 So this phase diagram that we understand a little bit better now, we call this a pressure composition phase diagram just naming it after the axes. The vertical axis is pressure, the horizontal axis is the composition of a solution, either mole fraction in the liquid phase and or mole fraction in the vapor phase depending on which of these two curves we're using. So as with any phase diagram we can use it to tell what phase a system will occupy if we prepare it at a particular pressure and composition. It might be single phase or it might be phase coexistence. We can also use it for example to read off, if I say prepare a solution at this composition under what pressure will it first exhibit vapor forming in the liquid or will it first exhibit liquid condensing out of the vapor. Likewise we can say if I form the first droplet, if I have a gas and I compress it until I form the first droplet, what will be the composition of that droplet? It will happen at this pressure and that droplet which is liquid I could read over to this curve and read the liquid composition. So there's a lot of ways we can use this pressure composition phase diagram. But for now I want to talk about a different axis, the temperature composition phase diagram and that's because pressure is actually not the most convenient axis to use for a phase diagram. If I say composition is fine, if I say prepare a solution that's 40%, 60%, ethanol, methanol as a mole fraction, that's easy enough to do. But if I say and make sure and do it under conditions where it generates a pressure above the liquid of 70 torr, that's a little bit hard to engineer, hard to do. What's much easier would be if I were to say prepare that 60-40 solution but do it at a temperature of 30 degrees Celsius. Temperature is much easier to control than directly controlling the pressure of the system. So we need to think about how this diagram would look at temperature coordinates in addition to pressure coordinates. And there's a connection of course between the pressure at which a liquid evaporates and becomes a gas or the pressure at which it condenses. There's a connection between those pressures and the temperatures at which it would do the same thing. For example, when the pressure is equal to, and now I'll be thinking primarily about single component systems so I can write P star as a vapor pressure. If the pressure is exactly equal to the vapor pressure, then I know I have equilibrium between two phases, the gas and the liquid phase. On the other hand, if the pressure is less than the vapor pressure, then the system will have evaporated and be in the gas phase. If the pressure is greater than the vapor pressure, then I'll have liquid phase. If I want to make those same statements about temperature, I have liquid and gas coexisting in equilibrium whenever the temperature is equal to the boiling point, the vaporization temperature. I have a gas whenever the temperature is greater than the vaporization temperature. And I have a liquid whenever the temperature is lower than the boiling point or the vaporization temperature. So knowing what the boiling point is is equivalent in temperature terms to knowing what the vapor pressure is. But the signs of these two are different. A substance with a high vapor pressure is going to have a low boiling point and vice versa. A volatile liquid with a high vapor pressure is going to boil relatively easily at a low temperature. Luckily we know something about the connection between the vapor pressure of a substance and its boiling point. And we know that from the Clausius-Clapeyron equation. If you remember the Clausius-Clapeyron equation in one form that we've seen it, that says the log of P2 over P1 is equal to enthalpy of vaporization over R with a negative sign times the difference not of the boiling points but of one over the boiling points. So remember on a phase diagram, a single component phase diagram, the temperatures and the pressures along the phase coexistence line between the liquid and the gas, that line is described by this P1, P2, T1, T2 type of coordinates. This much detail is actually not necessary for us right now. What we need to know is that the log of the pressure is proportional to and we don't much care about the exact magnitude of the proportionality but the log of the pressure varies with one over the temperature. In fact, the log of the temperature varies with one over the temperature and again that is confirming our statement that when the vapor pressure gets larger the boiling point gets lower. More volatile substances have lower boiling points. So that's enough at least in principle for us to say if I can draw a graph of P as a function of composition I could plug, I could transform those pressures and write them instead as temperatures rather than vapor pressures. So we won't do that mathematically, we won't do it quantitatively, we will just make use of this qualitative observation that says as the vapor pressure goes up the boiling point goes down and so substances with a high vapor pressure have a lower boiling point so when I redraw this diagram over here next to this one, if I redraw not a pressure composition phase diagram but a temperature composition phase diagram of these two solvents A and B I had written A with a higher vapor pressure so I'll write A with a lower boiling point so vaporization temperature of A, B has a lower vapor pressure so I'll write it with a higher boiling point, temperature of vaporization of B. Again these two end points are going to be connected by lines connected by the bubble point and the dew point curves. On the pressure diagram the bubble point curve where the liquid exists and is in