Understanding Moles and Molar Mass

Now that we know how to write formulas and name different compounds, we are ready to talk about how we measure them out. So this section on moles and molar mass is the introduction to that topic. So atoms and molecules are really tiny and sometimes we need a really specific number of them, but we're definitely not going to be sitting around and counting atoms or molecules. So We need a way to do that and that's what moles are. We count atoms by weighing them and a mole is just a specific number of atoms. It's kind of like the chemist's version of a dozen and there's a really great video on Canvas that will go into a little bit of history but also show some great examples because atoms and molecules are not the only thing that we count by mass. One mole of particles is equal to 6.022 times 10 to the 23rd particles. So it's an enormous number. But since atoms and molecules are really small, this is pretty reasonable. We need a ton of them to get some kind of mass that we could actually weigh out. And this number... 6.022 times 10 to the 23rd is known as Avogadro's number, after the person who came up with this number, and we sometimes abbreviate it with a capital N and then a subscript capital A. So let's apply this to a bunch of different things. If you had one mole of marbles, you would have 6.022 times 10 to the 23rd marbles. That's a lot of marbles. If you had one mole of carbon atoms, you would have 6.022 times 10 to the 23rd carbon atoms. Also a lot of carbon atoms, but imagining a pile of that many marbles versus a pile of that many carbon atoms, you can see there's a pretty distinct difference. This also applies to molecules. So one mole of carbon dioxide molecules is 6.022 times 10 to the 23rd. molecules. Now the way that we take this measurement of number of particles or number of atoms and get it to equal a mass is that it turns out that one mole of carbon atoms is equal to 12.011 grams of carbon atoms, which just so happens to be the atomic weight from the periodic table. When we scale this up to talking about other things, we'll refer to this as molar mass, or you might see molecular weight kind of used interchangeably. They both mean the same thing. The abbreviations, you'll either see two capital M's for molar mass, or maybe a fancy italicized capital M. or you'll see Mw for molecular weight. Either way, this means the mass of one mole of atoms of an element. In grams per mole, this is numerically equal to the element's atomic mass in AMU. So that means when we look at the periodic table, technically the 12.011 that we see for carbon is the atomic weight in atomic mass units. that is the weighted average of the naturally abundant isotopes. However, that also scales, and you have a molar mass of carbon atoms of 12.011 grams per mole. And so now this is giving us a way to take a mass in grams and relate that to the number of carbon atoms in moles. Because a mole is 6.022 times 10 to the 23rd things, if I have a mass, I can find out exactly how many atoms are in that sample. And if I need to get a specific number of atoms, I can find out what mass I need to weigh out to get that. Let's do carbon dioxide. One molecule of carbon dioxide has one carbon atom that weighs 12.011 amu and two oxygen atoms that weigh 15.999 amu each. So these are, right, we're taking the atomic mass unit atomic weight from the periodic table. We're using the subscripts from each atom in the formula and adding them up to find out how much one molecule would weigh. And that would be 44.01 amu. And you could call this the formula mass. This will end up just normally calling the molecular weight because it's from a molecule or generically calling it the molar mass of CO2. So carbon dioxide, one molecule weighs 44.01 amu. which means that one mole weighs 44.01 grams. So the molar mass of carbon dioxide is 44.01 grams per mole. For another example, let's look at C6H12O6. So carbon, hydrogen, and oxygen, I can get the atomic weight of each element. from the periodic table, and then the number from the subscript tells me how many of each atom. So if I wanted the molar mass of this molecule for carbon, I need to take 12.011 and multiply by 6. Hydrogen is 1.008 times 12. Oxygen is 15.999 times 6. I've given the individual results of those multiplications here. You don't necessarily need to do that, but it's a good check for your calculation. And when you add these up, the molar mass is 180.16 grams per mole. Now, why do we need this? I've kind of mentioned why we would need it, but let's do an example that shows exactly why we need it. So the question is, how much sodium oxide should you weigh to obtain? 