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# Empirical formula from mass composition

## Video transcript

Sal: What I want to do in this video is start with mass composition and see if we can figure out the empirical formula of the molecule that we're dealing with based on the mass composition. Let's say that we have a bag and we're able to measure that this bag is 73 percent, it's 73 percent mercury and it is, the remainder of the bag, 27 percent chlorine. Based just on this can we figure out the likely empirical formula for the molecule that we have in that bag? 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 is let's just assume a number. This is all the information we have, let's just assume we have 100 grams of it. We could assume a thousand grams or 10,000 grams or 57 grams, but I'll pick 100 grams because it will make the numbers easy to work with in our head. 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 percent mercury and 27 percent chlorine. If I assume that that means that the 73 percent that is mercury is going to be 73 grams and the 27 percent that is chlorine is going to be 27 grams of chlorine. Let me 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 and how many moles of chlorine is 27 grams. To do that I'll look up the periodic table right here. I have the atomic weight which is the weighted average of the atomic masses that's found in nature. The atomic weight here for mercury is 200.59. That means, let me write this right over here. One mole of, one mole of mercury is, we could say is 200.59 grams, 200.59 grams. Similarly we could look up the atomic weight for chlorine. Chlorine right over here, 35.453. 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. I guess we'll just go with that number. One mole of chlorine is going to be 35.453, 35.453, 35.453 grams. Given this information right over here how many moles of mercury is this, roughly, and how many moles of chlorine is this, roughly? I say roughly because getting an empirical formula from measurements of mass composition is going to be necessarily a messy affair, it'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? This is going to be 73 over 200.59 of a mole. If a mole is 200.59 we have 73, this is the fraction of a mole that we have, moles of mercury. Remember, moles are just a number, Avogadro's number of something, but let's just figure out what it is. 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. We can do the same thing for chlorine. This is going to be 27 over 35.453 moles of chlorine, which is approximately equal to, get our calculator out. 27 divided by 35.453 is equal to .76, I'll just say two. So 0.762 moles of chlorine. What's going to be the ratio of mercury to chlorine? Or I guess we could say since chlorine, there's more of that, chlorine to mercury. Remember, this is just a number. When 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. We can literally think of this as the ratio. This is a certain number of moles, this is another number of moles. Well what's the ratio, let's see. What's the ratio of chlorine to mercury? Well you can eyeball it, it looks like it's roughly two to one, and you can verify that if you take that number and you divide it by .3639, and once again I'm just going to get the rough approximate. You can see it's pretty close to two. So when you see something like this the simplest explanation is often the best. Okay, there probably will be some measuring error right over here, but you can say that it looks like roughly, this is what I'm talking about when you're trying to find the empirical formula for mass composition it tends to be a rough science. You can say roughly the ratio of chlorine to mercury is two to one. You have two chlorines for every mercury. And because of that you can say this is likely to be, so likely, for every mercury you have two chlorines, you have two chlorines. Based on these measurements right over here it's very likely that you have mercury two chloride. 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 electrons. In this case it's hogging, since each of the chlorine likes to hog one electron, 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, so the oxidation state on mercury right over here is two. Two of its electrons are being hogged, one by each of the two chlorines. This is mercury two chloride, where the two is the oxidation state of the mercury. This is what we likely have. The ratio, we have two chlorines for every one mercury, roughly.