 So as we begin to think about how to talk about multi-component systems, systems with more than one component in them, an awful lot of interesting multi-component systems are solutions, can be described as solutions. So let's make sure we understand the terminology, how to use some vocabulary that we use to describe solutions typically. So first question is maybe what is a solution? So a solution is a mixture of two substances in which, importantly, one substance is homogeneously dispersed within the other. So you're familiar with solutions. Let's take as our first example, I don't know, let's say sugar and water. So if you just dissolve some sugar and water, you've created a solution, let's say homogenous mixture, and the reason we can call this a solution is because after I've stirred the sugar into the water, the sugar molecules are dissolved in the aqueous solution. They're homogeneously dispersed. Everywhere I look I can find an equal proportion of sugar molecules and water molecules in that mixture, in that solution. So since the mixture is a homogenous mixture at every length scale, no matter how finely I look, I get the same proportion of sugar molecules in every portion of that solution. So that's what a solution is. We often talk about solutions in terms of solutes and solvents. The solute is usually considered to be the minority component of that solution. If I dissolve a small amount of sugar in a larger amount of water, we say that the sugar is the solute, the water is the solvent. So the solvent is the background into which I'm dissolving the solute to make this homogenous mixture that I'm calling a solution. So not everything is a solution, of course, and I can give you some counter examples. So sugar water, I'll say, is a solution. If I mix other things with water, they may not form a solution. If I mix oil and water, let's say you mix yourself some salad dressing, which I guess would be oil and vinegar, same idea, but let's just mix two-component solution, oil and pure water. I can shake them up like you would with a salad dressing, for example, and get them to appear to mix. But if I let them rest, of course, the oil and the water will separate. The oil will float on top of the water. So the fact that it doesn't remain dissolves, the two separate from one another, means the mixture is not homogenous. There's oil on the top and water on the bottom. So that's not a homogenous mixture. I can call it a mixture, perhaps, but I can't call that a solution. That's not a solution because the oil doesn't dissolve in the water. It doesn't mix homogeneously with the water. Terminology we would use in that case is to say those two fluids, those two liquids are immiscible, which just means not mixable. I can't mix the oil in the water to form a solution. They will separate from one another. So they're immiscible. I can also say that one of them is insoluble in the other. If I can't dissolve oil in water, then oil is insoluble in water. I can dissolve sugar in water, so sugar is soluble in water. Let's do another food-related example. So here's another mixture. Milk is actually a very complicated mixture with lots of components, of course. And it certainly looks like one solution. It won't separate the way oil and water will. Your milk sitting in your refrigerator is going to remain some substances mixed throughout other ones. If you have full fat milk mixed throughout the water, that is the solvent of the milk mixture. But in fact, this is not a solution. Maybe difficult to tell with a naked eye. But if you look very closely, especially under some magnification, what you'll see is there's globules or clusters of fat molecules near each other and other regions that are mostly aqueous. So the fat is not homogeniously dispersed throughout the solvent, but it's located in little pockets throughout the solvent. So the fact that it's not perfectly homogeniously mixed means that we don't actually call milk a solution. We would call that an emulsion. So if we manage to get the fat not separating, not floating on top of the water, well distributed throughout the entire sample, but persisting in clusters, like dissolving like the oil sticking with the oil and the water sticking with the water, and clusters separated from one another, we typically call that an emulsion. And there's interesting chemistry to explore about how it is the fat becomes suspended within that emulsion without fully dissolving. But we'll postpone those for another day. And in order to talk about more features of solutions, and we can also talk about what phases a solution has to have. So everything I've talked about so far has been liquids. Sugar water, oil and water, milk, those are all liquids. Solutions don't actually have to involve liquids. Let's say I have a solid chunk of brass. It turns out is what we call an alloy. An alloy is a mixture of more than one metal. So this is a binary alloy composed of two different metals. If I mix the correct proportions of copper and zinc, they will essentially dissolve one another. If I have a homogeneous mixture of copper and zinc, normally we would call that an alloy. It's a little bit unusual to call it a solution, but it's certainly possible to call that a solid solution. We can say that brass is a solid solution of copper and zinc. So you don't have to have solutions that are composed purely of liquids, although that's the more traditional case where you'd use the terminology of a solution. And in fact, when we're thinking about phases, although the solvent is usually but not always a liquid, we can dissolve any sort of material in that liquid solvent to obtain a solution. So for example, we've talked about several examples up here of solutions. In fact, I'll come back to this one of liquids. Here's an example. If I have carbonated water, the way to prepare carbonated water, the solute was originally carbon dioxide, probably in the gaseous phase. If I take gaseous carbon dioxide and dissolve it in water, what I get is a solution of CO2 in water or perhaps the chemical byproducts that CO2 produces when it dissolves in water. But the point is I've dissolved a gas in a liquid to make that solution. If I want to dissolve a liquid in another liquid, maybe an example I could use here would be any sort of alcoholic beverage. So that is typically have more than two components. But if I take ethanol and I dissolve it in water in some proportions, then I've got an alcoholic beverage. Alkali beverage is not pure water. They're not pure ethanol. They're a solution of ethanol and water. So that's an example where a liquid has been dissolved in another liquid. Here's a gas dissolved in another liquid. We've seen one example where we have a solid dissolved in a liquid. I can give a different example. Salt water, ocean water would be solids like sodium chloride or other salts dissolved in water. So the phase of the solute before you dissolve it in the solution, before you prepare the solution, might have been a gas, might have been a liquid, might have been a solid. Completely irrelevant what the phase of the solute is before it dissolves. It might end up in a liquid solution. In some cases, we might even talk about solid solutions. So those are several terminological features of solutions that are important to be able to talk about as we move forward and talk about multi-component thermodynamics. And what we'll do next is move on to talk about how to talk about the properties of a solution. In particular, we need to be able to talk about not just what the components of a solution are, but the relative amounts of those two components. So we need to be able to talk about concentration. And that's coming next.