 Okay, so to see if we can understand what's going on in non-ideal solutions and how to quantify the behavior of non-ideal solution, let's consider a case with a volatile solvent A and a non-volatile solvent B just to make some of our graphs a little less complicated. So this would be an example like water is the solvent and sodium chloride, salt water as our solution. So sodium chloride, salt doesn't have a significant vapor pressure at all. It doesn't escape into the vapor phase. So pretty much the only vapor pressure, partial pressures we're going to have to worry about are those of the volatile solvent water or A in this case. So in that case, if I draw the partial pressure of my volatile solvent as a function of its concentration mole fraction on the right side of the graph, when it's pure solvent, it has a partial pressure equal to its vapor pressure on the left side of the graph instead of drawing vapor pressure of B, the vapor pressure of B is zero. It's non-volatile. So Raoult's law predicts this behavior. The partial pressure goes up linearly with the mole fraction of the solvent. As we've seen, non-ideal solutions can have either positive or negative deviations from Raoult's law. So a system with positive deviations will typically have a, so this is the Raoult's law curve, this is the positive deviations curve, might have a vapor pressure that goes up too rapidly at first and then comes back in line with Raoult's law at high concentrations. And a system with negative deviations from Raoult's law will do something more like this. Its pressure will be lower than predicted by Raoult's law at first and then it eventually comes back in line with Raoult's law as we approach the pure solvent. So if we want to understand these curves quantitatively instead of just using a straight line to describe the Raoult's law curve, we can consider doing what physical chemists usually do. After we've defined an ideal model, we want a model that describes reality a little more accurately. We can start introducing some corrections into that ideal equation. So perhaps one thing we could do would be to rewrite this equation in the way that we've rewritten idealized equations in the past. If that equation is not good enough, if the ideal behavior doesn't perfectly describe what's going on, we can add some correction terms on top of that. So first term is the linear term. We could add another term that looks like the quadratic term, maybe some constant in front of there. If we need to, we could add a cubic term with a different constant and so on. So as I said, that's sort of a typical physical chemistry approach. Take the ideal behavior. If that's not working well enough for you, throw on some non-ideal corrections to explain the non-ideal behavior. That's not what we're typically going to do. We certainly can do that. We could describe these curves with quadratic and cubic and more terms if we want to. It's not the approach we typically do take for modeling non-ideal solutions. Instead, what we usually do is to engage in a little bit of wishful thinking. An ideal solution says the partial pressure is a straight line function of the mole fraction. It's a mole fraction multiplied by the vapor pressure. It would be nice if that worked, but it doesn't work for most combinations of real solvents. What we can do instead is say it would be so nice if that linear equation worked that we're going to keep the equation linear. We're going to say that partial pressure is indeed something multiplied by the vapor pressure, but now the something is no longer x, but it's some different number. Instead of for this solution, instead of multiplying the vapor pressure by the mole fraction to get this value, we'll multiply by a larger number to get this value, or perhaps a smaller number to get this value. That quantity that we multiply by is called the activity of the solution, the activity of the solvent in that solution. Essentially, the equation I've written down there is a definition of activity. We can define the activity of a component A in a solution to be the partial pressure of A above that solution divided by its vapor pressure. That's a triple equal sign. That's a definition of the activity. If we can measure the vapor pressure and the partial pressure, we can calculate the activity, and that's going to tell us something about the actual partial pressure rather than the relative pressure. It's all fine as a definition. What does that mean? Why do we call it activity? What is activity telling us about a solution? In some sense, activity plays the same role as mole fraction does. What the activity tells us is the system, if I draw a sketch of, so here's a system with some A's and B's in it in the liquid phase escaping into the gas phase to form gaseous molecules of A, what the activity is telling us is, let's suppose I tell you that the activity of this particular A in this particular solution is 0.6. What I've told you is, rather than using Raoult's law with the mole fraction, we're using something that looks like Raoult's law with the activity. What I've said is this system, regardless of what the actual mole fraction is, this system behaves as if it were an ideal solution with a mole fraction of 0.6. This is telling you a fake mole fraction, a wishful thinking version of the mole fraction of the solvent. It may or may not actually have a mole fraction of 0.6 of the actual solvent, but we can continue to use our simple equation if we pretend that this is like a mole fraction. That's one meaning of the activity is it's a wishful thinking version of the mole fraction. A more physical way of understanding what the activity means is to think of it in terms of the physical behavior of these molecules, A molecules that are present in the liquid along with B molecules escape into the gas phase. The reason we call this quantity an activity is that the solvent A is active, what solvents do in this circumstance when we're talking about liquid gas equilibrium, what solvents do is escape into the gas phase, a solvent that is very active is going to escape a lot and enter the gas phase in large numbers of molecules, a solvent that is inactive is going to remain in the solvent and is not going to escape into the gas phase. So by describing the activity of the solvent, what we're saying is how active the solvent is in escaping the solution. So an activity of 0.6 in addition to meaning it has the same vapor pressure, some partial pressure as an ideal solution with mole fraction 0.6, it's saying the solvent molecules are as active, their activity is 0.6 meaning that's a description of how active they are in evaporating from the liquid phase and entering into the vapor phase. So those are two different ways of understanding what the activity means. One more thing I'll point out about activity before we talk about something else is to point out one of the very nice features of this wishful thinking sort of version of defining equations. Using an equation we've already got that we know is not accurate with a different definition of a variable. It allows many of our equations that we've developed for ideal solutions to be used in very similar forms for non-ideal solutions. For example, we've obtained an equation earlier that said the chemical potential in a solution of a component in a solution is equal to the chemical potential in the pure substance plus rt natural log of the mole fraction in the solution, the mole fraction that component has in the solution. So that was an equation that was only true for ideal solutions. We derived it specifically for the case of ideal solutions. For non-ideal solutions, since activity plays exactly the same role as mole fraction previously paid for ideal solutions, we can write an equation that says the chemical potential of the solvent in a solution in a non-ideal solution is equal to its chemical potential in the pure liquid phase plus rt natural log and instead of using the mole fraction, we just substitute the activity. So that would be the version of this equation that we would use in a non-ideal solution. So again that's one of the main advantages of this particular definition of treating non-ideal solutions by defining this activity is many of the ideal solution equations we have are very similar to the equations we use for non-ideal solutions. One caveat, one warning I'll give you at this point. It's a very common mistake to think of the activity since we define it to understand non-ideal solutions as a method of understanding how ideal or non-ideal the solution is. That's not true. So it's incorrect, slightly tempting but incorrect to assume that activity is telling us something about the ideality of a solution. If I say the activity solution is 0.6, it doesn't mean the solution is 60% ideal, doesn't mean anything like that. What it means remember is the solution behaves as if it were an ideal solution that had a mole fraction of 0.6. So it's telling us really something more about the concentration of the solution or a wishful thinking version of the concentration rather than the ideality of the solution. So it is useful to be able to talk about how an ideal or non-ideal in one direction or the other a solution is. So we will have a measure that tells us something about how ideal a solution is and we'll explore that next.