Two-component mixtures

Indicator Mixtures (Two-Component). An important criterion for the selection of an indicator is an transition interval which is clear, visually well detectable, and as sharp as possible. Ideally, the acidic and the alkaline forms should possess complementary colors, for example, red and green. Unfortunately, no individual indicator fulfills all these requirements. Furthermore, the mixture of colors in the transition range often deteriorates the quality of color change. 

Many binary mixtures (two components) will form a compound which will be in equilibrium with liquid of the same composition. In many cases, such as with benzophenone and diphenylamine, compound formation may be detected by the appearance of a species with a new melting point in the melting point-composition curve (Fig. 2-15), and... 

In a binary mixture, two components are separated from the feedstock. In this example, our distillation system has a 40/60 mixture of butane (water) and pentane (propylene glycol and red dye). Three butane analyzers are used to monitor the concentration of butane in the various streams. 

In principle, extractive distillation is more useful than azeotropic distillation because the process does not depend on the accident of azeotrope formation, and thus a greater choice of mass-separating agent is, in principle, possible. In general, the solvent should have a chemical structure similar to that of the less volatile of the two components. It will then tend to form a near-ideal mixture with the less volatile component and a nonideal mixture with the more volatile component. This has the effect of increasing the volatility of the more volatile component. 

For a binary mixture of two components A and B in the gas phase, the mutual diffusion coefficient such as defined in 4.3.2.3, does not depend on composition. It can be calculated by the Fuller (1966) method ... 

So far we have considered only a single component. However, reservoir fluids contain a mixture of hundreds of components, which adds to the complexity of the phase behaviour. Now consider the impact of adding one component to the ethane, say n-heptane (C7H.,g). We are now discussing a binary (two component) mixture, and will concentrate on the pressure-temperature phase diagram. 

When the two components are mixed together (say in a mixture of 10% ethane, 90% n-heptane) the bubble point curve and the dew point curve no longer coincide, and a two-phase envelope appears. Within this two-phase region, a mixture of liquid and gas exist, with both components being present in each phase in proportions dictated by the exact temperature and pressure, i.e. the composition of the liquid and gas phases within the two-phase envelope are not constant. The mixture has its own critical point C g. 

Figure A2.5.3. Typical liquid-gas phase diagram (temperature T versus mole fraction v at constant pressure) for a two-component system in which both the liquid and the gas are ideal mixtures. Note the extent of the two-phase liquid-gas region. The dashed vertical line is the direction x = 1/2) along which the fiinctions in figure A2.5.5 are detemiined.

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].

While the phase rule requires tliree components for an unsymmetrical tricritical point, theory can reduce this requirement to two components with a continuous variation of the interaction parameters. Lindli et al (1984) calculated a phase diagram from the van der Waals equation for binary mixtures and found (in accord with figure A2.5.13 that a tricritical point occurred at sufficiently large values of the parameter (a measure of the difference between the two components). 

All the experimental teats described so far have been confined to binary mixtures, but of course it is also desirable to know whether flux relations adequate in binary mixtures are still successful in mixtures with more than two components. Even in the case of ternary mixtures the form of explicit flux relations is very complex, and a complete investigation of the various matrix elements, in their dependence on both pressure and composition, would be a forbidding undertaking. Nevertheless some progress in this direction has beet made by Hesse and Koder [55] and by Remick and Geankoplis [56]. 

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... 

In just the proportion to give a sharp-melting eutectic mixture is so remote that this possibility may be neglected. [Occasionally arbitrary mixtures of two substances which (usually) are chemically related may melt fairly sharply at temperatures intermediate between the melting-points of the two components, but this phenomenon is rarely encountered.]... 

An illustrative example generates a 2 x 2 calibration matrix from which we can determine the concentrations xi and X2 of dichromate and permanganate ions simultaneously by making spectrophotometric measurements yi and j2 at different wavelengths on an aqueous mixture of the unknowns. The advantage of this simple two-component analytical problem in 3-space is that one can envision the plane representing absorbance A as a linear function of two concentration variables A =f xuX2). 

System in which the solid phases consist of the pure components and the components are completely miscible in the liquid phase. We may now conveniently consider the general case of a system in which the two components A and B are completely miscible in the liquid state and the solid phases consist of the pure components. The equilibrium diagram is shown in Fig. 1,12, 1. Here the points A and B are the melting points of the pure components A and B respectively. If the freezing points of a series of liquid mixtures, varying in composition from pure A to pure B, are determined, the two curves represented by AC and BC will be obtained. The curve AC expresses the compositions of solutions which are in equilibrium, at different temperatures, with the solid component A, and, likewise, the curve BC denotes the compositions... 

Figure 3 19 (page 123) shows how the composition of an equilibrium mixture of two components varies according to the free energy difference between them For the equi librium shown in the accom panying equation AG = —4 kj/mol (—1 kcal/mol)... 

Spectrophotometric titrations are particularly useful for the analysis of mixtures if a suitable difference in absorbance exists between the analytes and products, or titrant. Eor example, the analysis of a two-component mixture can be accomplished if there is a difference between the absorbance of the two metal-ligand complexes (Eigure 9.33). 

Beer s law can be extended to samples containing several absorbing components provided that there are no interactions between the components. Individual absorbances, A , are additive. For a two-component mixture of X and Y, the total absorbance, Atot, is... 

Quantitative Analysis of Mixtures The analysis of two or more components in the same sample is straightforward if there are regions in the sample s spectrum in which each component is the only absorbing species. In this case each component can be analyzed as if it were the only species in solution. Unfortunately, UV/Vis absorption bands are so broad that it frequently is impossible to find appropriate wavelengths at which each component of a mixture absorbs separately. Earlier we learned that Beer s law is additive (equation 10.6) thus, for a two-component mixture of X and Y, the mixture s absorbance, A, is... 

This experiment describes the application of multiwavelength linear regression to the analysis of two-component mixtures. Directions are given for the analysis of permanganate-dichromate mixtures, Ti(IV)-V(V) mixtures and Cu(II)-Zn(II) mixtures. 

Blanco and co-workers" reported several examples of the application of multiwavelength linear regression analysis for the simultaneous determination of mixtures containing two components with overlapping spectra. For each of the following, determine the molar concentration of each analyte in the mixture. 

There is a parallel between the composition of a copolymer produced from a certain feed and the composition of a vapor in equilibrium with a two-component liquid mixture. The following example illustrates this parallel when the liquid mixture is an ideal solution and the vapor is an ideal gas. 

Blending behavior of a binary mixture may be characterized by a linear blending value (LBV). Figure 4 shows the response curve of a hypothetical two-component mixture. The LBV for each of the components at any composition is defined by the tangent at that point according to the formula. 

A third pumping method (Fig. Ic) uses an electrical discharge in a mixture of gases. It relies on electronic excitation of the first component of the gas mixture, so that those atoms are raised to an upper energy level. The two components are chosen so that there can be a resonant transfer of energy by collisions from the upper level of the first component to level 3 of the second component. Because there are no atoms in level 2, this produces a population inversion between level 3 and level 2. After laser emission, the atoms in the second component return to the ground state by collisions. 

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