 Okay, guys. I sent an email out this morning because apparently there was a misprint on one of the practice exam questions. There was an incorrect answer that was given as correct. Hopefully, if you guys examined that answer in a little more detail, you would have noticed that it was incorrect, but it said that sodium chloride breaks up into sodium minus ions and chlorine plus ions. Instead of giving you that as the correct answer on the test, because I don't want you guys to believe that sodium would ever break up into minus ions or chlorine would ever break up into plus ions, no matter what the practice exam tells you. Instead, I'm going to go back and regrade all the tests, throwing that question out, and giving more points for the rest of the questions. Okay? So, I think that's the most fair way of doing it, just again, so we won't get in our heads that it's the right answer that I'm giving you credit for. So, we'll just throw it out. That being said, of course, there's no test to hand back today. So, what I'll do is probably just hand it back when I was going to originally on Friday. So, just you're going to have to wait until Friday to get your exam back. Okay? So, but if there are any questions or you think that, you know, something was misgraded, please bring it to my attention. Of course, I want to know all about that. You know, I don't want to discourage anybody from doing that. But, yeah, so when it, but when it is wrong, we'll just throw the question out. The other thing is, is today I'm trying to, trying something new. I put a microphone on, I hopefully, for the online people or those of you who watch the lectures. Yeah, sometimes they're hard to hear. Hopefully, this will alleviate all of those problems with, you know, audio. So, if this, if this works out, if anybody could listen to it, email me and tell me what they hear, if it's much better, or whatever, we'll use this microphone from now on. Okay? Hopefully, you won't hear all of my extra noises while I'm like my burps and stuff like that. Okay? But anyways, so I think the last thing we talked about last time, I think we got past wait, wait percent. And I think we started talking about parts per thousand parts per million, right? And we talked how these are exactly like the weight volume percentage questions, except where instead we've got weight volume percent. Let's just write these out all together. So we got percent weight volume equals parts per thousand remember is grams of solute over mills of solution multiplied by 1000 or 10 to the 3rd is 1000 PPT. When we look at weight volume, it's grams of solute over mills of solution times 100. PPT, remember is this is the units for parts per thousand, just like percentage is the units for parts per hundred or weight, parts per hundred and weight, weight, or percent weight volume is like the same thing. Okay? So you can see these formulae are very similar. And if we looked at parts per million, the only difference would be, so you guys know if I do that, that means the same thing, right? The only difference would be instead of a thousand here, it'd be a million. And I'm not going to write all those zeros. I'll just put 10 to the 6th that PPM and that's parts per million. Oh, grams, okay, so they're doing this in, oh, wait, wait, sorry. Let's just do it in wait, wait, the same thing. Thanks for pointing that out. When you're doing water, when you're doing water solutions, a lot of times the mass of the solution will be the same as the number of mills of the solution due to the density. But, again, when you increase the concentration of solute, your density also increases. So, yeah, it's good to do it in grams of solution, I guess, yeah. Okay, so let's talk about molarity and, or remember molarity and then talk about equivalence per liter and realize this is similar to molarity. So, if we looked at this question here and it asks, what does it ask? One molar Na3PO4, so one molar sodium phosphate, right? And it asks us, well, what's the concentration of, well, let's just do sodium ions and you can do the concentration of phosphate ions on your own. So it's asking us, well, what's the concentration of sodium ions? Well, how do we figure that out? Remember, the chemical equation gives us the ratio. So, remember, we have this 1 mol Na3PO4 ratio. So we're going to have this conversion factor of 1 mol Na3PO4 to 3 mols of Na plus ions. And then all we've got to do to figure out the concentration of Na plus is say, well, we've got 1 molar Na3PO4. Multiply that by, well, we want to cancel molar Na3PO4. Sorry, I guess I should have written this, too. So, this, I don't like this. 1 mol per liter, like that. So, remember, mol per liter is 1 molar. So to cancel that out, you have 1 molar Na3PO4 to 3 molar Na plus ions, like that, like that. And then 1 times 3, of course, is 3. So we've got 3 molar Na plus ions. So, again, you can use the chemical equation just like we could with moles