Vapor pressure

We know that when we have some substance in a liquid state, it has enough kinetic energy for the molecules to move past each other, but still not enough energy for the molecules to completely move away from each other. So, for example, this is a liquid. Maybe they're moving in that direction. These guys are moving a little bit slower in that direction so there's a bit of this flow going on, but still there are bonds between them. They kind of switch between different molecules, but they want to stay close to each other. There are these little bonds between them and they want to stay close. If you increase the average kinetic energy enough, or essentially increase the temperature enough and then overcome the heat of fusion, we know that, all of a sudden, even these bonds aren't strong enough to even keep them close, and the molecules separate and they get into a gaseous phase. And there they have a lot of kinetic energy, and they're bouncing around, and they take the shape of their container. But there's an interesting thing to think about. Temperature is average kinetic energy. Which implies, and it's true, that all of the molecules do not have the same kinetic energy. Let's say even they did. Then these guys would bump into this guy, and you could think of them as billiard balls, and they transfer all of the momentum to this guy. Now this guy has a ton of kinetic energy. These guys have a lot less. This guy has a ton. These guys have a lot less. There's a huge distribution of kinetic energy. If you look at the surface atoms or the surface molecules, and I care about the surface molecules because those are the first ones to vaporize or-- I shouldn't jump the gun. They're the ones capable of leaving if they had enough kinetic energy. If I were to draw a distribution of the surface molecules-- let me draw a little graph here. So in this dimension, I have kinetic energy, and on this dimension, this is just a relative concentration. And this is just my best estimate, but it should give you the idea. So there's some average kinetic energy at some temperature, right? This is the average kinetic energy. And then the kinetic energy of all the parts, it's going to be a distribution around that, so maybe it looks something like this: a bell curve. You could watch the statistics videos to learn more about the normal distribution, but I think the normal distribution-- this is supposed to be a normal, so it just gets smaller and smaller as you go there. And so at any given time, although the average is here, there's some molecules that have a very low kinetic energy. They're moving slowly or maybe they have-- well, let's just say they're moving slowly. And at any given time, you have some molecules that have a very high kinetic energy, maybe just because of the random bumps that it gets from other molecules. It's accrued a lot of velocity or at least a lot of momentum. So the question arises, are any of these molecules fast enough? Do they have enough kinetic energy to escape? And so there is some kinetic energy. I'll draw some threshold here, where if you have more than that amount of kinetic energy, you actually have enough to escape if you are surface atom. Now, there could be a dude down here who has a ton of kinetic energy. But in order for him to escape, he'd have to bump through all these other liquid molecules on the way out, so it's a very-- in fact, he probably won't escape. It's the surface atoms that we care about because those are the ones that are interfacing directly with the pressure outside. So let's say this is the gas outside. It's going to be much less dense. It doesn't have to be, but let's assume it is. These are the guys that kind of can escape into the air above it, if we assume that there's some air above it. So at any given time, there's some fraction of the particles or the molecules that can escape. So you're next question is, hey, well, doesn't that mean that they will be vaporized or they will turn into gas? And yes, it does. So at any given time, you have some molecules that are escaping. Those molecules-- what it's called is evaporation. This isn't a foreign concept to you. If you leave water outside, it will evaporate, even though outside, hopefully, in your place, is below the boiling temperature, or the normal boiling temperature of water. The normal boiling point is just the boiling point at atmospheric pressure. If you just leave water out, over time, it will evaporate. What happens is some of these molecules that have unusually high kinetic energy do escape. They do escape, and if you have your pot or pan outside or, even better, outside of your house, what happens is they escape, and then the wind blows. The wind will blow and then blow these guys away. And then a few more will escape, the wind blows and blows them all away. And a few more escape, and the wind blows and blows them all the way. So over time, you'll end up with an empty pan that once held water. Now, the question is what happens if you have a closed system? Well, we've all done that experiment, either on purpose or inadvertently, leaving something outside and seeing that the water will evaporate. What happens in a closed system where there isn't wind to blow away? So let me just draw-- there you go. Let's say a closed system, and I have-- it doesn't have to be water, but I have some liquid down here. And there's some pressure from the air above it. Let's just say it was at atmospheric pressure. It doesn't have to be. So there's some air and the air has some kinetic energy over here. So, of course, do the water molecules. And some of