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# Another mass composition problem

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I said I would get you a more interesting mass composition to empirical formula problem, one that doesn't just have a straight-up 2:1 ratio. And so here it is. I have a bag of stuff. Or let's call this a bottle of stuff. Maybe it's in its liquid form. And it happens to be 2.04% hydrogen, 65.3% oxygen, and 32.65% sulfur. What is the empirical formula, what's our best stab at the empirical formula, of this substance? So what we would do, like we do in all these problems, let's just assume we've got 100 grams of the stuff. So we have 100 grams of the stuff. So we assume 100 grams. Let me do that in a good yellow. So let's say, assume I have 100 grams. How many grams of hydrogen do I have? If I have 100 grams total, 2.04% of that is hydrogen, so I have 2.04 grams of hydrogen. I have 65.3 grams of oxygen. And I have 32.65 grams of sulfur. Now, what we need to do now is figure out how many moles of hydrogen is this. How many moles of oxygen. And how many moles of sulfur. Then we can compare the ratios and we should be able to know the empirical formula. So how much 1 mole of hydrogen? What is the mass of 1 mole of hydrogen? Let me write that. So 1 mole of hydrogen. Well we know what the mass number for hydrogen is. It's 1. And especially, the atomic weight, also for hydrogen, if we were to take it on Earth. The composition, you pretty much just find hydrogen nucleuses. If it's neutral, it has an electron, but it has no neutrons. So it has an atomic mass of one atomic mass unit. So one mole of hydrogen. If you have a ton of hydrogens together, or a mole of them, not a ton, I shouldn't say, you have a mole of them. you have 6.02 times 10 to the 23 hydrogens. Then you take hydrogen's atomic mass number in atomic mass units. And you say, well, it'll be that many grams of hydrogen, right? So if you immediately look up here, if we have 2.04 grams of hydrogen, how many moles of hydrogen do we have? Well, one mole is one gram, so we have 2.04 moles of hydrogen. Notice, this said what the mass of the hydrogen is. This tells us how many hydrogen molecules we have. Remember, this is 2.04 times 6.02 times 10 to the 23 hydrogen atoms. Moles of hydrogen. Maybe I should write that down. So one mole of hydrogen. There you go. And then oxygen. One mole of oxygen. Oxygen's mass number, in case you forgot, is 16. Right there. Oxygen's mass number is 16. So one mole of oxygen has a mass of 16 grams. 6.02 times 10 to the 23 oxygen atoms has a mass of 16 grams. So how many moles do we have here? Let's see. So if we take 65.3 grams of oxygen. And we have 16 grams per mole, so you divide by 16. It equals 4.08125. I don't want to get too precise here. But let me just write that. 4.08 moles of oxygen. So I'm going to write that in oxygen color. So I have 4.08 moles of oxygen. And then finally, sulfur. What is sulfur's atomic mass? The one thing I'll never forget about sulfur is its smell. There's a city in Louisiana which we used to drive to all the time -- I think we had some family friends there --called Port Sulfur. And they did a lot of sulfur processing there. And lucky for the residents, at least at the time -- I apologize if they fixed the issue -- it smelled like sulfur, which smells like rotten eggs. But anyway, one mole of sulfur. One mole of sulfur. So sulfur's atomic mass is 32 atomic mass units per sulfur atom. So a whole mole of it is going to have a mass of 32 grams. So a mole of sulfur-- not a mule. Maybe I should invent a new unit called the mule. So a mole of sulfur is 32 grams. So how many moles do we have? We have a little bit more than one, but let's be precise here, because everything else is a little bit of a decimal. So if we have 32.65 grams of sulfur and we divide by the number of grams per mole -- divided by 32 grams per mole we have 1.02 moles of sulfur. This was hydrogen up here. So here, you should hopefully see a pretty good ratio, here. For every one sulfur atom-- I mean, the ratio worked exactly out and that's because I did this problem before. I actually made up this problem before we worked, so I made it so the numbers worked out. But one mole of sulfur, for every mole of sulfur, so for every 6.02 times 10 to the 23 sulphur atoms, you have two moles of hydrogen, right? This ratio is 1:2. Two times 1.02 is 2.04. And then, for every one mole of sulfur, you have four moles of oxygen. Right? Literally, if you multiply this times four you get 4.08. So the ratio of hydrogen to sulfur to oxygen is for every one sulfur, we have two hydrogens and we have four oxygens. So the empirical formula of this is H2. And then we have one sulfur. And then we have four oxygens. And this is sulfuric acid, one of the things you would least like poured on you most of the time. Anyway, hope you found that useful.