 Okay, so we've been using phase diagrams to talk about immiscible liquids or partially miscible liquids, liquids that may be miscible at some temperatures, but if I cool the temperature down low enough below this consulate temperature or critical solution temperature, then the two liquids become partially miscible, become immiscible below that temperature, and I have a phase separation between two different liquid phases. There's some more to understand about this phase diagram because we know of course that when we heat a liquid up to higher temperatures that liquid can boil. So we not only have phase equilibrium between two immiscible liquids, liquid-liquid equilibrium, but if we heat the system up to form a gas or a vapor, we can have equilibrium between the liquids involved and their vapors as well. So that's the next thing to understand is how does that work when we heat up these solutions involving partially miscible liquids. And we already understand liquid-vapor equilibrium, so it's just a matter of combining two things that we already know. So first thing to recognize is that for any mixture that has immiscibility between the two liquids, that's going to be a system with positive deviations from Reld's law. So this would be something like, for example, oil and water, which phase separate because they don't mix well, and that's because the interaction between the two types of molecules, the heterogeneous interaction is going to be weaker than the average of the homogeneous interactions. And as we've seen when we talked about ideal solutions, that's a situation where we're going to get positive deviations from Reld's law when I mix the two solvents together to make a solution. When A's are surrounded by B's, they're held into the liquid less strongly than when they're surrounded by their own type of molecule. So they leave the liquid phase more readily and go into the gas phase. We're going to have positive deviations from Reld's law. Or if these solvents are interacting strongly enough, deviating strongly enough from Reld's law to form an aziotrope, then we're going to have a minimum boiling aziotrope. So if I combine that information, these solvents will form a minimum boiling aziotrope with what I know about the liquid-liquid phase diagram. Then we can have what we know about aziotropes. So I've just drawn an aziotrope on this diagram at temperatures above the temperature where the two solutions become miscible. So if we heat the system up to high enough temperatures, the solution will boil and become a gas. That boiling happens over a range of temperatures. So these are two-phase regions showing the coexistence of a liquid phase and a gas phase, just like we've talked about for solutions and for aziotrope forming mixtures. So that's one thing that a phase diagram can do if I have partially immiscible liquids that form an aziotrope that the phase diagram can look like this. This would be a case where the boiling point of the aziotrope, so this point right there, this temperature that is the boiling point of the aziotropic mixture of those two solvents, I've drawn this phase diagram so that that aziotropic boiling point is above the critical solution temperature or the consulate temperature. That's not necessarily the case. That's true in this case for this amount of deviations from Reld's law. But imagine that the interaction between the two solvents causes even stronger deviations from Reld's law or even a lower boiling aziotropic mixture. So in that case, when the solvents are even more ideal, I'll draw another version of this phase diagram. So again, there's some phase separation between two liquid phases at low temperatures. But what I want to draw now is the case where this boiling point of the aziotrope has dropped low enough that it's below, actually below the critical solution temperature. So with roughly the same boiling points for these two pure solvents, if the boiling point of the aziotrope was dropped way down here, then I can draw curves corresponding to what that aziotrope mixture would look like. But now the aziotropic liquid vapor equilibrium curves are going to intersect the liquid-liquid phase equilibrium curves, and I'm going to get a phase diagram that looks like this. Essentially this is just a version of the phase diagram where the aziotrope has dropped below the point where the solvents become admissible. So notice what I have here. Again, the high temperature phase is the gas phase. I can boil these liquids if I raise their temperature high enough. I have a pure liquid phase over here and a pure liquid phase over here, but they're no longer part of all the same liquid phase. This is the liquid phase here. I can have liquid phase that's enriched in A, nearly pure A, or enriched in B, nearly pure B, and I can get from one side of this diagram to the other. Here I have two different phases. As with this diagram, I can drop the temperatures where the A-rich liquid and the B-rich liquid are not admissible with one another. So here's my A-rich liquid phase, and here's my B-rich liquid phase. Now not only are they not admissible, but I have no path connecting the two of them. So I essentially have two entirely separate phases. The B-rich liquid exists at compositions that don't overlap with the compositions of this A-rich liquid phase. I can be at particular points on this phase diagram. Let's say I'm at this point in the phase diagram in this liquid vapor coexistence region. If I prepare a system at this composition and this temperature, I'll be in this liquid vapor coexistence region. The tie line at that temperature tells me that what I actually have prepared when I reach equilibrium is a mixture of a liquid that's at an even more B-enriched composition than what I prepared and a vapor that is less B-enriched, more A-enriched. So coexistence between those two phases. Likewise, I can mix two liquids together. The one special case that appears on this diagram that hasn't appeared on any diagram we've seen before is this point right here, which is a triple point. If I prepare the solution at exactly this composition and exactly this temperature, the temperature, this flat line where the azeotropic curves, the bubble point curve has begun to intersect this liquid miscibility diagram. At that temperature in this composition, at this point I have coexistence of three different phases. I have the B-rich liquid and the gas phase and the A-rich liquid all coexisting with each other. The tie line right here tells me I have this phase and this phase and this phase all existing with one another. The gas at the composition I formed as well as an A-rich liquid and the B-rich liquid. So qualitatively, that phase diagram is a little bit different than this one, but the features are generally the same except for the addition of this triple point. And this gives us a way to understand the interaction, the very non-ideal interactions for an azeotropic forming pair of liquids that are also not fully miscible at all temperatures. So now that we understand what happens up here in the vapor phase, there's a few more things to point out about the consulate temperature, the temperature at which these two solvents become fully miscible. And we'll do that in a separate video.