them start to evaporate. So some of the water molecules that are up here in the distribution, they have enough energy to escape, so they start hanging out with the air molecules, right? Now something interesting happens. This is the distribution of the molecules in the liquid state. Well, there's also a distribution of the kinetic energies of the molecules in the gaseous state. Just like different things are bumping into each other and gaining and losing kinetic energy down here, the same thing is happening up here. So maybe this guy has a lot of kinetic energy, but he bumps into stuff and he loses it. And then he'll come back down. So there's some set of molecules. I'll do it in another set of blue. These are still the water-- or whatever the fluid we're talking about-- that come back from the vapor state back into the liquid state. And so what happens is, there's always a bit of evaporation and there's always a bit of condensation because you always have this distribution of kinetic energies. At any given moment in time, out of the vapor above the liquid, some of the vapor loses its kinetic energy and then it goes back into the liquid state. Some of the surface liquid gains kinetic energy by random bumps and whatever else and goes into the vapor state. And the vapor state will continue to happen until you get to some type of equilibrium. And when you get that equilibrium, we're at some pressure up here. So let me see, some pressure. And the pressure is caused by these vapor particles over here, and that pressure is called the vapor pressure. I want to make sure you understand this. So the vapor pressure is the pressure created, and this is at a given temperature for a given molecule, right? Every molecule or every type of substance will have a different vapor pressure at different temperatures, and obviously every different type of substance will also have different vapor pressures. For a given temperature and a given molecule, it's the pressure at which you have a pressure created by the vapor molecules where you have an equilibrium. Where you have just as many things vaporizing as things going back into the liquid state. And we learned before that the more pressure you have, the harder it is to vaporize even more, right? We learned in the phase state things that if you are at 100 degrees at ultra-high pressure, and you were dealing with water, you would still be in the liquid state. So the vapor creates some pressure and it'll keep happening, depending on how badly this liquid wants to evaporate. But it keeps vaporizing until the point that you have just as much-- I guess you could kind of view it as density up here, but I don't want to think-- you have just as many molecules here converting into this state as molecules here converting into this state. So just to get an intuition of what vapor pressure is or how it goes with different molecules, molecules that really want to evaporate-- and so why would a molecule want to evaporate? It could have high kinetic energy, so this would be at a high temperature. It could have low intermolecular forces, right? It could be molecular. Obviously, the noble gases have very low molecular forces, but in general, most hydrocarbons or gasoline or methane or all of these things, they really want to evaporate because they have much lower intermolecular forces than, say, water. Or they could just be light molecules. You could look at the physics lectures, but kinetic energy it's a function of mass and velocity. So you could have a pretty respectable kinetic energy because you have a high mass and a low velocity. So if you have a light mass and the same kinetic energy, you're more likely to have a higher velocity. You could watch the kinetic energy videos for that. But something that wants to evaporate, a lot of its molecules-- let me do it in a different color. Something that wants to evaporate really bad, a lot more of its molecules will have to enter into this vapor state in order for the equilibrium to be reached. Let me do it all in the same color. So the pressure created by its evaporated molecules is going to be higher for it to get to that equilibrium state, so it has high vapor pressure. And on the other side, if you're at a low temperature or you have strong intermolecular forces or you have a heavy molecule, then you're going to have a low vapor pressure. For example, iron has a very low vapor pressure because it's not vaporizing while-- let me think of something. Carbon dioxide has a relatively much higher vapor pressure. Much more of carbon dioxide is going to evaporate when you have it. Well, I really shouldn't use that because you're going straight from the liquid to the solid state, but I think you get the idea. And something that has a high vapor pressure, that wants to evaporate really bad, we say it has a high volatility. You've probably heard that word before. So, for example, gasoline has a higher-- it's more volatile than water, and that's why it evaporates, and it also has a higher vapor pressure. Because if you were to put it in a closed container, more gasoline at the same temperature and the same atmospheric pressure, will enter into the vapor state. And so that vapor state will generate more pressure to offset the natural inclination of the gasoline to want to escape than in the case with water. Now, an interesting thing happens when this vapor pressure is equal to the atmospheric pressure. So right now, this is our closed container and you have the atmosphere here at a certain pressure. Let's say until now, we've assumed that the atmosphere was at a higher pressure, for the most