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Molecular and empirical formulas from percent composition

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Using all of the major components in oil of cloves. It has a molar mass of 164.2 grams per mole, and is 73.14% carbon, and 7.37% hydrogen. The remainder is oxygen. What are the empirical and molecular formulas for eugenol? And just as a refresher, empirical formula is the simplest ratio of the atoms in the molecule. And we'll see that in a second. And the molecular formula is the actual number of atoms in the molecule. So let's see if we can figure this out. So the first piece of information they gave us is that, the molar mass of eugenol is 164.2 grams per mole. So just to simplify things in our head, let's just assume that we have 1 mole of eugenol. And just as a bit of a refresher, a mole is just a huge number. It's like saying we have a million molecules of eugenol, but a mole is just an even bigger number. And we know that the molar mass of eugenol-- if we have that many molecules of eugenol, then since we have 1 mole, we know that, that is going to have a mass of 164.2 grams. So another way to say it is, we have 164.2 grams of eugenol. Now they gave us the composition. They tell us what percentage is carbon, what's hydrogen, and the remainder is oxygen. So if we assume we have a mole of eugenol and we know that mole will have a mass of 164.2 grams, we can just use the percentages to figure out what is our mass of carbon, hydrogen, and oxygen. So let's figure this out. So let's start off with this. So 164.2 grams of eugenol times-- let me do it in another color-- times 73.14%. This will tell us what is our mass of carbon that we're dealing with. So let's figure this out. So our mass of carbon-- get the calculator up here. All right, so we have 164.2 times-- so 73.14% is the same thing as 0.7314. So we have 120.1. Let's go with that. We have four significant digits in each of these numbers, so let's just go with 120.1 grams of carbon. So this is 120.1 grams of carbon. Now let's do the same thing for the hydrogen and the oxygen. So we have 164.2 grams of eugenol times-- what's our percent composition of hydrogen? It's right here, 7.37%-- so times 7.37%. What is this going to be equal to? Get the calculator out. So we have 164.2 times-- 7.37% is 0.0737. And we will get 12.1. So we have 12.1 grams of carbon. And they don't give us, explicitly, the percent composition of oxygen. But we could figure it out fairly easily, because we know everything left over is oxygen. So we could take the mass of carbon, the mass of hydrogen-- oh sorry, this isn't grams of carbon. That's grams of hydrogen. We could take the mass of hydrogen, the mass of carbon, subtract them both from 164.2, and whatever is left over will be oxygen. So let's do it that way. Or we could figure out the percentage that's oxygen, because these all have to add up to 100%, and then multiply. Either way would work. So let's do that. So if we have 1 mole of eugenol, it's 164.2 grams. We just figured out that 120.1 of those grams are carbon, and that 12.1 of those grams are hydrogen. So what's left over? We have exactly 32 grams of oxygen. So what's left over when you subtract these two guys out? I'll do that in green. We are left with 32 grams of oxygen. So if you have a mole of eugenol, it has a mass of 164.2 grams. And if you break it down by the masses of the constituent molecules, 120 grams of carbon, 12 grams of hydrogen, 32 grams of oxygen. Now what we need to do is figure out how many moles of carbon this is, how many moles of hydrogen this is, and how many moles of oxygen. And this is maybe something that you should have memorized at some point, because these are the three most common elements you'll ever deal with. But just as a refresher, you could look up on any periodic table for carbon, you would see in the periodic table the atomis-- well, most periodic tables will give you the atomic weight, which is the weighted average of the different isotopes of carbon around. But in general, the atomic weight, or the weighted average of the atomic masses of the different isotopes. But carbon, you just remember that the atomic weight is pretty close to 12 atomic mass units. Which means, that carbon has a molar mass of 12 grams per mole. Or if you have a mole of carbon molecules, it will have a mass of 12 grams. We do the same thing for the hydrogen and the oxygen. Hydrogen has, whether you take a single isotope or you take the weighted average, its atomic weight or mass, depending which 1 you use, is pretty darn close to 1. And so hydrogen's molar mass is 1 gram per mole. There's some decimals here if you look it up on a periodic table, but I just remember carbon as 12, hydrogen is 1, and then finally, oxygen is 16. So oxygen's is approximately 16 atomic mass units. I guess, if you take a specific isotope, atomic mass. If you take its weighted average, atomic weight. And that means that its molar mass is 16 grams per mole. Now we have the number of grams of oxygen, hydrogen, and oxygen. So now we should be able to use this information down here to figure out how many moles this is. So let's do this. So it's 12 grams per mole, but we want to divide by grams because we want this gram to disappear in the numerator. So what we could do is, if it's 12 grams per mole, that's the same thing as 1 mole for every 12 grams. All I did is, I took the reciprocal of this right here. If we have 12 grams for every mole, that's also true that we have 1 mole for every 12 grams. And the grams cancel out. And we are left with 120.1 divided by 12, which is pretty close to 10. So this is equal to 10 moles of carbon. So we know how many moles of carbon we have in 1 mole of eugenol. Now let's do the hydrogen. So we do the multiplication here. And so here we have 1 mole of hydrogen-- if we take the inverse of this, or the reciprocal of this-- has a mass of 1 gram. So really, this is just going to multiply out. So we literally have, we could say 12.1 moles of hydrogen. But because we're looking for formulas, that's pretty darn close to 12. So we should just say 12 moles of hydrogen. And then finally, we have our oxygen. And we have 1 mole of oxygen for every 16 grams of oxygen. 32 divided by-- the grams cancel out, of course-- 32 divided by 16 is 2. So this is equal to 2 moles of oxygen. So if we have 1 mole of eugenol, we have 10 moles of carbon, 12 moles of hydrogen, and 2 moles of oxygen. So we now have the ratio. Or you could even think of, if you had 1 molecule of eugenol, we would have 10 carbons, we have 12 hydrogens, and we have 2 oxygens. And we're done. This is the molecular formula we have for every mole. We could think of it in moles which is a huge number. Or you could think of, for every molecule of eugenol, we have 10 molecules of carbon, 12 molecules of hydrogen, 6 molecules of oxygen. This right here is molecular formula. And the empirical formula is essentially taking this ratio to the simplest terms. And all of these have a common factor of 2. So the empirical formula, we essentially just put this ratio in simplest terms. So we can divide all of them by 2. So let's divide all of them by 2. And you have 5 carbons for every 6 hydrogens. This isn't O,6. This is 2 oxygens. So let me make that clear. I'll have to erase a lot of stuff to get there. There you go. That was 2 oxygens. Don't want to make that blunder. We saw we have 2 moles of oxygen, so this is the molecular formula. And the empirical formula, at least the 2 is still divisible by 2. So you divide all of these by 2. You get the simplest ratio. For every 5 carbons, you have 6 hydrogens, and you have 1 oxygen. Or you can put a 1 right there if you like. And we're done.