 OK, so let's go back to this idea of a pressure-composition phase diagram for ideal and for non-ideal solutions and observe something very interesting about these solutions that we can conclude by looking at them a little bit closer. First of all, here's the Raoult's Law curve. So this is Raoult's Law, the bubble point line for an ideal solution, straight line connecting the vapor pressures of the two solvents of this binary solution. We've seen how if we have negative deviations or if we have positive deviations from Raoult's Law, the bubble point curve and the dew point curve can either sag downward for this case of negative deviations. That's for this curve or for positive deviations where the pressures are greater than they would be expected to be from Raoult's Law. Turns out in drawing these relatively minor deflections from Raoult's Law, I've understated the case. For most pairs of solvents, or at least for many pairs of solvents like the chloroform acetone pair that we've talked about, this actually considerably understates the deviation from Raoult's Law. So if I were to try to draw what that pressure composition phase diagram looks like for a pair of solvents with relatively strong interactions and strong deviations from Raoult's Law, let's first stick with a case with negative deviations, but let's make that some strong, just TRONG, strong negative deviations as opposed to this case with weak negative deviations. So you might think the only thing I need to do is make these curves sag downward a little bit more. So here's pressure of pure solvent B, here's the vapor pressure of pure solvent A. I could make, let's say the dew point curve sag down a lot and the bubble point curve sag down a little less, and I won't draw that curve yet. In fact, what I'll do is I'll draw over here maybe what would be tempted to draw. And this is going to be the wrong answer, so I'll draw it off to the side. If I draw a curve that looks like this and this, for example, as you might expect would be the case for some even stronger deviations from ideality in this case, think about what this means. We've got composition on this axis, pressure being measured on this axis. At high pressures we have a liquid, at low pressures we have a gas, in between we have a phase coexistence region. The way we interpret this phase coexistence region, this liquid plus gas region, at a particular composition, we can read up and say, well I should say at a particular pressure we can read across and determine the composition of the liquid phase that's in equilibrium with the composition of the gas phase. Same thing is true on all these pressure composition diagrams. The tie lines tell us the composition of the two phases that are in equilibrium with each other at the opposite edges of this tie line. Think about what the tie lines would look like for this diagram, this incorrect diagram that I've sketched. If we're at a pressure down here, the tie line connects to gaseous phases. So what that suggests is if I have a pressure, this pressure, I have a gas phase with this concentration in equilibrium with the gas phase at this concentration. And of course we know that can't be the case. If I have two gases with different concentration of species A and I mix them together, they're going to equilibrate and come to a single concentration. The two gases will diffuse into one another and equilibrate their concentrations. So we'll never have a phase diagram that looks like this. I can't have two gas phases at different concentrations in equilibrium with each other. And the reason we ran into that problem is because this lower curve has a minimum. It undergoes a minimum on this curve. Whenever, in this case the dew point curve on this pressure composition diagram goes through a minimum, what necessarily must happen is that the bubble point curve connects to that minimum. So we do still have liquids at high pressure, gases at low pressure. We can still have deviations from Raoult's law that bend the curve downward, not just a little bit, but quite a lot. So the pressure drops much below what Raoult's law would have predicted. But again, when this curve undergoes a minimum, we're always going to have equilibrium between a liquid phase and a gas phase, never between a gas phase and a different gaseous phase. So these tie lines will always connect liquid on one side and gas on the other. So the liquid phase dips down and meets the gas phase curve at this point. So I have tie lines over here that connect the liquid phase with the gas phase as well. So this is what the pressure composition phase diagram looks like for the case where we have strong deviations, strong negative deviations from Raoult's law. I can draw a similar curve over here for strongly positive deviations, pressure and composition, vapor pressures of the pure components. Instead of the straight line Raoult's law behavior connecting the two of them, I might have very positive deviations from Raoult's law. But again, if this curve exhibits a maximum, if in this case the bubble point curve exhibits a maximum, the dew point curve is going to have its maximum meet at exactly the same place. So again, this coexistence region must be a liquid and gas coexistence region. The tie lines must connect liquid on one side and gas on the other side. So these two unique points where the minima of the curves meet, when I have negative deviations or where the maxima of the pressure curves meet, when I have strongly positive deviations, those points are called aziotropes. In particular, a solution with a concentration that is the concentration of this special point on these diagrams, that solution is called an aziotropic mixture of the two solvents. So it turns out that aziotropes are very important for being able to understand all sorts of components, all sorts of properties of solutions, such as whether we can separate them by distillation, what their boiling points are and so on. So we'll explore the properties of these aziotropic mixtures of solvents quite a bit and that's coming up next.