 Okay, so when we start talking about bonafide chemical properties, it's going to be very useful to distinguish between two different flavors of properties, those we call extensive and those we call intensive properties. So let me explain what those terms mean. First, an extensive property is one that is proportional to the size of the system. So what I mean by that is when the system gets larger, the value of this property gets larger in the same proportion. So I'll give you some examples of what I mean by that. Typically, the way to think about that is if you were to double the size of the system, would the value of the property double as well or would it not? So if let's say I have a beaker containing, let's say, 100 grams of water or 100 milliliters of water, your choice, both are roughly true. So I've got a beaker of water. If I were to double the size of that system, let's say I take two identical beakers of water and I pour them together. So now I have a beaker of water. So the mass when I double the system will be 200 grams instead of 100 grams. When I double the system size, its volume doubles to 200 milliliters. If I were talking about the number of molecules or the number of moles, there's roughly five and a half moles of water and 100 milliliters of water. When I double the system size, that doubles as well. I can think of other properties as well. The energy of the water over here will double to become twice as large on this side. So there's a lot of properties like the mass and the volume and the moles and the energy. Those are all extensive properties, meaning that when I double the system size, the property doubles. Or if I triple it, the property would triple. The other way to think about extensivity, a property that's extensive, is if I have two systems, they don't have to be identical beakers of water. They could be non-identical as well. If I have 100 grams of water and a 50-gram block of copper, and I put the 50-gram block of copper in the water, its mass is still going to be 100 from the water and 50 from the iron. So an extensive property, whether it's mass or volume or whatever, whatever the property is I'm interested in, the total value of that property will be the sum of the value for two different subsystems. If I have system A and system B and I combine them, if I have an extensive property, I just add the two properties together to get the property for the total system. So that works with properties like mass. So another way to think about an extensive property is it's one that's additive. If I have two different systems and I combine them together, I add the value of the property to get the value for the combined system. That's different than an intensive property, which doesn't change when I change the system size. So an intensive property is independent of the system size. Changing the system size doesn't have any effect on the property. So for example, other properties I could give you that describe this beaker of water. It's 100 grams and 100 milliliters, and it's got a certain number of moles and a certain amount of energy. I could also tell you that beaker of water is at, let's say, 300 Kelvin. If I take two beakers of water, both at 300 Kelvin and I combine them, their temperature isn't 600 Kelvin. I don't add those two temperatures together. The temperature remains the same when I combine the two of them together. Likewise, the water has a density of one gram per milliliter. Regardless of whether I have a small beaker or a large beaker of water, that density is still the same. I could tell you the pressure of the water, if it's under an atmospheric pressure of one atmosphere. If I double the everything in the system, it's still under a pressure of one atmosphere. So there's other properties like the temperature and the pressure and the density that are intensive properties. So again, extensive properties scale with the size of the system. Intensive properties don't change at all when all I do is change the size of the system. So a couple of important things to point out about extensive and intensive properties. If I were to take the ratio of two extensive properties, let's say, let me just write down the extensive property divided by another extensive property gives an intensive property. The reason for that, of course, is if I double the system size, the numerator and the denominator both get twice as large, so the ratio didn't change at all. So an example of that would be something like if I were to take the mass divided by the volume, that's the mass density. So mass is an extensive property, volume is an extensive property, if I take the ratio of two extensive properties, I get an intensive property like the density. So that's a pretty common way of converting extensive properties to intensive properties is take one extensive property and divide it by another. A very common way of doing exactly that is dividing by the number of moles or molecules in a system. So for example, if I have volume and I divide it by the number of moles or if I, let's take an example you're more familiar with, first if I take the mass of the system divided by a number of moles, if I tell you that there's a hundred grams of water in the system and I divide it by the five and a half moles of water in that system, then I'll find out that the mass per mole is 18 grams per mole. So that's the quantity we call the molar mass. So it's the mass divided by the number of moles, so it's mass per mole or the molar mass. Likewise, if I take the volume of the system, 100 milliliters divided by the five and a half moles that are there, it's going to turn out to be 18 milliliters per mole. So that's telling me a quantity that we call the molar volume, we normally represent that with a bar on top. So the molar volume would be the volume divided by the number of moles. These are both examples of an extensive property divided by moles as another extensive property, and that's a common way of converting this extensive property to an intensive property. The molar mass of water is 18 grams per mole no matter how much of it we have, but the mass of the total water scales with the amount of water in the system. So these extensive properties and intensive properties will help us understand the different properties we're interested in, and the next step will be in particular the property that we found as useful for predicting whether a change in a system is likely or unlikely, the multiplicity of the system. We'll need to think a little bit about whether the multiplicity is an extensive or an intensive property, and we'll do that in the next video lecture.