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Problem 92 Hard Difficulty

Calculate the mass of carbon in grams, the percent carbon by mass, and the number of individual carbon atoms present in each of the following samples.
a. 7.819 g of carbon suboxide, $\mathrm{C}_{3} \mathrm{O}_{2}$
b. $1.53 \times 10^{21}$ molecules of carbon monoxide
c. 0.200 mole of phenol, $\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}$

Answer

A.$2.076 \times 10^{23}$ atoms $\mathrm{C}$
B.$1.53 \times 10^{21}$
C.$1.20 \times 10^{23} \mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}$ molecules

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Video Transcript

All right. So here we have the green, um, compounds carbon containing compounds we have over here feen on, which is like benzene with an alcohol group. If that Since Steve our door about it, We have carbon monoxide and, like try carbon dioxide known ascribe in Suboxone. So listen to where you worry too much about the names, but let's just tryingto solve some things over here. So they have access to find mass percent of carbon just of carbon, which let's just quickly remind results of that formula. It would be basically the mass of carbon over the mass of the molecule. We simplify it well, it's no m for molecule C for carbon. Let's go a step further. So it's not just any regular mess. It's the mass of one mole of compound. So we know that my physical went to malls multiplied by more maps and we are always working in one war. Yes, always. One more. This is the standard matloff compound are a molecule and one mole of whichever element carbon here. So you just multiply the moans by the molar mass of carbon for the more massive compound, you know? Okay, so that's how we're gonna sell from the molar mass or the mass percent of carpet. So we're also looking for, um, the number of Adam's Karpin's, so to find that number of Adams number of atoms is always related to number of mall kills. So let's just first, I copied down the number of molecules formula, which is just n for malls multiplied by N A. I have a gorgeous constant. Okay, this right here will give us number of molecules, but we then have to multiply by. I'll just call. You have to multiply by the particular number of carbon atoms in the compound. So just put brackets and see number of carpets. Yeah, love carbons, right? And where they're also asking us lastly, for the mass of carbon Jefty White weird. So here is the mass of carpets of oxide. But they want to know the mass of just the carbon in this compound. So might be a little tricky, but the way was thought for that is just take the total mass and multiplied by the mass percent of carpet. So simplest way to do it right. So let's get started of a lot to do. So we must find number Adams of carbon mass carbon and the mass percent carpet. Okay, um, so right now we have this compound. We were given total mass. So let's start off by finding the mass percent. So I have simplified the mass percent home formula, So these basically cancel out. It's okay. All we're left with is mass of carbon over mass of molecule C for car pump it ups, but too confusing. Let's just call it Mom too. So you're going to need our, um, periodic table. But I know the mass small amounts of carbon You should know as well. It's just 12 the most balconies units, because this is a mass we're talking about the mass equivalent toe a molar mass. I just use the property. It's grams and the molar mass of those carbon dioxide 68. Then if you were to multiply each of these Mueller masses by, um, one more, then that's how we get them to be, Gramps. But since it's just one moment, cancel that out. No. This gives us a mass percent of 52 0.9. There we have it. The first answer, 52.9%. So then to find the mass of carbon will take the total mass intrudes like seven points eight 19 I'm also quite that by the mass percent in a decimal, not in, you know, person thing. And it's his grams. This will give us a massive carbon of being four point 14 rooms. Okay. And lastly, we're looking for Adams number of Adam's, so just use this space number of Adams. It's a club. Went to malls. Times have a guy just constant times number off carbon atoms in one compound. Oh, so we I don't have morals, but we do have we do know that most is equivalent to massive Imola mass. We have the mass. And here this would not be the massive carbon. No way. This is, you know, the mass of the compound. We're gonna just for this to be, like just carbon by multiplying by this factor over here, this is still total moles off the compound. This factor will adjust it to just being carbon. That make sense. I think it does. So that's an A from a gorgeous number times number of carbon atoms, which it's just this little sub script, which is three. Okay, so it's just quickly plunged this all these figures in have mass over molar mass again of the whole compound, which is over here. We sought to be succeed. Ain't DRAMs and grams per mole. I'm not gonna write out. I got this constant, you know, it's six point. Oh, it's 6.22 times 10 to the 23 and then multiply all by three to give us a very large number. It's gonna get messy. Is all equivalent to two point 07 times tend to the exponents 23. So, yes, but you're so yeah, these that this would be Adams of carbon. Just highlight. I hope this works. Oh, yes, it does work. These are the answers. I agree. Right? Let's move