Henry's law

Let's say you're taking a look at the interface between a gas-- I'm going to do in yellow-- and a liquid down here in blue. And the liquid I'm going to use is H2O, or water. And you actually want to kind of keep your eye on exactly what's happening right here. So this is your eyeball, and you're watching exactly what's happening right at that surface layer. In fact, let me write that down because it ends up being kind of an important idea. You're just watching the surface layer of water. And you really want to make sure that you keep your eye on how the molecules are moving around. So let's say you've got some molecules in purple, and you've got some green molecules here as well. And four of each, so overall it's 50% purple and 50% green. And down below, you've got some water molecules. Let's draw some oxygens here. And I'm going to draw some hydrogens as well. So these are little hydrogens on my water molecules. So these are H2Os, and all this is happening in a giant cup of water. So this is a big cup of water. And the purple and green molecules represent some sort of molecule. Who knows what kind of gas that is, but some hypothetical gas. And to think through this, I want to kind of get to the idea of partial pressure. So we know total pressure is one atmosphere, or you could write it as 760 millimeters of mercury. But if I'm only interested in the green molecules, then I would really rephrase that as partial pressure. And if I wanted to calculate what that would be, I could say, I know that there are 4 green molecules out of a total of 8, and that is 50% green molecules. And I know that the overall pressure is 760-- actually let me leave it in the same color-- 760 millimeters of mercury. And I've got 50%, I said, that are green. So that means that the green partial pressure is going to be half of 760, which is 380. So this is the partial pressure of the green molecules. I figured it out. And I could actually complicate this a little bit. I could say, well, what if I got rid of those two and replaced them with green molecules? So now the gas is looking different. I've got 6 out of 8 molecules that are green. So what is the new partial pressure looking like? Well, 6 out of 8 means that the percentage is going to be different. So I've got a new number here and here. So I'd say 75% is the new number. And I've got 75% times 760 is 570 millimeters of mercury. This is my new partial pressure. And the reason I actually went through that is because I wanted to show you a way of thinking about partial pressure, which is that if the number of molecules in a group of molecules-- if the proportion goes up-- then really that's another way of saying the partial pressure has gone up. And if you have more molecules, what does that mean exactly? Well, from this person's standpoint, this person that's watching this surface layer, they're going to see, of course, molecules going every which way. Every once in a while, these green molecules are going to go down and into the liquid. They're going to bounce in different ways, and just by random chance, a couple of these green molecules might end up down here in the surface layer. So that's something that you would observe. And you'd probably observe it more often if you actually have more green molecules. In other words, having a higher partial pressure will cause more of the molecules to actually switch from the gas part of this cup into the liquid part of the cup. So I don't want to be too redundant, but I want to point out that as the partial pressure rises, we're going to have more molecules, more green molecules, going into the liquid. So now let me actually ask you to try to focus on this little green molecule, this little fella right here, this guy. Now imagine, he's just entered our world of H2O's, and he's trying to figure out what to do next. And one thing he might do is pop right back out. You'd agree that that's something he could do, right? If he entered the liquid phase, he could also just re-enter the gas phase. He could leave. And a lot of molecules want to do that. They want to actually get out of the liquid because the liquid is a little stifling. It's kind of crammed in there, a lot of H2O molecules around in this case may not like that. So it turns out you can actually look up, in a table, this value called K with a little h. And this H with a little h is just a constant. So this is just a constant value that's listed on a table somewhere. And this K sub h actually is going to take into account things like which solute are we talking about. When I say solute, you basically can think of these green molecules. So which is it? Is it a green molecule or a purple one or a blue one? What exact solute are we talking about? And what solvent are we talking about? Are we talking about water? Or is it dish soap or ethanol or some other liquid that we're worried about in this case? And finally, what temperature are we talking about? Because we know that molecules are going to want to leave. Especially molecules that prefer to be in a gas phase, they're going to want to leave the liquid, and they're going to do it much, much more if the temperature is high. Because when the temperature is high, remember, the little H2O molecules are dancing around and shaking around, And that allows them to free up and leave. So these are three important issues. What is the solute? What is the solvent? And what is the temperature? And if you know these three things, you can actually-- like I said, you could look up in a table what the Kh is. And that tells you a little bit about that red arrow. What is the likelihood of leaving the surface layer? So just as before, where we talked about going into a liquid, this is now going out of liquid. So Kh, these values that I said you can find in a table, tell you about the likelihood of going out of a liquid. And the partial pressure tells you the likelihood of going into a liquid. So if you are looking now-- let's go back to this person that's been very patiently observing. If you're looking at this surface layer, you can actually do a good job of checking how many molecules are entering, how many molecules are exiting, and you can now calculate a concentration of the molecule in the surface layer. You could actually say something like this-- pressure, or partial pressure, divided by K over h equals concentration. So let me write all this out. Concentration is here. And the other two are what we've already been talking about. The p just partial pressure, and that is right there. And the K with a little h is the constant, and that is right there. So that's this guy. So if you just divide the two, you can figure out the concentration, and specifically, I mean the concentration of green molecules in the surface layer. And what does that really tell you? OK, so now you figure out the concentration of green molecules in the surface layer. What the heck does that mean? Well this, my friends, this formula-- actually, I don't know if you recognize it, but this is Henry's law. So a guy named William Henry-- and actually Henry was his last name-- came up with this fantastic formula. And sometimes you see it rewritten. You might see p equals concentration times K with the little h. It depends on how you're going to present it, but it's the same formula. And basically what it says-- and it's a very clever way of saying it-- is that you can take a look at the molecules that are going into a liquid and the molecules that are going to want to leave a liquid. And basically it gives you a sense for the concentration of molecules in the surface layer. In fact, another way of saying is that there's a relationship between partial pressure and concentration within the liquid. So it's actually a pretty powerful way of thinking about it. And I hope that by describing K with a little h in this way you get a more intuitive feel for what it stands for.