Concentration space binary mixture

Figure 2.13b shows a structure of concentration space of mixture benzene (entrainer) (1) -isopropyl alcohol(2)-water(3). The mixture has a ternary azeotrope and three binary azeotropes. 

Fig. 40. Schematic description of unstable thermodynamic fluctuations in the two-phase regime of a binary mixture AB at a concentration cb (a) in the unstable regime inside the two branches tp of the spinodal curve and (b) in the metastable regime between the spinodal curve tp and the coexistence curve The local concentration c(r) at a point r = (x. y, z.) in space is schematically plotted against the spatial coordinate x at some time after the quench. In case (a), the concentration variation at three distinct times t, ti, u is indicated. In case (b) a critical droplet is indicated, of diameter 2R , the width of the interfacial regions being the correlation length Note that the concentration profile of the droplet reaches the other branch ini, of the coexistence curve in the droplet center only for weak supersaturations of the mixture, where cb -

The calculation of the minimum reflux and reboil ratios of nonpreferred separations is based on the fact that, in ideal mixtures, the states of constant reflux ratio = const, constitute a straight line in the triangular concentration space of Fig. 5.2-30. Their endpoints on the side lines of the triangle can easily be determined from the McCabe-Thiele diagram showing the equilibrium curves of the binary mixtures a-b and a-c. From a first estimation of the reflux ratio the operating line is drawn. Its points of intersection with the equilibrium lines dehver the endpoints... 

The (n - 1) concentration for an n-component mixture can be fixed independently because concentration of the nth component can be found from Eq. (1.2). That is why the dimensionality of the concentration space of binary mixture Ci is one, of ternary mixture C3 - two, of four-component mixture C4 - tree, etc. 

Concentration space is the number of points representing all possible compositions of an n-component mixture. Concentration space of a binary mixture C2 is a segment of unit length the ends correspond to pure components, and the inner points correspond to mixtures of various compositions (Fig. 1.1a)... 

We examine separation of the mixtures, concentration space of which contains region of existence of two hquid phases and points of heteroazeotropes. It is considerably easier to separate such mixtures into pure components because one can use for separation the combination of distillation columns and decanters (i.e., heteroazeotropic and heteroextractive complexes). Such complexes are widely used now for separation of binary azeotropic mixtures (e.g., of ethanol and water) and of mixtures that form a tangential azeotrope (e.g., acetic acid and water), adding an entrainer that forms two liquid phases with one or both components of the separated azeotropic mixture. In a number of cases, the initial mixture itself contains a component that forms two liquid phases with one or several components of this mixture. Such a component is an autoentrainer, and it is the easiest to separate the mixture under consideration with the help of heteroazeotropic or heteroextractive complex. The example can be the mixture of acetone, butanol, and water, where butanol is autoentrainer. First, heteroazeotropic distillation of the mixture of ethanol and water with the help of benzene as an entrainer was offered in the work (Young, 1902) in the form of a periodical process and then in the form of a continuous process in the work (Kubierschky, 1915). 

The binary eutectics are represented by points A (31.5 °C 72.5 per cent O, 27.5 per cent M), B (33.5 °C 75.5 per cent O, 24.5 per cent M) and C (61.5 °C 54.8 per cent M, 45.2 per cent P). Curve AD within the prism represents the effect of the addition of the component P to the 0-M binary eutectic A. Similarly, curves BD and CD denote the lowering of the freezing points of the binary eutectics B and C, respectively, on the addition of the third component. Point D, which indicates the lowest temperature at which solid and liquid phases can coexist in equilibrium in this system, is a ternary eutectic point (21.5 °C 57.7 per cent O, 23.2 per cent M, 19.1 per cent P). At this temperature and concentration the liquid freezes invariantly to form a solid mixture of the three components. The section of the space model above the freezing point surfaces formed by the liquidus curves represents the homogeneous liquid phase. The section below these surfaces down to a temperature represented by point D denotes solid and liquid phases in equilibium. Below this temperature the section of the model represents a completely solidified system. 

For a three-component mixture, it is convenient to present the composition space C3 as an equilateral triangle, the height of which equals one (Fig. 1.1b). The triangle s vertexes represent pure components, the points within its sides, represent the binary constituents of the three-component mixture, and the inner points of triangle represent the three-component mixture compositions. The lengths of the perpendiculars to the triangle s sides correspond to the concentrations of the components indicated by the opposite vertexes. The described system of coordinates, which bears the name of the system of uniform coordinates, was introduced by Mobius and was further developed by Gibbs. 

Figure 14 (a) Illustration of the state diagram of asymmetric binary star mixtures (small star concentration C2 against small-to-large star size ratio). (b) The cartoon from MD simulations depicts the large-star cage and the small stars filling in the loose space. ... 

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