Vapor-Liquid System:
Diagrams

Upon studying this section, you should be familiar with the following:

Phase Diagram: Single Component

Explanation:

A pure component, like water for example, can exist in multiple phases: as a solid, liquid, or a vapor/gas. Say, we put a pan of water in the freezer where it freezes the water in it. If we take it out, place it on a burner, and turn on heat, we will eventually melt the ice. The temperature throughout the melting is constant, and for water, it is its melting point of 0°C. That is, from the moment that the first drop of liquid forms until the point at which we have almost completely melted the ice, it is at 0°C. After it is all liquid, we can simply add heat to the system until the temperature of the solution reaches 100°C, where the temperature again stays constant until the liquid is completely vaporized. If we trapped the vapor after it is formed, we could continue to heat it to raise its temperatures far above 100°C. Note, for this process, the pressure was held constant; we were at constant atmospheric pressure.

The following phase diagram is representative of water. The path just discussed is the red path A on the diagram. That is, taking ice from sub-cooled temperatures (say, in the freezer it was -8°C) is to left of the orange line. We raise the temperature to its melting point where the temperature is constant (from the point the first drop forms to the point were the last bit of ice melts) is the temperture right on the orange line. Between the orange and green line, the liquid is being heated. When it gets to the green line, it begins vaporization until the last drop of liquid turns to vapor. Then the vapor temperature can be increased. At high temperatures, we define the vapor as a gas as it gets far from its condensation conditions. Again, the pressure was constant, so the red dash at the intercept of the pressure axis would, of course, represent 1 atm.

We could also put water vapor in a piston. Push down on it to increase the pressure (and as the phase diagram reveals with the blue path B), condense the vapor. It would continue at the same pressure until the last vapor molecules condense. Then we could continue to increase the pressure.

A few more points about the features of the pure component phase diagram. The purple line constitute the sublimation curve, while the boiling point and melting point curves have already been discussed. The triple point is the unique pressure and temperature were we could have all three phases present simultaneously. At that temperature and pressure in our piston, we could have ice floating in water, and water vapor above it. Once we change the temperature or pressure just a little bit, we can go right to a single phase. For example, increasing the temperature by 1°C would immediately give a system of only vapor; decreasing the temperature one degree puts every molecule in a solid lattice (ice); and increasing the pressure by any amount places the entire system in the liquid phase.

The critical point, labeled cp, is the point at which we can no longer distinguish the liquid from the gas phase, or better said, we have a phase that is neither a gas nor a liquid, but rather one that has properties intermediate of the two phases. And lastly, at high temperatures, such as those higher that the critical temperature, our vapor becomes a gas because it is far from its condensation temperature.

Txy/Pxy Diagrams

Explanation:

For a two component system, such as water and ethanol, we now have to take into account the respective mole fractions of each component in a phase diagram. We didn't have this for pure component phase diagrams because the mole fraction there is always 1 because it was a pure component. Since we need take mole fractions into account here, we have to take a different approach to plotting the phase equilibrium for the system. Two common ways are plotting mole fractions vs. temperature (at some constant P), or plotting mole fractions vs. pressure (at some constant T), referred to as Txy and Pxy diagrams. Here, Psub>xy diagrams are discussed thoroughly, and Tsub>xy diagrams are briefly commented on later.

Psub>xy Diagrams:



Psub>xy and Tsub>xy diagrams give us information on vapor-liquid equilibrium. This is denoted by the enclosed yellow section on this graph. The yellow region constitutes the two phase (vapor and liquid) region. The red curve designates the bubble point curve, where the first formulation of a vapor occurs. The blue curve designates the dew point curve, where the first drop of liquid condenses from a vapor. Now, consider the phase diagram below.

At P1, we only have a liquid, and at P6 we only have a gas. Thus, for P1, we only have a liquid, but we don't know the mole fraction of the first component (only that the mole fraction of the gas phase is zero cause there is no gas phase). For P6, we can apply an analagous explanation with zero liquid phase.

If we were at P1 initially, where we have a liquid mixture, and we reduce the pressure to P2, the first vapor molecule forms at the pressure (and temperature) of the pure component (the pure boiling point). Similarly, P5 is the pressure (and temperature) at which the phase change (either vaporization of the liquid or condensation of the gas) takes place.
For the equilibrium tie line at P3, it is important to note that the upper curve (red) gives the liquid mole fraction of component one, x1, and the lower curve (blue) gives the vapor mole fraction for component 1. So, at P3, our line shows that x1 » .6 (interception of the bubble point curve (red)), and y1 » .8 (interception of the dew point curve (blue)). And, of course we have two components, and the second component mole fractions would just be one minus the first (ex, at point 3, x2 = .4, and y2 = .2). At P4, our line shows that x1 » .45 (interception of the bubble point curve (red)), and y1 » .7 (interception of the dew point curve (blue)).

We could easily derive this phase diagram experimentally. Because we are changing pressure, we could do this by placing water and ethanol in a piston (corresponding to P6 below). We would press down until we see condensate where we could stop and take a sample of both the vapor and of the condensate in the system(P5 below). We could continue to do this (giving data such as those at P4, P3, and P2 below), pushing down, increasing the pressure, and sampling the vapor and condensate several times as more vapor continues to condense until we have completely condensed the vapor. After that, increasing the pressure would provide no further information.

If this were a binary phase diagram for a water-ethanol system and we called water component one, and ethanol component two, at P1 we would have a liquid mixture of water and ethanol with negligible vapor above it. However, the diagram does tell us the mole fractions (again, here, there is only one phase, a liquid phase (these are called two phase diagrams for a reason). The diagram gives us concentration information only if we are in two phase equilibrium, and not, for example, at P1 or P6. At P2, our line at that pressure (tie line) shows the vaporization (or condensation) conditions of pure water. At P3, our line at that pressure (tie line) shows that both xH20 » .6 and yH2O » .8. Thus xetOH » .4 and yetOH » .2. And similarly, we can determine the vapor and liquid mole fractions for water and ethanol at P4. P5 tells us the boiling point of pure ethanol, and all P6 tells us is that there is only a vapor phase present.

Txy Diagrams:


The Txy diagram is read analogously to the Pxy diagram. The information about vapor-liquid equilibrium is given by horizontal tie lines that intersect the yellow region, as was the case with the Pxy diagrams. Experimentally, we were able to obtain the Pxy diagram by slowly adding pressure to an all vapor water-ethanol mixture and recording the condensate composition at several different times until the vapor was completely condensed. To derive a Txy diagram, we could simply heat a bulb of a water-ethanol liquid mixture (keeping the pressure of the system constant by keeping it open to the atmosphere, P = 1 atm), and take sample of the vapor and the liquid at different temperatures, until all the liquid has been vaporized.



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