'only N - 1 mole fractions are required, because
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xi xi = 1
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103 VLE: Qualitative Behavior
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Figure 101 P T x y diagram for vaporlliquid equilibrium
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103 VLE: QUALITATIVE BEHAVIOR
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VaporAiquid equilibrium (VLE) is the state of coexistence of liquid and vapor phases In this qualitative discussion, we limit consideration to systems comprised of two chemical species, because systems of greater complexity cannot be adequately represented graphically When N = 2, the phase rule becomes F = 4 - nSince there must be at least one phase(n = I), the maximum number of phase-rule variables which must be specified to fix the intensive state of the system is three: namely, P, T, and one mole (or mass) fraction All equilibrium states of the system can therefore be represented in three-dimensional P-Tcomposition space Within this space, the states of pairs of phases coexisting at equilibrium (F = 4 - 2 = 2) define surfaces A schematic three-dimensional diagram illustrating these surfaces for VLE is shown in Fig 101 This figure shows schematically the P-T-composition surfaces which contain the equilibrium states of saturated vapor and saturated liquid for a binary system The under surface contains the saturated-vapor states; it is the P-T-yl surface The upper surface contains the saturated-liquid states; it is the P-T-xl surface These surfaces intersect along the lines U B H C ,
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CHAPTER 10 Vapor/Liquid Eauilibrium: Introduction
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and KAC2, which represent the vapor pressure-vs-T curves for pure species 1 and 2 Moreover, the under and upper surfaces form a continuous rounded surface across the top of the diagram between Cl and C2,the critical points of pure species 1 and 2; the critical points of the various mixtures of the two species lie along a line on the rounded edge of the surface between C1 and C2 This critical locus is defined by the points at which vapor and liquid phases in equilibrium become identical Further discussion of the critical region is given later The subcooled-liquid region lies above the upper surface of Fig 101; the superheatedvapor region lies below the under surface The interior space between the two surfaces is the region of coexistence of both liquid and vapor phases If one starts with a liquid at F and reduces the pressure at constant temperature and composition along vertical line FG, the first bubble of vapor appears at point L, which lies on the upper surface Thus, L is a bubblepoint, and the upper surface is the bubblepoint surface The state of the vapor bubble in equilibrium with the liquid at L must be represented by a point on the under surface at the temperature and pressure of L This point is indicated by V Line VL is an example of a tie line, which connects points representing phases in equilibrium As the pressure is further reduced along line F G , more and more liquid vaporizes until at W the process is complete Thus W lies on the under surface and represents a state of saturated vapor having the mixture composition Since W is the point at which the last drops of liquid (dew) disappear, it is a dewpoint, and the lower surface is the dewpoint surface Continued reduction of pressure merely leads into the superheated vapor region Because of the complexity of Fig 101, the detailed characteristics of binary VLE are usually depicted by two-dimensional graphs that display what is seen on various planes that cut the three-dimensional diagram The three principal planes, each perpendicular to one of the coordinate axes, are illustrated in Fig 101 Thus a vertical plane perpendicular to the temperature axis is outlined as AL B D EA The lines on this plane form a P-xl - y phase diagram at constant T If the lines from several such planes are projected on a single parallel plane, a diagram like Fig 102(a) is obtained It shows P-xl-yl plots for three different temperatures The one for T represents the section of Fig 101 indicated by ALB DEA The horizontal , lines are tie lines connecting the compositions of phases in equilibrium The temperature Tb lies between the two pure-species critical temperatures identified by C1 and C2 in Fig 101, and temperature Td is above both critical temperatures The curves for these two temperatures therefore do not extend all the way across the diagram However, the first passes through one mixture critical point, and the second through two such points All three of these critical points are denoted by the letter C Each is a tangent point at which a horizontal line touches the curve This is so because all tie lines connecting phases in equilibrium are horizontal, and the tie line connecting identical phases (the definition of a critical point) must therefore be the last such line to cut the diagram A horizontal plane passed through Fig 101 perpendicular to the P axis is identified by H I J K L H Viewed from the top, the lines on this plane represent a T-xl-y diagram When lines for several pressures are projected on a parallel plane, the resulting diagram appears as in Fig 102(b) This figure is analogous to Fig 102(a), except that it represents values for three constant pressures, Pa, Pb, and Pd Other possible plots are vapor mole fraction yl vs liquid mole fraction xl for either the constant-T conditions of Fig 102(a) or the constant-P conditions of Fig 102(b) The third plane identified in Fig 101, vertical and perpendicular to the composition axis, is indicated by MNQRSLM When projected on a parallel plane, the lines from several
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