Transcript for:
Understanding Chemical Composition and Moles

In this video we're going to cover chapter 6 which talks about chemical composition. So let's start off with this idea of trying to buy nails in a hardware store. Okay, so let's say you want to buy a bunch of nails.

And if you take it to the cash register, you know, the person, if they charge per nail, the person at the cash register is going to have to count how many nails you have and charge you for each one of them. But, you know, depending on how many you have, that could take quite a while. So a much quicker and easier way is to just weigh all the nails. together and then assuming that they're all the same size and they all weigh the same you can then figure out how many nails you have very quickly just by weighing all of them and then the person would know exactly how much to charge you okay so let's do an example let's say one nail Okay, so let's say one nail weighs five grams.

And let's say you buy, there's about, well, you take a bunch of nails to the counter. And let's say they weigh 280 grams. Okay, so if that's the case, how much or how many nails did you bring to the counter? Okay, if one nail weighs 5 grams and all the nails that you brought to the counter weigh 280 grams, how many nails did you just bring to the counter? Okay, so how can we figure that out?

Okay, well, we know that one nail... weighs 5 grams, that's our conversion statement. So our conversion factor is going to be 1 nail over 5 grams. Okay, so the grams will cancel, and this will tell us how many...

Let me get my calculator. This will tell us how many nails we have. Okay, so that's 280 divided by 5. Okay, so that means there are 56 nails that we brought to the counter. And then, you know, each nail is a dollar.

The person at the cash register would charge you $56. Okay, so it's much. Easier and quicker when you have a bunch of objects, they all weigh the same, instead of counting them one by one, it's much quicker just to weigh them all together and then knowing how much each one weighs, figuring out how many nails you have.

So the idea is the exact same way. or works the exact same way with atoms. Okay?

In this picture on the left, we have a bunch of nails that we could weigh all at once to figure out how many we have. And on the picture on the right, what we have in this are not nails, but are a bunch of carbon atoms, which when we put them together looks like this black powder. Okay, so this is all carbon. in carbon atoms in this container. And let's say it weighs, after we subtract the boat out, let's say we put the boat on, we tiered it to zero, and then it reads 8.25 grams.

So we know we have 8.25 grams of carbon. Okay, so if we come back here, and if I tell you 1, I tell you that one carbon atom weighs. You can then tell me exactly how many carbon atoms I have.

So it's one carbon atom weighs 12.01. But those are what are called atomic mass units. And how do I know that? Well, if you look at the periodic table, it tells you, okay, so carbon has the symbol C.

So right underneath that, you can read the atomic mass of carbon. So 12.01. And for one carbon atom, It's measured in AMUs, atomic mass units. So back to our case, the scale is not reading AMUs, it's reading grams.

So we need a way to convert AMUs to grams first. Okay, that can be done. So AMUs...

Let's see the conversion factor for AMUs to grams. It's 6.022 times 10 to the 23rd AMUs will make up 1 gram. Okay, so we can find out...

How much one carbon atom weighs in grams if we know it weighs 12.01 amu? Just use this conversion factor. So we have to convert amu to grams, so we'll put the 1 gram up top and the 6.0.

We'll talk more about this number soon. It's a very large number. You can see 10 to the 23rd amu.

AMUs will cancel, and we'll get the mass of one carbon atom in grams, and then we can figure out, okay, how many carbon atoms we actually have in that container. So let me do the math here. So I'm going to take 12.01, divide it by 6.022 times 10 to the 23rd. Gives me, keeping, let's see, four sig figs, that gives me a value of 1.994 times 10 to the minus 23 grams. Okay, so it's a very small number.

One carbon atom weighs this many grams, 1.99. 4 times 10 to minus 3 minus 23 grams. So very small number but now we know how much one carbon atom weighs in grams and we know that in this container there's a bunch of carbon atoms all of them together weigh 8.25 grams. So if I want to figure out how many carbon atoms there are in that container instead of counting them trying to count them one by one which would take a long time.

time. That would be very difficult to do because they're too small to see anyway. So yeah that leaves me no choice but to use this method. Okay so if I had 8.25 grams of carbon, C for carbon, and I know that one carbon atom Weighs 1.994 times 10 to the minus 23rd grams. I can then figure out, since the grams cancel, I can figure out how many carbon atoms I have.

