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### The thermite reaction,  \mathrm{Fe}_{2} \math…

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Problem 114

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, principally $\mathrm{N}_{2}(\sim 79 \%)$ and $\mathrm{O}_{2}(\sim 20 \%) .$ In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called "${NO}_{x}$" gases. In $2009,$ the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this? (c) The production of $\mathrm{NO}_{x}$ gases is an unwanted side reaction of the main engine combustion process that turns octane, $\mathrm{C}_{8} \mathrm{H}_{18},$ into $\mathrm{CO}_{2}$ and water. If 85$\%$ of the oxygen in an engine is used to combust octane and the remainder used to produce nitrogen dioxide, calculate how many grams of nitrogen dioxide would be produced during the combustion of 500 g of octane.

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## Discussion

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## Video Transcript

So in first part of this problem, we have to go balance the reaction off the formation ofthe night Greek oxide from the reaction of nitrogen and houses and gas. And also you have to ban is a creation of the formation of nitrogen dioxide from nitric oxide and oxygen gas. So the first twenties, the reaction of nitrous and gas and foxes and gas which will give us nitric oxide, I guess. Soto banning the situation. We can see that we have two nitrous and in the reactant side, but one natural in the production side. So what we can do, we can just multiply this by two tohave to nitrogen in the peroxide. Also. Now we have component resenting the reactor's side and unity in the peroxide. And we have two oxygen in the reactor inside and docks in the port side. That means this's are balanced regulation for the production of nitric oxide. Now will, I don't aggression for in the formation ofthe nitrogen dioxide from nitric oxide in oxygen so nitric oxide will react oxygen to give us nitrous and die aside. Now we have one night risen in both side, but we have one has to three ox is in in the reactor inside and talks in the peroxide. Right? So if we place it too here, we'LL have now for accident in the reactor sign and also to night frozen in the north. Now we have four oxen in the in this side and three olsen in the reactor inside a second. If we since we have now two nitrogen the peroxide well multiplied thesis by two tohave tonight chosen the reactions that also now if he recounted, we have two night rosen in both side and we have Truex isn't blast rocks and four oxen in the reactor sign and times two for us in the product side, that was This is our ballistic question for the reaction of the formation ofthe nitrogen dioxide. Now, in second part of this question were asked to find out how many grams of nitrogen dioxide is nineteen million dawns off *** than the outside. So nineteen milion tons it means nineteen dimes, six don's And we know that one tone is equal to nine o seven, nine hundred seven point one eight five kids genes. We can write it nineteen times generally burst six times and your six tone's names. Nine hundred seven planned. I wanted to fight kid T is one Thanh. So from here we can right this calculation Give us a hello off one point seven two time state with the poor Stan kids he and again if we wantto convert this to Graham, came to multiply this by one thousand gram since one thousand gram is one G and that really was a fellow off one point seven to times the power tired Dana Graham. So this is the amount are the massive nitrogen dioxide in grams for nineteen million Don self um, nitrogen dioxide. Now in Percy of this problem, we have to find out how many grams of nitrogen dioxide would be pretty was during the compassion off five hundred gram off oxygen. So for that first you have to find out how many um also fucked in his five hundred gram off walked in. And from there we'LL have to find out how many moles off oxygen we will require two combust that minimal Zoff octane. From there, we'LL have to find out the massif oxygen which will be required to combust five hundred gramophone then and from there we can find out Ah, how many grams off oxygen will will be used toe form or produce nitrogen dioxide. And from there you can find how many grams of nitro lento said we will have so first period ce we will have a balanced decoration for the reaction of the compassion of walked in like this. So here you can see that Ah, from the balanced equation For the compassion of walked in, we can see Bluemel off Ock ten is combusted by twenty five mall off oxygen that men's So now if we know the number ofthe mall off octane for the five hundred Gamma fucked, then we can use this relation to find out how many more of oxygen we will require for the specific creation. So first you have to find out the number off more off then for five hundred grams of Oakton So five hundred grams octane is the five hundred gram over the molar mass off Ock ten, which is one hundred fourteen point two three. Crump are small and it will give us the number of malls of octane which is four point three eight more now. So from here, you can see that too will opt in, will be combusted by are identical toe twenty five more oxygen that men's four point three eight more locked in will be combusted by or is identical to twenty five over two times four point three eight mall off oxygen, which is equal to, um fifty four point seven. One more oxygen. This is the mass. This's the number of most off oxygen, which you require. Arto combines two four point three eight more all five hundred gram off Ogden. Now, from here you can find the massive oxygen, which is required to combust this much. Um, Stockton. So we can do that by so we can find out the mass off oxygen by multiplying the mall's off oxygen fifty four point seven one mall by the molar mass of oxygen, which is thirty two Grandpa, our mall and it will give us a value off one seven five zero point eight five gram oxygen. So this is the massive oxygen, which you required to combust. Five hundred grandma walked in. Now you're saying that this is the seventy five percent off. Also, this is the eighty five percent all the oxygen in an engine that means So if this is the eighty five percent we confined, what is the wrist off? Um, in the oxygen, which we will use in finding out are how much oxygen we will have for the production of nitrogen dioxide. So we can write one seven five zero point eight five gram is eighty five percent or point eight five. So if we just write it the other way, point eight five or eighty five percent, is one seven five zero point eight five gram. That means so one hundred percent minus eighty five percent is fifteen percent. So the fifteen percent oxygen we will have for the for the reaction off nitrogen dioxide or the food for the production of nectar. And I've seen. So if a seventeen fine if seventeen fifty point eight five gram is eighty five percent or point eight five, that means fifteen percent or point one five is seventeen, fifty point eight five times, point one five over point eight five and it will give us fellow off on three or eight point nine seven nine seven gram. So this is the mass of oxygen. Wait, which will be used for the production off the the nature's Indios. Say so now from here we can find out the value ofthe our deaf. We can find out the number of malls off oxygen for this much mass of oxygen. It's a member ofthe malls of oxygen for dead myself. Oxygen will be mass over molar mass. That means two eight point nine seven gram over the molar mass of oxygen, which is thirty two cramp our mole, and this will give us value off nine point six six ah, more oxygen. So this is the number of mole off oxygen, which will be used for the production of nitrogen dioxide. Now from the balanced equation for the production of nitrogen does that. We can see that one more off oxygen can peruse to mall of nitrogen dioxide. That means we can write one mole off oxygen is identical to two more nitrogen dioxide or produces two monitors in their sight. That means nine point six six small oxygen will produce two times nine point six six mall nitrogen dioxide R nineteen point three one, nineteen point Truan, Moloch, nitrous and day outside. So this is the number of mall of nitrogen dioxide, which will be a realist in this variation conditions. And from here we can find a mass of nitrogen dioxide which will be produced. So the mass of nitrogen dioxide, which will be produced his the number of malls of nitrogen dioxide, which is nineteen point three one more times the molar mass of nitrogen dioxide, which is forty six. Grandpa are more. And from here we will have a fellow off eight hundred eighty eight point for zero graham nitrogen dioxide. So this is the massive nitrogen dioxide, which we'LL have formed, um, in the compassion off five hundred gram off Oakton.