Vapor-liquid equilibria curves

Figure 8-2 illustrates a typical normal volatility vapor-liquid equilibrium curve for a particular component of interest in a distillation separation, usually for the more volatile of the binary mixture, or the one where separation is important in a multicomponent mixture. 

Most batch distillations/separations are assumed to follow the constant relative volatility vapor-liquid equilibrium curve of... 

For continuous systems, molar flow rates Q can be used instead of n. The thermodynamic activity (ax) can be calculated according to Equation 2, but requires knowledge of the saturation pressure of the pure compound (Ppsatx). This data can be obtained from the saturation curves (vapor-liquid equilibrium curves) and is taken at the working temperature of the gas stream. The thermodynamic activity is then calculated using the following equation ... 

The data in Tables I-XVI (see Appendix for all tables) show the isobaric vapor-liquid equilibrium results at the boiling point for potassium, ammonium, tetramethylammonium, tetraethylammonium, tetra-n-propylammonium, and tetra-n-butylammonium bromides in various ethanol-water mixtures at fixed liquid composition ratios. The temperature, t, is the boiling temperature for all solutions in these tables. In all cases, the ethanol-water composition was held constant between 0.20 and 0.35 mole fraction ethanol since it is in this range that the most dramatic salt effects on vapor-liquid equilibrium in this particular system should be observed. That is, previous data (12-15,38) have demonstrated that a maximum displacement of the vapor-liquid equilibrium curve by salts frequently occurs in this region. In the results presented here, it should be noted that Equation 1 has been modified to... 

Figure 8.4. Equilibrium constant (log K) for the reaction HCC>3 + H+ — CC>2(gas) + H20(aq) as a function of temperature at different pressures. SAT refers to the vapor-liquid equilibrium curve for pure H2O. (After Bowers et al., 1984.)...

FIG. 13-4 Isobaric vapor-liquid equilibrium curves for benzene-toluene. Brian, Staged Cascades in Chemical Processing, Frentice-Hall, Englewood Cliff , N.J., 1972.)... 

Because of the wide range of fixed x values for which data had been taken, it was possible to use interpolated data from Table II to construct a family of vapor-liquid equilibrium curves for the ammonium bromide-ethanol-water system at various constant salt concentration values—the condition most closely representing that existing from tray to tray in a... 

If r and P correspond to a point on the vapor-liquid equilibrium curve for a substance, P is the vapor pressure of the substance at temperature T, and T is the boiling point (more precisely, the boiling point temperature) of the substance at pressure P. 

The vapor-liquid equilibrium curve terminates at the critical temperature and critical pressure (7c nnd Pc). Above and to the right of the critical point, two separate phases never coexist. 

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. 

Let us again consider the vapor-liquid equilibrium curve for benzene and toluene (Fig. 1-25). If one started with a mixture of 20 mole per cent benzene and 80 mole per cent toluene, the vapor in equilibrium with this mixture (upper curve) would have about 40 mole per cent benzene. This percentage corresponds to the composition of... 

Plot the vapor-liquid equilibrium curve from data available at the column operating pressure. In terms of relative volatility... 

For the small concentrations of interest in flashing furfural residues (5 % by weight of furfural in water corresponds to a mere 0.977 % by mole), this ratio can be well approximated by the initial slope of the vapor/liquid equilibrium curve. Referred to mass fractions, this slope is known as the amplification factor k . Its dependence on pressure is illustrated in Figure 124. As can be seen, k increases strongly with decreasing pressure. 

The saturation ratio is greater than unity when p and T correspond to a vapor state on the liquid side of the vapor-liquid equilibrium curve. For S > I, the system is said to be supersaturated. The supcrsaiuration is given by (/) — pA/p.t-... 

Figure 3.24 Comparison of the schematic P-T diagrams for small molecule systems with those for polymer-solvent systems (A), type-lll system for a small molecule system where the vapor-liquid equilibrium curves for two pure components end in their respective critical points,...

Reversible Reaction. This type of absorption is characterized by the occurrence of a chemical reacting between the gaseous component being absoibed and a component in the liquid phsee to form a compound the exerts a significant vapor preasure of the absorbed component. An example is the absorptina of carbon dioxide into a monoethanoismine solution. This type of system is quite difficult to analyze bacause the vapor-liquid equilibrium curve is not linear and the race of absorption may be affected by chemical reactiou rates. 

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. 

Although the separation achieved in a column depends to some extent on all components in the feed, an approximate value of the minimum reflux ratio can be obtained by treating the mixture as a pseudobinary. Taking only the moles of light key and heavy key to make a new pseudofeed, product compositions could be calculated along with a vapor-liquid equilibrium curve based on aLK-mt-Then could be obtained using Eq. (18.43) as illustrated in Fig. 18.19. An alternate equation for a saturated liquid feed gives the minimum ratio of liquid rate to feed rate for a binary mixture of A and B ... 

