Vapor-liquid equilibrium temperature diagrams

Once the equilibrium total pressure has been computed for a given liquid composition using Eqs. 10.1-2 or 10.1-4, the equilibrium composition of the vapor can be calculated using Eqs. 10.1-1 or 10.1-3, as appropriate. Indeed, we can prepare a complete vapor-liquid equilibrium composition diagram, or x-y diagram, at constant temperature by choosing a collection of values for the composition of one of the phases, say the liquid-phase composition x, and then using the vapor pressure data to compute the... 

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 schematic diagram of the high-pressure vapor-liquid equilibrium circulation-type apparatus is shown in Fig.l. The main piece of the equipment is a high-pressure phase equilibrium cell of approximately 100 cm3. The apparatus includes a compressed-air actuated piston-pump that allows to circulate one or both phases to bring the vapor and liquid in close contact with each other. This pump, the cell and all the related valves were placed in a constant-temperature water bath to have and to keep uniformely the desired temperature. 

Obtain (or plot from data) a phase diagram for the benzene/toluene system. Vapor-liquid equilibrium behavior of binary systems can be represented by a temperature-composition diagram at... 

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. 

The separation process depends on the nature of the vapor-liquid equilibrium relationships of the system, which can be represented on a ternary diagram. Figure 10.3a shows a ternary diagram at some fixed system pressure. Components A and B are close boilers, and A forms an azeotrope with the entrainer E. The curves in the triangle represent liquid isotherms. A corresponding vapor isotherm (not shown) could be drawn to represent the vapor at equilibrium with each liquid curve with tie lines joining vapor and liquid compositions at equilibrium. The temperature of the isotherms reaches a minimum at point Z that corresponds to the composition of the azeotrope formed between A and E. 

Figure 3.5d shows the construction of a P-x diagram at temperature Tj, an isotherm that intersects the vapor pressure curve of the less volatile component, the LLV line, and both branches of the critical mixture curve (see figure 3.5b). At low pressures, a single vapor phase exists until the dew point curve of the vapor-liquid envelope is intersected and a liquid phase is formed. Vapor-liquid equilibrium is observed as the pressure is increased further until the three-phase LLV line is intersected, indicated by the horizontal tie line shown in figure 3.5d. There now exists a single vapor phase and two liquid phases. 

The phase behavior for the polymer-solvent systems can be described using two classes of binary P-T diagrams, which originate from P—T diagrams for small molecule systems. Figure 3.24A shows the schematic P-T diagram for a type-III system where the vapor-liquid equilibrium curves for two pure components end in their respective critical points, Ci and C2. The steep dashed line in figure 3.24A at the lower temperatures is the P-T trace of the UCST... 

Example 18.1. A mixture of 50 mole percent benzene and 50 mole percent toluene is subjected to flash distillation at a separator pressure of 1 atm. The vapor-liquid equilibrium curve and boiling-point diagram are shown in Figs. 18.2 and 18.3. Plot the following quantities, all as functions of f, the fractional vaporization (n) the temperature in the separator, b) the composition of the liquid leaving the separator, and (c) the composition of the vapor leaving the separator. 

Few liquid mixtures are ideal, so vapor-liquid equilibrium calculations can be more complicated than is the case for the hexane-triethylamine system, and the system phase diagrams can be more structured than Fig. 10.1-6. These complications arise from the (nonlinear) composition dependence of the species activity coefficients. For example, as a result of the composition dependence of y, the equilibrium pressure in a fixed-temperature experiment will no longer be a linear function of mole fraction. Thus nonideal solutions exhibit deviations from Raoult s law. We will discuss this in detail in the following sections of this chapter. However, first, to illustrate the concepts and some of the types of calculations that arise in vapor-liquid equilibrium in the simplest way, we will assume ideal vapor and liquid solutions (Raoult s law) here, and then in Sec. 10.2 consider the calculations for the more difficult case of nonideal solutions.. ... 

For a binary (that is, two-component) mixture, if constant-pressure vapor-liquid equilibrium diagrams, such as Fig. 10.1-4 or that of Illustration 10.1-1. have been previously prepared, dewpoint and bubblepoint temperatures can easily be read from these diagrams. For the cases in which such information is not available, or if a multicomponent mixture is of interest, the trial-and-error procedure of Illustration 10.1 -2 is used to estimate these temperatures. 

