 Hello, I'm Professor Steven Neschiva, and I want to tell you a little bit about the relationships between boiling points, freezing points, and Raoult's law. So I'm first just going to talk a little bit about pure substances, because Raoult's law has to do with when you put, say, a salt into a liquid. But first I'll just talk about the phase diagram of, let's say, pure water. And here we have the phase boundaries between solid, liquid, and gas. And there's the triple point right there, which is a temperature of about 273 Kelvin. And just focusing on the part that's the equilibrium between liquid and gas, we can tell where the boiling temperature of a liquid is by just looking to see where the vapor pressure, the equilibrium vapor pressure of a body of water, equals about atmospheric pressure, or I'll say one bar. When that happens, then what we observe is that the liquid begins to boil. This kind of explains something that you might have noticed before, which is that if you try to boil water at a high altitude, the pressure is lower, which means that that curve would drop a little bit. And now what that would mean is that the water would boil at a lower temperature. How about the freezing temperature? For the freezing temperature, it's useful to think about the equilibrium with the vapor. So we'll talk about P star liquid vapor, that's that value there. What we say is that all along that curve is that the ambient vapor pressure equals the equilibrium liquid vapor pressure given by the Clausius-Clapeyron equation. That's why it's in equilibrium. If you want to have a visual, it means that the rate at which water molecules leave the liquid equal the rate at which water molecules come into the liquid from the gas phase. So at equilibrium, those two quantities are equal. How about along that part of the curve, the solid vapor curve, well it's the same kind of thing. We imagine that if I have ice in equilibrium with its vapor, then the rate at which molecules are leaving the ice and going into the ice is the same. So what we would say is that P star of the solid vapor curve equals the ambient vapor pressure. There's only one place where both of those equalities can hold true. That is to say, if that's equal to that, and that's equal to that, then that must be equal to that, and that is the triple point. This is the normal freezing temperature of water, so 273 and 373 here. So the last idea I just want to pitch at you is what happens when we have salt in the water? So I'm just going to put some salt water molecules in that water. Well, Raoult's law tells us something, and it goes something like this. It says that the equilibrium vapor pressure of that liquid is actually, it's equal to the mole fraction of water in here, and in the liquid times that same curve that we've been talking about, okay? And the mole fraction of water in a salty solution is smaller than one. So what we see is that the equilibrium vapor pressure of the water is smaller than P star. And I can draw that on here, so I'm just going to take that very curve here and drop it down to there. Okay? So now what I've really drawn is the Raoult corrected P liquid vapor curve. According to Raoult's law here, as you can see, it's a lower value than P star, so I've dropped it down. And you can see right away there are two conclusions that you can draw from this. One is that now in order to reach ambient vapor pressure when you're trying to boil salty water, you have to raise it to a higher temperature. So that's what we call boiling point elevation. It's you have to raise salty water to a higher temperature in order to see it boil. The other thing that happens is that now you can see that this condition of the equilibrium between the liquid and the ambient pressure, vapor pressure in the solid, that intersection now occurs at a lower temperature. So what we see here, if I can draw it, is a reduction in the freezing temperature, that is to say freezing point depression. So both freezing point depression and boiling point elevation can be traced back to the same idea, which is Raoult's expression for the reduction in the equilibrium vapor pressure over salty water.