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Jawaharlal Nehru Technological University KakinadaPresented byProf. K. V. RaoAcademic Advisor / Visiting ProfessorPetroleum CoursesJNTUKIII Year B. Tech. Petrochemical Engineering II Sem.Mass Transfer Operations II

DistillationVAPOR LIQUID EQUILIBRIUMVAPOR LIQUID EQUILIBRIUMTypes of phase diagram in vapor-liquid systems

The different types of phase behavior occurring in vapor-liquid systems can be described most readily by referring to a binary system and to a quantity known as relative volatility. The relative volatility is defined in terms of an equilibrium ratio, which is conventionally defined by

Where yi is the mole fraction of component i in a vapor phase that is at equilibrium with a liquid phase containing xi mole fraction of the same component. The relative volatility of component i with respect to j is conventionally defined by

In a binary system x2 = 1 = x1 and y2 = 1 y1. It is conventional in binary systems to choose as component 1 the component with the lower boiling point (the more volatile component), to express compositions in terms of component 1, and to drop subscripts, recognizing that x = x1, y = y1, and = 12. Thus the conventional binary equation is

Which, solved for y, becomes

The type of phase behavior exhibited by a binary system will be determined largely by the manner in which varies with composition. For binary systems three methods are commonly used to represent the phase behavior graphically:

A plot of y versus x, which may be done either with temperature constant or with pressure constant.A plot of total vapor pressure versus x (bubble-point curve) and of total vapor pressure versus y (dew-point curve) at constant temperature.A plot of equilibrium temperature versus x and equilibrium temperature versus y at constant total pressure.Ideal Solutions

The ideal solution has a constant value of throughout all concentration ranges at constant temperature and a very nearly constant at constant pressure.

An example of the type of phase diagram exhibited by an ideal solution is shown in Figure 1.

The y-x curve for such a system always lies above the y = x line, which is usually shown on such diagram, and exhibits no unusual behavior, such as maxima, minima, or discontinuities.

Since the more volatile component is taken conventionally as component 1, is always greater than unity.

The isothermal - composition curves are equally well behaved.

The -x curve is always above the -y curve, with neither showing any peculiar behavior.

The isobaric T-composition curves are similar,except that thy T-y curves lies above the T-x curve.

The benzene-toluene system is an example of an ideal solution.

Ideal Solutions

Figure 1: Phase diagrams for ideal solution: a)isothermal x y diagramb) isothermal -composition diagramc) isobaric T-composition diagram

7Nonideal systems, Nonazeotroping

Usually the value of varies with composition. When its value is always greater than unity, the system is typically represented by Figure 2.

In the system shown here is greater at low values of x than at high values. Therefore the y-x curve has a tendency to inflect near a mole fraction of 1.

The pressure-versus-composition and temperature-versus-composition curves also show this tendency to inflect, but there is no maximum nor minimum in any of the curves.

In a system in which is greatest at high values of x the inflection tendency is near x = 0.

The region of the inflection tendency is frequently called a pinch to indicate that separation by distillation are difficult in this region. Systems of this type are quite common; methanol-water at atmospheric pressure is typical example.

Figure 2: Phase diagrams for nonideal, nonazeotroping system:

y-x diagram b) isothermal phase diagramc) isobaric phase diagram9Low-Boiling Azeotropic system

If varies greatly with composition, it might conceivably have values greater than unity at some concentrations and lower than unity at other concentration.

Since is continuous in composition, it will equal unity at some concentration. If = 1, it gives y = x and the composition at which this occurs (i. e., vapor composition and liquid composition of a mixture are equal at equilibrium) in known as the azeotrope.

If > 1 at low concentration and < 1 at high concentration, the azeotrope will be low boiling. The term low-boiling azeotrope merely implies that, at a given pressure, the boiling temperature of the azeotrope is lower than the boiling temperature of either pure component.Figure 3 shows as a typical set of diagrams for a low-boiling azeotropic system.

The y-x curve crosses the y = x line at the azeotropic composition, the pressure-composition curves both exhibit maxima and coincide at the azeotropic composition, and for the isobaric system the temperature-versus-composition curves coincide at a minimum at the azeotropic composition.

