13.4 Osmotic Pressure

For osmotic pressure we don't use P like we do for gas pressure. For osmotic pressure we use the Greek letter P, which is pi. So in this case pi equals iMRT. So we still got to take into account the number of pieces here. And this is the one case where now we're not using molality anymore. For this one we actually use molarity. So one thing to note I put the Vant Hoff factor in each one of these equations. You'll see, depending on what textbook you use and whose professor's notes you're looking at, you'll see different variations of these equations. Some professors don't put the i in there. And they assume that the m here means the total molality of pieces, and takes the I already into account. So you may see it like that somewhere down the road. But I find students make less errors when it's all kind of spelled out for them. Sometimes you won't see the negative sign right there and the expect you remember that freezing points go down even though it's not built into the equation. Well I don't like that either. But it's there. So just one thing to note the i's may not show up and sometimes you may not see that negative sign, but keep those in mind. All right! So osmotic pressure. Let's get a little more room here. If you look at PV equals NRT, can somebody solve for P and tell me what it equals? What's P equal? NRT over V. If we rearrange this just a little bit we can say it's equal to n over V times R T. Same diff. Same diff. What's n? Moles of gas. What's V? Volume. Usually measured in? Liters. What's moles per liter? Molarity. Well technically this is gas pressure. But turns out, it's going to look pretty darn similar to what we define down here for osmotic pressure. That's not a gas pressure. We'll talk about it little bit. But the one thing we got to take into account again is that we're going to include the Vant Hoff factor into that equation. So let's talk about what osmotic pressure actually is. Alright. Let's say we filled this lovely vessel up so with water. With water. So and this dashed line right here represents what we call a semi permeable membrane. It lets water molecules pass back and forth no problem. But it doesn't let any solute molecules pass by at all. Solutes if they're on this side they're trapped on this side. If the solutes are trapped on this side, you know, they're on the side they're trapped on that side. Only water gets to pass back and forth through the membrane freely. So in this case we put a plunger or a piston on this side, and we put another one over on this side. These plungers can move up and down in the cylinders here on either side. So first of all what is osmosis? What is it. Movement of water from where? A little more specific. It's actually, we could call it the diffusion of water. And so if it's the diffusion of water, what was diffusion Brie? High to low. Movement of high concentrations to low concentrations. So if osmosis is the diffusion of water it's where water moves from a high concentration to a lower concentration. And so in this case, let's say I put pure water on one side and then I put one molar sodium chloride on the other side. Because there's a difference in concentration in water here, water needs to move. Osmosis is going to occur. It wants to move. Which way does water want to move? Good. Water is in its highest concentration over on this side. Notice one molar NaCl has a bunch of solutes. It's still mostly water, but there's NaCl there as well. And so it's tricky because we're not looking at solute concentrations now, we're looking at water concentrations. And where water is most pure, that is where it's highest in concentration and so it'll move from a higher concentration to areas of lower concentration. As a result where will this piston want to go? It's going to want to go up. And where's this piston want to go? Down. The amount of pressure we would have to apply to keep this one from going up and to keep this one from going down, would equal the osmotic pressure. So that's what it is. And in this case we could calculate it out. In this case we'd say pi equals the difference in concentration here. So i times M times R times T. And so again pi equals two for the vet Hoff factor, NaCl breaks up into two ions. The molarity is one molar in this case. R we can express in a couple of different units. I'm going to put it as 0.08206 liter atmospheres per mole Kelvin. And T wasn't given here, so I need to give you T as well. I'm just going tell you we're doing this at room temperature. So T equals 25 degrees Celsius. So what do I need to plug in for T here? Good. 273 plus 25. Got to be in Kelvin. So in this case 298 Kelvin. Cool. And if we look here, the Kelvins cancel. Molarity is the same as what? Moles per liter. And here we have liters per mole, so those cancel. And I'm going to be left with an answer, in this case, in atmospheres, based on the units of R that I used. Can somebody solve this for me? Because I definitely can't do this in my head very well. Maybe? 48.9. Okay. So 48.9 atmospheres. So, let's look at this for a minute. So this thing is going to want to push up on this piston with 48.9 atmospheres of pressure. What's going to happen if I push back with 20 atmospheres of pressure? Which way is the piston going to move? It's still going to move up. Cool. What if I push back with exactly 48.9 atmospheres? Then it's not going anywhere. It's balanced. What if I push back with a hundred atmospheres? Ooh. I'm going to push it down. Which is going to force some of the water to go across the membrane and will produce more pure water. What's that called? I'm reversing osmosis. So that's your RO system, your reverse osmosis system, creating more pure water. You have to push harder than osmosis is pushing back, so to speak, to create more pure water across a semipermeable membrane. Cool.