The semiconductor gallium arsenide, GaAs, is used in high-speed integrated circuits, light-emitting diodes, and solar cells. Its density is 5.32 $\mathrm{g} / \mathrm{m}^{3} .$ It can be made by reacting trimethylgallium, $\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Ga},$ with arsine gas, $\mathrm{AsH}_{3}$ . The other product of the reaction is methane, $\mathrm{CH}_{4}$ . (a) If you reacted 450.0 g of trimethylgallium with 300.0 $\mathrm{g}$ of arsine, what mass of GaAs could you make? (b) Which reactant, if any, would be left over, and how many moles of the leftover reactant would remain? (c) One application of GaAs uses it as a thin film. If you take the mass of GaAs from part (a) and make a 40 -nm thin film from it, what area, in $\mathrm{cm}^{2},$ would it cover? Recall that $1 \mathrm{nm}=1 \times 10^{-9} \mathrm{m} .$

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## Video Transcript

s O in this problem we're given and compassion reaction off a hydrocarbon which is burned in a limited amount off air and which is formed both Karen monoxide and carbon dioxide. And we had given the mass ofthe cover monoxide, carbon dioxide and water, which is farmed illustration. So in first part of the situation, we have to find out the empirical formal of the compound. So find out them bagel formal of the compound. First, we have to know how many grams off carbon and hide Rosen are in the compound. And we can find out the mass of carbon and hydrogen in the compound. Bye. Calculating their mass in the products which is carbon monoxide, carbon dioxide and each tour. So from carbon monoxide and carbon dioxide, we confined the mass ofthe carbon and from each tool we confined the mass ofthe head risen. So what we'LL do First we'LL find out the number of malls off Cara monoxide, carbon dioxide and water which is produced. From there, we will find out the number of mall off carbon and hydrogen which is being produced and from those number of moles, will find the mass of carbon and hydrogen in Graham and these masses will be the mass of carbon and hydrogen in the original compound. And from there massing original calm bone, we can find the number of malls off carbon and number of most ofthe hydrogen. Then we'LL divide each number of malls by the smallest number of malls to get a simplest hole number. Issue Barbara and hydrogen small number. From there we can find out and them bagel formula of the hydrocarbon. So our first table will be to find out the number of mole off each protect. So the number of full of carbon monoxide produced will be the mass of carbon monoxide, which is zero point four six seven gram over the molar mass of carbon monoxide, which is twenty eight point one Grandpa Ramon. And it will give us a value ofthe sirrah point zero one six seven more Now, since you can see that in one molecule of carbon monoxide, we have one carbon atom that means in one well off carbon monoxide. We'LL have one more of carbon and in parts around six seven Mall of caravan outside we'LL have the same number of mall of carbon, so the number of all of carbon here is also thereupon zero on six seven more. And from here we can find the mass ofthe carbon which is being produced in the form of Kara Monoxide, which will be just the number of mall's times. The Moler mass off Carmen, which is twelve point or one cramp our mall. It will give us a hello off zero point two zero zero Graham. So this is the mass ofthe carbon which is being produced in the form of carbon monoxide. Now we'LL find the mass of carbon in the form off carbon dioxide. And for that we'LL find out the number of malls off carbon dioxide first, which is again the mass of carbon dioxide produced over the molar mass of carbon dioxide, which is forty four point zero one. Cramp our mall and this will give us a value off zero point zero one six six mall again. In one molecule of carbon dioxide, we have one carbon. That means in this in a in a certain number of mall of coronary said we will have the same number of mall of carbon dioxide. That means this is the number of mole off carbon. In this, most malakar on our side and from air Recon directly find out the mass ofthe carbon here which will be the number of mole off carbon and carbon dioxide, which is Europe on zero on six, six more times the molar mass of carbon, which is still point one gram per mall. And from here we will have again the same a Mondo off Carbone in Colorado City. So this is the amount ofthe carbon which is being produced in the form of carbon dioxide. So the total carbon in the original hydrocarbon will be the some off the carbon produced in the form off carbon monoxide and ah ah, mess of carbon, which is produced in the form of carbon dioxide. So the total mass off Carmen will be point to Graham plus one two zero zero. Graham, we should give us a pint for Syria's program Carbon. So this is the mass of carbon. Now we'LL find out the mass ofthe hydro zin. So for that, we need to find out the number of more ofthe water first which is being produced. So the mass of water which is produced is, as you know, partner four five zero Graham and the molar mass of water is eighteen Point Cyril wants six. Grandpa. Our mall. So from here, we'LL have a value off. Is there a part zero to five more. Now, this is the number of Mall of H two, which is being produced. That means and again, we can see that in one molecule of phase two we have who had risen statements in a certain number of moral office tour. We'LL have good times that mole off head Rosen. So the number of ball of hydrogen will breed two times zero point zero two five mall, which will give us, um zero point zero five is serum all ofthe head rosen. Now, from here, we can find the mass ofthe address and Rachel. But just this number of most time, um, the molar mass of Hydra Zen, which is one point as Syria zero eight gram bar more. So it will give us a value off, um, again, zero point approximately the same massive