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Problem 56

(a) The characteristic odor of pineapple is due to ethyl butyrate, a compound containing carbon, hydrogen, and oxygen. Combustion of 2.78 mg of ethyl butyrate produces 6.32 $\mathrm{mg}$ of $\mathrm{CO}_{2}$ and 2.58 $\mathrm{mg}$ of $\mathrm{H}_{2} \mathrm{O} .$ What is the empirical formula of the compound? (b) Nicotine, a component of tobacco, is composed of $C, H,$ and $N .$ A 5.250 -mg sample of nicotine was combusted, producing 14.242 $\mathrm{mg}$ of $\mathrm{CO}_{2}$ and 4.083 $\mathrm{mg}$ of $\mathrm{H}_{2} \mathrm{O} .$ What is the empirical formula for nicotine? If nicotine has a molar mass of $160 \pm 5 \mathrm{g} / \mathrm{mol},$ what is its molecular formula?

Answer

a) $\mathrm{C}_{3} H_{6} O$

b) Above

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## Discussion

## Video Transcript

seeing this problem we air given to persevere in the first part. We're given thiss compound it help your chariot, which contains carbon, hydrogen and oxygen. And we're saying that the compassion off two point seven mini gram of this it'll beauty area producers six point three two milligram off carpet outside and took one five milligram off Hydra isn't have to find out the empirical formal of the compound. All right, so, um, before we solve this problem, lis, look at the steps will follow to solve it. So the first step here will be we'll find the number ofthe malls off Sciutto and issue which is produced from the compassion and from the number of moles of Syrian is tool. We will find the number of most ofthe carbon and hydrogen so we'LL find a number of most ofthe carbon in Soto and we'LL find the number most ofthe agent age tool and from this number of moles will find their massive that missed the mass ofthe carbon and the massive fight Rosen in Soto who's prettiest and since that it help you tear it is combusted too produced on li carbon dioxide and water. That means the mass of carbon hydrogen and we will calculate from this number off malls offs organise door that is the mass ofthe carbon and hydrogen in it'LL beauty. Right. So that way we can find the mass ofthe carbon hydrogen in the original sample or it'LL butor it. Then we will convert those masses in it'LL be a tirade Are those mice of carbon and hydrogen? It'll beauty right into their number of malls And then we will divide each number of moles. May the smallest number of malls to get the simplest hole number issue of most and in this case, are in the Step three. What we'LL do is here not only carbon hydrates and we will include since we have oxygen here also, since we are producing oxygen so we had given and the total mass of the tale beauty read so well of Subtract the mass of carbon and hydrogen from the massive little beauty did to get the mess off oxygen. And this way we'LL know the mass of carbon, hydrogen and oxygen And then we would find ah we'Ll find there, um number of bowls and then we'LL divide each number of moles by the smallest number of malls to get the simplest ratio are simple Asshole number shop the malls and from the simplest hole number issue we confined or deter mined the empirical formula off late A little. Great. So start either for us one Here, sir. Step one is we'll have to find out the number of most off carbon dioxide and a stool produced So we just do it. We just divide the massive Soto produced by smaller mass Maciver Muller must will give us the number of malls of superheroes and same way for the number of mull Selfish too. We divide the massive which to produce the bay smaller mass to get this number of most. Now, in step two, we will find the number of most ofthe carbon and hydrogen in those number most of Theo to manage tour. So since in one hour we can see that in one molecule of pseudo, we have only one atom off. See, that means one more of pseudo well produced one mall off carbon. That means the number of balls off Soto is also the number of most ofthe Kurban now from this number of most ofthe carbon, we confined a mass of carbon which is produced there simply were just multiply this number of moles by the molar mass off carbons. Since we know that number of malls is equal to mass over Moller Mel, that means mass is equal to number of most times smaller mass. And this is the mass ofthe carbon which is produced in cierto and in the same way we will find the number of months off Agent H two. And since in one ah molecule of history, we can see we have two each or to hide rosen atoms. That means in one mole off his tour will have to matloff hydro's, and that means will multiply the number of balls off each tour by to get the number of malls off hydrogen. Now, this is a number of months off treason. And from here we'LL find a massive hydro than in ah, water or massive entries and produce has the same way. We just multiply this number of most of hydrogen and by the molar mass of hydrogen get the massive hydrogen produced. So now we know the number of the mass ofthe carbon and massive hydrogen produced, and these are also our mass of carbon and hydrogen in the little beauty it since it's Alberta is completely combusted to produce commandoes and hydrogen on water That means the mass of carbon had risen Irrigating here at the massive Khurana had risen in our it'LL Beautiful dick. So now we will ah will deter mined the mass of carbon and hydrogen as we got in the the mass of carbon Henderson in the products. So these are massive head resident carbon and it helped it also and then will deter mined the mess off oxygen It'll booted by subjecting the mass ofthe carbon and hydrogen from the massive withheld beautifully to get the mass off oxygen in it'LL be great Now we know the mass of carbon we know mass of hydrogen in no mass off oxygen And now we'LL find out the number of malls off each ofthe thiss So here is how we find the number of multi Just divide each mass Ah, by their moral Irma's. So for carbon, the molar mass is twelve point all One way we divide them massive carbon by smaller months to get this more and same where we find out