 Okay, the topic of this presentation will be the mole, which we're going to abbreviate is MOL. And this is a topic that seems foreign to students and it seems to be one of the topics that is more difficult to grasp, but actually when we understand it, it's pretty straightforward. But the other thing is it's one of those, it's a basic understanding you have to have in biotechnology. It's like being able to tie your shoes. If you don't learn to tie your shoes, you may be able to walk around with them untied, but sometimes you're going to stumble and fall. So it's something that we're going to have to understand and embrace. So why, you know, I understand there's some reasons why students are kind of repelled a little bit, but because it's, you know, it's unfamiliar, right, so it isn't unfamiliar. The other term is we use it, you know, it's metric, right. And of course, the metric system, we're going to be using in biotechnology, so you're going to have to get an understanding of it, but it's tied in with the understand of mole. And this can be also a little confusion with the term, with the related term, molarity. Obviously they're related, but mole and molarity are not the same thing. So in this discussion, we're going to discuss both of them and come to an understanding of both. But we're going to start with the term the mole. What is a mole? A mole is a measure and you're familiar with measures. We've been talking a lot about different measures, but if, you know, if I sent you to the store and I said, if I want some milk, right, you know, you can get it as a quart or you can get it as a gallon. So those are the measurements of liquid. Now they're not metric, but for the sake of our discussion, we're going to be using temporarily these common things. You know, if I told you to get some sugar, right, you could go and get a five pound bag of sugar. Now so what if I told you to get some eggs, right, a dozen, right? Now the quart is a quantity, the pound is a quantity and those are used, a dozen is what? A dozen is a number, it's a number 12, right, and you know, it wouldn't matter if the eggs were little quail eggs or big extra large eggs and it wouldn't matter if they were free range eggs or whatnot. If they were a dozen, it would be 12 regardless of the size or shape or whatnot, it'd be a dozen. And this is like mole, a mole is a number, it's a number, right, so, you know, it happens to be a very large number, I'm going to say a big number, I have to, I have to. So it's a large number, the concept of the mole was developed by chemists in order to work with atoms and molecules, because they're very small and it takes a lot of them to have any mass. If you had your dozen eggs, that's something you can see and hold in your hand and that's a reasonable number. But a dozen atoms are, you know, incontestably small, so in order to get enough of them to be able to basically weigh them out, you have to have a lot of them. So that is the notion and the purpose of the mole is to bring the notion of atoms and molecules into a usable range to work on. So you need billions and billions of atoms for molecules to have enough to weigh. But it's just a number. And so let's write this number, not in scientific notation but in decimal form, just to see how large that number looks to us. So if you have a mole of anything, you have this number, 6.023 times 10 to the 23rd of that item. This is, you had a dozen of anything, you've got 12 of it. If you have a mole of anything, you have 6.023 times 10 to the 23rd of them. Give it a stop now, isn't it? Oh. Okay. So let's call this number, the 6.023 times 10 to the 23rd, as Avogadro's number. So Avogadro's number is just 6.02 times 10 to the 23rd, which gives us a number of atoms or molecules to determine their mass. And we get this information on the periodic table. If we look at the simplest element, hydrogen that has its atomic number is 1, and its atomic mass is equal to 1.01 gram per mole. So that information is on the periodic table. So for each element, it gives us individual atomic number and the mass of that atom. And it's the mass of 6.023 times 10 to the 23rd atom. Now another thing that can cause students to stumble is when we talk about molecules. There again, when we had sodium hydroxide, that was a molecule made up of sodium, hydrogen, and oxygen atoms. But we talked about the molar mass of it, 40 grams per mole. That was the mass of the individual sodium plus oxygen plus hydrogen. So the atomic mass is the mass of an atom, and the molecular mass is the mass of a molecule. But there again, it is a mole. So it's 6.02 times 10 to the 23rd hydrogen atom, or 6.02 3 times 10 to the 23rd, in this case sodium hydroxide molecule. So let's go to Avergado's Sandwich Shop and look at this concept. Avergado makes here he has two kinds of sandwiches. The first kind of sandwich is going to be the water sandwich. Now let's look at his recipe for water, or for the water sandwich. He has two pieces of bread and one slice of ham. So here in our example, the hydrogen atoms are the bread, two breads, and the oxygen is the slice of ham. So each sandwich, each water sandwich has two slices of bread, but one slice of ham. So if he has 100 water sandwiches, he's going to have to have 100 slices of ham, but 200 slices of bread. So there are twice as many slices of bread as there are ham. So they're the 2 to 1 ratio, and that's in the recipe. So a mole of water has two moles of hydrogen and a mole of oxygen. Let's look at Avergado's other sandwich. He has a sulfuric acid sandwich, has more components. It still has two hydrogen, so it still has two slices of bread. Oh, it has ham, or oxygen is ham. It's got four slices of ham, so it'll cost more money, or he's going to have to buy more ham. Oh, it has an S, so this one S is going to make it be Swiss cheese. So for each sulfuric acid sandwich he makes, he's going to have to have two slices of bread, a slice of Swiss, and four slices of ham. So each molecule, he would have to have two moles of hydrogen, four moles of ham, and one mole of Swiss. So let's go to the periodic table and look at our sandwiches and see how we do the molecular mass of these molecules. Well, here we've got H2O, and so what we said for each molecule, there are two H's and one oxygen. So if we go to the periodic table, we find that the mass of hydrogen we said was 1.01 grams per mole, and the mass of oxygen is 16.0 grams per mole. So looking at abrogato sandwich, for each sandwich there's two hydrogens and one oxygen, so we have to have 2 times 1.01, and then 1 times 16. So this is 2.02, and this is 16. So we get 18.02 grams per mole for the molecule of water. Okay, going on, looking at the sulfuric acid sandwich, right, here we've got two high hydrogens, one sulfur, and four hydrogen. So once again, hydrogen, its atomic mass is 1.01 grams per mole. The sulfur is 32.07 grams per mole, and once again, oxygen is still 16 grams per mole. So we do 2 times 1.01 is 2.02, 1 times 32. 2.07 is 32.07, and 4 times 16 is 64. So the molecular mass of sulfuric acid is 98.09 grams per mole. So let's do one more with sugar, called sucrose, if you've had your coffee today. And here's the molecular formula for that. Okay, it's a bigger molecule, more participants in it, but we're still talking about if we have one mole, we have carbon, hydrogen, and oxygen. So for each one, we have 12, 22, and 11. So for carbon, we're going to use a mass of 12. And for hydrogen, we just go around it down to make it a little bit easier for one. And oxygen again is 16. So 12 is 144, 22 times 1, 22, and 11 times 16 is 176. So the mass of a molecule of sucrose is 342 grams per mole. It's no more complicated than that. So if we had 6.023 times 10 to the 23rd molecules of sugar, then it would be 342 grams. So that's something we could weigh out if we wanted to make...