So I have to do the math and I'll keep it. 3 sig figs. So I'm going to take 8.25 5 divided by 1.994 times 10 to the minus 23rd equals keeping three sig figs since 8.25 only has three sig figs this one has four I get 4.14 times 10 to the 23rd carbon atoms.

Okay, so that's a lot of carbon atoms in there. That's a very big number and it would take you forever to to be able to count them one by one. So it's much quicker just to weigh them and then knowing how much each of them weighs to find out how many there are. So in this container, yeah, I know there's 4.14.

times 10 to the 23rd carbon atoms. It's the exact same idea with the nails. If we know how much each nail weighs, instead of counting them, we can just weigh them all together and figure out how many we have.

Okay, so let's see. There's a few other things to consider. Oh yeah, so this...

Number here, let me write it again. Yeah, this number here is 6.022 times 10 to the 23rd is what we call a mole, but we abbreviate it as M-O-L. So M-O-L is the abbreviation for mole.

If you have this many of anything, that means you have one mole of it. So if you have 6.022 times 10 to the 23rd eggs, which is a lot of eggs, that means you have one mole of eggs. It's very similar to a dozen.

So a dozen is equal to, most people know it's 12. But a mole is not equal to 12. It's a different number. It's a much bigger number. It's this number, 6.022 times 10 to the 23rd. So if you have a dozen eggs, you have 12 eggs. If you have one mole of eggs, you have 6.022 times 10 to the 23rd eggs.

But it doesn't matter what you're talking about. It could be carbon atoms. It could be marbles. It could be eggs.

You have one mole of... whatever it is you're talking about you have this many of them okay so this number is also known as Avogadro's number that's the person who came up with it his last name Avogadro and so again it's just 6.022 times 10 to the 23rd That's equal to Avogadro's number, which is sometimes written like this. N for number, A for Avogadro's number is this value.

So we're going to see that come up a lot. Okay, so back to the periodic table. Remember, if we're looking at, for example, carbon, Its atomic mass is 12.01.

So one carbon atom will weigh 12.01 amu atomic mass units. I showed you how to go from atomic mass units to grams, but if you have one mole of carbon atoms, so 6.0... 2, 2 times 10 to the 23 carbon atoms.

So you have one mole of carbon atoms. Then these units that we see in the periodic table are not going to be amu, but instead we can say they are grams, g for grams. So one carbon atom weighs 12.01 amu. One mole of carbon atoms weighs 12.01 grams. Okay, so it's the same thing with all the other elements.

If I have one mole of oxygen, I mean if I have one oxygen atom, it would weigh 16.00 amu. But if I had one mole of oxygen atoms, it would weigh 16.00 grams. Okay, so that's why you don't see any units behind this number because it depends.

You're talking about just one atom or one mole of atoms. If it's one atom, use amu. If it's one mole, use grams. Very important. Okay, so let's move on.

Okay, I'm going to kind of jump around here. So... Those problems in a second.

Okay, so if we look at the periodic table for sulfur, and we already looked at for carbon, right? So we know, I just told you, if we have one mole of carbon atoms, we'll have 12.01 grams. But if we look at the periodic table for sulfur, We have one mole of sulfur.

Sulfur is right there. It would be 32.06 grams. Well, here they have 32.07, but close enough. Okay, so yeah, one mole of sulfur atoms, which is what we see in this picture, would weigh 32.07 or six grams. Every periodic table is going to be a little bit different.

That's why we're probably seeing this variation. But one mole of carbon atoms, which is what we have here in this picture, will weigh 12.01 grams. Okay, so because why? Sulfur atoms are bigger than carbon atoms, so they weigh more.