the number of most of high treason and oxygen. And then in the next step, we will divide each number of malls by the smallest number of malls. And here you can see there, the smallest number of Moses, this one that Mr Divide. Each number of malls made the smallest number of malls to get more ratio. And here is our moral issue. So here you can see that for carbon, their issues three for hydro zeros five point nine seventy is close to six. And, well, just as a meat as six and four oxen, it's one that men's. The ratio here is first see H or their issue is three six one. That means, um so from their issue, we confined our them pickle formula. And we're going right. You see, three, eight, six. Oh, since our issue is three six one, we'LL just write to see three It's six Oh, as our empirical formula. So this is the empirical formal off it'LL build right? No, I'm off dourness problem. In the second problem, we're given a sample off nicotine, which is a complaint of tobacco and is composed of carbon, hydrogen and nitrogen and were given a specific massive sample off nicotine combusted producing governments. And I'd rosen water and we have to find out the m brickell formal off nicotine. So there's the same procedure as the previous problem. But in this case, we have a little extension where we're given the molar mass of the nicotine and they have to find out the molecule of formal. So start finding out the empirical formal of recording first following the previous proceed eoe. So first, what we do is we find out the number of also sealed manage to as before, which is divided the massive sciutto and age to abi there, Mohler masses to get the number of most ofthe theater in its tour. And then again, we shall we find out the number of most ofthe Carbone inside here too, which is same our number of also Soto as one molecule of Seo to convince one atom of carbon. That means the number of most of theater is same as number of C and from the number of malls off. See, we find a massive since your toe, Mr Marty, play this number of malls by the molar mass of carbon to get the mass ofthe carbon produced, say, where we find the number of most of hydrogen in age tour and since in one is too we have to age. That means one more office too will produce two more off Ah ah h And that means this mole off Vegeta will produce two times the small off hydrogen gas and this is the number of most of hydrogen produced and we just multiply this by the more mass of hydra sent to get the massive hydrogen produced. Now we know the mass ofthe carbon and hydrogen produced, and from here we will find the mass ofthe nitrogen. So since the nicotine is being combusted too produced, see it when it's too. Only that means the mass of carbon and hydrogen in see what When it's tool is also the mass ofthe governor had risen in nicotine. So we assumed this messes and carbon and hydrogen in decoding. And then we subtract thiss masses from the mass of nicotine to get the mass of nitrogen. Now we know the mass of nitrous and we know that now, even though the mass of carbon, hydrogen and nitrogen and what we'LL do is we will find out the number of malls off each element just by dividing each mass by their Mueller masses. So we divide each mess by their Mueller masses to get the number of most ofthe carbon, hydrogen and nitrogen. And then we move to our next step, where we are divided east number of moles by the smallest number of months to get the simplest race you. So the simplest one number issues we Ah, we divide each number of most by the smallest one and we get for carbon their issues five, four hundred years seven and for nitrogen is one. So the simplest hole number issue here is five seven one. And from here we can easily find out the empirical formal off nicotine. And here is our empirical formula, which is C five eight, seven n. Since we had five, carbon seven had risen and one night chosen the simplest one number issue there. So this is the empirical formal off in the nicotine. Now, from here we can find out the molecular formula of nicotine, which is simply we put an end over this empirical formula. Are in Is the Moler master molecular weight off nicotine over its empirical formal away and in should be and must be whole number multiple. That means if we get a fraction off in Well, ah, John Sener. The nearest hole number as the veil off end. So we're given Ah, the molar mass or the molecular weight of nicotine. We have to find out Ah, the empirical formal await of nicotine. Get the value ofthe end and there's very simple howto find them pickle formal Await. What we do is we simply add the atomic weight off each he check in prison. So we have carbon here and car bombs at iniquitous development. All one and we have five carbon. That means multiple ID's been five. Then we have seven had risen and we multiply the hide Rosen's atomic weight by seven. And then we have, um we have night rose and so this will not be Amy. It is Graham Barmal since all the values are given in. So since you're given the molar mass of nicotine, we'LL have tto consider the Moler mass off each at present. And if we're given the molecular weight off nicotine In that case, we had to consider the atomic mass unit off each atom present Okay, so no, That way we find out the Moler mass off the of them bagel formula, or we find out them pickle for Muay. Now we know them brittle formula. Wait and we will simply divide the molar mass of nicotine. How much is one sixty and were given one sixty plus minutes. Five. We just ignored those past satisfy, because that will not give us that much difference in values. We just consider it one sister Graham Permal, as the nickel in smaller mass. And we divide that by the empirical formula mus off nicotine. I don't give us one point nine seven. It is close to two. So our molecular formula will be well. Just replace the value ofthe iness too. And that means they multiply each of these by two we had. Now we have, ah sit in its foreign and toe. And this is the molecular formula off nicotine

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