## Vapor Liquid Phase Diagrams

Vapor-liquid equilibrium data may be obtained by experiment, by thermodynamic calculation, or in published sources. It is typically presented either in tabular form or as an equilbrium diagram. Diagrams may take several forms:

• boiling point diagrams
• Txy, Pxy diagrams
• ternary diagrams
• solubility diagrams
Each of these has specific uses. We'll begin by discussing "boiling point" diagrams, which are more precisely called Txy or Pxy diagrams.

### Txy Diagrams

You may have seen some of these diagrams in your material balance and stoichiometry class (for instance, see Felder & Rousseau (3rd ed.), Section 6.4d).

The figure (see Figure 9.1 in the text, also Fig 21.3 in MSH6) shows one common way of plotting equilibrium data -- the Txy diagram. It represents a binary mixture, and all compositions are expressed as mole fractions of the more volatile component; x in the liquid phase or y in the vapor phase. (The less volatile component is thus 1-x and 1- y.)

For a given temperature and composition, this diagram tells us the nature and composition of each phase of the mixture that is present. Similar drawings can be constructed at constant temperature while allowing pressure to vary. These will look basically the same, only the shape of the phase envelope will be inverted. (If a Txy slants down left-to-right, the Pxy will slant up L-to-R).

When a pure component boils, it does so at a temperature fixed by the pressure (or vice versa). This temperature remains constant from the time the first bubble vaporizes until all of the pure substance is vaporized. When a mixture boils, the temperature varies, because as vapor forms and boils off the composition of the remaining saturated mixture is changes. We call the temperature at which a mixture begins to boil (when the first bubble of vapor forms) the bubble point temperature (or pressure) of the mixture. The bubble point as a function of composition is shown on a Txy diagram as the line forming the bottom of the phase envelope.

When a vapor mixture is condensed, the less volatile component will tend to condense first and the condensing temperature will change as the less volatile exponent is depleted. We call the temperature where the first drop of condensate liquid forms the dew point temperature. This is shown by the line along the top of the phase envelope.

At temperatures between the bubble point and the dew point, a mixture will be partially vaporized, thus we call the interior of the phase envelope the two-phase region.

### Calculations

The calculations we make using Txy or Pxy diagrams begin with mass and component balances. Assume that a binary feed stream F is split into a liquid portion L and a vapor portion V. Each stream has its own unique composition, so that the balances become:

The equations are often rearranged in terms of the fraction vaporized or other ratios. This calculation is a very simple form of a "flash calculation", which we'll examine in greater detail later on.

References:

1. Elliott, J.R. and C.T. Lira, Introductory Chemical Engineering Thermodynamics, PTR Prentice-Hall, 1999, pp. 285-87.
2. McCabe, W.L. and J.C. Smith, Unit Operations of Chemical Engineering (3rd Edition), McGraw-Hill, 1976, pp. 485-86.
3. Treybal, R.E., Mass-Transfer Operations, 3rd Edition (Reissue), McGraw-Hill, 1987, pp. 343-46, 347-48.

R.M. Price
Original: 3/6/97, 1/5/98; 8/13/2002; 7/20/2004
Modified: 1/8/98, 1/8/99; 2/10/2003