So that's why even though you have the same number of atoms, the weight is going to be more. for the bigger atom just like bigger nails the same number of nails in each case the bigger nails are going to combine are going to weigh more because each nail weighs more than a smaller nail okay so okay so now what we need to do is to be able to know how to convert between Here I'll make a little diagram between those three sets of units. So I'm going to add a slide here.

I'm going to get rid of that. Get rid of this. So I'm going to write down this mnemonic that you can use, this device to.

help you memorize how to convert between all of those units. So we'll put mol on the top, and we'll put grams down here, and then over here we'll put atoms. And later you'll see it can also be... molecules.

Right now we'll just talk about atoms. So you can go between, you can convert between moles of an element, like carbon, and grams of that element. And you can also convert between moles of an element and atoms of that element.

So you have to know how to go convert between those different units. Okay so let's start off with an example. Let's say you had somebody gave you let's make up a number okay nine point seven five grams of sulfur. So we'll write S for sulfur. And we want to know...

So we're right over here. Right now we're dealing in units of grams. We want to know how many moles of sulfur we have.

So what we need to do is go back to the periodic table, look at sulfur. Here it is. And we see that it has atomic mass of 32.06. So one mole of sulfur atoms is going to weigh... 32.06 grams.

So I'm going to go back to my slide over here. Okay, so I have to convert this to moles. I know that one mole of sulfur weighs 32.06 grams of sulfur.

Okay. How do I know that? I got that from the periodic table.

So now the grams of sulfur will cancel, and I can then calculate how many moles of sulfur that is. So 9.75 divided by 32.06. Keeping 3 sig figs, I have 0.304 moles of sulfur.

Okay, so that's how I can convert from grams of sulfur to moles of sulfur. So I went from here to there. Okay, but now let's say we want to go from... moles to grams.

Okay, so what if somebody tells you that you have 41.28 moles of sulfur? How many grams is that? Okay, so now we can use this same conversion factor, but we're going to flip it.

We know that 32.0. Six grams of sulfur is what one mole of sulfur weighs. So if we want to go from moles to grams, moles of sulfur to grams of sulfur, we can cancel the moles of sulfur, and I can do the math. Keep being four sixths, 41.28 times 32.06.

Keeping four sig figs, I get 1,323 grams of sulfur. Okay, so we went in both directions, between moles and grams. Okay, but now let's go from, what if we wanted to go from this many moles? 41.28 moles of sulfur to atoms of sulfur.

Okay, how are we going to do that? Well, remember I said if you have one mole of anything, you have 6.022 times 10 to the 23rd of those objects, Avogadro's number. Okay, so if I have one mole of sulfur, I have, that means I have 6.022 times 10 to the 23rd sulfur atoms. And one mole of sulfur, there are this many sulfur atoms. Okay, so if I have 41.28 moles of sulfur, how many sulfur atoms do I have?

Well. Now the moles of sulfur cancel and I can calculate what that is. 41.28 times 6.022 times 10 to the 23rd. Keeping four sig figs I get 2.486 times 10 to the 25th sulfur atoms.

Okay, that's a lot of atoms. Okay, and I could go the other way. If somebody gives me a certain number of atoms, I can tell you how many moles I have.

Okay, so if somebody says you have, I'm just going to make up a number, 5.867 times 10 to the 24. Sulfur atoms. How many moles do I have? Okay, well, I know that in one mole of sulfur, there are 6.022 times 10 to the 23rd sulfur atoms. So, sulfur atoms will cancel, and I can find out how many sulfur... or moles I have in this many sulfur atoms.

So keeping four sig figs I get 5.867 times 10 to the 24 divided by Avogadro's number. Keeping four sig figs I get 9.743. Oh. 7, let me erase that, okay so 743 moles of sulfur, okay?

So that's how many moles of sulfur there are in this, if I have this many sulfur atoms, okay, but now We could also do that, I want to introduce the concept of how we could figure out, do this with not just elements, single elements, but actually molecules, which could be made up of more than one element. So let's add another slide, that and this, okay. Now let's consider water.

Okay, so water has the chemical formula H2O. Okay, remember, it kind of looks like a Mickey Mouse head. That's the oxygen atom. The two hydrogen atoms kind of look like the airs, but they're connected.

