O2 and CO2 solubility

Let me do a little experiment. Let's say I have oxygen here, and we know that oxygen is about 21% of the atmosphere. And I decide to take a cup, let's say a cup like this-- simple cup of water. And I leave it out on the counter. And it's about room temperature, about 25 degrees Celsius here. And I want to know, how much oxygen is really going to enter that cup at that surface layer? So let's say I want to measure the concentration of oxygen in that surface layer of water. Well, you know, I say 21% so, of course, there's some molecules of oxygen here. And it's only 21%, it's not like it's the majority. So I've got to draw some other molecules. This could be nitrogen or some other molecule, let's say. But I'm focused on the blue dots, because the blue dots are the oxygen dots. And so over time I let this kind of sit out. And maybe I come back and check, and a little bit of oxygen has entered my surface layer of water. In fact, if I measured it, I could say, well, the concentration, C, at that level is 0.27 millimoles per liter. And this number is literally just something that I would have to measure, right? I would actually measure the concentration there, and that's the measure of oxygen. So I've learned about Henry's law, and I can think well, you know, I know the partial pressure now. And I can rearrange the formula so that it looks something like this. I can say, well Henry's law basically is like that. So if I know the pressure and I know the concentration, I should be able to figure out the constant for myself. I can figure it out and kind of give it in units that I like. So I'm going to write the units of the KH down here. I can say, well, 769 liters times atmospheres over moles. And that's something that I've just calculated. I've just taken two numbers and I've divided them by each other. So this is my calculation for oxygen. And so far, so good, right? But now I decide to challenge myself and say, let's do this again. But instead of with oxygen, I'm going to create an environment that's 21% carbon dioxide, which is way more carbon dioxide than we actually have. But imagine I could actually do that. I actually find a way to crank up the carbon dioxide, and I do the exact same thing. I take a cup of water and I keep it out at room temperature, 25 degrees Celsius. And I say, OK, let's see how much carbon dioxide goes into my cup. I've got my carbon dioxide out here. And over time more and more molecules kind of settle in here. And, of, course the atmosphere is not going to run out of carbon dioxide molecules. They're just going to keep replacing them. But they keep settling into this top layer, this surface layer, of my water. So it's actually looking already really different than what was happening on the other side. We only had a little bit of oxygen but now I've got tons of carbon dioxide. And I don't want to make it uneven. I mentioned before, we have nitrogen-- so let me still draw a bunch of nitrogen-- that will outnumber the carbon dioxide dramatically. Because we have here about, let's say, 79% nitrogen and we only had 21% carbon dioxide. So it'll look something like that. But there's lots and lots of carbon dioxide there. In fact, if I was to calculate the concentration on this side, the concentration would be pretty high. It would be 7.24 millimoles per liter. And Again, these numbers, I'm assuming that I'm doing the experiment. This is the number I would find if I actually did the experiment. So it's a much bigger number than I had over here. On the oxygen side, the number was actually pretty small, not very impressive. And yet on the carbon oxide side, much, much higher. Now that's kind of funny. It might strike you as kind of a funny thing. Because look, these partial pressures are basically the same. I mean, not even basically, they're exactly the same. There's no difference in the partial pressure. And yet the concentrations are different. So if you keep the P the same, the only way to make for different concentrations is if you have a different constant. So let me actually move on and figure out what the constant is. So what do you think the constant on this side would be, higher or lower? Let's see if we can figure it out together. The K sub H on this side is going to be lower. It's going to be lower. It's 29 liters times atmosphere divided by moles. So it's a much lower number. And I don't want you to get so distracted by this bit. This is kind of irrelevant to what we're talking about. It's just the units, and we can change the units to whatever we want. But it's this part-- it's the fact that the number itself on the carbon dioxide side is lower. Now let's think back to this idea of Henry's law. Henry's law told us that the partial pressure, this number, tells you about what's going to be going into the water, and that the K sub H tells you about what's going out of the water. And so if what's going in on both sides is equivalent, then really the difference is going to be what's the leaving. And on this side, on the first side of our experiment, we had lots of oxygens leaving this water. They didn't like being in water. They were leaving readily. And so you didn't see that, but they were actually constantly leaving. And on the carbon dioxide side, you had maybe a little bit of leaving, but not very much. The carbon dioxide was actually very comfortable with the water. In fact, to see that as a chemical formula, you might recall this. Remember, there's this formula where CO2 binds with water and it forms H2CO3. Well, think about that. If it's a binding to the water then it's not going to want to leave. It's pretty comfortable being in the water. And so the moment that carbon dioxide goes into water, it does something like this. It binds to the water. It turns into bicarbonate and protons. And so it's a very comfortable being in water, and that's why it's not leaving. In fact, I can take this one step further and even compare the two. I could say, well, 769 divided by 29 equals about 26. So that's another way of saying that carbon dioxide is 26 times more soluble than oxygen. I'll put that in parentheses-- than oxygen. And I should make sure I make it very clear. This is at 25 degrees Celsius, and this is in water. Now, you might say, well, that's fine for 25 degrees Celsius. But what about body temperature? What's happening in our actual body? What's happening in our lungs? So in our lungs, we have 37 degrees Celsius. And instead of water-- actually, I shouldn't be writing water-- instead of water, it's blood, which is slightly different than water. The consistency is different. And so these K sub H values are actually temperature dependent. And they're going to change as you increase the temperature. So at this new temperature, it turns out that carbon dioxide is about 22 times more soluble than oxygen. So it's still pretty impressive. Sometimes you might even see 24 times, depending on what numbers you read. But this is an impressive difference. And actually, what I wanted to get to is the fact that it goes back to the idea of what's going in and what's coming out. And the net difference is why you end up with a huge difference in concentrations between carbon dioxide and oxygen.