4.02 times 10 to the minus 2 moles of sodium oxide. And then how many molecules is this? So just for the first part, this is where using molar mass like a conversion factor is how we are going about solving this problem, right? When I referred to it earlier, I said, if you know how many you want to count, right? How many... Atoms or molecules, in this case molecules, you want to have counted out. That's a number of moles. If you know the molar mass, you can figure out how many grams that would be. So that's our first question. I want to go from moles to grams. If I know how many grams there are per mole for sodium oxide, I can do that. But I'm not given the molar mass, of course, so I have to calculate the molar mass first. In sodium oxide, I have two sodium atoms that are 22.99 grams per mole each, and one oxygen atom that's 15.999 grams per mole each. And when you add this up, you get 61.979 grams per mole. And you'll notice that I've stopped using the AMU labeling completely. We will jump directly to the grams per mole. Because that's what's going to be on the macroscopic level. It's going to be what we deal with on a regular basis. Now, for solving the problem, I have 4.02 times 10 to the minus 2 moles of sodium oxide. This is what I'm trying to weigh out. I'm going to put this over 1 like I always do. But you don't have to, again, like always. And I know how many moles I want to weigh out. And then I know the relationship between grams and moles. So if I multiply with grams on the top and moles on the bottom, moles will cancel and I'll be left with grams. And this would be 2.492 grams of sodium oxide. Now, in the interest of our COAST framework, does this make sense? So think about this answer. I am weighing out 2.492 grams of sodium oxide. That's much less than a mole because one mole would be nearly 62 grams but The number of moles I was asked to weigh out is pretty small, right? 4 times 10 to the minus 2, so 0.04 moles. So way less than 1 mole, so way less than 62 grams makes sense. The next thing that we were asked to calculate is the number of molecules. So in a 1 mole sample, how many molecules are there? Well, any... How many numbers of atoms? How many numbers of molecules? That's always a relationship with Avogadro's number because that is the specific number that relates to one mole. So I know that I will be weighing out 4.02 times 10 to the minus 2 moles and that one mole of anything is 6.022 times 10 to the 23rd molecules or atoms. in this case molecules. So if I have the 6.022 times 10 to the 23rd in the top and then moles in the bottom, moles will cancel and this will give me 2.42 times 10 to the 22nd molecules. So again, does this answer make sense? It does. It should be a really big number. If it's asking us how many atoms or how many molecules, it will be a very big number. So 10 to the 22nd makes sense. The units have cancelled so that seems good. It's less than one mole but for the same reasons that our small mass made sense, a less than times 10 to the 23rd answer here also makes sense. Let's do this for C6H12O6. We set this up a little bit earlier. So we got the molar mass of C6H12O6 in an earlier example. And what I have here, I've got the generic outline of the calculation that we did, but just a bit of a breakout and a little bit of kind of a reminder or kind of bringing some of this maybe hidden information to the forefront. When we have six carbon atoms per molecule, That also means that one mole of C6H12O6 has six moles of carbon atoms in it, right? If you have one mole of C6H12O6, you have 6.022 times 10 to the 23rd molecules. Each molecule has six carbons. So you have six moles of carbon atoms. that sample. It also means that you have 12 moles of hydrogen atoms in that sample and 6 moles of oxygen atoms. So this question says how many moles of carbon could be extracted from 1 kilogram of C6H12O6? So the reason that we just looked explicitly at those subscripts and what it means in terms of moles is because we're going to need it. to solve this problem. So I've set this up like a unit conversion. You could set this up in any way that makes sense to you. But here's what I know. I know how many kilograms of C6H12O6 I have. I want to get to moles of carbon. Well, from kilograms, I know that I can get to any other prefix or base unit that has grams in it. So the first thing that I did was convert this to grams. So there are 1000 grams in one kilogram. Now that I know how many grams of C6H12O6 I have, because I calculated the molar mass earlier, I can convert this to moles of C6H12O6. So If I were to get a final answer here, right, I would know how many moles of C6H12O6 are in one kilogram. And then the new piece of information that I've added, I know within one mole for in each mole of C6H12O6, I have six moles of carbon. And so I can use the formula as a conversion factor here. So six moles of carbon on top. one mole of C6H12O6 on the bottom. That will cancel out my moles of the molecule and leave me with moles of carbon. And that ends up being 33.3 moles of carbon, which sounds huge, right? So we should think about this and see if this answer makes sense. Well, 180 grams would be one mole of the molecule. So 180 grams would be six moles of carbon. I have a thousand grams, so I have way more than one mole. So way more than six moles of carbon makes sense.

