 Alright, so now it's time to confess one other simplification we've been making in talking about solutions, which is that up till now we've been talking about solutions as if any possible concentration of the solvent is allowable anywhere between no solvent up to 100% solvent. So essentially what we've been doing is assuming we can combine these solvents A and B in any proportion we want that we can mix them in any proportions that we want. And we know of course that that's not true. We can take liquids like an oil and water and mix them and they won't dissolve. I can't dissolve oil and water. So there are pairs of solvents that are immiscible, essentially not mixable. Those two solvents can't be mixed, can't form a solution at any concentration we want them to. It's not quite correct to say that they're completely immiscible. It's probably more correct, it's definitely more correct to say that oil and water, oil might be only sparingly soluble in water and vice versa. I can dissolve a few drops of oil in water and when I dissolve them, mix them up, they won't phase separate out again. But in fact many pairs of solutions can be mixed at some concentrations but not mixed at other concentrations. So we would say that that type of solution pairing would be partially miscible. There might be some concentrations I can prepare a mixture or a solution of and other concentrations where they will not mix fully and will phase separate. So let me give you just a visual picture of how that might work with the pairing of two solvents, phenol and water. Phenol looks like it should be fairly hydrophobic but it's got a hydroxyl group so that hydroxyl group is fairly hydrophilic so that solvent might bond well with water under some conditions. Turns out that that mixture of phenol and water I can prepare solutions with some concentrations. I cannot prepare solutions with other concentrations. For example, if I try to make a solution with phenol concentration 0.25 mole fraction, mix one mole of phenol with three moles of water, what I will see is that I'll get phase separation. I will get a layer of the solution that looks like water. It won't be pure water and pure phenol as we'll see and just admit. But I'll get a water-rich portion of the solution that phase separates apart from the phenol-rich portion of the solution that floats on top. On the other hand, if I were to try to mix those solutions with a different mole fraction, if I make it more rich in phenol, 50% mole fraction phenol, then I just get a fully mixed solution. The phenol and the water dissolve each other relatively well at this mole fraction. So I get only a single phase rather than two phases. I can go too far in the other direction as well. If I put only a tiny fraction of phenol in solution, if I say I have a beaker of water and I mix in only 1.99 as many moles of phenol as I have moles of water, again, I'll get a solution that is mostly water, a lot of water molecules and only a rare phenol molecule floating around in that solution, but that's going to be a single phase. So they can mix at that concentration, mix at this concentration, they'll phase separate at this concentration. To make things even more complicated, if I take my immiscible solution, I could not prepare a solution in a single phase at a concentration of 0.25 mole fraction phenol. If I do that at 25 degrees Celsius, what I've told you is true. I can't mix those solutions in that concentration, but if I heat them up to, let's say, 60 or 70 degrees Celsius, they will mix. As I heat those phase separated phenol and water layers, I'll get a single phase. So the phase behavior of these materials depends on temperature, depends on composition. So what I've been describing is essentially the temperature composition phase diagram of these two solvents. So let's go ahead and show that on a phase diagram. If I pull up a graph here of the temperature composition phase diagram for phenol water, that's what this graph is showing. And in fact, that's what we see here. If I try to prepare a solution that is 25% mole fraction of phenol at a temperature of 25 degrees Celsius, so a point here somewhere, this is in a two phase liquid plus liquid portion of this phase diagram. It will phase separate into a portion of a liquid phenol rich portion and a liquid phase rich portion or phase as well. On the other hand, this concentration at 0.5 mole fraction phenol and 25 degrees Celsius, I'm out here in the single well mixed liquid phase. So everything out here is a solution that I can form. Turns out as long as I have a lot of phenol, a little bit of water will dissolve in and I can make those waters be solvated by the phenol molecule. On the other side, things are not as good. I have to go down to very low mole fractions of phenol. So I said 0.01, so somewhere way down here in 25 degrees Celsius. Somewhere right about there is I'm in a phenol rich, I'm sorry, a water rich, mostly water only a little bit of phenol. So this pure liquid phase down here, I'm in what I would call a phenol rich phase. In this little sliver down in here, that would be a water rich phase. And if I'm at relatively mild temperatures, I have a phase coexistence region where the phases will separate. This temperature behavior, if I take this system that's 25% mole fraction of phenol and I heat it up to 60 degrees, then I've entered the single phase region, the liquid phase region. So once I cross the temperature of somewhere around 40 degrees Celsius or so, those two phases mixed and became just a single phase. So as with all two phase regions, this liquid-liquid region consists of tie lines. So in fact, if I take one mole of phenol and three moles of water to form this 25% phenol solution, attempt to prepare a solution with this concentration at this temperature, I can't form a single phase. What the tie lines tell me is that what I actually get when those phases separate is systems with the two concentrations given at either end of that particular tie line. I'll have a phenol-rich solution with a concentration of maybe 31% or 32% phenol by mole. And the water-rich phase will be at the other end of this tie line. That's down here at about 2% or 3% phenol in that water-rich phase. So this is a phase diagram much like the other temperature composition phase diagrams we've talked about before, except instead of showing liquid-vapor coexistence, here I'm showing liquid-liquid coexistence. I can have, as you've seen before in everyday life, two phases, two liquid phases in coexistence with each other with different concentrations of two different substances. And this phase coexistence region is describing the two, the concentration of the two phases that are in the coexistence with each other at various different temperatures. The special point that's up here at the top of this curve, what that means is the temperature above which I can always mix these solutions. If I have water and phenol at 80 degrees or 90 degrees Celsius, any composition of the solution will mix just fine. And below this temperature that I might sometimes get phase separation between the two. This temperature, we can call it a critical temperature. It looks like the critical temperature we've talked about for gas-liquid phase diagrams before on a pressure-volume phase diagram. So we can call that a critical temperature to distinguish that from a gas-liquid critical point. We more specifically call it a critical solution temperature. Or the other name that's sometimes given to that is a consulate temperature. It's a somewhat fancier word to describe that critical point. But that consulate temperature or critical solution temperature tells us the temperature below which we may see phase separation, above which we'll never see phase separation between the two liquids. So it may have occurred to you that on this liquid phase diagram, we don't have evidence of gas anywhere. I've cut the graph off below the temperature at which the solution would boil. But of course if we continue heating these liquids up to the point where either phenol or liquid would boil, phenol or water would boil or their solutions would boil, then we're going to see liquid vapor coexistence as well. So if we look a little closer at these phase diagrams, we'll see not just liquid-liquid phase separation, but also liquid-vapor phase separation at higher temperatures. And that's coming up next.