The first commercial application of pervaporation was for ethanol-water separation. The dilute solution produced by fermentation is distilled to produce an overhead product with 90 to 95 percent alcohol (close to the azeotrope), and this solution is fed to the membrane unit to give nearly pure ethanol (99.9 percent). The permeate stream with about 20 to 40 percent alcohol is recyled to the distillation column. The vapor-liquid equilibrium curve and the vapor and liquid compositions for a poly(vinyl alcohol) membrane are shown in Fig. 26.16. The membrane gives a permeate that is always richer in water than the liquid, in contrast to distillation, where alcohol is the more volatile component over most of the range. The shape of the curve for permeate composition indicates strongly... 

Figure 11.3-3 shows the vapor-liquid and liquid-liquid equilibrium behavior computed for the system of methanol and n-hexane at various temperatures. Note that two liquid phases coexist in equilibrium to temperatures of about 43°C. Since liquids are relatively incompressible, the species liquid-phase fugacities are almost independent of pressure (see Illustrations 7.4-8 and 7.4-9), so that the liquid-liquid behavior is essentially independent of pressure, unless the pressure is very high, or low enough for the mixture to vaporize (this possibility will be considered shortly). The vapor-liquid equilibrium curves for this system at various pressures are also shown in the figure. Note that since the fugacity of a species in a vapor-phase mixture is directly proportional to pressure, the VLE curves are a function of pressure, even though the LLE curves are not. Also, since the methanol-hexane mixture is quite nonideal, and the pure component vapor pressures are similar in value, this system exhibits azeotropic behavior. 

At the lowest pressure in the figure, P = 0.133 bar, the vapor-liquid equilibrium curve intersects the liquid-liquid equilibrium curve. Consequently, at this pressure, depending on the temperature and composition, we may have only a liquid, two liquids, two liquids and a vapor, a vapor and a liquid, or only a vapor in equilibrium. The equilibrium state that does exist can be found by first determining whether the composition of the liquid is such that one or two liquid phases exist at the temperature chosen. Next, the bubble point temperature of the one or either of the two liquids present is determined (for example, from experimental data or from known vapor pressures and an activity coefficient model calculation). If the liquid-phase bubble point temperature is higher than the temperature of interest, then only a liquid or two liquids are present. If the bubble point temperature is lower, then depending on the composition, either a vapor, or. a vapor and a liquid are present. However, if the temperature of interest is equal to the bubble point temperature and the composition is in the range in which two liquids are present, then a vapor and two coexisting liquids will be in equilibrium. 

Equilibrium methods, as proposed originally by Silver [200] and extended by Bell and Ghaly [201] and others, all assume that there is local equilibrium between the vapor and the condensate throughout the condenser. Even though condensation is a nonequilibrium process, the gas temperature Tg is assumed to follow a vapor-liquid equilibrium curve at T, as the vapor mixture is cooled from the mixture dew point 7"dew to the mixture bubble temperature Tbub. These methods therefore require the generation of a cooling or condensation curve (not to be confused with the condensation curve described in Fig. 14.1), as shown in Fig. 14.25,... 

Binary Vapor-Liquid Equilibrium Curves Based on Constant Relative Volatility... 

BC Evaporate liquid - -V increases, system remains at point on vapor - liquid equilibrium curve as long as some liquid is present. T = 100° C. 

Figure 8.6 Vapor-liquid equilibrium curve for the substance of Figure 8.4, computed from the Redlich-Kwong equation of state. The critical point is marked with a filled square. Also shown is the 250 K isotherm taken from Figure 8.4. At this temp>erature the Redlich-Kwong equation gives P = 40.8 bar the saturated vapor and liquid volumes occur at the filled circles. The van der Waals loop is that part of the 250 K isotherm between the saturated phases.

This linear relationship between the total pressure, P, and the mole fraction, x, of the most volatile species is a characteristic of Raoult s law, as shown in Figure 7.18a for the benzene-toluene mixture at 90°C. Note that the bubble-point curve (P-x) is linear between the vapor pressures of the pure species (at x, = 0, 1), and the dew-point curve (P-yJ lies below it. When the (x, yi) points are graphed at different pressures, the familiar vapor-liquid equilibrium curve is obtained, as shown in Figure 7.18b. Using McCabe-Thiele analysis, it is shown readily that for any feed composition, there are no limitations to the values of the mole fractions of the distillate and bottoms products from a distillation tower. 

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