on. As tried to use a bit quicker. All right, so here we have a number off carbon monoxide molecules so we can straight ahead, jump into number of Adams, whichever, you know. So the my recorder we go number Adams is equivalent to number of molecules. Judges hop right in to see. This is this 11.53 times tend to the explain it. 21 cripes, that's it. Here we have per one molecule of carbon monoxide, always the exact same one carbon. So it's a 1 to 1 ratio. Here there's nothing which means one. So, yeah, I just think about the spatially. Every molecule of carbon monoxide has one molecule or one atom of carpet. So yeah, just just copy and paste straightforward. If there were to be like a to die carbon monoxide, you know that sort of thing. If we're to be that, then we would multiply this by a factor of two. No, we're going Teoh, find mass percent. Let's do them here. So in mass percent of just carbon. So let's quickly remind ourselves it's basically mullah maths of carbon over molar mass of the compound. Malkin. Because we even multiplied by 11111 And that gives us a mass Great. So here we have 12 divided by when you which will give us 42. Who are you? 2.87 Her sense right now, let's find must find the total mass worry. You know, less confusing. You will just multiply this total mass, but mass percent carbon to find massive carbon itself. So we know that mass is equivalent to moles multiplied by, um, Momus. And we all have moments, but we know that malls is equivalent Teoh Number of molecules. Slush member of alums, gemstone A way out. The number. So most sickle to number of molecules. Oh, for our cadres number. And then let's not forget molar mass right to the Momus. We already figured out to be 28 so if we just collect all of those figures in, we would get a total mass. Uh mm. Give me a second to use my calculator to find them. Right? So that is what the toll mass of this is you have went to. So then if you multiply that by the mouse percent of carbon, we get 0.0. It's a bit of her. Be a 0.0 305 05 When you see 15 continue right. Also here we could have got another out, you know, even straight away found the mass of carbon by multiple by the moles of Karpin. Since we know the exact well since we know the atoms of carbon and our bodies number well, the molar mass of carbon that would have straight away given us surprise to euro three to Europe from five. That's another potential path, but same number. So it doesn't matter now. We have a penal or C six h 60 and we have a number of moles so we can find Let's start off with a fine moles now of carbon, Can't you just equal to the total moles multiplied by, you know? Ah, factor of you know how many moles of carbon are there para Mull Chul. So your point, you most hall and let's find that factor. So as you can guess the factor six to snow for one wall of fino. We have sex moles of carbon atoms. I just want to put up by Big Six and we got most of carbon to being 1.2. So now we can take this number to find massive Karpin using your mouse and number of atoms of carbon straight without even ever using total anything or anything. Master Mel's of the compound. Everything here is just in numbers of carpet. That's why it can be a bit tricky knowing whether is that massive Karpin or mass total. So just try to keep it. You know, Constant to try those keeper so mass of carbon now is equivalent to the moles of carbon. Just 1.2 occupied by the molar mass of carbon, which we know is 12. So that leads us to finding it. 14. But if you know where to carry on all of these digits, we would get 14 for one grams. Come try include some units, grams per mole. So similar mass. And this is malls. Yeah. So now let's find number one again. Number of carbon atoms. Yeah. Okay. So, like, for this question, there's, like, many different ways that we can go. Just choose one and stick to it. Right? So in a number of Adams is equivalent to malls, which we know it was 1.2 months time that we got just a number. Jenny Mark went right out. And a so then that will lead us to. So when I point to true six times 10 to the exponents. 23. Now, lastly mass percent. Last percent of carp in. Of course. So you remember from above it's the mass percent of the element or the molar mass of the elements This is through the shortcut. The molar mass of the compound of the element over the mole mass of the compound, which you can calculate. I'll let you take you like that. That I pregnant. Okay, Actually, the molar mass of the combat is like 94. This gives us mass percent. See the years, Where is hungered sexual cuts? So it's actually 12 times six something. So, yeah, let's try to. So there's how do explain. So there's one mall. So we did one more multiplied by more amounts of compound. So in one mole of compound, we have six malls of penal or of, um, Harbin, one more six months. So that's why that's a 72. Mm. Yeah. And there should have been 12 times three, which is 36. Which is why that probably in Hank sent. Mm. Sorry about that. Because then I could Why? More of compound? I'm just three malls off carbon Annam. One mole off carbon atom here. Six months of carbon on, which would lead us to 76 point 57 percent. There we have it. Mean six. That's six

McMaster University
Top Chemistry 101 Educators
Stephen P.

Drexel University

Allea C.

University of Maryland - University College

Morgan S.

University of Kentucky

JH
Jacquelin H.

Brown University