 Okay, so the next thing we need to consider is if solutions are not ideal, how do we deal with those non-ideal solutions? And the idea is going to be similar to what we've considered for the ideal gas model in the past. The whole purpose of the ideal gas model is not to make a claim that all gases are ideal. We know that none of them actually are. But once we've described the ideal gas model, we know what assumptions we've made and writing it down, then we can understand better when those assumptions are not true and how to improve the model for gases that don't behave ideally. So let's start by summarizing everything we know about ideal solutions. First of all, our model for an ideal solution is essentially the same as saying the interaction between the two different solvents in the solution, the A-B interaction, is the average of the homogeneous A-A interaction and the homogeneous B-B interaction. Structurally, what that means about an ideal solution, I've drawn two different types of molecules here, A's and B's, for example, is that if, for example, half of the molecules are A molecules, then they appear distributed randomly throughout the system. And if they're only half of the molecules at the surface are A molecules, then instead of having the vapor pressure equal to the pure solvent, it's equal to only half of that. The partial pressure above the solution is only half or whatever the mole fraction is times the vapor pressure of the solvent. That's Raoult's law. And by looking at that in a little more detail, we've seen that these pressure composition or vapor, I'm sorry, temperature composition diagrams describe two different types of phase diagrams that tell us whether we're in the liquid phase or the vapor phase, liquid phase or vapor phase, as a function of temperature, and we have these liquid gas coexistence regions that we can use with tie lines to decide what are the compositions of the vapor and what are the compositions of the liquid that are in equilibrium with one another at a particular total pressure or at a particular temperature. All right, so those are the things we want to understand for non-ideal solutions where the results will be different than ideal solutions. So if things are not ideal, if this assumption doesn't hold, we can go back to the beginning and ask ourselves what would be non-ideal about them and see what the consequences would be. So we consider two different cases. First of all, if the heterogeneous interaction, the A-B interaction is not the average of the A-A and B-B interactions, there's only two other options that can be stronger than or weaker than that average predicts. So we'll consider those two cases separately. So for the first case, let's say that V-A-B and to avoid getting hung up in inequalities and signs when these interaction energies are negative, that might be a little bit confusing. So I'll just say, if the A-B interactions are stronger than ideal, so instead of the average of the A-A and B-B interactions, A and B hold onto each other a little more tightly, their interaction energy is more favorable, more negative than the ideal case predicts. So what that's going to mean is rather than A molecules escaping from the solution to produce a partial pressure of A as predicted by Raoult's law, because those A molecules will tend to be surrounded sometimes by some amount of B molecules. They will be held back into solution more tightly by these stronger A-B interactions. In the ideal solution, every A-A and B-B interaction, they're all the same. In this non-ideal solution, the A-B interactions are stronger, so the A molecules escape from solution less often than they would in the ideal case. So again, strong heterogeneous interactions mean fewer of the molecules escape. So we call that situation negative deviations, because in particular, we're used to using Raoult's law to make predictions about the pressure, and in this non-ideal case, the pressure is lower than the Raoult's law of prediction, so it's deviating in a negative direction from the Raoult's law of prediction. So if we move over to the pressure composition diagram, just to remind you where this diagram came from originally, Raoult's law for component A says the vapor pressure, I'm sorry, the partial pressure piece of A increases linearly with concentration of A. Partial pressure Pb increases linearly with the concentration of B. We add those two curves together, we get the dew point curve, I'm sorry, the bubble point curve, which is a straight line of the system of Bayes Raoult's law. The sum of this straight line and that straight line gives us this straight line. What would that look like for a system with negative deviations from Raoult's law? I'll draw the same axes, pressure, composition, the pure substances are still going to have the same vapor pressures they've always had, so we're still going to connect those two dots with a bubble point curve and a dew point curve, but now, because we have negative deviations, instead of a straight line and a straight line, I won't draw these curves because it will clutter up my diagram a little too much, but actually maybe I will. Instead of a straight line, I'll draw a curve that sags a little bit. Likewise, for B, I'll draw a curve that sags a little bit below what we would predict for Raoult's law. So these