here. We could do it with moles per liter. And moles per liter, remember, is molar. Okay, so very similar, but slightly different. Unit is the equivalence per liter. And equivalence is the number of charge or the number of moles of charge per liter. So let's do this same problem, except let's talk about phosphate and talk about equivalence per liter. So, if we've got 1 mol per liter, 1 molar Na3PO4, and we wanted to know how many equivalence per liter of phosphate we would have. Well, equivalence per liter, so instead of moles, it's actually moles of charge is equivalence, okay? So when you're asked, well, how many equivalence does sodium have? It's because you only have a plus 1 there, it's going to be 1 equivalence, okay? If we look at phosphate, it's got 3, a minus charge of 3. So we could say that has 3 equivalence. So you want to think of equivalence per liter kind of equal to moles of charge per liter. So if we wanted to ask, well, if we've got 1 molar Na3PO4, well, the number of equivalence per liter of phosphate, so equivalence per liter of phosphate would be 1 mol, I'll just do it this way, 1 mol per liter Na3PO4, and for every 1 mol of Na3PO4, we're going to have what? 3 equivalence of phosphate, like that. Where did we get this 3 from? Right there, okay? So like that. So we're going to have 3 equivalence per liter of phosphate, okay? So if we ask the same question, if we have 1 molar, sorry, 1 molar sodium phosphate, how many equivalence per liter of sodium would we have? What do you guys think would be the answer there for sodium? Think it would be 1? It would be actually 1 times 3, okay? Because you've got to multiply it by the coefficient, okay? Because it's going to be here, right, 3 equivalence because of this, but it's also going to be 3 equivalence of sodium because for every 1 mol of sodium phosphate, you've got 3 mols of sodium ions, okay? So you're going to have to convert that first, okay? So I'd like you guys to try that one on your own and make sure you can cancel out your units to get to 3 equivalence of sodium as well, okay? So it should come logically that it should be 3 equivalence because we've got 1 equivalent for every sodium ion, right? And for every 3 sodium ions, we only have 1 sodium phosphate, okay? So try to cancel them out on your own. So that's essentially this problem. Here we did the phosphate portion of it. And then there you go. You can do mols to mols of charge, mols of charge to equivalence. Okay, so let's talk about colloids now. This will be the last topic we talk about and the properties of colloidal solutions. In chapter 7, okay? Maybe get through with it today, maybe not. Okay, so what's the difference between a colloid and a solution? Well, a colloid, unlike a solution, contains solute particles which are not uniformly distributed. So what does that mean? Unlike a solution where if you look at a solution, right, the solution is clear. It doesn't appear to have particles in it if we're visually inspecting it, okay? A colloidal suspension, you can see the actual particles in the suspension, okay? So this is due to the larger size of these particles. So these particles are from 1 to 200 nanometers, okay? So it appears identical to the solution from the as a solution from the naked eye, but you can visually inspect them. I don't know if you guys can see it very well. If you shine a light through them, here let's see if we can turn off. Okay, so if you shine a light through it, right, you can see here we've got a solution. We can't see any of the particles. Here we've got the particles diffracting there and we can actually see them, okay? And then smaller than 1 nanometer, you have a solution larger than 1 nanometer as a precipitate. This effect that we're seeing here, the colloidal suspension, the particles will scatter light like we're showing here. If we compare it to a solution, we see no quote-unquote haze, right? We call this the Tyndall effect named after some guy Tyndall. So the Tyndall effect is this ability of a colloidal suspension to scatter light. So this is this haze you see when shining light through the mixture and with the solution, the particles are so small that the light doesn't bounce off of them, okay? Or at least you can't see the light bouncing off of them. Okay, so let's talk about colligative properties and colligative properties is just properties of colloidal suspensions, okay? Or sorry, properties of solutions, but so these properties of the solution depend solely on the number of moles of solvent particles and they don't depend on the identity of those particles. So these particles can be polar, nonpolar, small, large, so on and so forth. It doesn't matter. It only matters the concentration of the solute particles, it should say, not their identity. So there's four colligative properties that we're going to talk about. The first one is vapor pressure lowering. The second one is boiling point elevation, freezing