 Okay, so let's talk a little more about the liquid-vapor equilibrium for a mixture of two substances in a slightly different way. So what we've seen so far is for a non-ideal solution, we've defined this quantity called the activity, which is the partial pressure of some substance over the liquid divided by the vapor pressure, the pressure it would have if it were a pure solvent. And if the solution's ideal, that ratio is going to be equal to the mole fraction of that particular solvent or component of the solution. But if it's not ideal, then we use the activity. And activity may or may not be the same as the mole fraction. So if I rearrange this and say we can predict the, if we know the activity, we can predict the partial pressure of A above a mixture as the activity times the vapor pressure. What we know is that the activity, even if A is a solvent and it's nearly pure solution and I've only dissolved a little bit of something else in there, the activity of A is always going to be less than one. For a pure solution, the activity is one. So what activity means is how active the solvent is relative to the pure solvent. So the activity is going to be less than one if the solution is not pure solvent. So if this number is less than one, the partial pressure is going to be less than the vapor pressure. So we can think about that as the vapor pressure has always been lowered. The partial pressure is always lower than the vapor pressure. So we can think of the vapor pressure of the solution as having been lowered relative to the pure solvent. So in fact, often rather than talking about what is the actual partial pressure above that solution, often what we talk about instead is by how much has the vapor pressure been lowered. So we can define that change in the partial pressure to be what it would have been for the pure solvent minus that slightly lower value for this particular solution. So that's our definition of a new quantity, the vapor pressure lowering, the amount by which the vapor pressure has been lowered. But since we know what the partial pressure is, I can write activity times vapor pressure. So that this works out to be one minus the activity times the vapor pressure. So far, so good. That's the amount by which the vapor pressure is lowered. And dilute solution meaning I don't have very much of the solute. I have nearly 100% of the solvent. The activity is going to be close to one and this difference is going to be pretty small. In fact, in that solution that's dilute in the solute relatively concentrated nearly pure in the solvent, that solution will be close to ideal. If we assume that's an ideal solution because it's near pure solvent, then I can write that as one minus mole fraction because in an ideal solution activity and mole fraction are the same thing. But then one minus mole fraction of A, one minus the fraction of the solution that's solvent, that's just going to be the fraction of the solution that's solute. So let me go ahead and rewrite that up here so we can talk about it a little bit. What we've discovered is the vapor pressure lowering in an ideal solution is the concentration of the solute as a mole fraction multiplied by the vapor pressure of the solvent. So there's a couple of interesting things to point out about that equation. That's our equation for vapor pressure lowering. If we want to know, for example, let's say at room temperature, the vapor pressure of water is 24 Torr. If I mix in 1 mole, 1.01 mole fraction of some solute. If I dissolve some salt or some sugar or something else at a mole fraction of 0.01, then what this tells me is 0.01 times 24 Torr. So I've lowered the vapor pressure by 1% of the 24 Torr. So notice what that means is these two different terms, the amount of this vapor pressure lowering is proportional to the concentration of the solute. In other words, the amount of the solute that I've dissolved in the solution. Notice that I don't have to know what the solute is. It could have been 1% mole fraction sucrose. It could have been 1% mole fraction ethanol. It could have been 1% mole fraction anything. It doesn't matter what the identity of B is, it just matters how much of it there is. So that vapor pressure lowering depends on the amount or the concentration of the solute, but not what the solvent solute is. On the other hand over here, it does depend on the identity of the solvent. The vapor pressure of water is 24 Torr. The vapor pressure of acetone or ethanol or some other volatile salt event is a different value. So it depends on, it does depend on the identity, the chemical identity of the solvent, because each solvent has a different vapor pressure from others. So that general pattern of some property depending on how much solute I dissolve in a solution and what the chemical character of the solvent that I dissolve it in, that's a pretty common pattern that we'll see over and over. And properties that have this type of behavior we're going to call colligative properties. And we'll see a number of examples of those, many of which you may have heard of before. Freezing point depression, boiling point elevation, osmotic pressure, vapor pressure lowering. Those other three that I just named, we'll talk about in other videos coming up, but they're all examples of these colligative properties that have the same property where it only matters how much solute I dissolve, not with the chemical content of that solute is.