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103 VLE: Qualitative Behavior
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Figure 105 P T diagram for ethaneln-heptane (Redrawn from F H Barr-David, AlChE J, vol 2, pp 426-427, 1956 with permission)
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The P-T diagram of Fig 105 is typical for mixtures of nonpolar substances such as hydrocarbons A P-T diagram for a very different kind of system, methanol(l)/benzene(2), is shown in Fig 107 The nature of the curves in this figure suggests how difficult it can be to predict phase behavior for species so dissimilar as methanol and benzene Although VLE in the critical region is of considerable importance in the petroleum and natural-gas industries, most chemical processing is accomplished at much lower pressures Figures 108 and 109 display common types of P-x-y and t-x-y behavior at conditions well removed from the critical region Figure 108(a) shows data for tetrahydrofuran(l)/carbon tetrachloride(2) at 30315 K (30 C) Here, the P-xl or bubblepoint curve on a P-xl-yl diagram lies below the linear P-xl relation characteristic of Raoult's-law behavior, as described in the following section When such negative departures from linearity become sufficiently large relative to the difference between the two pure-species vapor pressures, the P-x curve exhibits a minimum, as illustrated in Fig 108(b) for the chloroform(l)/tetrahydrofuran(2)system at 30315 K (30 C) This figure shows that the P-yl curve also has a minimum at the same point Thus at this point where xl = yl the dewpoint and bubblepoint curves are tangent to the same horizontal line A boiling liquid of this composition produces a vapor of exactly the same composition, and
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CHAPTER 10 Vapor/Liquid Equilibrium: Introduction -
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Figure 106 yx diagram forethaneln-heptane (Reproduced by permission from F H Barr-David, AIChE J, vol 2, p 426-427, 1956)
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the liquid therefore does not change in composition as it evaporates No separation of such a constant-boiling solution is possible by distillation The term azeotrope is used to describe this state3 The data for furan(1)lcarbon tetrachloride(2) at 30315 K (30 C) shown by Fig 108(c) provide an example of a system for which the P-xl curve lies above the linear P-xl relation The system shown in Fig 108(d)for ethanol(l)/toluene(2) at 33815 K (65 C) exhibits positive departures from linearity sufficiently large to cause a maximum in the P-xl curve This state is a maximum-pressure azeotrope Just as for the minimum-pressure azeotrope the vapor and liquid phases in equilibrium have the identical composition
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3~ compilation of data for such states is given by J Gmehling, Azeotropic Data, John Wiley & Sons, Inc, New York, 1994
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103 VLE: Qualitative Behavior
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Figure 107 P T diagram for methanollbenzene (Redrawn from Chem Eng Sci, vol 19, J M Skaates and W B Kay, "The phase relations of binary systems that form azeotropes," pp 431-444, copyright 1964, with permission from Elsevier Science Ltd, Pergamon Imprint, The Boulevard, Langford Lane, Kidlington OX5 IGB, UK)
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Appreciable negative departures from P-xl linearity reflect stronger liquid-phase intermolecular attractions between unlike than between like pairs of molecules Conversely, appreciable positive departures result for solutions for which liquid-phase intermolecular forces between like molecules are stronger than between unlike In this latter case the forces between like molecules may be so strong as to prevent complete miscibility, and the system then forms two separate liquid phases over a range of compositions, as described in Sec 144 Since distillation processes are carried out more nearly at constant pressure than at constant temperature, t-xl-y, diagrams of data at constant P are of practical interest The four such diagrams corresponding to those of Fig 108 are shown for atmospheric pressure in Fig 109 Note that the dewpoint (t-yl) curves lie above the bubblepoint (t-xl) curves Moreover, the minimum-pressure azeotrope of Fig 108(b) appears as a maximum-temperature (or maximum-boiling) azeotrope on Fig 109(b)There is an analogous correspondence between Figs 108(d) and 109(d) The yl-xl diagrams at constant P for the same four systems are shown in Fig 1010 The point at which a curve crosses the diagonal line of the diagram represents an azeotrope, for at such a point yl = XI
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