 Okay, so here's what we understand so far about binary ideal solutions, a mixture of two different substances, A and B, in a liquid phase. They're vapors in equilibrium with them in the vapor phase. Raoult's law tells us the pressure as a function of the mole fraction in the liquid phase is the straight line connecting vapor pressure of B, vapor pressure of A. If we instead think about how the pressure depends on the mole fraction in the vapor phase, y sub A, that's not a straight line and appears below the Raoult's law curve. So it turns out this diagram that I've been talking about, that is a phase diagram. The reason we know it's a phase diagram is because it describes, first of all, the equilibrium condition, the condition that must be obeyed for a system to have two different phases in equilibrium with each other. If we're on this line, if we have a particular mole fraction in the liquid phase, if the pressure is exactly equal to the value predicted by this curve, then the two phases are in equilibrium. If not, then they won't be in equilibrium and we can't have just a single phase. Likewise, on this curve, the lower curve, if I have at the same pressure, that's in equilibrium with a different concentration in the vapor phase. So when I read from this point downwards, I'm reading to the x-axis, the mole fraction in the liquid phase. When I read over to this lower curve, I have to read down and think of it as the mole fraction in the vapor phase, the y sub A axis. So these two different curves are telling me as a function of pressure, I can learn the mole fraction in the liquid phase or the mole fraction in the vapor phase. And remember, for example, the example we've been talking about so far. If I have a 50-50 mixture, if the vapor pressure is 300 Torr in this example, it worked out to be 50-50 in the liquid phase and two-thirds, one-third in the vapor phase. Let's think a little more about what the other positions, other than sitting on this line, tell us about the phase diagram that we're talking about. Let's suppose I have, so here's my liquid of A and B, and I'm going to put a lid on that liquid and I'm going to press down on it with a pressure that's bigger than 300 Torr. So I'm going to press with a pressure that's bigger than the equilibrium vapor pressure. So the pressure, if it's bigger than 300 Torr, I'm going to be somewhere up here on the phase diagram. If I'm exerting more pressure than the total partial pressure in the system, I'm not in equilibrium. I'm no longer on a phase coexistence line, and what happens is because the pressure I'm exerting is larger than this total, some of the partial pressures, those vapors are going to condense and become liquid. So I've drawn this as purely liquid phase. I have a liquid phase solution with no vapor, single phase system. So I'm up here, we've just learned that this entire upper portion of the phase diagram is for the liquid phase, not liquid coexisting with gas, because just like for a single component system, if I exert a pressure greater than the vapor pressure, it will all condense. In this case, I've exerted a pressure greater than the Raoult's law pressures combined together, so I'm in the liquid phase. So I can imagine slowly reducing the pressure on this liquid, so let off the pressure a little bit, and when I do that, if I decrease down until I get exactly to the Raoult's law pressure, 300 Torr in our example, if I decrease the pressure until I get to exactly the Raoult's law pressure, what's going to happen then is once I reach this liquid vapor coexistence line, I will have two phases in coexistence with each other. I'll have vapor coexisting with liquid. I started out with just liquid, the way to get vapor in coexistence with the liquid is I have to form a bubble of the vapor, some vapor has to form. So what I get here is a system almost exactly the same volume, but now I've formed a little bubble of vapor at the top of the system. So I've still got A and B in the liquid phase, and I've got, so that's liquid, and I've got a tiny little bubble of gas phase that's formed. This is the type of system that we've talked about when we considered the Raoult's law examples. If the liquid state is 50-50 for a particular choice of 200 Torr, 400 Torr for our vapor pressures, then the vapor pressure will be 300 Torr, and the composition of the vapor phase will be two-thirds, one-third. So the relevant thing to remember is the vapor phase will be enriched in this more volatile component. A has a higher vapor pressure, it escapes from the liquid phase more readily. So the mole fraction in the vapor phase of that more volatile phase, more volatile component will be larger than the mole fraction in the liquid. I can continue reducing the pressure, so at this point I was exerting a pressure of exactly equal to the sum of the Raoult's law pressures, in this case 300 Torr. I can try to reduce the pressure a little more, and what will happen is more liquid will evaporate, become vapor. As I continue to do that, remembering that the vapor that gets formed is enriched in the more volatile phase, I am evaporating more molecules of A out of the liquid than I am of B. So in other words, I'm depleting the liquid of the more volatile component A. So as this happens, the mole fraction in the liquid phase is going to decrease because more of those molecules are leaving and entering the vapor phase. What that looks like on this phase diagram, I've decreased the pressure a little bit. I'm in coexistence along these two curves. I can, at this lower pressure, I can read off the mole fraction in the liquid phase from this P of x curve is lower than it used to be. The mole fraction in the vapor phase is still enriched compared