The figure-that follows for the ethanol + water sy.s-tem is an unusual one in that it shows both vapor-liquid equilibrium and the enthalpy concentration diagrams on a single plot. This is done as follows. The lower collection of heavy lines give the enthalpy concentration data for the liquid at various temperatures and the upper collection of lines is the enthalpy-concentration data for the vapor, each at two pressures, 0.1013 and 1 013 bar. (There are also enthalpy-concentration lines for several other temperatures.) The middle collection of lines connect the equilibrium compositions of liquid and vapor. For example, at a pressure of 1.013 bar, a saturated-vapor containing 71 wt % ethanol with an enthalpy of 1535 kJ/kg is in equilibrium with a liquid containing 29 wt % ethanol with an enthalpy of 315 kJ/kg at a temperature of 85°C. Note also that the azeotropes that form in the ethanol -f water system are indicated at each pressure. 

Figure 3.2b, an x-y vapor-liquid equilibrium diagram, is an alternative way of presenting some of the information in Fig. 3.2a. Here each point on the x-y equilibrium curve is at a different but undesignated temperature. Figure 3.2b is widely used in calculating equilibrium-stage requirements even though it contains less information than Fig. 3.2a.

A schematic of the entropy diagram and the thermodynamic cycle is shown on the right side of the diagram. Temperature is shown on the x-axis and entropy is on the y-axis. The lines identified as h, and hz represent constant enthalpy. Lines P, and P2 are constant pressure. The parabolic curve is the locus of points representing the vapor-liquid equilibrium. The thermodynamic cycle is traced by the points labeled 1 through 7. 

As an example, consider the system formed by liquid water in equilibrium with its own vapor. The pressure—temperature diagram for this system has been constructed over the range of 1-99°C [10] and is shown in Fig. 1. The characteristics of a univariant system (one degree of freedom) are evident in that for each definite temperature value, water exhibits a fixed and definite pressure value. 

Figure 9.8 Pressure-temperature diagram for the alkane(l)-aromatic(2) mixture in Figures 9.4-9.7. Solid lines are pure vapor-pressure curves, ending at pure critical points (filled circles). Dashed line is the mixture critical line. Dash-dot lines are liquid constant-composition lines small dashed lines are vapor constant-composition lines. Filled square at A is a vapor-liquid equilibrium point it occurs at 14.5 bar, 386.7 K, Xj = 0.25, t/j = 0.75.

An accurate but simple way to quantily the vapor—liquid equilibrium relationships is to generate T y diagrams at two different pressures. Over a fairly small composition range at a constant pressure, a linear dependence of composition on temperature should provide... 

The cubic form of an equation of state is the simplest form which enables the description of the PvT behavior of gases and liquids and thus the representation of the vapor-liquid equilibrium with only one model. At constant temperature and aL a given pressure this equation has three solutions. These solutions may be - depending on the values of temperature and pressure - all of real type or of mixed real and complex type. Figure 2.14 shows an isotherm in the Pv-diagram, calculated with the Soave-Redlich-Kwong equation for ethanol at 473.15 K. The cho.. en temperature is lower than the critical temperature of ethanol (T = 516.2 K),... 

FIGURE 8.4 Vapor-liquid phase diagrams of methane in a graphite pore with fluid-solid interaction of ejkg = 21.5 K and pore width of H = lOo, where o is diameter of methane. Temperature, T, and density, p, are in adimensional form in the plot. The open circles and dashed and solid lines represent the results from the simulations, MFT, and MFWDFT, respectively. The dotted curve represents the bulk vapor-liquid equilibrium obtained from simulation. (From Vishnyakov, A., et al. Langmuir 17 4451, 2001 Adapted from Peng, B. and Yu, Y.-X., J. Phys. Chem. B. 112 15407, 2008.)... 

It is usually desirable to present the experimental vapor-liquid equilibrium data graphically. A number of methods of presentation have been developed, but the most important are the temperature-composition and the vapor-liquid composition diagrams. 

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