So We need a way to do that and that's what moles are. We count atoms by weighing them and a mole is just a specific number of atoms. It's kind of like the chemist's version of a dozen and there's a really great video on Canvas that will go into a little bit of history but also show some great examples because atoms and molecules are not the only thing that we count by mass.

One mole of particles is equal to 6.022 times 10 to the 23rd particles. So it's an enormous number. But since atoms and molecules are really small, this is pretty reasonable.

We need a ton of them to get some kind of mass that we could actually weigh out. And this number... 6.022 times 10 to the 23rd is known as Avogadro's number, after the person who came up with this number, and we sometimes abbreviate it with a capital N and then a subscript capital A. So let's apply this to a bunch of different things.

If you had one mole of marbles, you would have 6.022 times 10 to the 23rd marbles. That's a lot of marbles. If you had one mole of carbon atoms, you would have 6.022 times 10 to the 23rd carbon atoms.

Also a lot of carbon atoms, but imagining a pile of that many marbles versus a pile of that many carbon atoms, you can see there's a pretty distinct difference. This also applies to molecules. So one mole of carbon dioxide molecules is 6.022 times 10 to the 23rd. molecules.

Now the way that we take this measurement of number of particles or number of atoms and get it to equal a mass is that it turns out that one mole of carbon atoms is equal to 12.011 grams of carbon atoms, which just so happens to be the atomic weight from the periodic table. When we scale this up to talking about other things, we'll refer to this as molar mass, or you might see molecular weight kind of used interchangeably. They both mean the same thing.

The abbreviations, you'll either see two capital M's for molar mass, or maybe a fancy italicized capital M. or you'll see Mw for molecular weight. Either way, this means the mass of one mole of atoms of an element. In grams per mole, this is numerically equal to the element's atomic mass in AMU. So that means when we look at the periodic table, technically the 12.011 that we see for carbon is the atomic weight in atomic mass units.

that is the weighted average of the naturally abundant isotopes. However, that also scales, and you have a molar mass of carbon atoms of 12.011 grams per mole. And so now this is giving us a way to take a mass in grams and relate that to the number of carbon atoms in moles.

Because a mole is 6.022 times 10 to the 23rd things, if I have a mass, I can find out exactly how many atoms are in that sample. And if I need to get a specific number of atoms, I can find out what mass I need to weigh out to get that. Let's do carbon dioxide.

One molecule of carbon dioxide has one carbon atom that weighs 12.011 amu and two oxygen atoms that weigh 15.999 amu each. So these are, right, we're taking the atomic mass unit atomic weight from the periodic table. We're using the subscripts from each atom in the formula and adding them up to find out how much one molecule would weigh.

And that would be 44.01 amu. And you could call this the formula mass. This will end up just normally calling the molecular weight because it's from a molecule or generically calling it the molar mass of CO2. So carbon dioxide, one molecule weighs 44.01 amu.

which means that one mole weighs 44.01 grams. So the molar mass of carbon dioxide is 44.01 grams per mole. For another example, let's look at C6H12O6.

So carbon, hydrogen, and oxygen, I can get the atomic weight of each element. from the periodic table, and then the number from the subscript tells me how many of each atom. So if I wanted the molar mass of this molecule for carbon, I need to take 12.011 and multiply by 6. Hydrogen is 1.008 times 12. Oxygen is 15.999 times 6. I've given the individual results of those multiplications here. You don't necessarily need to do that, but it's a good check for your calculation. And when you add these up, the molar mass is 180.16 grams per mole.

Now, why do we need this? I've kind of mentioned why we would need it, but let's do an example that shows exactly why we need it. So the question is, how much sodium oxide should you weigh to obtain?

4.02 times 10 to the minus 2 moles of sodium oxide. And then how many molecules is this? So just for the first part, this is where using molar mass like a conversion factor is how we are going about solving this problem, right? When I referred to it earlier, I said, if you know how many you want to count, right?

How many... Atoms or molecules, in this case molecules, you want to have counted out. That's a number of moles.

If you know the molar mass, you can figure out how many grams that would be. So that's our first question. I want to go from moles to grams.