So that's one molecule of water. Okay, well... How much does one molecule of water weigh? Okay, well, let's look at the periodic table.

We see that hydrogen has atomic mass of 1.01, oxygen atomic mass of 16.00. So let's go back to that slide here. Okay, and I'll write that down. So hydrogen. Equals 1.01, right?

I just got that from the periodic table, AMU. But we have two of them in water. So one molecule of water has two hydrogens, right?

Look at it. And oxygen weighs 16.00 AMU. So... If one molecule of water looks like this, it's H2O. That means we have two hydrogens.

They each weigh 1.01. One oxygen weighing 16.0, so we add them together, and we get 18.02 amu. So that's what one molecule of water weighs.

One molecule of H2O. weighs that many amu but what if i had one mole of water molecules well then that would weigh we just changed those units from amu to grams just like we did for the element okay so one mole of water molecules weighs 18.02 grams So now going back to this. Mnemonic, you know, we can go between molecules and moles, moles and grams, exactly the same way we did for atoms. Okay, so I'll show you an example. So let's say you have 2 moles of, or let's call it 2.5 moles, 2.50 moles.

of water. I want to know how many molecules of water you have in 2.5 moles of water. Okay, so that means we want to go from moles to molecules.

So what we'll do is keeping in mind that one mole of water will contain how many molecules? Well one mole of anything, it's always Avogadro's number, so 6.022 times 10 to the 23rd water molecules. Okay that's how I'm going to convert from moles of water to molecules of water.

One mole of water will contain Avogadro's number of water molecules. So I'll use my calculator. I'll keep three sick figs. I get 2.5 times Avogadro's number 6.022 times 10 to the 23rd gives me 1.51 times 10 to the 24. water molecules. Okay, so that's how I know how many molecules of water there are in this many moles.

Okay, but let's say somebody says, now we want to go from grams of water to moles of water. So let's say you have 495 grams of water. How many moles of water is that?

Well again we want to go from grams to mole so we know how to do that so we can use the conversion factor now that we're going to use is that one mole of water weighs 18.02 grams right So we have 495 divided by 18.02. Keeping 3 sig figs I get 27.5. This cancelled.

27.5. moles of water. Okay.

And then we can also go from moles of water to grams of water. You just flip this conversion factor. Okay. So you could also go, yeah, from molecules to moles to grams.

All right. Okay, so let's continue. Alright, so as many of you know, the chemical formula for table salt is sodium chloride. So every, you know, it looks to us like a white solid, right? But if you were to look more closely, you'd see that.

Every one of these green spheres is a chloride ion, and every one of these sodium spheres, I mean the purple spheres, is a sodium ion. Okay, so the chemical formula for table salt is NaCl. Okay, so when you eat sodium chloride salt, you're eating some sodium and some chlorine.

Food and Drug Administration says that, oh, you shouldn't eat more than two 2.4 grams of sodium per day. That's not sodium chloride. They're talking about sodium because you could eat other things that contain sodium like baking soda, sodium bicarbonate, and that total should still be less than 2.4 just for sodium. So we want to know, so let's say for example, that you ate, let's say, come up with a value, let's call it, let's say you ate 8.64 grams of sodium chloride.

If that were the case, how many grams of sodium did you just eat, if you ate? 8.64 grams of sodium chloride. So that's what we want to know, how many grams of sodium are in 8.64 grams of sodium chloride.

Some of this 8.64 grams comes from sodium and some of it comes from chlorine. If we look at the periodic table we see that sodium, we'll record the numbers here, has an atomic mass of 22.99. Chlorine, atomic mass of 35.45. So let's write those down over here.

So sodium is 22.99 amu. Chlorine, 35.45 amu. Okay, so using this information, we can now figure out exactly how many grams of sodium that we consumed if we ate 8.64 grams of sodium chloride. Okay, how are we going to do this? Well, one mole of sodium...

