of the pure substance these two lines coincide, and the critical temperature and pressure are the maximum for both variables that can exist and have coexistence of liquid and vapor phase. In the case of the mixture the maximum temperature does not coincide with the maximum pressure.

For a pure component at the critical condition, the properties of the vapor and the liquid phases become identical in all respects. In the

Fig. 4-2. Pressure-temperature curves for butane-hexane system.

and the liquid are in general different, both at the point of maximum temperature and at the point of maximum pressure. There is a point on the loop, usually between the maximum temperature and the maximum pressure points, at which the properties of the liquid and the vapor are identical. This is taken as the critical of the mixture. This critical point K is shown on Fig. 4-1. Figure 4-2 shows loop curves for three different mixtures of butane and hexane, and a curve indicating the loci of critical points is shown. If the conditions inside a single loop curve are analyzed, it is found possible to plot lines of constant fraction vaporized; such curves for 0, 20, 40, 60, 80, and 100 per cent vapor have been drawn in Fig 4-3. All these curves converge to a common point at the critical.

The curves of Fig. 4-3 indicate the phenomena of retrograde condensation, i.e., conditions under which an increase in pressure causes vaporization instead of condensation, or in which a decrease in temperature causes vaporization instead of condensation. Thus, start ing at point A, Fig. 4-3, and increasing the temperature at constant pressure, the bubble-point curve is first contacted and vapor begins to form. An increase in temperature causes more vaporization up to about 20 per cent. Higher temperatures then cause a decrease in vapor until the mixture is again all liquid at point C. A similar type of phenomenon is exhibited by curve EL. If at constant temperature the pressure is lowered from point E, the conditions first reach the dew-point curve; i.e., the mixture is all vapor. On lowering the pres sure, the mixture becomes more and more liquid until about 25 per cent is condensed. In this region it has exhibited the retrograde phenomena. At still lower pressures, the mixture behaves normally and vaporizes with decrease in pressure.

In a binary mixture, if two of the loop curves intersect, i.e., if the vapor curve of one crosses the liquid curve of the other, then the two compositions determine a vapor-liquid equilibrium point. This is due to the fact that, for a binary system of two phases, the phase rule allows two degrees of freedom. However, the value may not be unique, i.e., in the higher pressure region, particularly very near the critical, it is possible for a given vapor to have two possible equilibrium liquids of different compositions. These two conditions can be at the

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