[MUSIC] In this lecture, I'll begin what will be a series of discussions about chemical composition. Because atoms and molecules are very light, it's difficult to take the mass of them one at a time. So in this lecture, we'll talk about how you can count items by taking their mass. But before I do that, you might wonder why you want to know about chemical composition. Well, there's a large number of reasons that people are interested in knowing how much of a chemical is in a particular sample. Here's a whole bunch of examples. For example, your doctor might tell you to cut back on sodium, and so then you'd have to know how much sodium is in certain foods, and how much sodium overall is in my diet. This could happen, for example, if you had high blood pressure. Another practical application is someone might be interested in knowing how much iron content there is, in some ore that is going to be used for steel production. That would tell you the value of that ore. Or, in another case that is very applicable today, someone who has a well for oil might be interested in knowing how much octane is in that crude oil. Sometimes there's negative effects of chemicals. For example, we might want to know how much chlorine is in freon, because the chlorine atoms in freon contribute to ozone depletion. There might be a side-effect causing contaminant in a drug formulation. And so people would be very interested in determining how much of that is there, and finding ways to remove it. The same is true for pollutants in our air and in our drinking water. So obviously there are many reasons why we might want to know the chemical composition of a sample. Let's make an analogy with something that's larger and easier to count by hand. For example, some nails. I might wish to by a certain number of nails from the hardware store, but the hardware store doesn't tell me how much one nail costs. They have a sign that says that they sell the nails by the pound. So, if I'm going to buy a pound of nails, how would I know how many nails I am buying? There's a chemical analogy for this. And that is, how many atoms are in a given mass of an element? Let's do an example of counting nails by the pound. So in this problem, I'm the customer and I'll buy 2.6 pounds of the certain type of nail. There's a pricing sign near those nails that says one dozen of those nails has a mass of 0.150 pounds. So in that case, the customer took the nails up to the front of the store, where there was a scale and a clerk weighed the nails for them. We know these conversion factors. We know from the sign that that particular type of nail had a mass such that 1 dozen nails weighs 0.150 pounds. We also know that there's 12 nails in a dozen, just like there's 12 cookies in a dozen cookies. So we can write a couple of conversion factors as ratios or fractions. What we want to do ultimately is convert the pounds of nails that we're buying into the number of nails that we have. That way we'll know if we have enough nails to do the project that we have in mind. So our solution map would be to convert the pounds of nails into dozens of nails, and then because every dozen nail has twelve in it, we can convert that to the total number of nails. We can write these conversion factors that were given to us initially as fractions, or ratios. We know that one dozen nails weighs 0.150 pounds, and we know that there's 12 nails in a dozen. So, the equation that we would set up would look like this. We started with 2.6 pounds. There's one dozen nails in 0.150 pounds. That came from the sign in the store. So that was a conversion factor that we were given. There's twelve nails in a dozen. That's just a relationship that we know, right? There's twelve, there's twelve in any dozen. Right, twelve in a dozen of anything. So we've set up this calculation by doing a unit analysis. I can cancel out the pounds and I can cancel out a dozen nails. Of course, it should say nails right there, right? Twelve nails in a dozen nails. And the answer then is that we have bought 208 nails. Let me ask you a question though. What if we were going to buy a second type of nail that is smaller? In other words, our first purchase was of nails of this size, these large nails. Our second purchase will be of some smaller nails. Let's think about some of these questions. So the customer is going to buy a different size of nail. Would the mass of a dozen of the smaller nails still be 0.150 pounds? What do you think? No, of course it wouldn't be. A dozen of the large nails weighed 0.150 pounds. The smaller nails weigh less per nail, so a dozen of those nails would weigh less than 0.150 pounds. Here's another question. Are there still twelve nails in a dozen? Well, of course there are. There's always twelve in a dozen, that never changes. So the first conversion factor can change depending on the size of the nail, but the second conversion factor doesn't depend on the size of the nail. There's always twelve in a dozen. Here's another question. In the first problem that we did, there were 208 nails in 2.60 pounds. Is that true, if we buy 2.60 pounds of the smaller nail, are there still 208 nails in the 2.60 pounds, but now we're looking at the smaller nails? That's right, you would expect to have to more, or a greater quantity of the smaller nails in a mass of 2.60 pounds. So, I would expect to