Empirical formula from mass composition edited

0:00- [Voiceover] What I want to do in this video is start with mass composition and then see if we can figure out the empirical formula of the molecule that we're dealing with based on the mass composition. So let's say that we have a bag, and we're able to measure that this bag is 73%, it's 73% mercury, and it is the remainder of the bag, 27% chlorine.

0:26Now based just on this, can we figure out the likely empirical formula for the molecule that we have in that bag? And I encourage you to pause the video and try to see if you can figure it out on your own. Well, one way to think about it, well let's just assume a number.

0:43This is just all the information we have, but let's just assume we have 100 grams of it. We could assume 1,000 grams or 10,000 grams or 57 grams, but I'll pick 100 grams because it will make the numbers, it will make the numbers easy to work with in our head. So let's just assume, let me make it clear that I'm assuming this, I'm going to assume that I have 100 grams of this molecule that is 73% mercury and 27% chlorine.

1:09And if I assume that, that means that the 73% that is mercury is going to be 73 grams, and the 27% that is chlorine is going to be 27 grams of chlorine. I'm going to make it clear this is mercury, and this is chlorine. Now I just need to think about, well how many moles of mercury is 73 grams?

1:34And how many moles of chlorine is 27 grams? And to do that, I'll just look up this periodic table right here. I have the atomic weight, which is of course the weighted average of the atomic masses as kind of found in nature. And the atomic weight here for mercury is 200.59.

1:53So that means, so let me write this right over here, so one mole of mercury is, we could say, is 200.59 grams. And similarly, we could look up the atomic weight for chlorine. Chlorine, right over here, 35.453, and so we could say, one mole of chlorine, and once again this is a weighted average of all of the isotopes of chlorine as found in nature, and I guess we'll just go with that number.

2:32So one mole of chlorine is going to be 35.453, 35.453 grams. So given this information right over here, how many moles of mercury is this, roughly, and how many moles of chlorine is this, roughly? And I say roughly because getting an empirical formula from measurements of mass composition, it's going to be necessarily a messy affair.

3:00It's not going to come out completely, the numbers aren't going to work out completely exact, so that's why I said roughly. So how many moles is this? Well this is going to be, this is going to be, 73 over 200.59 of a mole. If a mole is 200.59 and we have 73, this is the fraction of a mole that we have.

3:22Moles of mercury. And remember, moles are just a number, Avogadro's number of something. But let's just figure out what it is. So, so if we take 73 divided by 200.59 we get .36, I'll just say 0.364, and once again, this is, so approximately 0.364. That's how many moles of mercury that we have, and we could do the same thing for chlorine.

3:59This is going to be 27 over 35.453 moles of chlorine, which is approximately equal to 0.762. Now, moles of chlorine. So, what's going to be the ratio of mercury to chlorine? Or I guess I could say, since chlorine, there's more of it, chlorine to mercury, remember, this is just a number.

4:29When I say 0.762 moles, this is just 0.762 times Avogadro's number of chlorine atoms. This is 0.364 times Avogadro's number of mercury atoms. And so this, we can literally think of this as the ratio. This is a certain number of moles, this is another number of moles.

4:47Well, what's the ratio? Let's say, what's the ratio of chlorine to mercury? Well, you can eyeball it. It looks like it's roughly 2:1, and because of that, you could say, well this is likely to be, so likely for every mercury, you have two chlorines. So, based on these measurements right over here, it's very likely that you have mercury two chloride.

5:17And the reason why it's called mercury two chloride is because, well, I won't go into too much detail right over here, but chlorine is highly electronegative. It's an oxidizing agent. It likes to take other people's electrons, or hog other people's electrons. In this case it's hogging, since there's, each of the chlorine likes to hog at least, likes to hog one electron, so in this case, two chlorines are going to hog two electrons, so it's hogging two electrons from the mercury, when you lose electrons, or when your electrons are being hogged, you're being oxidized.

5:51So the oxidation state on mercury right over here is two. Two of its electrons are being hogged, one by each of the two chlorines. So this is mercury two chloride, where the two is the oxidation state of the mercury. But this is what we likely have, the ratio, we have two chlorines for every one mercury, roughly.