part keeping these molecules contained. Maybe some atmosphere molecules are coming in here, and maybe some of the vapor molecules are escaping a bit, but it's keeping it contained because this is at a higher pressure out here than this vapor pressure. And of course the pressure right here, at the surface of the molecule, is going to be the combination of the partial pressure due to the few atmospheric molecules that come in, plus the vapor pressure. But once that vapor pressure becomes equal to that atmospheric pressure, so it can press out with the same amount of force-- you can kind of view it as force per area-- so then the molecules can start to escape. It can push the atmosphere back. And so you start having a gap here. You start having a vacuum. I don't want to use exactly a vacuum, but since the molecules escaped, more and more of these molecules can start going out. And at that point, you've reached the boiling point of the substance when the vapor pressure is equal to the atmospheric pressure. Just to get a sense of what all of this means, let's look at the vapor pressure for water. This is water right here, H2O. I should do that in black. And so you see at 760-- so atmospheric pressure, we're in torr now, but that's just a different-- 760 torr is equal to 1 atmosphere, so that's about right. That's about right there, so it's 1 atmosphere. So at atmospheric pressure, the vapor pressure at 100 degrees Celsius for water-- the vapor is at 100 degrees Celsius for water. Or I guess another way to put it, at 100 degrees Celsius, you have 760 torr of vapor pressure, which is exactly the atmospheric pressure, or 1 atmosphere, at sea level. So at 100 degrees, vapor pressure is equal to atmospheric, or sea level atmospheric. And so you're going to boil, which we all know is true. And then at lower temperatures, your vapor pressure is going to be lower than the atmospheric pressure, right? Let's see, here it looks like 300 something. But then what happens? If you lowered the atmospheric pressure enough, if you were to pump air out of the container, or whatever, low enough, so if you brought the atmospheric pressure down to this vapor pressure, then again, you will have boiling. And we saw that in the phase change diagrams, that you can boil something at a lower temperature if you lower the atmospheric pressure. And that's because you're lowering the atmospheric pressure to the vapor pressure of the substance. And here's a comparative chart, and this is interesting. You see this is kind of an exponential increase with temperature of vapor pressure. And that's because, if you think about that distribution we did before, this is at one kinetic energy. If you increase the amount of kinetic energy, then your distribution will look like this. The temperature has gone up. And now you have a lot, lot more. It's not just linear. You have a lot more particles that can now escape and have the kinetic energy to evaporate. And you can see it's this exponential increase as you increase the temperature. Now, here's another chart. You say, hey, where's that exponential increase going? That's because this is a logarithmic chart. You can see the scale. It increases exponentially as opposed to linearly, so it goes from 0.1 to 10, so equal distances are actually up by a factor of 10, so that's why you don't see that logarithmic move. But these are just for different substances. Propane, you see at any given-- so let's go at like a decent temperature. Let's go 20 degrees Celsius. At 20 Celsius, propane has the highest vapor pressure. So this is 1 atmosphere, so propane will actually evaporate, will actually boil at 20 degrees Celsius. It will actually completely boil and go into the gaseous state. Because its vapor pressure is so much higher than atmospheric pressure, if we're assuming we're at sea level. And you could do that for different molecules. Methyl chloride is the next one. It's a slightly lower vapor pressure, but still very volatile. It would still definitely boil and turn into the gaseous state at 20 degrees Celsius if we're at sea level because sea level is right there. Let's see, at sea level, if you wanted to keep something-- so sea level is this pressure-- if you wanted to keep let's say, methyl chloride. If you wanted to keep methyl chloride in the liquid state, or in equilibrium with the liquid state instead of boiling, you would have to be at least at around-- what is this? Minus 25 degrees Celsius in order for that. Propane, even at minus 25 degrees is still in the gaseous state because its vapor pressure is still higher. And then, of course, if you have butane, for example. Butane I think is what they put in lighters, but butane will be in the liquid state as long as you're at around roughly 0 degrees. In a lighter, you might say, oh, it's in a liquid state. They probably increase the pressure so the pressure in the lighter is probably something higher. Maybe it's at 2 atmospheres or something, so that the butane at room temperature will stay in the liquid state. Who knows? I don't know what the pressure is in there. This is just an interesting chart to look at, that there's actually a bunch of different vapor pressures. You can see at atmospheric pressure what's likely to be a gas or a liquid at different temperatures, and then you could see at different temperatures, which are the things that are most volatile and how much do you have to increase or decrease the pressure to evaporate something or to boil it. Anyway, hopefully you found that useful. Vapor pressure is something that we encounter every day, and I'll see you in the next video.