 Okay. Again, this little exercise may seem kind of dumb, but it's designed to put you in the right frame of mind for what's coming up. So, I think everyone who listens to this probably knows the answer to this. How much is a dozen? It's one group of twelve things. That's what one dozen means. So, you can have one dozen eggs. That's one group of twelve eggs. You can have a dozen roses. I think that's coming up. It's one group of twelve roses. You can have a dozen donuts. So, hopefully, that's what my wife gets me for Valentine's Day. Not that I need it. You can also have, again, a dozen doesn't really tell you what you have. It just tells you how many groups of twelve you have. So, you can have a different type of dozen eggs. You can have the local eggs, right? One dozen of those. You can have bigger eggs, right? You can have the jumbo eggs or something like that. If you had a dozen of those, it doesn't really tell you what type of thing you have. It just tells you how many you have. So, a dozen means twelve. And at this point, I usually ask my students in the on-ground class, well, how do you know this? And, you know, invariably they say something like, I learned this in second grade or I learned it in third grade. And so, if you were maybe a foreigner, the word dozen might seem a little strange. It doesn't really come as part of our normal assortment of numbers. It's not, you know, one, two, three, four. It's a little bit of a weird word and it's tied to this number. And the only reason that it doesn't seem weird to most of us is because we've heard of it all of our lives. There's a number coming up that you probably have not heard of all of your life. It's a little bit of a weird number, but the idea behind it is very similar to the idea behind a dozen. A dozen just means twelve of something. The number that we're going to talk about a little later will mean a different number of something. So, keep that in mind. Again, two dozen of something is just twenty-four things. Or, if you want to, you can say two groups of twelve things. But two groups of twelve things is twenty-four things. So, if I have two dozen eggs, I have twenty-four eggs. Two dozen roses, you know, that's twenty-four roses. And if my wife really likes me this year, two dozen donuts. So, again, there's nothing earth shattering behind two dozen. That's just twice as much as one dozen. Again, just trying to get you in the right frame of mind. So, we're going to shift gears now and talk about counting atoms and weighing atoms. So, first of all, we're going to play How Much Does It Weigh? It's a very exciting game, I know. This is supposed to be a typical hydrogen atom. That's one red circle. That's one proton, very tiny one, written there. How much does this hydrogen atom weigh? Well, it weighs about, that's my about symbol, about one AMU. If I have two hydrogen atoms all together, both of them together, they weigh about two AMU. The question that I'm going to pose to you, you can think about your answer to this, is if I had a scale in the lab, just a conventional scale, or, you know, let's say your bathroom scale, and I had a bag of hydrogen atoms. I know you can't really have a bag of hydrogen atoms, but pretend you did. Could you actually scoop out and assume that you could scoop out two hydrogen atoms from your bag? Could you put them on a scale and actually weigh them? The answer to that is no, because, well, they're too light. Conventional scales just can't, they can't weigh one atom. They can't weigh two atoms. Could you, if you had three atoms, that would be about three AMU. Could you weigh those on a scale? Could you scoop them out and weigh them on a conventional scale? Again, the answer is pretty clearly no. These things are really, really tiny, and you just can't weigh them on a conventional scale. Here's another question, maybe a little bit more difficult to answer. It's 100,000 billion. What if I had a billion? What if I could scoop out a billion hydrogen atoms? Would I be able to weigh a billion hydrogen atoms out on a conventional scale? If you're honest with yourself, or maybe if you're not delusional, the answer to this is I don't know. Or at least if you haven't had much chemistry before, your honest response to this question should be, I don't really know. I don't know if a billion is enough to actually put on a scale or not. Seems like a lot, so maybe I can weigh it out on a scale, but maybe it isn't. Maybe it isn't as much as I think it is. The answer to that is going to be no. Even a billion hydrogen atoms, if you put them on a conventional scale, even a very good scale in a lab, you wouldn't be able to weigh them out. These things are really tiny. So this begs the question, how many atoms do I actually need to have before I can weigh them out on a conventional laboratory scale? This is a question that people thought about for a long time. They might have even thought about it in the backward sense, that they were weighing out certain amounts of chemicals, and they wanted to know, well, look, I'm weighing out a bunch of water or some other type of chemical. How many water molecules do I actually have that I'm pouring into a little container? How many of those little guys are there running around in there? It turns out that you need to have about one times 10 to the 23 atoms before you can get to weights that are enough to be measured on conventional scales. This is a rough number. You don't have to be exactly at one times 10 to the 23. You could be a little bit under, and you can definitely be over, but you have to be in this neighborhood, and this is a lot more than a billion. It's a heck of a lot more. It's this many zeros, right? That's about, that should be about 23 zeros. So that's a lot of atoms. Again, some of the stuff that I'm going to tell you is a little bit, let's just say I'm bending history a little bit, but it doesn't really matter. All you really need to know is that this was sort of done in relation or with these types of numbers in mind. When you look at hydrogen, I said your average hydrogen atom weighs about 1.0079 AMU. That's the average weight of hydrogen atoms. What people did, what chemists did, is they reused this number. But AMU is a unit, and one AMU is not really enough to weigh out on a conventional scale. And what they basically said is, look, why don't I use this number, but shift to a unit that actually can be weighed out on a scale? What if I had 1.0079 grams, and the abbreviation for grams is just a lowercase g. What if I had 1.0079 grams of hydrogen atoms? How many hydrogen atoms would there actually be in my 1.0079 grams? So ignore the dolns here. 1.0079 grams is about the weight of a paperclip. So imagine that I had a paperclip's worth of hydrogen atoms. How many h's, how many little h atoms are there in my paperclip's worth of hydrogen atoms? It's going to be somewhere