Chloride, table salt, would weigh, if we add these together, let's see, what are we going to get? 9 and 5 is 14, and 1, that's 10, that's another 14, and a 1 there, so that's 3, that's 8, and 2, okay. So we get 58.44 amu. But that's just for one sodium atom and one chlorine atom together would weigh 58.44 amu. But if we had one mole of that combination, this is just one formula unit, this is how much it would weigh.

But if we had one mole of sodium chloride formula units together, it would weigh not 58.44 amu, but... 58.44 grams, g for grams. Okay, so now we can ask the question, we can ask the question, 8.64 grams weighs, or is how many moles?

Okay, well, we know that one mole of sodium chloride weighs 58.44 grams. Okay, we got that from here. So the grams will cancel. We'll find out how many moles we have.

So I'm going to take 8.64 divided by 58.44. Keep three sick figs. I have... 0.148 moles of sodium chloride.

Okay, so if that's true, if I have 0.148 moles of sodium chloride in 8.64 grams of sodium chloride, how many moles of sodium do I have? Well, Based on the formula, I can see that. One mole of sodium chloride must contain one mole of sodium, right?

Because it's a one-to-one ratio. So you have one mole of sodium chloride. That means in that one mole of sodium chloride, there's one mole of sodium. So if I have 0.148 moles of sodium chloride, I can then use that conversion factor, which tells me that one mole of sodium chloride will contain one mole of sodium. So that's an easy calculation to do.

One over one is one. So I have 0.148 moles of sodium in... 0.148 moles of sodium chloride. And now, if I have this many moles of sodium, I can convert that to grams. So, do that here.

I know that one mole of sodium weighs 22... 0.99 grams. Why?

Because we're talking about one mole of sodium. So I can now calculate how many grams of sodium I have. So I'll do 0.148 times 22.99. Keeping three sig figs, I get three point 3.40 grams of sodium.

Okay, so when I ate 8.64 grams of sodium chloride, I ate 3.40 grams of sodium. Okay, so that would be more than the recommended amount. Remember, the FDA, the Food and Drug Administration said, oh, you should need more than 2.4. grams of sodium, so I just ended up eating 3.4, which is more than 2.4, so that would not be good for your health, right?

It leads to high blood pressure and other problems. Okay, so that's just one way how we could figure out that 8.64 grams of sodium chloride contains 3.40 grams of sodium. The other way is just by looking at the formula.

We know that it's a one-to-one ratio of sodium to chlorine. So because one mole of sodium chloride weighs this many grams, and we know that one mole of sodium weighs this many grams, 22.99 grams, and one mole of chlorine weighs 35. 5.45 grams, right, just convert amu to grams when we're talking about moles, then I can get the mass percent of sodium and sodium chloride, right, because one mole of sodium weighs 22.99 grams and one mole of sodium chloride weighs 58.5 grams. for 4 grams so the um oh times 100 percent that will give me the mass percent of sodium in sodium chloride so let's do that calculation and i get 22.99 divided by 58.44 four times 100 keeping four sig figs I get 39.34 percent.

Okay so what that means is that any sample of sodium chloride that you have will be 39.34 percent sodium. So we had 8.64 grams of sodium. chloride so I can use this percentage Find out how many grams of sodium chloride I have. So I'll take 8.64 grams.

That was my mass of sodium chloride. Times it by this percentage. So 39.34% is the same as 0.3934, right? Just divide by 100, get rid of the percent.

And that will give me the mass of sodium, which should be coming out to be equal to 3.4. We did everything correctly. So let's see if that's the case. So 8.64 times 0.3934. Keeping three sig figs, yeah, I get 3.4.

Zero grams for sodium. Okay? So that's an important problem. Okay.

So let's move on to this. Slide over here. Well, let me insert, before we get to slide 42, let's just do another example.

Okay, so let's, this time let's consider water, just to help you calculate the mass percent. So let's consider water, H2O. I would like to know... What is the mass percent of oxygen in water? So H2O, remember water, it's got one oxygen, two hydrogens, it looks like that.

