 Okay, in one of our previous sessions, we discussed the concept of the mole. I remember that we abbreviated as MOL. And in that discussion, we mentioned that one source of confusion for students was the similar term polarity. And so the purpose of this session is to try to further our discussion of the mole and sort out how it fits into polarity to understand the relationship. So if we recall, we said that the mole was equal to Avogadro's number of some item, be it an element or a molecule, which was 6.023 times 10 to the 23rd. Therefore, there are 6.023 times 10 to the 23rd atoms in a mole, an element. Likewise, there are 6.023 times 10 to the 23rd molecules in a mole. So let's put this in terms of some units. We'll be using units of polarity and units are important to keep straight what we're talking about. So we could say that there's 6.023 times 10 to the 23rd atoms per mole, or likewise 6.023 times 10 to the 23rd molecules. So we could say that there's 6.023 times 10 to the 23rd marbles in a mole of marble. So once again, the mole is just this Avogadro's number of units to make up the mole. So that if we had half a mole, 0.5, we would have 3.0 times 10 to the 23rd, say atoms, if we're doing atoms. So if we divided or multiplied 0.5 times the 6.023, or we divided by 2, so we just took half the number of atoms in half a mole. So once again, mole is a number. Now, so what is molarity? Molarity is a concentration. Important. Molarity is a concentration. What is a concentration? It is a concentration of defined as moles per liter. And our abbreviation for molarity is a big M. So molarity big M is equal to moles per liter. So we talk about concentrations of solutions. And in this class, we talk a lot about solutions. It's one of our key skills. If we had a one molar solution, that's one molar solution, then we would have one mole per liter. Or we could say one for big L. So once again, unit. A mole per liter is a concentration. Or as a mole is what is a number. Mole is a number. Molarity is a concentration. But it's a concentration defined in terms of a mole per liter. So let's look at an example of its use. Let's say if we have a one molar solution of saline. What is saline? Saline is just an aqueous solution. That means it's made in water of sodium chloride in ACL. So this is a molecule made up of atoms of two elements. Sodium and chlorine. And so let's determine what the molecular weight of sodium chloride is. So again, we've got, if we did a mole, we've got one per molecule. We've got one atom of sodium and one of chlorine. So if we go to our periodic table and we look at sodium, we find a value in the atomic mass of sodium of 22.99 grams per mole for chlorine. We find an atomic mass of 35.45 grams per mole. So that's one times that. So if we have one of each, we can just add those together. And so the atomic mass or the molecular mass of sodium chloride is 58.44 grams per mole. So if we have one mole of sodium chloride, we'll have to weigh out 58.44 grams. Okay, so back to our solution. We're interested in one molar solution of sodium chloride. We said that the definition of that, of a molarity, was one mole per liter. So if we wanted one molar sodium chloride, we need one mole of sodium chloride in one liter of water. So if our instructions were to make one liter of one molar sodium chloride, we would go way out 58.44 grams, right? I mean one mole, right? And bring it to volume in one liter of water. So there we are. We now know what molarity is. It's a concentration defined as moles per liter, moles per liter. So if we had a 0.5 molar solution of sodium chloride, then we would have 0.5 moles per liter. So we wanted to make that up, but what we would do, we would have to say, okay, one mole of sodium chloride is 58.44 grams per mole. So if we take 58.44 grams times 0.5, so we will have a mole, then that's going to be 29.22 grams of sodium chloride, 0.5 moles. So if we take that 29.22 grams and we put it in one liter, now we've got 0.5 molar, big M, sodium chloride. Now let's look at a cabinet. That's defined in terms of a liter. So if our instructions, we didn't need a liter. Let's say we needed 500 milliliters, then we're going to have half the volume of a liter. So if we needed 29.5 liters of the 0.5 molar, if it took us 29.22 grams in a liter or half molar, 500 milliliters, if we just said here is 0.5. So we need half as much. So we say 0.5 times 29.22 is equal to 14.61 grams of sodium chloride into 500 milliliters. It's going to give us 500 milliliters of 0.5 molar sodium chloride. So the way to get a handle on this and to achieve an understanding of it is to go through and work some problems on your own, work some of the sample problems using moles and molarity to get a mastery of it. But once again, the point is to remember that the mole is a number. 6.023 times 10 to the 23rd of something. And molarity is a concentration defined as moles per liter. So when you're going to be making solutions, which you'll be doing a lot of and it's defined as molarity, then you're going to have to take it back to your chemical formula. Like ours for NaCl are in previous things, like sulfuric acid H2SO4. You're going to have to take your chemical formula and then your periodic table and determine the moles. How much the mass of the mole, how many moles do you need or what part of a mole do you need and what volume do you need because your solutions will just be defined in molarity, which is the concentration and usually it will specify a volume because you need moles per liter or basically moles for some volume that you have to do a proportion if you're making more or less than one liter. So work on some problems, work on a lot of problems. So this becomes kind of second nature to you. Thanks for listening.