If I know how many grams there are per mole for sodium oxide, I can do that. But I'm not given the molar mass, of course, so I have to calculate the molar mass first. In sodium oxide, I have two sodium atoms that are 22.99 grams per mole each, and one oxygen atom that's 15.999 grams per mole each. And when you add this up, you get 61.979 grams per mole. And you'll notice that I've stopped using the AMU labeling completely.

We will jump directly to the grams per mole. Because that's what's going to be on the macroscopic level. It's going to be what we deal with on a regular basis. Now, for solving the problem, I have 4.02 times 10 to the minus 2 moles of sodium oxide. This is what I'm trying to weigh out.

I'm going to put this over 1 like I always do. But you don't have to, again, like always. And I know how many moles I want to weigh out. And then I know the relationship between grams and moles. So if I multiply with grams on the top and moles on the bottom, moles will cancel and I'll be left with grams.

And this would be 2.492 grams of sodium oxide. Now, in the interest of our COAST framework, does this make sense? So think about this answer. I am weighing out 2.492 grams of sodium oxide. That's much less than a mole because one mole would be nearly 62 grams but The number of moles I was asked to weigh out is pretty small, right?

4 times 10 to the minus 2, so 0.04 moles. So way less than 1 mole, so way less than 62 grams makes sense. The next thing that we were asked to calculate is the number of molecules.

So in a 1 mole sample, how many molecules are there? Well, any... How many numbers of atoms?

How many numbers of molecules? That's always a relationship with Avogadro's number because that is the specific number that relates to one mole. So I know that I will be weighing out 4.02 times 10 to the minus 2 moles and that one mole of anything is 6.022 times 10 to the 23rd molecules or atoms. in this case molecules. So if I have the 6.022 times 10 to the 23rd in the top and then moles in the bottom, moles will cancel and this will give me 2.42 times 10 to the 22nd molecules.

So again, does this answer make sense? It does. It should be a really big number. If it's asking us how many atoms or how many molecules, it will be a very big number.

So 10 to the 22nd makes sense. The units have cancelled so that seems good. It's less than one mole but for the same reasons that our small mass made sense, a less than times 10 to the 23rd answer here also makes sense. Let's do this for C6H12O6. We set this up a little bit earlier.

So we got the molar mass of C6H12O6 in an earlier example. And what I have here, I've got the generic outline of the calculation that we did, but just a bit of a breakout and a little bit of kind of a reminder or kind of bringing some of this maybe hidden information to the forefront. When we have six carbon atoms per molecule, That also means that one mole of C6H12O6 has six moles of carbon atoms in it, right?

If you have one mole of C6H12O6, you have 6.022 times 10 to the 23rd molecules. Each molecule has six carbons. So you have six moles of carbon atoms.

that sample. It also means that you have 12 moles of hydrogen atoms in that sample and 6 moles of oxygen atoms. So this question says how many moles of carbon could be extracted from 1 kilogram of C6H12O6?

So the reason that we just looked explicitly at those subscripts and what it means in terms of moles is because we're going to need it. to solve this problem. So I've set this up like a unit conversion.

You could set this up in any way that makes sense to you. But here's what I know. I know how many kilograms of C6H12O6 I have. I want to get to moles of carbon.

Well, from kilograms, I know that I can get to any other prefix or base unit that has grams in it. So the first thing that I did was convert this to grams. So there are 1000 grams in one kilogram. Now that I know how many grams of C6H12O6 I have, because I calculated the molar mass earlier, I can convert this to moles of C6H12O6. So If I were to get a final answer here, right, I would know how many moles of C6H12O6 are in one kilogram.

And then the new piece of information that I've added, I know within one mole for in each mole of C6H12O6, I have six moles of carbon. And so I can use the formula as a conversion factor here. So six moles of carbon on top.

one mole of C6H12O6 on the bottom. That will cancel out my moles of the molecule and leave me with moles of carbon. And that ends up being 33.3 moles of carbon, which sounds huge, right?

So we should think about this and see if this answer makes sense. Well, 180 grams would be one mole of the molecule. So 180 grams would be six moles of carbon.

I have a thousand grams, so I have way more than one mole. So way more than six moles of carbon makes sense.

Transcript for:Understanding Moles and Molar Mass

Transcript for:
Understanding Moles and Molar Mass