At low-to-moderate pressure ranges typical of most industrial applications, the fundamental composition relationship between the vapor and liquid phases in equilibrium can be expressed as a function of the total system pressure, the vapor pressure of each pure component, and the liquid-phase activity coefficient of each component i in the mixture:
In systems that exhibit ideal liquid-phase behavior, the activity coefficients, y(, are equal to unity and Eq. (13-124) simplifies to Raoult's law. For nonideal liquid-phase behavior, a system is said to show negative deviations from Raoult's law if y( < 1, and conversely, positive deviations from Raoult's law if y( > 1. In sufficiently nonideal systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as shown in each of the three parts of Fig. 13-57. At such maxima or minima, the equilibrium vapor and liquid compositions are identical. Thus, y( = x( for all i = 1, ...n (13-125)
and the system is said to form an azeotrope (from the Greek, meaning to bo(l unchanged). Azeotropic systems show a minimum in the T-x,y diagram when the deviations from Raoult's law are positive (Fig. 13-57a) and a maximum in the T-x,y diagram when the deviations from Raoult's law are negative (Fig. 13-57b). If at these two conditions, a single liquid phase is in equilibrium with the vapor phase, the azeotrope is homogeneous. If multiple liquid-phase behavior is exhibited at the azeotropic condition, the azeotrope is heterogeneous. For heterogeneous azeotropes, the vapor-phase composition is equal to the overall composition of the two (or more) liquid phases (Fig. 13-57c). Mixtures with only small deviations from Raoult's law may form an azeotrope only if the components are close-boiling. As the boiling-point difference between the components increases, the composition of the azeotrope shifts closer to one of the pure components (toward the lower-boiling pure component for minimum-boiling azeotropes, and toward the higher-boiling pure component for maximum-boiling azeotropes). Mixtures of components whose boiling points differ by more than about 30°C generally do not exhibit azeotropes distinguishable from the pure components even if large deviations from Raoult's law are present. As a qualitative guide to liquid-phase activity-coefficient behavior, Robbins [Chem. Eng. Prog., 76 (10) 58 (1980)] developed a matrix of chemical families, shown in Table 13-15, which indicates expected deviations from Raoult's law.
The formation of two liquid phases within some temperature range for close-boiling mixtures is generally an indication that the system
FIG. 13-57 Schematic isobaric-phase diagrams for binary azeotropic mixtures. (a) Homogeneous minimum-boiling azeotropes.
FIG. 13-57 (Continued) Schematic isobaric-phase diagrams for binary azeotropic mixtures. (b) Homogeneous maximum-boiling azeotrope.
will also exhibit a minimum-boiling azeotrope, since two liquid phases may form when deviations from Raoult's law are extremely positive. The fact that immiscibility does occur, however, does not guarantee that the azeotrope will be heterogeneous. The azeotropic temperature is sometimes outside the range of temperatures at which a system exhibits two liquid phases. Moreover, the azeotropic composition may not necessarily fall within the composition range of the two-liquid-phase region even when within the appropriate temperature range
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