Equilibrium line vapor-liquid diagrams

Using the vapor-liquid equihbrium data, plot a y-x diagram. Draw a number of operating lines at a slope of 0.75. Note the composition at the 45° intersection, and step off seven plates on each to find the equilibrium value of the bottoms. Some of the results are tabulated in the following table ... 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

At high pressures, solid II can be converted (slowly) to solid III. Solid III has a body-centered cubic crystal structure. Line bd is the equilibrium line between solid II and solid III, while line be is the melting line for solid III.P A triple point is present between solid II, solid III, and liquid at point b. Two other triple points are present in this system, but they are at too low a pressure to show on the phase diagram. One involves solid II, liquid, and vapor while the other has solid I, solid II, and vapor in equilibrium. 

The liquid line and vapor line together constitute a binary (vapor + liquid) phase diagram, in which the equilibrium (vapor) pressure is expressed as a function of mole fraction at constant temperature. At pressures less than the vapor (lower) curve, the mixture is all vapor. Two degrees of freedom are present in that region so that p and y2 can be varied independently. At pressures above the liquid (upper) curve, the mixture is all liquid. Again, two degrees of freedom are present so that p and. v can be varied independently/... 

Thus, by knowing aAB from vapor-liquid equilibrium and by specifying xA, A can be calculated. Figure 4.3a also shows a typical vapor-liquid equilibrium pair, where the mole fraction of benzene in the liquid phase is 0.4 and that in the vapor phase is 0.62. A diagonal line across the x-y diagram represents equal vapor and liquid compositions. The phase equilibrium behavior shows a curve above the diagonal line. This indicates that benzene has a higher concentration in the vapor phase than toluene, that is,... 

The conditions that apply for the saturated liquid-vapor states can be illustrated with a typical p-v, or (1 /p), diagram for the liquid-vapor phase of a pure substance, as shown in Figure 6.5. The saturated liquid states and vapor states are given by the locus of the f and g curves respectively, with the critical point at the peak. A line of constant temperature T is sketched, and shows that the saturation temperature is a function of pressure only, Tsm (p) or psat(T). In the vapor regime, at near normal atmospheric pressures the perfect gas laws can be used as an acceptable approximation, pv = (R/M)T, where R/M is the specific gas constant for the gas of molecular weight M. Furthermore, for a mixture of perfect gases in equilibrium with the liquid fuel, the following holds for the partial pressure of the fuel vapor in the mixture ... 

If you plot the temperature and vapor pressure data given in Table 1, you reconstruct the liquid-vapor equilibrium line in the phase diagram of that liquid (Fig. 139). The equation of this line, and you might remember this from your freshman chemistry course, is the Clausius -Clapyron equation ... 

Fig. 3.2. A stylized phase diagram for a simple pure substance. The dashed line represents 1 atm pressure and the intersection with the solid-liquid equilibrium line represents the normal boiling point and the intersection with the liquid-vapor equilibrium line represents the normal boiling point.

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

The three sets of vapor-liquid equilibrium data appearing on the x-y diagram show some disagreement, so that great accuracy cannot be expected from determination of tray requirements, particularly at the low water concentrations. The upper operating line in the first column is determined by the overall material balance so it passes through point (0.995, 0.995), but the initial point on the operating line is at x = 0.53, which is the composition of the reflux. The construction is shown for 50% vaporized feed. That result and those for other feed conditions are summarized ... 

Let s see how this simple expression applies to the phase diagrams we have been considering. When two phases are in equilibrium, such as liquid water and water vapor, we set p = 2 and obtain f = 3 — 2=1. One degree of freedom means that we can vary either the pressure or the temperature. To preserve the equilibrium when we vary the pressure, we have to adjust the temperature by an appropriate amount to preserve the equilibrium when we vary the temperature, the pressure must change appropriately. That is, the pressures and temperatures at which two phases are present in a one-component system are not independent of each other, and the relation between them is represented by a line on the phase diagram. As the temperature is changed, the pressure changes as indicated by the phase boundary. 

FIGURE 8.40 A temperature-composition diagram for benzene and toluene. The lower, blue line shows the boiling point of the mixture as a function of composition. The upper, orange line shows the composition of the vapor in equilibrium with the liquid at the boiling point. Thus, point B shows the vapor composition for a mixture that boils at A. 

FIGURE 11.18 A phase diagram of temperature versus composition (mole fraction) for a mixture of benzene and toluene. Liquid composition is given by the lower curve, and vapor composition is given by the top curve. The thin region between curves represents an equilibrium between phases. Liquid and vapor compositions at a given temperature are connected by a horizontal tie line, as explained in the text. 

Figure 14.10 The five types of (fluid + fluid) phase diagrams according to the Scott and van Konynenburg classification. The circles represent the critical points of pure components, while the triangles represent an upper critical solution temperature (u) or a lower critical solution temperature (1). The solid lines represent the (vapor + liquid) equilibrium lines for the pure substances. The dashed lines represent different types of critical loci. (l) [Ar + CH4], (2) [C02 + N20], (3) [C3H8 + H2S],...

The phase diagram (Figure 1-18) indicates the existence of three phases solid, liquid, and gas. The conditions under which they exist are separated by three equilibrium lines the vapor pressure line TA, the melting pressure line TC, and the sublimation pressure line BT. The three lines meet at point T,... 

A portion of the McCabe-Thiele diagram for the simulation involving plug flow of vapor and dispersion flow of the liquid is shown in Fig. 13-55. For a nonequilibrium column these diagrams can only be constructed from the results of a computer simulation. Note that the triangles that represent the stages extend beyond the curve that represents the equilibrium line this is so because the efficiencies are greater than 100 percent. 

The effect of the solute on the solution boiling point is easy to see from the diagram. Recall that the boiling point of a liquid at a given pressure is the intersection of a horizontal line at that pressure with the vapor-liquid equilibrium curve. At pressure Po, the pure solvent boils at temperature Tbo, while the solution boils at a higher temperature. Tbs. 

Vapor-liquid equilibrium is a mapping from a liquid composition to a vapor composition. It can be done by including tie lines from one to the other for all compositions. On a line, such a mapping is very difficult to visualize, so we typically use a second dimension where we can plot vapor composition versus liquid composition as in a McCabe-Thiele plot or as in a temperature versus composition diagram. For three or four species, showing tie lines is fairly direct. The important point is that equilibrium is not a line (as we might think because of our familiarity with McCabe-Thiele plots) but a mapping. 

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