point depression, and osmotic pressure. And each property depends on the solute molecules to not be able to cross a phase barrier, okay? So this is a phase change recall would be like going from a liquid to a gas or a solid to a liquid or something like that, okay? So these properties depends on the solute molecules not being able to do that, cross the barrier from going from, in the case of boiling point elevation, liquid to vapor or freezing point depression, liquid to solid, okay? Osmotic pressure is to go between or be able to get through a semipermeable membrane, which we'll talk about later. Okay, so let's talk about non-volatile, non-electrolytes, and this is what we'll think of all of the solutions of questions that have to deal with colligative properties, okay? We'll think of all of these solutions as having solutes that are non- volatile and non-electrolyte, non-electrolytic, okay? So recall what that means, non-volatile, volatile means to be able to go into the vapor phase, okay? So a non-volatile solute would be something that's, you know, rather heavy that you can expect that it's not going to go from the liquid to the vapor phase or from the solid to the vapor phase, okay? That's all that means, it's non-volatile. Non-electrolyte, do you guys remember what an electrolyte is? It's kind of that question that was incorrect on the practice exam, too. Anybody can tell me what an electrolyte is? So what is it? When something, what? Yeah, so when it gets dissolved into a solute or solution, right, it'll break into its ions instead of just dissolving whole, right? Like sodium chloride is a very good example of something that's an electrolyte. When we dissolve that into water, it breaks into its ions, like that, okay? So what do you think it means to be a non- electrolyte? It doesn't break up into ions, okay? So these are things that when dissolved don't break up into ions, okay? So those would be what? Covalent compounds, okay? So non-ionic compounds, okay? So you can think of a non-volatile non-electrolyte as something that's not going to go into the vapor phase or break up into ions, okay? So what is vapor pressure? Let's talk about vapor pressure. This picture here actually gives you a good idea about what's going on. So we've talked about this before when we evacuate, we have a flask, right? And we evacuate it, we take all the air out of the flask and we put a liquid in that flask. So say we sucked all the air out and we put a liquid in, right? So the only thing that's in there is liquid particles. What's going to happen is because there's no air up here, right? The surface particles are going to go up, vaporize and go into the vapor phase and, you know, rest on top of the liquid solution here. And over time, of course, we're going to have a lowering of that solvent level, but we're going to have particles in the vapor phase now and some particles still in the liquid phase, okay? So the pressure of these particles pushing back down onto the liquid, we call that the vapor pressure, okay? So on the earth, right, the relative humidity is like the vapor pressure, okay? What you find is that when you put a solute in there, a non-volatile non-electrolyte, so what can't, if it's a non-volatile non-electrolyte, what can't it do when we're looking at something going from the liquid to the vapor phase? What can't it do? We just talked about that for like 10 minutes. It's not going to vaporize, right? Thank you. It's not going to vaporize, so only the solvent particles will vaporize, not the solute particles, right? That's why when we look at A to B here, right, when we've got these solute particles in there, we don't see any of them above the liquid phase in this mixture, okay? So what is this saying is that when we compare the solvent by itself relative to the solution, right, over time more particles from the solvent alone will be able to vaporize from the liquid to the vapor phase, okay? But if we look at the solution, because there's the particles that on the surface, right, so we've got solute particles, our solvent particles, and some solute particles, every once in a while we'll have a solute particle, these guys can vaporize, but when we get here these guys can't, so this one won't be able to vaporize, okay? So due to this phenomenon of these solute particles on the surface blocking the lower ones to be able to vaporize, what you'll find is that the vapor pressure will be relatively lower in a solution than it will be in the pure solvent because the molecules underneath the surface that are the solvent molecules can't vaporize, okay? Because there's this physical barrier, right? It's like a wall, like if there's a door here, right? I could get through there, but if there's a wall, you know, I'll just bash my head against the wall until, you know, the wall moves or something, right? Or I open the door, so it's like, here's the solvent particle, or the solute particle, I'm a solvent