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 just kind of 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 hydrogen's as well so these are little hydrogen's on my water molecules so these are h2o s and all this is happening let's say 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 can write it as 760 millimeters of mercury right but if I'm only interested in the green molecules then I would really rephrase that as partial pressure and if I want to calculate what that would be I could say well I know that there are four green molecules out of a total of eight and that is 50% green molecules right 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 360 or 760 which is 380 so this is the partial pressure of the green molecules I've figured it out right and I could actually complex this a little bit I could say well what if I got rid of those two and replace them with green molecules so now the gas is looking different I've got six out of eight molecules that are green so what is the new partial pressure looking like well six out of eight means that the percentage is going to be different so I've got a new number here in here so I'd say 75% is the new number right 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 want to show you a way of thinking about partial pressure which is that if the number of molecules in a group of molecules you know 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 right 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 'a' 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 a 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 right 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 to 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 I 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 K with a little H is just a constant so this is just a constant value that's you know listed on a table somewhere and this K sub H actually is going to take into account things like well which solute are we talking about when I say solute you basically can think of these green molecules so which which is it is it a green molecule or a purple one or a blue one what what exact solute are we talking about and what solvent are we talking about you know 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 shakin around and that allows them to free up and leave so these are three important issues right 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 can 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 you know we're we talked about going into a liquid this is now going out of liquid out of liquid so KH these values that I've 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 kind of been very patiently observing if you're looking at this surface layer you can actually kind of 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 can actually say something like this pressure a partial pressure / k / 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 is 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 of green molecules in the surface layer in the surface layer and what does that really tell you I mean okay so now you figure out the concentration of green molecules and surface layer what the heck does that mean well this my friends this this formula actually I don't know if you recognize it but this is Henry's law Henry's law so a guy named William Henry 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 a 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 gives you a sense for the concentration of molecules in the surface layer in fact another way of saying it is that there's a relationship 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 you know in this way you get a more intuitive feel for what it stands for