to the liquid. It's still more molecules of A in the liquid, higher mole fraction of A in the vapor phase than in the liquid, but it has also become a slightly lower concentration of A. If I draw a picture of what's going on here, I've got some A and B in the liquid phase and now maybe a substantial amount of A and B have evaporated into the vapor phase. Again, the pressure is a little bit lower. I have this mole fraction in the liquid phase, this mole fraction in the vapor phase. I can continue that further. I still have higher mole fraction of A in the vapor phase than the liquid phase as this diagram shows me, but if I continue to evaporate more and more, again, pulling a higher ratio of A out of the liquid than B, because A is more volatile, if I get to a point where I've only got a tiny little bit of liquid phase left, A and B coexisting in this little drop-wit at the bottom of the container and most of the volume of this container now is being occupied by gas phase. So I've evaporated almost all of the liquid, just a little bit of it left, mostly gas phase remaining. In this case, I'll reduce the pressure down to the point where almost all the molecules are in the gas phase. If I ignore the few molecules left in the liquid phase, the composition in this vapor phase has to be the same as the composition I started with. Molecules have not left the container, so if it was a 50-50 mixture in the liquid to begin with, I'm going to end up, after I've evaporated it all, as a 50-50 mixture in the gas phase. So just before I evaporate the last drop of liquid, it's going to be nearly the same composition in the vapor. So the gas phase composition will be back to the original composition that I started with. At that pressure, the liquid phase composition will be substantially reduced in A, so it will be now quite depleted in that more volatile component, because almost all of the A has evaporated in earlier stages of this process. So as I drop the pressure, I've moved from liquid and vapor composition equal to these values, and they've slid down these coexistence curves until they've ended up here. And then as a last step, if I evaporate the last bit of the liquid, reduce the pressure even further. Now I've got purely A and B in the gas phase, none left in the liquid phase, so that would be a point like this on the phase diagram. If I'm at a pressure below this lower curve, then I'm no longer in coexistence. I have only one phase, and that phase is the gas phase. So two important things left to say about this diagram. Number one, interpreting it as a phase diagram, clearly on the upper side of this diagram is liquid phase, below the lower curve is the gas phase. What's going on in between these two curves? If I try to compose a system that is at a pressure and a composition that is between the two curves, that corresponds to the case like when we had phase coexistence here. It's below the upper curve, above the lower curve, in this region, just like in each of these three diagrams, I have a mixture of liquid and gas coexisting. So unlike, say, a pressure, temperature, or single component phase diagram, I don't have a phase coexistence line, I have a phase coexistence region. This region that's filled with these horizontal tie lines is the liquid gas coexistence region of this phase diagram. The other thing we can point out about this diagram is some names of the curves on this diagram. I've been calling these the upper curve and the lower curve, or perhaps the Raoult's law line, and this lower curve, which is not a straight line. The more common way to refer to these curves on this diagram, let's go back and think about what happened when I go from the liquid phase and first encounter this phase coexistence line. This boundary of the phase coexistence region. I can tell physically when I've reached that point because I formed the first bubble in my liquid. So in fact, at this composition, the pressure at which I see the first bubble form, that's called the bubble point, the pressure at which the first bubble forms in my liquid. So for that reason, we call this upper curve, the Raoult's law curve, the bubble point curve. If I have a liquid, I can reduce the pressure when I get to this line, when I get to the bubble point curve, that's when I'll see the first bubble of vapor forming inside my system. Likewise, if I start the system as a gas and I do these steps in reverse, if I am exerting a pressure on this and I increase the pressure, raise the pressure, raise the pressure, raise the pressure, at first I just compress the gas, but at some point I've compressed the gas to a point where the gas will begin to condense. And when I first begin to see condensation, when I see the first droplet form on the bottom of the container, that's when I know I've encountered, I've raised the pressure to the point where I've encountered this lower boundary of the phase coexistence region. And we call that not a droplet curve, which we could call it because it's when we see the first droplet, but we call that curve the dew point curve because, for example, that's what happens if you have condensation or dew forming from the vapor phase condensing onto a surface, in some circumstances we call that dew, so the first invisible existence of this dew occurs when we get to the dew point line. So these two curves, the bubble point curve and the dew point curve, are the boundaries of this phase coexistence region and knowing where we are in this liquid vapor coexistence, liquid vapor phase diagram expressed as a function of pressure and either gas or liquid phase composition can tell us whether we're in a single phase liquid, single phase gas or coexistence of the liquid and gas phase together.