Vapourliquid Equilibrium

The composition of the vapour in equilibrium with a liquid of given composition is determined experimentally using an equilibrium still. The results are conveniently shown on a temperature-composition diagram as shown in Figure 11.3. In the normal case shown in Figure 11.3a, the curve ABC shows the composition of the liquid which boils at any

Temperature Composition Diagram Toluene
Figure 11.1. Separation of a binary mixture
Atmospheric Distillation Column
Figure 11.2. Multicomponent separation

given temperature, and the curve ADC the corresponding composition of the vapour at that temperature. Thus, a liquid of composition x1 will boil at temperature T1, and the vapour in equilibrium is indicated by point D of composition y1. It is seen that for any liquid composition x the vapour formed will be richer in the more volatile component, where x is the mole fraction of the more volatile component in the liquid, and y in the vapour. Examples of mixtures giving this type of curve are benzene-toluene, n-heptane-toluene, and carbon disulphide-carbon tetrachloride.

In Figures 11.3b and c, there is a critical composition xg where the vapour has the same composition as the liquid, so that no change occurs on boiling. Such critical mixtures are called azeotropes. Special methods which are necessary to effect separation of these are discussed in Section 11.8. For compositions other than xg, the vapour formed has a

Azeotropes Carbon Disulfide Acetone

Mole fraction in liquid (x) Mole fraction in liquid (x) Mole fraction in liquid (x)

(a) Benzene-toluene (&) Acetone-carbon disulphide (c) Acetone-chloroform

Mole fraction in liquid (x) Mole fraction in liquid (x) Mole fraction in liquid (x)

(a) Benzene-toluene (&) Acetone-carbon disulphide (c) Acetone-chloroform

Figure 11.3. Temperature composition diagrams different composition from that of the liquid. It is important to note that these diagrams are for constant pressure conditions, and that the composition of the vapour in equilibrium with a given liquid will change with pressure.

For distillation purposes it is more convenient to plot y against x at a constant pressure, since the majority of industrial distillations take place at substantially constant pressure. This is shown in Figure 11.4 where it should be noted that the temperature varies along each of the curves.

Figure 11.4. Vapour composition as a function of liquid composition at constant pressure

11.2.1. Partial vaporisation and partial condensation

If a mixture of benzene and toluene is heated in a vessel, closed in such a way that the pressure remains atmospheric and no material can escape and the mole fraction of the more volatile component in the liquid, that is benzene, is plotted as abscissa, and the temperature at which the mixture boils as ordinate, then the boiling curve is obtained as shown by ABCJ in Figure 11.5. The corresponding dew point curve ADEJ shows the temperature at which a vapour of composition y starts to condense.

Boiling Point Diagram Acetone Toluene
Figure 11.5. Effect of partial vaporisation and condensation at the boiling point

If a mixture of composition x2 is at a temperature T3 below its boiling point, T2, as shown by point G on the diagram, then on heating at constant pressure the following changes will occur:

(a) When the temperature reaches T2, the liquid will boil, as shown by point B, and some vapour of composition y2, shown by point E, is formed.

(b) On further heating the composition of the liquid will change because of the loss of the more volatile component to the vapour and the boiling point will therefore rise to some temperature T'. At this temperature the liquid will have a composition represented by point L, and the vapour a composition represented by point N. Since no material is lost from the system, there will be a change in the proportion of liquid to vapour, where the ratio is:

Liquid MN Vapour ML

(c) On further heating to a temperature T1, all of the liquid is vaporised to give vapour D of the same composition y1 as the original liquid.

It may be seen that partial vaporisation of the liquid gives a vapour richer in the more volatile component than the liquid. If the vapour initially formed, as for instance at point E, is at once removed by condensation, then a liquid of composition x3 is obtained, represented by point C. The step BEC may be regarded as representing an ideal stage, since the liquid passes from composition x2 to a liquid of composition x3, which represents a greater enrichment in the more volatile component than can be obtained by any other single stage of vaporisation.

Starting with superheated vapour represented by point H, on cooling to D condensation commences, and the first drop of liquid has a composition K. Further cooling to T' gives liquid L and vapour N. Thus, partial condensation brings about enrichment of the vapour in the more volatile component in the same manner as partial vaporisation. The industrial distillation column is, in essence, a series of units in which these two processes of partial vaporisation and partial condensation are effected simultaneously.

11.2.2. Partial pressures, and Dalton's, Raoult's and Henry's laws

The partial pressure PA of component A in a mixture of vapours is the pressure that would be exerted by component A at the same temperature, if present in the same volumetric concentration as in the mixture.

By Dalton's law of partial pressures, P = that is the total pressure is equal to the summation of the partial pressures. Since in an ideal gas or vapour the partial pressure is proportional to the mole fraction of the constituent, then:

For an ideal mixture, the partial pressure is related to the concentration in the liquid phase by Raoult's law which may be written as:

where PA is the vapour pressure of pure A at the same temperature. This relation is usually found to be true only for high values of xa, or correspondingly low values of xb, although mixtures of organic isomers and some hydrocarbons follow the law closely.

For low values of xa, a linear relation between PA and xa again exists, although the proportionality factor is Henry's constant H', and not the vapour pressure PA of the pure material.

For a liquid solute A in a solvent liquid B, Henry's law takes the form:

If the mixture follows Raoult's law, then the vapour pressure of a mixture may be obtained graphically from a knowledge of the vapour pressure of the two components. Thus, in Figure 11.6. OA represents the partial pressure PA of A in a mixture, and CB the partial pressure of B, with the total pressure being shown by the line BA. In a mixture of composition D, the partial pressure PA is given by DE, PB by DF, and the total pressure P by DG, from the geometry of Figure 11.6.

Figure 11.7 shows the partial pressure of one component A plotted against the mole fraction for a mixture that is not ideal. It is found that over the range OC the mixture follows Henry's law, and over BA it follows Raoult's law. Although most mixtures show wide divergences from ideality, one of the laws is usually followed at very high and very low concentrations.

If the mixture follows Raoult's law, then the values of yA for various values of xa may be calculated from a knowledge of the vapour pressures of the two components at

Fractionating Reflux Still
Figure 11.6. Partial pressures of ideal mixtures
Fractionating Reflux Still
Figure 11.7. Partial pressures of non-ideal mixtures

various temperatures.

Thus: and:

giving:

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Responses

  • David
    What is the ideal ratio for a reflux column?
    7 years ago
  • angela castiglione
    Where is equilibrium shown on a heating curve?
    6 years ago

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