and a relative volatiHty of 2.0. The feed is 100 mol of = 0.6 the required distillate is x = 0.95, and the bottoms x = 0.05, with the compositions identified and the lighter component E. The feed is at the boiling point. To calculate the minimum reflux ratio, the minimum number of theoretical stages, the operating reflux ratio, and the number of theoretical stages, assume the operating reflux ratio is 1.5 times the minimum reflux ratio and there is no subcooling of the reflux stream, then ... 

As shown by Marek and Standart [Collect. Czech. Chem. Commun., 19, 1074 (1954)], it is preferable to correlate and utilize hquid-phase activity coefficients for the dimerizing component by considering separately the partial pressures of the monomer and dimer. For example, for a binary system of components 1 and 2, when only compound 1 dimerizes in the vapor phase, the following equations apply if an ideal gas is assumed ... 

In this paper we give a few examples from our work on the monatomic materials and present some new results on how our method extends to binary systems. 

Referenced to 806 data points for binary systems. Equation 8-70A gives absolute deviation of 13.2%, which is about as accurate, or perhaps more so, than other efficiency equations. Equation 8-70B uses the same data and has an absolute average deviation of 10.6%. See Example 8-13 for identification of dimensionless groups. 

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. 

Equilibrium Basic Consideration, 1 Ideal Systems, 2 K-Factor Hydrocarbon Equilibrium Charts, 4 Non-Ideal Systems, 5 Example 8-1 Raoult s Law, 14 Binary System Material Balance Constant Molal Overflow Tray to Tray,... 

The dilated van Laar model is readily generalized to the multicomponent case, as discussed in detail elsewhere (C3, C4). The important technical advantage of the generalization is that it permits good estimates to be made of multicomponent phase behavior using only experimental data obtained for binary systems. For example, Fig. 14 presents a comparison of calculated and observed -factors for the methane-propane-n-pentane system at conditions close to the critical.7... 

Electrolytic conductivity has also been measured in many binary systems. " Although data on conductivities in binary mixtures are very useful for practical purposes, the information from such data alone is limited from the viewpoint of elucidation of the mechanism. For example, the empirical Markov rule is well known for the electrical conductivity of binary mixtures. However, many examples have been presented where this rule does not hold well. 

Adrian et al. (2000) have reported a novel high-pressure liquid-liquid extraction process with reference to processing in biotechnology the example of cardiac glycosides (digitoxin and digoxin) is cited. A completely miscible, binary system of water and a hydrophobic organic solvent like ethanol can split into two liquid phases when a near-critical gas (e.g. CO2) is added. The near-critical C02/water/l-propanol system is reported, for which possibilities for industrial exploitation exist. 

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. 

Connors and Jozwiakowski have used diffuse reflectance spectroscopy to study the adsorption of spiropyrans onto pharmaceutically relevant solids [12]. The particular adsorbants studied were interesting in that the spectral characteristics of the binary system depended strongly on the amount of material bound. As an example of this behavior, selected reflectance spectra obtained for the adsorption of indolinonaphthospiropyran onto silica gel are shown in Fig. 1. At low concentrations, the pyran sorbant exhibited its main absorption band around 550 nm. As the degree of coverage was increased the 550 nm band was still observed, but a much more intense absorption band at 470 nm became prominent. This secondary effect is most likely due to the presence of pyran-pyran interactions, which become more important as the concentration of sorbant is increased. 

Figure 3.9 An illustration of low-order terms in the Taylor series expansion of In y for dilute solutions using lnyT1 for the binary system Tl-Hg at 293 K as example. Here lny i =-2.069,fij11 =10.683 and/J1 =-14.4. Data are taken from reference [8],...

Equations (4.7) and (4.8) may be solved numerically or graphically. The latter approach is illustrated in Figure 4.2 by using the Gibbs energy curves for the liquid and solid solutions of the binary system Si-Ge as an example. The chemical potentials of the two components of the solutions are given by eqs. (3.79) and (3.80) as... 

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