particle, I can't get out, right, until it moves out of the way, then I can get out of there, right? Okay? So it's going to take a long time, it's going to take a lot more energy, right? To get into the vapor phase, okay? Does that make sense? So if there's something in the way, I can't go, right? But if there's nothing in the way, then I can go. It can, it can, but, right? But it can, but it takes more energy, right? And over time, it'll take more, the ones that don't have to move around will be jumping off faster, right? Getting out of there faster. The ones that do have to move around, it'll take time, right? That's why, like, when you go to the grocery store, you go into the shorter line, then you go into the longer line. You go into the longer line, like do this, do this experiment. Two of you go into the grocery store, one of you go to the longer line, one of you go to the shorter line, see who gets out faster, right? That's like colligative properties, okay? So all of the colligative properties are like that, okay? They're all this physical barrier that this thing has to get through. Therefore, you're going to have vapor pressure lowering, boiling point elevation, freezing point depression, same as the lowering, and osmotic pressure. Of course, it's not just as simple as that, right? There's an equation behind this that you're just going to have to do some math problems about. But it's not so bad, okay? It's called Rawl's Law, and it's Rawl's Law vapor pressure lowering, and it states, Rawl's some guy who's dead, right? When non-volatile solute is added to a solvent, the vapor pressure of the solvent decreases in proportion to the concentration of solute added. So that makes sense, right? All that saying is that the more solute I add, the lower the vapor pressure is going to be, okay? The more and more barriers I add, the harder it's going to be to get through there, right? If there's only one short line at the grocery store, right? It's going to take you much longer time, unless there are much longer time than if there was only one long line, okay? So that's kind of like the saying, okay? So the pressure of, and here's the note, sorry, this should say solution, pressure of solution equals the, X is the mole fraction of the solvent times the original vapor pressure, or the vapor pressure of the pure solvent. All of this stuff has to be given to you. Just going to multiply them together, okay? And then you're going to have this, so you got the original, subtracted the new, that equals the change, okay? So whenever you got this symbol, remember this delta symbol? This delta means change of, okay? So this is the change in the pressure. So this is going to be, the change in the pressure is going to be the original pressure minus the new pressure, right? Does that make sense? So this is the original of the solvent, and this is the new of the solvent, so this is like the solution, but we'll just say the new of the solvent, okay? And that actually equals the mole fraction of the solute times the original pressure of the solvent, okay? So that's all you got to really realize. So I could give it to you, give you the change this way, or I could give you these numbers and you could figure out the change, okay? So again, all this is, is trying to get through these barriers, okay? It's going to be the same thing for all four of these types of properties. Here's a problem that you go through in detail. I'd like you to go through this one on your own. Notice here the mole fraction. This might be something that we talked about. So the mole fraction is just what you would expect it to be. X is the mole fraction here. Let's just go over that portion of this calculation. Mole fraction is just like percentage. So what is this saying here? So it's saying that we have 10 mls of glycerol and it's giving us the density of glycerol and we're going to have to figure out the molecular weight of glycerol. All of that gives us the number of moles of glycerol and if we figure out, and we've got the density of water here, we've got the number of mls of water so we can figure out the number of moles of water, okay? So from those two equations you get the number of moles of the two different things that are in your solution, the solvent and the solute, okay? So let's just look at how they're calculating the mole fraction, okay? Remember this is an integral part of the Raoult's law, this X here, this mole fraction. So the mole fraction of the solute, which is what you're looking for, is going to be the moles of solute divided by the total number of moles, right? Total number of moles. And what's the total number of moles? What do you guys think that is? Number of moles of what plus number of moles of what? Yeah, solvent plus solute. So here we figured out that this was 27.4 moles plus 0. what was it, 1, 3, 7 moles, okay? So that number there is going to be that number there and then of course this number here