## Y i

1.1.3 Phase Diagrams

Phase diagrams- are- uaed to describe binary systems by plotting two out of the three "ariables - composition, temperature and pressure, at a constant value of the remaining one. The most popular of these plots are the T-x plot and the x-y plot.

TEMPERATURE - COMPOSITION (T-x) DIAGRAMS (Figure 1.2) Curve ABC shows the composition - temperature relationship for the saturated liquid. At temperature T]_ and liquid composition X]_, point B is the condition at which the liquid is ready to start boiling. Point B is termed the bubble point.

When the liquid starts to boil at temperature T]_ (point B), the first vapor formed has a composition yi and is therefore at its dew point. At this point, the vapor is as rich in the light component as it will ever be. As temperature is further raised, more of the heavier component is boiled off. The quantity of vapor formed increases, but the mole fraction of the light component in both vapor and liquid drops. At temperature T2, the liquid composition is X2 and the vapor composition is y2• Some of the initial charge is now vapor and some is liquid. A further increase in temperature to T3 will vaporize the rest of the liquid. The vapor composition will now be x^, and the last drop of liquid vaporized has a composition X3.

From the above discussion, the liquid always travels along its bubble point curve (BEH) while the vapor always travels along the dew-point curve (DFG). Therefore, in distillation, bubble-points liquid is always in equilibrium with dew-point vapor.

x-y DIAGRAMS Another way of portraying the difference in composition of the liquid and vapor phase is by plotting one against the other (Figure 1.3). Such a plot is called an x-y diagram. Each point on the x-y diagram corresponds to a fixed equilibrium temperature on the T-x diagram. The 45* diagonal line represents points at which vapor and liquid compositions are the same.

The concept of dew points and bubble point is useful in the construction of x-y diagrams. When bubble-points and dew-points can be readily calculated for a mixture of components, the saturated liquid and saturated vapor curves can be plotted for the system as in Figure 1.2. From these data, values of x and y can be obtained for a number of temperatures, and used to construct the x-y diagram. Similarly, bubble-point calculations yield the equilibrium vapor compositions, giving the values of both x and y. These can also be derived from dew point calculations in a similar manner. Xt MOLE FRACTION IN LIQUID