partial pressures are the things that are exhibiting the negative deviation from Raoult's law, and then when I add those two curves up, instead of getting a straight line, I get a line that sags a little bit. So it's not the straight line, it's decreased by just a little bit. That's the bubble point curve, the dew point curve, the curve that describes the composition of the gas, pressure of the gas is a function of composition. That's still below the bubble point curve, so we still have a liquid phase at high pressures, a gas phase at low pressures, and a coexistence of the liquid and gas phase in this coexistence region, which again is connected with tie lines. So only difference between the two is the actual data are different for the real gas with negative deviations than Raoult's law predicts, and these pressures are reduced by a little bit because of those negative deviations. If I use the same logic for the temperature composition diagram, so temperature composition, the boiling point of these solutions, we can draw this same curve just inverted because systems with a high vapor pressure are more volatile, they will have a lower boiling point, but again, instead of a nice, smooth looking, lenticular, lens-shaped surface up here, it's going to, instead of deviating downward in the pressure, it's going to deviate upward in the temperature. So it's going to look something like that, liquid, gas coexistence, tie lines inside the coexistence region. So again, qualitatively the same as the Raoult's law case, but the boiling points are elevated for this case because if the Raoult's law pressure is lower, if the pressure is lower than the Raoult's law pressure, the boiling points will be higher than the Raoult's law boiling points. So now that leads us to the last case, which is the opposite situation of positive deviations, and I suppose before I describe that case, I can give you an example, a real world example of what would a system be that does or doesn't behave like Raoult's law? If I want to have a system with negative deviations, a system where A molecules interact more strongly with B molecules than they do with themselves, or with the B, than the B molecules do with themselves, the stereotypical example to give in that case would be acetone interacting with chloroform. So in this case, so acetone has this carbonyl bond, chloroform has this very polar hydrogen because of the electron withdrawing character of these chlorine atoms, so this very polar hydrogen can hydrogen bond in solution very well with the oxygen of the carbonyl bond in acetone. In pure chloroform, there's no oxygens or fluorines or nitrogens to hydrogen bond with, so it doesn't exhibit hydrogen bonding homogeneously. Likewise, these hydrogens are not polar enough to hydrogen bond with the oxygen in acetone, so there's no strong hydrogen bonding in acetone and pure acetone or in pure chloroform, but if I make a mixture of the two solvents, then I've got this strong hydrogen bond between solvents A and B, acetone and chloroform, and the AB interactions are stronger than they are in the pure solvent. So that's a standard case to use as an example when you want to illustrate negative deviations from Raoult's law. Positive deviations are the exact opposite. That would be a case where the AB interactions are weaker than the average of the AA and the BB interactions, so that would be most solvent pairs exhibit positive deviations from Raoult's law. That would be a case like, for example, most aqueous solutions. If I combine water and ethanol, water's got very strong hydrogen bonds with itself. It doesn't hydrogend as well with ethanol as it does with itself, so that would be a case where we will see positive deviations from Raoult's law, meaning that the pressure of either one of these solvents is going to be greater than predicted by Raoult's law, and you can probably guess what these diagrams are going to look like if the pressures are deviating in a positive direction, so rather than the straight line Raoult's law connecting the vapor pressures of the two pure solvents, those are deviated upwards a little bit, so liquid phase at high pressure, gas phase at low pressure, coexistence region between the two, so I've drawn the upper curve as bowing upwards from the Raoult's law behavior a little bit. Likewise, when we think about boiling points, if the pressures are deviated in the upward direction, the temperatures are going to deviate in the negative direction, so rather than the Raoult's law type curve, the boiling points are going to be lower for the solution with positive deviations, so you'll notice that I've made these deviations relatively slight. We will see in the future systems that have relatively minor deviations from Raoult's law, like the cases I've drawn here and cases that have more significant deviations from Raoult's law, so what I've drawn here are systems that have relatively minor deviations from Raoult's law, and then what we'll do next is, now that we at least understand how to categorize solutions either as being ideal, deviating in one direction or the other direction from Raoult's law, of course the next thing we'll need to want to do is to get a little more quantitative and ask if the system is non-ideal and we can't use Raoult's law, is there something else we can use instead?