In this video, we examine the conditions under which real gases are most likely to deviate from ideal behavior: low temperatures and high pressures (small volumes). At low temperatures, attractions between gas particles cause the particles to collide less often with the container walls, resulting in a pressure lower than the ideal gas value. At high pressures (small volumes), finite particle volumes lower the actual volume available to the gas particles, resulting in a pressure higher than the ideal gas value. Created by Sal Khan.
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- Can we say that in container with small volume and very low temperature, the ideal gas law would be completely inaccurate(5 votes)
- We can say inaccurate, but not completely inaccurate because that's saying that no part of it is true which is incorrect.(5 votes)
- [Instructor] We've already spent some time looking at the ideal gas law, and also thinking about scenarios where things might diverge from what at least the ideal gas law might predict. And what we're going to do in this video is dig a little bit deeper into scenarios where we might diverge a little bit from the ideal gas law, or maybe I guess, a lot of it in certain situations. So I have three scenarios here. This first scenario right over here, I have a high temperature, high temperature, and I have a large volume. And both of these are really important because when we think about when we get close to being ideal, that situation's where the volume of the particles themselves are negligible to the volume of the container. And at least here, looks like that might be the case 'cause we're dealing with a very large volume. Even this isn't drawn to scale. I just drew the particles this size just so that you could see them. And high temperature, that helps us realize that well maybe the intermolecular interactions or attractions between the particles aren't going to be that significant. And so in a high temperature, large volume scenario, this might be pretty close to ideal. Now it's not gonna be perfectly ideal because real gases have some volume, and they do have some intermolecular interactions. But now let's change things up a little bit. Let's now move to the same volume. So we're still dealing with a large volume. But let's lower the temperature. So low temperature. And we can see because temperature is proportional to average kinetic energy of the particles, that here, these arrows on average are a little bit smaller. And let's say we lower the temperature close to the condensation point. Remember, the condensation point of a gas, that's a situation where the molecules are attracting each other, and even starting to clump up together. They're starting to, if we're thinking about say, water vapors, they're starting to get into little droplets of liquid water, because they're getting so attracted to each other. So in this situation, where we have just lowered the temperature, the ideal gas law would already predict that if you keep everything else constant, that the pressure would go down. If we solve for pressure, we would have P is equal to nRT over V. So if you just lowered temperature, the ideal gas law would already predict that your pressure would be lower. But in this situation with a real gas, because we're close to that condensation point, these gases, these particles are more and more attracted to each other. So they're less likely to bump into the sides of the container, or if they do, they're going to do it with less vigor. So in this situation for a real gas, because of the intermolecular attraction between the particles, you would actually have a lower pressure than even the ideal gas law would predict. Ideal gas law would already predict that if you lower the temperature, pressure would go down. But you would see that a real gas in this scenario, P, even lower, even lower for a real gas. Now let's go to another scenario. Let's go to a scenario where we keep the high temperature that we had in the original scenario, but now we have a small volume, small volume. Maybe this top of the container is a piston, and we push it down like this. Well the ideal gas law, if we just solve for P again, P is equal to nRT over V. It would already predict that if you decrease the denominator here, that's going to increase the value of the entire expression. So it would already predict that you would have a higher pressure, that the particles will bounce into the sides of the container more frequently, and with more vigor. But if we have a really small volume of the container, we no longer can assume that the volume of the particles themselves are going to be negligible compared to the volume of the container. And so the effective volume, to move around in is even lower than we're seeing in this equation. So these particles have even less space to bounce around in because they take up some of the space. So they're going to bounce off the sides of the container more frequently and even more vigor. So here, pressure even higher for a real gas than what is predicted by the ideal gas law.