near this number, because I said you had to be near this number before you can actually start weighing things out. And a paperclip is definitely in the neighborhood of things that you can weigh out on fancy scales. Turns out that the number of atoms that you have, if you have 1.0079 grams of hydrogen is about 6.02 x 10 to the 23 hydrogens, which is close to this number up here, right? It's about six times bigger. This is 1 x 10 to the 23. This is 6.02 x 10 to the 23. It took people a long time to figure out what this number is. If I have 1.0079 grams of hydrogen, how many hydrogens do I have? And this number, it's not complete. There are more digits that go on after this. And people still don't know all of the digits, but it's usually written as about 6.02 x 10 to the 23. And we're going to sort of skip the extra digits that we may or may not know that come after this 2. This number is a special number in chemistry. It has a couple of special names. It gets used a lot. And guess what? You're going to use it a lot. And it is related conceptually to the dozen that we talked about earlier. 6.02 x 10 to the 23 things is called one mole of things. So if I have a dozen things, one dozen things, I have 12 things. If I have one mole of things, then I have 6.02 x 10 to the 23 of them. I have an awful lot. That may be confusing, but I think part of the reason or two of the reasons is this is a new word that you haven't heard every other day since second grade. And this is a weirder number. But the idea is very similar to the idea behind a dozen. One dozen things is 12 things. Two dozen things is two times as many things. One mole of things is this many. It's 6.02 x 10 to the 23 things. And we're going to practice this coming up and we're going to sort of do little drills and hopefully pound this into everybody's head. But this is a new term that you should know. It's going to show up a lot for the rest of the course. One mole of something is 6.02 x 10 to the 23 things. And that's about the smallest number of things in the neighborhood of the smallest number of things of atoms or molecules that you can have before you can actually start to weigh them out on a conventional scale. This number is also sometimes called Avogadro's number or Avogadro's constant sometimes as well. It's there's a dead Italian guy named Avogadro. He is not the person who discovered this number, but they named it in honor of him. So sometimes this number, this name is used as well. Okay, I want to go back to counting and weighing. We said that one hydrogen atom is about one AMU, two hydrogen atoms together weigh about two AMU, three hydrogen atoms together weigh about three AMU. I want to talk about helium now. And we need to pay attention to this number down here. One helium atom weighs about four AMU. So if I compare that to one hydrogen atom, like I did much earlier in this unit, the helium atom one helium weighs four times as much as one hydrogen because this guy weighs four AMU, this guy weighs one. So the helium is four times heavier. If I have two helium atoms, they weigh about eight AMU altogether. And two helium atoms weigh four times as much as two hydrogen atoms because the two hydrogens weigh about two AMU and eight divided by four, I'm sorry, eight divided by two is four times heavier. Three helium atoms weigh about 12 AMU. So three helium atoms are still going to be three times heavier than three hydrogen atoms. Sorry, let me rephrase that. So three helium atoms are going to be four times heavier than three hydrogen atoms for the same reason that two helium atoms were four times heavier than two hydrogen atoms, et cetera, et cetera. No matter as long as I have, as long as I have equal numbers of heliums and hydrogens, my pile of heliums will always weigh four times much as my pile of hydrogens. And you can kind of see that here as well. This means the heliums are about four times heavier than the hydrogens. So to summarize, the average helium atom weighs about four times more than the average hydrogen. Two heliums weigh four times more than two hydrogens. 100 heliums should weigh four times more than 100 hydrogens. Hopefully that makes sense. A billion heliums weighs four times more than a billion hydrogens, correct? Because as long as I have equal numbers, my pile of heliums will always weigh four times more than my pile of hydrogens. If that's all true, then 6.02 times 10 to the 23 helium atoms must weigh four times more than 6.2 times 10 to the 23 hydrogens, because I have the same number of each and every helium is four times heavier. If that is all true, how much does 6.02 times 10 to the 23 helium atoms actually weigh in grams? And you can think about this. You can pause and unpause. But the answer is that it has to weigh this many grams, because I told you on the previous slide that 6.02 times 10 to the 23 H atoms weighs this number, but not in AMU. It weighs that number in grams. People reused this number. They switched the units from AMU to grams and they said, look, if I have one, roughly one gram of hydrogen, how many do I have? I have 6.02 times 10 to the 23 of them. What that means is 6.02 times 10 to the 23 H atoms weighs about one gram. Now weighs about 1.0079 grams, but I'm just rounding to the nearest number. If that's true and your average helium is four times heavier, approximately, then 6.02 times 10 to the 23 helium atoms is going to weigh four times more than this. It's going to weigh four times more than a gram, roughly. And what it's actually going to weigh is this number, but without the AMU unit and instead it's going to have a gram unit. So if I have 6.02 times 10 to the 23 helium atoms, it weighs about four paperclips or approximately four grams. So now we have a way of converting between number of atoms and mass of atoms or weight, if you want, in grams. Grams is something that we're at least somewhat familiar with. I'm telling you a gram is about the weight of a paperclip. So for the longest time, people wanted a way of figuring out, look, if I weigh out some chemical in grams, I want to be able to count how many things are there. I want to be able to know how many things are there. What I'm giving you now is a conversion and it deals with this number and whatever number is the average atomic mass in a box for an element. So 6.02 times 10 to the 23 H atoms weighs about one gram. 6.02 times 10 to the 23 helium atoms weighs about four grams. And you can do this for any of the elements in the periodic table. It's not just hydrogen and helium, it's all of them that you can use this number and this number as a way to interconvert between how much some material, some pile of atoms weighs and how many atoms are in that pile. So I think this is probably a good point to stop. Maybe you can digest what we just covered and we'll cover more going forward. How well everybody said about the bird.