 Okay, so let's continue our discussion of ideal and non-ideal solutions, and in particular let's look a little closer at what happens on the limiting cases on this graph. Either when the mole fraction approaches one, we have something verging on pure A, or when the mole fraction approaches zero, and what we have here would be the pure solute. So this will be the case where mole fraction is approaching one, and down here mole fraction of A is approaching zero. So just as a reminder, this is a pressure composition diagram. The straight line is Raoult's law telling us that the pressure goes up linearly with the mole fraction. We might have systems that deviate positively or deviate negatively from Raoult's law for non-ideal solutions. But as I said, we're going to be interested for now in focusing a little more on what happens on the edges of this pressure composition diagram. So let's go back to a structural picture. So I'll draw a picture of the molecules in a beaker of solution in this limit where the mole fraction of A is approaching one. Not quite 100% A, but nearly pure A. So I've got molecules of A in this solution. I'll draw A as these open circles, got many, many molecules of A, and a relatively small number of a different type of molecule B. So there's a few molecules of B scattered throughout the solution, those I'm drawing as filled circles, so nearly pure A. So Raoult's law tells us, well first of all, for the pure solvent, if this molecule at the surface weren't here, molecules would be escaping from the surface at the same rate that they would in the pure solvent. The partial pressure would be the same as the vapor pressure. I've got a few of these B molecules lying around, some of which are going to be at the surface, so that's going to reduce the partial pressure a little bit. Raoult's law says it reduces in straight line proportion to the fraction of these molecules that are A or B molecules. Notice though that every one of these A molecules, not every one, but nearly all of these A molecules are surrounded completely by A molecules. In a nearly pure solvent, almost all the solvent molecules see nothing but solvent molecules, so they're going to behave just as the pure solvent would. They're going to behave like A molecules surrounded by A. Only a small number of the solvent molecules even have a B molecule anywhere nearby because we're nearly pure. So Raoult's law says the only molecules that don't escape into the solution as they would in the pure solvent are the ones that are B molecules. An ideal solution says, well that may or may not be true because the ones near the B molecules might be held into the solution more strongly or less strongly because of those non-idealities, but there's not very many of those molecules. So in that sense, as the mole fraction becomes one, relatively few molecules even have a chance to be perturbed by a B molecule. The overwhelming majority of the molecules are going to behave just like solvent. So in the limit as the mole fraction of A approaches one, the activity of A is going to be the same as the mole fraction, and likewise in the limit of that pure solution the activity coefficient of the solvent is going to approach one. The solvent is going to behave ideally in this limit of a pure solution, and that's why when we draw these curves or when we measure this data, regardless of whether we have a positive deviation or a negative deviation, as we approach a pure solvent, the system becomes more and more Raoult-like. The deviations from ideality begin to disappear as we reach pure solvent, and you can see from the way I've drawn this diagram that's not what happens at low concentration. In the case where the mole fraction of the solvent A is approaching zero, we can draw another picture to see what's happening in that system. So here I've got, let's see if I can use, I'll use filled circles for my B molecules, and there's a small number of these open circles that will be A molecules. So the A molecules, the open circles are the minority in this case. So mostly B molecules, a few of these A molecules. And again, we can ask ourselves, what will the partial pressure of A be above the solution, and how will that compare to what it would be in an ideal solution? Clearly the B molecules, whether they evaporate or not, don't affect the A pressure in the vapor phase. The only ones that can evaporate are the few A molecules that happen to be near the surface. And unlike this case where the A molecules behave just like A molecules in pure solvent, this A molecule is going to behave nothing like A molecule in a pure solvent. So it'll behave not very ideally at all if the solution is not an ideal. If the B molecules bind to A more tightly or less tightly than the A molecules do to themselves, then there's no reason to expect that the activity of this A molecule will be anything like the mole fraction of the A molecules. Likewise, there's no reason to expect that the activity coefficient will be anywhere near one. The solution won't be necessarily ideal in this limit of a dilute solution, because an A molecule surrounded by B molecules won't behave anything like an A molecule surrounded by A molecules. So the dilute solution limit down here is very different than concentrated, sorry, dilute A limit down here is very different than the concentrated pure solvent A limit down here, up here. And the system certainly has to approach vapor pressure or partial pressure of zero once the concentration gets to zero, but it doesn't have to approach it along the Ralph's Law slope. The activity coefficient doesn't have to approach one as we go down to small amounts of A in the solution. So that's on this diagram. The slope with which this negative deviation line, partial pressure is moving away from zero is a different slope than the Ralph's Law slope. Likewise, the positive deviation non-ideal solution is moving away from zero at a very different slope than the Ralph's Law slope. So in fact, high concentrations and low concentrations are both ideal in a certain way. They both look linear. The nearly pure solvent limit behaves like Ralph's Laws as it should. The very dilute amounts of A in the solution limit is behaving linearly, but not with a Ralph's Law straight line. And the straight line we use in that case is called Henry's Law, which says if I want to predict the partial pressure of component A, it is indeed a linear function of the mole fraction. Looks like a straight line when I'm at low concentrations, but that coefficient is no longer, though remember Ralph's Law says partial pressure is mole fraction times vapor pressure. The slope of this curve is the vapor pressure. The slope of this curve doesn't have to be the vapor pressure any longer. It's some different constant that we call k, k sub h for the Henry's Law constant. And this is one version of Henry's Law. It's a description of the straight line on this graph. This Henry's Law constant might be very different for a substance with negative deviations from Ralph's Law or with positive deviations from Ralph's Law or anywhere in between. There is unfortunately another version of Henry's Law, depending on whether you think, whether you're trying to predict the pressure as a function of the concentration or whether you're trying to predict the concentration in a solution as a function of the pressure above the solution. Both of these are relatively common things to do. And both of them just involve this proportionality constant. Unfortunately, they're both often called the Henry's Law constant. So oftentimes from context, you'll have to look at a Henry's Law constant. And say for example, in this case, Henry's Law, if I multiply a unit less mole fraction by a constant and get something with units of pressure, that means this Henry's Law constant is gonna have units of pressure. On the other hand here, I need to multiply a pressure by something with some units in order to get something unit less. So in this case, the Henry's Law constant is gonna have units of one over pressure, one over atmospheres, one over bar, something like that. So, it's unfortunate perhaps that there's two, actually more than two different versions of Henry's Law, depending on what type of concentration units we're interested in. But you can usually figure out from context from the units on the Henry's Law constant which version of this equation you're being provided with a constant for. So, in summary, we have two different types of ideal behavior. Henry's Law behavior at very low concentrations of the substance we're interested in, Raoult's Law behavior at very high concentrations of the substance we're interested in, nearly pure solutions. Those two limiting behaviors are both relatively simple. Things get more complicated and more interesting in the middle of this diagram. And that's also conditions where we often spend a great deal of time when we prepare solutions. So, what we'll do next is pay more attention to what happens away from the edges of the diagram toward the middle of the diagram.