have more than 208 nails, in the sample of 2.60 of the smaller nails. Assuming that the nails are made of the same material and have the same density of course. You can think about how this would affect the conversion factors. So the conversion factor that there's twelve nails in a dozen stays the same, doesn't it? So this one stays the same. [SOUND]. But the other two conversion factors that I've written here about there how many, about how much a dozen nails weighs and how many nails there are in 2.60 pounds. Those convert, conversion factors change because the nails now are lighter because they're smaller. Because atoms are very small and light, in practice, people who are using atoms and molecules use them in mole and gram quantities, not even by the dozen. We use them in very, very large amounts. So the first thing we need to remember is what is a mole. A mole is, of course, just a number, just like a dozen is number. It's a quantity. It's 6.022 times 10 to the 23rd items. And those items can be atoms or molecules. The mole is defined as being equal to the number of carbon atoms in a 12 gram sample of carbon-12. So this is review. One of atom of carbon-12, that's a carbon with 6 protons and 6 neutrons, weighs exactly 12 atomic mass units. And, one mole of carbon 12 weighs exactly 12 grams. That's the wonderful thing about the mole. So we can weigh grams, and know how many moles of carbon we have. In 12 grams of carbon, there are 6.022 time 10 to the 23rd carbon atoms. There's some useful ratios here. We know how many atoms there are in a mole and we can write that ratio as fractions. We can write it either this way or we can write it this way, right? We can write some other ratios that are also useful. For carbon, right, there's always 12 grams in one mole, or we could say that one mole weighs 12 grams. There's different ways we can write these ratios. Let's do a review example looking at carbon. One of the solid forms of carbon is diamond. Here's a beautiful one carat diamond. This particular diamond weighs 0.20 grams. So, if we have a sample of carbon diamond that weighs 0.20 grams, which of the following is true? Do you have less than 1 atom of carbon, or more than 1 atom of carbon in your diamond that is 0.20 grams of carbon? Of course, there is more than 1 atom of carbon here. Because atoms are very light. They have a mass that are tiny fractions of grams. So a single carbon atom would hardly weigh anything. And in fact, one carbon atom weighs 12.01 atomic mass units, which is only about 2 times 10 to the minus 23rd grams. So I have much more than that, I've got 0.20 grams here. And that must be more than one atom of carbon. Wonderful. So even though it looks like it's a fraction of a whole number, it's a fraction of a gram, and there's billions and billions of atoms in every gram. Let's look at this another way. Let's think about moles. Same sample of carbon, it's still this one carat diamond, diamond is one of the forms of solid carbon, there are other forms. Do we have more or less than 1 mole of carbon? So you have to think about this relationship, is 0.20 grams of carbon, is that more than 1 mole of carbon, or is it less than 1 mole of carbon? A mole of carbon atoms would be 6.02 times 10 to the 23rd atoms, and if we had an average sample of carbon atoms, which is a mixture of isotopes, then that sample would weigh 12.01 grams, so I could write that up here. 1 mole of carbon has a mass of 12.01 grams. One of the things you probably notice is that I use the word weight and mass interchangeably. I know that they're not exactly the same, and that weight depends on the gravity of where you're taking the mass but a lot of people use the weight commonly on Earth, and so I'm just going to use the word weight and mass interchangeably, and we're going to assume that we're always on Earth. If you were taking an astronomy class, that might not be the case, but we're going to do our chemistry all on Earth for now. Let's do a calculation and determine how many atoms of carbon there are in that 0.2 gram sample of carbon. We determined that it was more than one carbon atom, but less than 1 mole of carbon atoms. So, that's a pretty large range. Let's do an exact calculation. So here's the quantity we were given for that one carat diamond. We know that there's 12 grams per mole. I want the grams to cancel out, so I need to write the ratio with moles on top and grams on the bottom. The grams cancel out. And I see that I have 0.017 moles of carbon in that sample. So that's less than one mole of carbon of course. But I want to know how many carbon atoms there are. So I'm going to take that fraction of a mole that we have, and I'm going to multiply it by the number of atoms in a mole. So here's a conversion factor for the number of atoms in a mole. That's always the same. It's always 6.02 times 10 to the 23rd in one mole. Moles cancel, and now I have the number of carbon atoms, which is 1.02 times 10 to the 22nd atoms. So in those last couple of examples, b and c were true, and I know you got those correct. We have counted the number of carbon atoms by knowing the mass of the sample. Since many relationships in chemistry depend on stoichiometry, which is the mole ratio, you need to become very adapt at converting between grams and moles. We'll continue to practice with that throughout the semester.