Okay, so here is, oh no, okay, so that's, yeah, one water molecule right there, H2O. So what is the mass percent of oxygen? In H2O, mass percent of oxygen, in H2O what is that equal to? Well, there's a few ways to do it. We look at the periodic table, we know that hydrogen weighs 1.01 amu, one atom.

Oxygen weighs, one atom of oxygen weighs 16.00 amu. And, but remember, there's two hydrogens in one molecule of water. So the mass percent of oxygen in water, we have to, well, yeah, add up two hydrogens. So we add those together, we get 18.02 amu. That's just for one molecule of water.

One mole of water would weigh 18.02 grams. One mole of water, one molecule of water is that. Okay, so you could use either one, but let's do the grams since that's more common. Okay, so if we have one mole of water, that would weigh 18.02 grams. In one mole of water, how many moles of oxygen are there?

Well. In one molecule water, how many atoms of oxygen are there? Just one, right?

So that's the same for the moles of water. If you have one mole of water molecules, each one has one oxygen atom. So you have in one mole of water, you'll have one mole of oxygen atoms.

One mole of water will have one mole. of oxygen atoms. So to find the mass percent of oxygen, it's the mass of oxygen atoms divided by the mass of water molecules times 100%.

Okay, so what we would do... use in this equation the mass one mole of oxygen atoms will weigh 16.00 grams right and one mole of water will weigh 18.02 grams so times 100 percent this will give us our mass percent of oxygen and it will be 16 divided by 18.02 keeping Fosick figs times 100% is 88.79%. Okay, so that's the mass percent of oxygen.

That's for oxygen, okay? What about for hydrogen? Well, there's two ways to do it.

Since one molecule of water contains two hydrogen atoms, That means the mass percent of hydrogen is, and each atom of hydrogen, or each mole of hydrogen will weigh 1.01 grams, but you have two moles. One molecule of water has two hydrogen atoms, so one mole of water will have two mole of hydrogen atoms, so two moles of hydrogen atom will weigh 2.02 grams. g for grams and then one mole of water still weighs 18.02 grams times 100 percent so keeping three sig figs we'll get 2.02 divided by 18.02 times 100 is 11.2 percent and that's for hydrogen okay so the mass percent of hydrogen is 11.2 percent for oxygen is 88.79 so another way you could have got this number here is just do 100 minus this because there's only two elements in water hydrogen and oxygen so together they must equal 100 and let's see if that's the case yeah 88 and 11 is 99 99.99 but you can only go out to one decimal place so it becomes 100 percent right so let's do that this gets us to 99.99 but this only went out one decimal place so we can only go out one decimal place but because this is greater than five that gets bumped up to yeah 100 percent okay So now let's say that somebody does an experiment.

Okay, and they, where's that problem? And they find out, oh yeah, okay, they find out that, so basically we want to do this problem. So somebody does an experiment where they take titanium, which is a metal, Ti for titanium, they react it with oxygen gas, which has the formula O2, and they get an oxide of metal, but we don't know the formula for it, so we'll call it TiX.

x, o, y, where we don't know x and y. All we know is that it's a new chemical reaction took place to form an oxide of titanium, but we don't know the chemical formula, so that's why I'm putting x and y. We don't know what x and y are, but that's what we're trying to figure out.

But they did tell us that we started with 3.24 grams of titanium. And then after the reaction took place, we formed a compound of titanium. oxide that weighed 5.04 grams. Okay, so with this information we should be able to figure out what X and Y are.

Okay, so if we started, you know, assuming all the titanium went into this titanium oxide. We know that in this 5.40 grams are 3.24 grams of titanium and so the difference must be the grams how many grams of oxygen are in here right so what's 5.40 minus 3.24 it's 5.40 4.0 minus 0.24, 2.16 grams of oxygen, 0.16 grams, and that's of oxygen. Okay, so let's do this on a fresh slide. Okay, so I'll write it down here.

We had three point... So we have a compound. We don't know its formula.

All we know it contains titanium and oxygen. But we do know that the whole compound weighs 5.40 grams. Out of that is coming titanium at 3.24 grams, and therefore oxygen at 2.16 grams. Okay, so how are we going to figure out what X and Y are, which will be the empirical formula for this compound? Okay, well, if we have...