is equal to this number. So that's going to be 0.137 moles, okay? It's just like what you would expect it to be. The mole fraction is the number of moles of the 1 over the number of moles total, okay? So go through this problem on your own, calculate it all out and if you have any problems with it we can go over it next time, okay? It might be the first thing we do next time. But I want to see that you guys made an effort to do it, okay? If you don't make an effort then we won't go over it. If I'd be like, bam, tell me, you know? And you don't tell me then we won't go over it, okay? So just like vapor pressure lowering, boiling point elevation, you can imagine you're going to have to go from, you can imagine the boiling point, you're going to have to go through a phase change, right? So if I'm going from a liquid to a vapor, that's what boiling is, right? If I'm going from a liquid to a vapor, that's boiling, right? That's what you would expect. So I have to go through the phase change of liquid to vapor, okay? Remember we talked about when you have a solution there's going to be particles on the barrier of the liquid to the, or of the phase change, in this case the liquid to the gas phase change that are going to not allow those particles underneath it to go from the liquid to the gas, okay? So let's talk about this. Okay, remember the grocery store analogy. Okay, so here, how many people have ever boiled something on the stove? Yeah, everybody? Okay, good. Some of you haven't, I see, but those of you who haven't take what the other people have done when they say, yeah, I know that or whatever and realize that it's the truth. Okay, so when you boil like water, you want to cook something, a lot of times you'll add salt to the water, right? Why do you add salt to it? Well, not just to season the stuff, okay? Not just because it tastes better salty, that's not why. But some people said it boils faster, that's what some people said, that's not really the case. It actually takes a longer time to get to boiling temperature. But what's another, somebody else said the reason? Why? It boils, it raises the boiling point, boiling point elevation, right? So what happens is when you make a solution, the, so let's look at this, right? So here's the pure water, right? So all of those at the surface are water molecules, okay? Compare that to our salt solution that we're going to use to boil our spaghetti or whatever, okay? Not all of those will be water particles, right? One of those or a few of those will be salt molecules, right? In this case we're talking about non-electrolytes, so let's just pretend we put something else in there besides salt, but whatever. You can imagine some of them are not water molecules, remember? And they're not going to evaporate, okay? So what's going to happen? What's going to happen to this molecule here, this water molecule there? Is it going to be able to evaporate? No, because there's a barrier in the way, right? So it's trying to, because we got this thing, this burner on it, you know? It's like, man I gotta get out of here, it's getting too hot for me, but it can't because it's being stuck, right? So what's happening? Well, these guys, right, are able to take off at will, you know? They're taking off going wherever, right? After the same amount of time, what would you expect? Would you expect, so say when this one's all boiled away, would you expect these to still, some of this to still be here? Why is that? Because there's the things blocking, right? Remember the grocery store analogy, okay? If two of you go in at the same time, one of you stands in the longest line, the other one stands in the shortest line, which one is going to come out first, right? So it's not that actually it speeds up the boiling, it actually slows it down, that's what we proved here, right? It slows it down. But what it does is it increases the boiling temperature, right? Because at 100 degrees Celsius, these guys are taking off, right? Because that's the boiling point of water. When you get to 100 degrees Celsius here, these guys want to take off but they can't, okay? So what's actually happening is you've got to get them to a higher temperature before they'll start taking off and boiling, okay? Remember this is, again, remember that barrier, right? If I want to get out of here, I can't get out of here, right? Because there's a barrier in front of me. If there was no barrier there, then I could take off, okay? So just like vapor pressure lowering, this is this between phases things, okay? And here's the equation for boiling point elevation, okay? KB, this K, that's just a constant, okay? That's something I have to give you. And remember the little m, do you guys remember molality? Okay? So if you don't remember molality, you've got to go back and learn it, okay? So if I said, well, there's water, there's it's KB, okay? If I said I had, let's do a problem with change or boiling point