Point, azeotropic critical

Figure 2.2-1. Two phase equilibria three cases were the composition of the two phase are equal, a Pure component boiling point, b Azeotropic point, c Critical point.

Figure 5.100 Experimental and predicted VLE data, azeotropic points and critical data for the system CO2 (l)-ethane (2) using VTPR.

It has been shown that the principle of isomorphic critical behaviour accounts not only for the thermodynamic behaviour of mixtures near vapour-liquid critical points and near critical liquid-liquid mixing critical points, but also near special critical points, like azeotropic critical points, critical points where the critical temperature exhibits a maximum or a minimum as a function of temperature, re-entrant critical points and critical double points, depending on the values of the coefficients a,-, bi, and c,- in the expressions for the scaling fields. In this chapter we restrict ourselves to some more common cases of critical phase behaviour in mixtures. 

In cases where rAB>l and rBA>l or rAB<.l and rBAazeotropic composition1 or critical point where the copolymer composition will exactly reflect the monomer feed composition (Figure 7.1). 

According to this equation the maximum number of phases that can be in equilibrium in a binary system is = 4 (F= 0) and maximum number of degrees of freedom needed to describe the system = 3 (n=l). This means that all phase equilibria can be represented in a three-dimensional P,T,x-space. At equilibrium every phase participating in a phase equilibrium has the same P and T, but in principle a different composition x. This means that a four-phase-equilibrium (F=0) is given by four points in P, 7, x-space, a three-phase equilibrium (P=l) by three curves, a two-phase equilibrium (F=2) by two planes and a one phase state (F= 3) by a region. The critical state and the azeotropic state are represented by one curve. 

Often the essentials of phase diagrams in P,7,x-space are represented in a P,7-projection. In this type of diagrams only non-variant (F=0) and monovariant (F=l) equilibria can be represented. Since pressure and temperature of phases in equilibrium are equal, a four-phase equilibrium is now represented by one point and a three-phase equilibrium with one curve. Also the critical curve and the azeotropic curve are projected as a curve on the P, 7-plane. A four-phase point is the point of intersection of four three-phase curves. The point of intersection of a three-phase curve and a critical curve is a so-called critical endpoint. In this intersection point both the three-phase curve and the critical curve terminate. 

Since an azeotrope by definition has either a higher or a lower vapor pressure than that of any of the components, the azeotropic vapor pressure curve will always lie above or below the curves of the components. This is indicated schematically in Figure 1 where A and B are vapor pressure curves of the components and C is the vapor pressure of the azeotrope. If curve C crosses either A or B, the azeotropic vapor pressure is no longer greater or less than any of the components and the system will become nonazeotropic at the point of intersection. On the other hand, if the azeotropic curve is parallel to the other curves the system will be azeotropic up to the critical pressure. 

In cases where only the normal azeotropic boiling point is known, it is possible to predict the effect of pressure on the system by drawing the azeotrope curve through the normal boiling point with a slope equal to the average slopes of the component vapor pressure curves. This procedure will permit a fairly accurate prediction of whether the azeotrope will cease to exist below the critical pressure. 

Figure 14.11 The critical locus for (xiQHp + x2C6F6), a system with a maximum boiling azeotrope. In (A), the circles represent the critical points (a and b) of pure components (1) and (2) the solid lines represent (vapor + liquid) equilibrium for the pure substances the dashed line is the critical locus, and the short-dashed line represents the azeotrope composition, which intersects the critical locus at point c. (B) shows the intersection of the (vapor + liquid) equilibrium lines with the critical locus.

Figure 4.33 illustrates the PSPS and bifurcation behavior of a simple batch reactive distillation process. Qualitatively, the surface of potential singular points is shaped in the form of a hyperbola due to the boiling sequence of the involved components. Along the left-hand part of the PSPS, the stable node branch and the saddle point branch 1 coming from the water vertex, meet each other at the kinetic tangent pinch point x = (0.0246, 0.7462) at the critical Damkohler number Da = 0.414. The right-hand part of the PSPS is the saddle point branch 2, which runs from pure THF to the binary azeotrope between THF and water. 

If the components exhibit strong physical or chemical interaction, the phase diagrams may be different from those shown in Figs, 1,1 and 1,5, and more like those shown in Fig, 1.8. In such systems there is a critical composition (the point of intersection of the equilibrium curve with the 45 diagonal) for which the vapor and liquid compositions are identical, Once this vapor and liquid composition is reached, the components cannot be separated at the given pressure, Such mixtures are called azeotropes. 

Here, xt is the mole fraction of component i, n is the number of components, Tcl and Voi are the critical temperature and volume, and w, is the acentric coefficient for species i. In Eq. (3.21), 7h is the normal boiling point in Kelvin at atmospheric pressure, R = 1.987 cal/(molK), and A77v is in cal/mol. Table 3.2 shows the entropy of vaporization of some binary and ternary azeotropic mixtures obtained from the Lee-Kesler correlation. 

As tire pressure increases, line C D becomes shorter and shorter (indicated in Fig. 14.17 by lines CD and C"D"), until at point M it dimiirishes to a differential length. For still Irigher pressures (P4) the temperature is above tire critical-solution temperature, and there is but a single hquid phase. The diagram then represents two-phase VLE, and it has the form of Fig. 10.9(d), exhibiting a minimum-boiling azeotrope. 

Constituents from a particular homologous series, such as the normal paraffins, usually deviate from type-I phase behavior only when the size difference between them exceeds a certain value. This is because the constituents are so close in molecular structure that they cannot distinguish whether they are surrounded by like or unlike species. It is important to remember that the critical curve depicted in figure 3.1a is only one possible representation of a continuous curve. It is also possible to have continuous critical mixture curves that exhibit pressure minimums rather than maximums with increasing temperature, that are essentially linear between the critical points of the components (Schneider, 1970), and that exhibit an azeotrope at some point along the curve. 

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