coexistence with the vapor at a particular liquid state composition is the upper of the two curves. Once I'm talking about temperature again because of this inverse relationship between pressure and temperature the lower of the two curves, if there's two curves the lower of the two curves is going to be the bubble point curve. In addition to that it's no longer going to be a straight line, I'm not going to draw a straight line to connect the temperatures because this is not a linear relationship between pressure and temperature so again the exact mathematical form of the line isn't terribly important for us but I'll just draw a somewhat curved line rather than a straight line this will be our bubble point curve and below this temperature, below the temperature given by this bubble point coexistence curve will have liquid again because when I cool a liquid or a solution below the temperature at which it vaporizes given by this bubble point curve I'm going to have a liquid. On the other side what used to be the lower curve is now going to be the upper curve it's going to be the dew point curve. It used to not be a straight line I'm going to transform it by some function that is not a straight line it doesn't magically undo the nonlinearness of this curve I end up with still another nonlinear curve that ends up at the same end points and this dew point curve is again going to be nonlinear not a straight line if I heat the substance to above the dew point curve then I've got a pure single gas phase not pure it's still a solution but I have a single phase gaseous system if I have a temperature and a composition that fall in between these two curves then I have phase coexistence I have liquid coexisting with gas if I want if I have a system at this temperature for example it will be in equilibrium with a liquid at this composition and a gas at this composition so just as on the pressure composition phase diagram the temperature composition phase diagram has a liquid gas coexistence region the horizontal lines in this phase coexistence region are tie lines that tell us the composition of the liquid where the line encounters the liquid phase composition of the gas where the liquid encounters or the substance encounters the gas phase side of the phase diagram so everything is basically the same for the temperature composition diagram as it is for the pressure composition diagram with the one exception that has been turned upside down there's an inverse relationship nonlinear inverse relationship between boiling points and vapor pressures so it's often more convenient to use this temperature composition phase diagram to understand at what point a liquid will begin to evaporate or gas will begin to condense in fact we can draw some quick cartoons and illustrate how that would work much as we did for the phase I'm sorry the pressure composition phase diagram if I have a mixture of liquid A and B and the temperature is below so if I start here at a temperature below the bubble point curve I've got a pure liquid if I heat that system up until I get to the bubble point curve what will happen is what the name bubble point curve suggests will happen if I heat that system so temperature is increasing until I get to this point let me go ahead and label these this is diagram one this is point one when I get to the bubble point curve at this point two diagram two what will happen is I will have formed my first so I've got A and B in the liquid I'll form my first droplet my first bubble of vapor in this solution again the composition of the vapor will be different than the composition of the liquid I will it will be enriched in the more volatile component the one with the lower boiling point or the one with the higher vapor pressure I can continue to increase the temperature further until I've boiled away much of the liquid and I have now a substantial amount of A and B in the gas phase if I label that system number three that may be at a point like this line this horizontal line where the liquid composition and the gas composition are now substantially different than they were in my initial system the liquid system has been depleted substantially in that more volatile component because most much of it has evaporated into the vapor phase the vapor phase is more enriched in that volatile component a than the original system was because it evaporated out of the liquid more readily continuing even more to the point where now I've got a lot of A and B in the gas phase only a little bit of liquid left that would correspond to a point like this one this horizontal line this time line where the vapor composition is now almost exactly the same as the initial composition of the system was the liquid left behind is substantially depleted as about as depleted as we can make it in component a because it's the last little bit to evaporate so it's largely component B and if I continue to increase the temperature even more I get to a point like this one where that would be purely in the vapor phase all I've got is molecules of A and B in the vapor phase no liquid left at all and once I have passed that dew point curve I can continue to increase the pressure and all that's going to happen now I won't change the composition anymore I'll just heat the system further expand it further as I as I raise the temperature so again very similar to the process that happened as we crossed from one phase to another on the pressure composition diagram we can use the tie lines to read the compositions in the same way but now what we're talking about is boiling a system rather as by changing its temperature rather than condensing or evaporating a system by changing its pressure