elevation. So if I said I had a, I don't know, 0.1 molar sucrose, this is a non-volatile, non-electrolyte. This is like coffee, like sugar in your coffee or something like that, okay? Solution, which would be, you know, one of these things. What's the change in temperature of your boiling point? So we know that, oh, sorry, not molar, molar, little m, okay? So let's do this. We know T is this, KB times little m, okay? Little m, well, we got this up here, right? So KB, that's given to us on the list there, so 0.512 degrees Celsius per molar, molal, okay? So what's the, what's the new temperature of the boiling point in the solution? What's the new temperature? Let's figure that out. So KB, 0.512 degrees C over one molal times 0.1 molar, right? Cancel, cancel, and we get 5.12 times 10 to the negative 2 degrees C, right? Okay? That's the change in temperature, right? That's a very small temperature, if you would imagine that to be the temperature that it's boiling in. So if I asked you what's the new boiling temperature, you would have to add this to the original boiling temperature, which the boiling temperature for water is 100 degrees C, right? So the new boiling temperature would equal temperature boiling plus the change in temperature, right? As you would imagine. And then we would just add those two numbers together. Let's get something very, very close to 100 degrees. So with this number of sig figs, it won't matter, but let's just say we had a bunch of sig figs, just so we can emphasize what's going on. Notice the new boiling temperature is not at 100 degrees, but it's something that's higher than 100 degrees. So if we had a more concentrated solution, this would be more apparent, okay? So try it instead of with a .1 molar or a molal solution, try this on your own with a 10 molal solution and see what our new boiling temperature is, okay? Then go home and dump a bunch of salt into your stovetop boiling water and measure your temperature. See if it really does happen and you'll see that it really does happen. So I think I have a, oh, the freezing point depression is the exact same thing, okay? The exact same thing except I'm going from instead of liquid to gas, I'm going liquid to solid, right? Has anybody ever lived somewhere other than Texas? Anybody ever, okay. Maybe if you've lived somewhere where it snows. Has anybody ever lived somewhere where it snows? Huh? Well, somewhere where it snows where they put salt on the road. Has anybody ever done that? Yeah, so Colorado. So you ever ask yourself, why do they put salt all over the world? Why is it? Because when it dissolves into the water, that's the ice, it'll lower the freezing point, okay? So what'll happen is that when you dissolve that salt into your water, right? And it gets down to zero degrees Celsius, which is the freezing point of water, okay? Our 32 degrees Fahrenheit in the United States, right? When you get down to that temperature, right? It's very cold, right? And everything freezes over and then cars start sliding all over the place and smashing into each other and causing wrecks and killing people and stuff. So in order to prevent that, put salt on the road. So when it gets down to 32 degrees Fahrenheit, right? There's that solution that's not going to freeze at that temperature. So it actually freezes at a lower temperature and that lower temperature is, in fact, much lower because they actually don't put a salt solution down. They put pieces of salt, right? So you can imagine at the point of dissolving in one big chunk of salt into a little piece of ice that concentration of that solution is very, very astronomical, almost infinite, right? So it decreases the boiling point quite substantially, okay? But anyways, it's the same sort of thing as increasing the boiling point, decreasing the freezing point. It's this constant which I have to give you, which is listed here. So what I'll probably do is give you this table on a test, okay? And you'll have to figure out through these numbers on this table what's going on. And I'll say, what's the new boiling or freezing point? Or I could say for an easier question, what's the change in freezing point? Okay? Remember the new freezing point would make you take this change, add it to the original freezing point and see what happens. You would expect one other thing I should say about this freezing point, right? You would expect it to be a negative number, okay? Because you're lowering the freezing point, okay? So here's, there you go. So notice your final temperature here is a negative number, okay? Most of these solutions we'll be dealing with are water, okay? So add 0 degrees Celsius water freezes. I don't want to talk about osmotic pressure right now, so I'll let you guys go three minutes early. Okay, so if there's any questions, I know if anybody has any questions about grading or anything like that, you can come up and talk to me. I know I haven't given the test back, but...