Such azeotropic systems frequently occur when the two components are dissimilar functionally and the boiling points are not greatly different (about 250C for most systems, although much greater difference are noted in some systems).

Ethanol-water is a typical example. An extensive tabulation of tabulation of known azeotropes is given by Horsley [1].

A very important characteristic of this type of system is that it is impossible by successive distillation at a pressure (or at a given temperature) to obtain from a mixture both components as pure products.

At some point in the procedure the azeotropic composition will be reached;

when an azeotrope feed is partially vaporized, the vapor has the same composition as the liquid and no separation of component is effected.

Figure 3: Phase diagrams for low-boiling azeotropic system:

y-x diagram b)isothermal phase diagram c) isobaric phase diagram13High-Boiling azeotropic systems

If varies with composition in such a way that it is less than unity at low concentration and greater than unity at high concentration, a high-boiling azeotrope occurs.

This type of system differs from the low-boiling azeotrope in that the temperature-versus-composition curves of the isobaric plot exhibit maxima and the pressure-versus-composition curves of the isothermal plot exhibit minima.

Typical diagrams for this type of systems are shown in Figure 4. The high-boiling azeotrope is less common than the low-boiling azeotrope; it generally occurs between components whose molecules are somewhat attracted to each other.

Acetone-chloroform is an example of this type of systems.

Figure 4: Phase diagrams for high-boiling azeotropic system:

y-x diagram b)isothermal phase diagram c) isobaric phase diagram15Heterogeneous azeotropic systems

Frequently a system with a strong tendency to form a low-boiling azeotrope will consist of two components that are not completely miscible in the liquid phase.

In such a system there will be a maximum solubility of component 1 in components 2, designated xs, and a maximum solubility of component 2 in component 1, designated 1 xs.

If a liquid mixture is prepared with overall composition between xs and xs, it will separate into two layers, or phases.

One phase will have composition xs and the other xs; the relative quantities of the two liquid phases can be determined by material balance from the overall composition. A typical set of diagrams for this type of system is shown in Figure 5. The composition xs and xs both have the same bubble point, and the equilibrium vapor composition ya is the same for both liquid compositions.

A vapor having the azeotropic composition will, when condensed, form two liquid phases having mole fractions xs and xs; thus the vapor having composition ya is known as a heterogeneous azeotrope.

Heterogeneous azeotropes are invariable low-boiling azeotropes, and this behavior is exhibited by most liquid with limited solubility.

Since the liquid-phase composition is never equal to the vapor-phase composition, it is possible to obtain both components pure by distillation a mixture;

However, in a continuous distillation at least two columns are required, and in a batch distillation at least two runs are required. The -butanol-water system is an example of this type of system.

Figure 5: Phase diagrams for heterogenous azeotroping system:

y-x diagram b)isothermal phase diagram c) isobaric phase diagram18Heterogeneous, Nonazeotroping System

It is possible for a partially miscible system not to exhibit an azeotrope. Such a system will have the equilibrium solubilities xs and xs, and the same vapor composition will exist in equilibrium with both these liquid compositions. However, the equilibrium vapor composition will not lie between xs and xs, as is the case with the heterogeneous azeotrope, and the boiling point of the xs (or xs) composition lies between the boiling points of the pure components. Figure 6 shows the typical phase diagrams of such a system. Systems of this type are not numerous; an example is the propylene oxide-water system.

It is conceivable that a system might exhibit partial miscibility and have an azeotrope in the homogeneous region. The author is not aware of the actual existence of such systems. Problem 1: Compute the vapor-liquid equilibria at constant pressure of 1 std atm for mixtures of n-heptane with n-octane, which may be expected to form ideal solutions.Solution: The boiling points at 1 std atm of the substances are n-heptane (A), 98.40C and n-octane (B), 125.60C. Computations are therefore made between these temperatures. For example, at 1100C, pA = 1050 mmHg, pB = 484 pt = 760 mmHg.

In similar fashion, the data of the following table can be computed:

Problem 2: A mixture containing 50 g water and 50 g ethylaniline, which can be assumed to be essentially insoluble, is boiled at standard atmospheric pressure. Describe the phenomena that occur.Solution: Since the liquids are insoluble, each exerts its own vapor pressure, and when the sum of these equals 760 mmHg, the mixture boils.

The mixture boils at 99.150C.

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