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- [Instructor] So let's review our knowledge of what it means to be an ideal gas. What key assumptions do we make about an ideal gas? Well, the first assumption is no intermolecular interactions, and what do we mean by that? Well, an example of an intermolecular interactions are something like, say, a hydrogen bond. Well, let's say that you have two water molecules, two neighboring water molecules, and that is... So you have an oxygen with two hydrogens. We know that the oxygen end of a water molecule... And this is the gas form, so we're talking about water vapor here. So we know that the oxygen has a partially negative charge, and that the hydrogen end has partially positive charge and these are attracted to each other. These are our famous hydrogen bonds. So that is an intermolecular interaction. We can think about dipole-dipole forces, which is similar because of the polarity of the molecules. We can think about van der Waals forces. These various molecular interactions where just random chance one side gets a temporary polarity and might be attracted or repulsed from the other side of a neighboring molecule. For ideal gases, and for the application of the ideal gas law, we assume that there are no intermolecular interactions or, if there are, that it's very.... We assume an ideal gas has none of them. And, in real gases, in order to assume they're like an ideal gas, we assume this is very limited or that we can assume they're not happening. The second key assumption is that the volume of the gas itself, the molecules of the gas, is negligible relative to the volume of the container. So, gas molecule volume is negligible. Now, it turns out there are no gases that are absolutely true ideal gases. Obviously, all gases, their actual molecules, do take up some volume and there will be some type of intermolecular interactions in terms of even van der Waals forces and whatever else. But it turns out, under most conditions that we're dealing with in a lot of gases, that these are reasonable assumptions. Or at least many conditions these are reasonable assumptions. In particular, these are reasonable.... So, this is reasonable for real gases.... Reasonable assumptions for real gases at relatively high temperatures and low pressures. And, obviously, that's going to depend on which gas we're talking about how high of a temperature you need or how low of a pressure. Or another way of thinking about it is these assumptions where gases become less and less ideal as you approach their condensation point. So, if you start to really lower the temperature or increase the pressure, you're more likely to go from a gas form to liquid form. And, as you approach that condensation point, your gas is going to behave less and less like an ideal gas. But, as we've seen in many videos, if your gas is... If you can make these assumptions, then it's reasonable to apply the ideal gas law. That the pressure times the volume of your ideal gas is going to be equal to the number of moles times the universal gas constant times the temperature measured in Kelvin. Now, let's, first of all, think about why this is reasonable for most gases at relatively high temperatures and low pressures. And then, we'll think about where this breaks down as we can approach the condensation point where the temperature is lower or where the pressure is a lot higher. So, let's do these three cases. So, the first... Let me do it in this color right here. So, high temperature/low pressure. Then, I'll do a case of low temperature. And then, I'll do a case of high pressure. So, first, why is it reasonable for real gases to behave this way at high temperatures and low pressures, relatively high temperatures and low pressures. Well, let me draw a container here. This is the walls of my container. Obviously, this container will be in three dimensions. But I will just draw... Imagine it as a cross-section or a two-dimensional version of it. And let me draw the gas molecules bouncing around. So, it's high temperature. So, these things are really moving around quite fast. But it's low pressure, so there's not a lot of bouncing, especially with the walls of the container. So, this is a real gas. Its molecules clearly take up some volume. And we'll assume that they're in the real world. There are some intermolecular interactions with neighboring molecules. But, because it's such a high temperature, these things are really buzzing around super fast, you really don't have the closeness and the time for these things to really interact. And the attractive forces that you might get from, say, hydrogen bonding or whatever else, it really doesn't come into play. Likewise, since it's low pressure, there aren't a lot of collisions. It's reasonable to assume that the gas, that the volume is negligible relative to the volume of the container. At least my brain visualizes that there's just not... That the container's huge relative to these gas molecules. And so, when we consider how they might interact, it's okay to not think about their interactions with each other. Either in terms of colliding with each other and having this electrostatic repulsion or they're gonna be so far away from each other most of the time that some type of attractive force, whether it's a hydrogen bond or dipole-dipole interactions, that it's not really gonna come into play. So, this is why, in these conditions, it's okay, it seems reasonable that most real gases.... Let's assume the ideal gas conditions and that we can apply the ideal gas law. Now let's go into more of the, I guess you could say, boundary cases. Let's assume you have low temperature. So, in a situation with low temperature.... I'll draw the same container. We'll draw the same container. And so, now low temperature. If you are an ideal gas, a truly, this kind of mythical, ideal gas, Well, the temperature shouldn't matter so much. But now that we actually have a low temperature, now neighboring molecules, especially things like attractive forces, are going to have a chance to come and play. They're not whizzing by each other so fast. And so, if attractive forces are starting to come in play, do you think holding the volume constant and holding the temperature constant at this low temperature and holding the number of molecules constant... Do you think that a real gas at a low temperature would have a lower pressure or higher pressure than a ideal gas? I encourage you to pause the video and think about it. So, it's low temperature. And so, we're assuming... So, hold T temperature, volume, and number of moles for ideal and real constant. So, if we were to compare the pressure of the real gas to the pressure of the ideal gas, what do we think it will be? Well, the real gas, these things are gonna be kind of moseying past each other. So, they're gonna have more time to attract each other with these hydrogen bonds and these van der Waals forces. And so, they might spend more time bumping into each other or clumping closer to each other than they would be bouncing into the walls. So, you can imagine, if you hold this low temperature constant for the two different situations, ideal versus real... If you hold the volume constant, if you hold the number of molecules constant, you would imagine that the pressure for the real gas is going to be lower than the pressure for the ideal gas. And think about taking the temperature so low that you, once again, get to the condensation point. Then these things are going to be moving so slow that they're going to start really attracting each other or they're gonna have a chance that attractive interaction can overpower, I guess you could say, the kinetic movement past each other due to the low temperature. And so, you can think of it, capture each other. And they could go to a liquid state. And this would happen with water vapor molecules as you lower the temperature closer to the, I guess you could say, closer to the condensation point or the boiling point, depending on which direction you are coming from. Now, let's go the other way. Let's think about high pressure. And let's hold... Let's compare what a real gas would do to an ideal gas. But we're gonna compare volume. So, we wanna compare the volume of a real gas compared to the volume of an ideal gas. And we're going to hold temperature, pressure, and number of moles constant. So, an ideal gas... Let me draw my container again. An ideal gas, right over here, it shouldn't matter that it's high pressure. We're assuming these things here. So, these things are really knocking into each other very, very frequently. Not only into the containers, but into each other. And, depending on how much you view the volume negligible, for an ideal gas, you think about more about the interactions with the container. But, if the pressure is high enough, well, then there's so many collisions going on, that, if you really wanted to hold the pressure constant, especially if this volume becomes consequential because there's so many collisions going on, well, then if you wanna hold the pressure constant for the ideal gas versus the real gas, you would have to give the real gas more space. You'd have to give it more space because the volume of the molecules are becoming consequential. You're starting to challenge assumption number two. So, to have the same pressure, in this case, the same high pressure, your volume of the real gas would have to be higher than the volume of the ideal gas. So, once again, getting something really, really, really high pressure is another way to get closer to that condensation point. In general, if you lower the temperature, increase the pressure, you're getting closer and closer to the molecules interacting with each other, capturing each other so that you get to a liquid state. So, the whole takeaway here, ideal gas assumptions and the ideal gas law reasonable for most gases when we have a high temperature/low pressure. But then, when we test those things, low temperature/high pressure, well, things might start to break down a little bit.