hundreds. And so this is the mass of hydrogen, which is being produced in the form of his two. And since, um, this is formed from the compassion of the original hydrocarbon. That means this is the mass of hydrogen in the origin. Hydrocarbon, too. We know the mass ofthe Carbone and head rose. And in the original hydrocarbon. So from here you can find the number ofthe mall of carbon hydrogen in the original hydrocarbon. So we will write the mass ofthe carbon, which is, as you know, blind for Syria zero and mass off hide. Rosen is zero point zero five zero Graham. So these are the mass of carbon and hydrogen in the original hydrocarbon. Now we'LL find out their number of malls in the origin hydrocarbon. So the number of Matloff Carbone Well, hey, zero point four zero zero graham over the molar mass of hydrocarbon Stuart ponder on gram bar more and it will give us value off. Ah, zero point zero three three more And the number of mole of hydro season will be the massive head rosen over the molar mass of had risen and she'LL give us a bell off zero point zero five zero more. Um, so now we'll divide each number of mall by the smallest number of moral And for American, see that the smallest number of mole is thiss so we'LL divide each number of more by the smallest number of Malta Get the simplest hole number Asia So the whole liberation for carbon will be zero point zero three three mall move over zero point zero three three more which will give us about off one and for hydro's and it'LL be syrup find zero five serum all over zero point is you know three, three more which will give us valuable one point five two. So since we need a simp asshole number Atia And since this is not a whole number, we have to go convert this tree hole number and the smallest possible hole number. We can convert it to his way, multiplying by two which will give us approximately three year. And since you're multiplying this by two, we have to multiply the ratio of carbon by two also, which will give us well off too. So that means the simplest hole number issue of carbon and hydrogen here is tour is two three. That means the empirical formula will be see too age three. So this is the empirical formula off. The hydrocarbon were given here now in the second part of the question, we have to find out the mass off oxygen which is provided the as you know, that from the love conservation of mass on the mass ofthe reactant CE is equal to the mass of products. So we know that all the masses of products and we know the other reacted mass. So just subjecting the mass of the other reactor and from the sum of the mass of products we confined the mass off oxygen, which is we're just taking part in this reaction. The massive oxygen will be the sum of the mass of the products upon for six seven gram class zero point seven three three Graham class zero point four five zero grams that this is the total mass of the products. Mine is the mass of other reacting or the hydrocarbon which is so refined four five zero Graham. And this will give us a value off one point to Syria. Zero Graham Oto. That means this is the mass off oxygen which has taken part in the reaction. Now, in third part of the problem, we have to find out how much more ox is in. We would require toe completely combusts The hydrocarbon sentence of complete compassion will not have any carbon monoxide being produced. Ten minutes There will be no carbon monoxide and all will be carbon dioxide. That means for complete compassion. We need toe convert the carbon monoxide which is produced, um, do carbon dioxide. And if you want to balance this creation Ah, we have to put it to here. And then we have to put, um yeah, and two here. Then we'LL have to carbon on his sign and for oxygen on the site. This is our balanced reaction in question. That means two I'm a true convert to true molecule of carbon monoxide. Our woman of Carolina sign. We need one molecule or one mole off oxygen. That means we have to know how many carbon, how many? Most of carbon monoxide. We have being bored, Joost, in the reaction given and from there we have to find out how many more oxygen we we would require for a complete ah, compassion of the hydrocarbon. So they have calculated the number of mall of carbon monoxide, which is being I'm being farmed here, which was so here it is. So this is the number of mall of carbon monoxide about here. So zero point zero one six seven more So to convert this much more of carbon monoxide, we will need since to convert to mull of carbon monoxide. A convertible of Caroline aside, we need one more off oxygen that Mr Convert. This much more of carbon monoxide will lead half off the small off oxygen which is ultimately zero point zero zero eight for more off oxygen. So we need this much more off oxygen for complete our toe. Just convert the excess carbon monoxide which is being produced here. So we have to find out the mass of oxygen forthis much more off oxygen. So the massive for oxygen to convert the excess carbon monoxide. They called her the number of mole off oxygen which is required this barn zero zero four more on the molar mass of oxygen, for although it is started to cramp our mole, which will give us a value off zero point two six seven gram or two. So this is the massive oxygen which we need in excess. Ah, to convert, um, all the carbon monoxide being produced to carbon dioxide. So the total amount of oxygen which you need for a complete compassion will be equal to the massive oxygen which wass provided. Which is this. This must oxygen. We were Ah, we were being provided in the reaction. So the total will be one point to Syria. Zero Graham glass this much oxygen which you need to convert the carbon monoxide being produced plus one, two, six, seven gram. The total will be one point four six seven gram oxygen. So this is the massive oxygen which would have been required for a complete compassion of the hydrocarbon.

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