This many grams of titanium, we can convert that to moles. So I have to look at the periodic table for titanium and oxygen to do the conversion. And I see that titanium right here is 47.88.

and oxygen 16.00 so 40 write that down over here we have yeah titanium coming in at 47.88 grams is what one mole of titanium Well, weigh. So this tells me I have, um, this will tell me how many moles of titanium I have. So 3.24 divided by 47.88.

Keeping three sig figs, I get 0.0. 677 moles of titanium. Okay, and for oxygen, 2.16 grams. And one mole of oxygen weighs 16.00 grams. So I can figure out how many moles of oxygen I have.

So keeping three safe figs, it's 2.16 divided by 16.00 is 0.135 moles of oxygen. Okay, so remember, these subscripts... in a chemical formula referred to the either number of atoms or number of moles of atoms.

Just like in, you know, let's look at H2O. H2O looks like that. That's the oxygen atom, two hydrogen atoms as the ears.

So, you know, that's really a one. So that means there's one atom of oxygen. This two means there's two atoms of hydrogen. in one molecule of water. But it could also refer to not just atoms, but moles.

Because if you had one mole of water molecules, you'd have one mole of oxygen atoms. If you had one mole of water molecules, you'd have two moles of hydrogen atoms. So what we could do is, since these numbers are moles, we can put them in the formula.

So for titanium, we could write the formula. I mean this x would be how many moles we have so that's 0.0677 moles and for oxygen y would be this many moles 0.135 okay but usually you know we want whole numbers we don't want these fractions or decimals. So what you do is take the smallest value out of these two, which in this case is this one, and divide both of the numbers by that smallest value. Do the same thing over here and then simplify. So this divided by itself is easy.

That's one. And the oxygen, let's see, okay, 0.135 divided by 0.0677, keeping, well, I get 1.99, keeping three sig figs, but the closest whole number, that's very close to two. Okay, so basically...

What we get is this, titanium dioxide. There's two oxygens for every one titanium. So this would be the empirical formula, which is what we wanted to determine. Okay? So that's how we would do a problem like this.

But sometimes... They want you to calculate what's called the chemical formula if you're given the molar mass. So for example, let's just say you did another experiment, just like the one that we just did, but you found it was a sugar compound.

It only contained carbon, hydrogen, and oxygen. The empirical formula came out to be this. So one carbon for every two hydrogens for every one oxygen. But then somebody told you, oh, one, the molar mass of this compound is 180.2 grams per mole. In other words, yeah, 180.2 grams of this substance.

is what one mole of that substance would weigh. Okay, so one mole weighs 180.2 grams. So the way, this is the empirical formula, the way to calculate the molecular formula is to calculate, okay, how much, if this was the chemical formula, what would be the molar mass of this compound?

well carbon weighs 12.01 grams per mole hydrogen 1.01 grams per mole and oxygen i'm just getting these from the periodic table 16.00 grams per mole but for hydrogen we have to multiply that by two since we have two of them so you add these together What do you get? 12.01 plus 2.02 plus 16 gives me 30.03 grams per mole. If this was the chemical formula, then one mole of that would weigh... 30.03 grams. But they told us no.

One mole of that compound, which contains only carbon, hydrogen, and oxygen, actually weighs 180.2 grams. So what you do is you take this mass that they gave you and divide it by the mass of what this, what we got here, 30.03. and see what you get. Should be a nice round number. So 180.2 divided by 30.03.

Okay, basically comes out to be six. Okay, so what that means is the real molecule has 6 carbons, 12 hydrogens, and 6 oxygens. So I just multiplied.

This is really a 1, so it's that. I just multiplied all these subscripts through by 6 to get C6H12O6, which is the chemical formula of fructose. Okay, so we call...

Remember, we called this... So this is the molecular formula of fructose, but the empirical formula is... this one. It just simplified. Okay, so I think that is pretty much it for chapter 6. I will see you in chapter 7.