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Problem 68

The complete combustion of octane, $\mathrm{C}_{8} \mathrm{H}_{18},$ a component of gasoline, proceeds as follows:

$$

2 \mathrm{C}_{8} \mathrm{H}_{18}(I)+25 \mathrm{O}_{2}(g) \longrightarrow 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} \mathrm{O}(g)

$$

(a) How many moles of $\mathrm{O}_{2}$ are needed to burn 1.50 $\mathrm{mol}$ of $\mathrm{C}_{8} \mathrm{H}_{18}$ ?

(b) How many grams of $\mathrm{O}_{2}$ are needed to burn 10.0 $\mathrm{g}$ of $\mathrm{C}_{8} \mathrm{H}_{18}$ ?

(c) Octane has a density of 0.692 $\mathrm{g} / \mathrm{mL}$ at $20^{\circ} \mathrm{C} .$ How many grams of $\mathrm{O}_{2}$ are required to burn 15.0 $\mathrm{gal}$ of $\mathrm{C}_{8} \mathrm{H}_{18}$ (the capacity of an average fuel tank)?

(d) How many grams of $\mathrm{CO}_{2}$ are produced when 15.0 gal of $\mathrm{C}_{8} \mathrm{H}_{18}$ are combusted?

Answer

a) 18.75 moles of $O_{2}$ are needed.

b) See explanation for solution.

c) 400.5$g$

d) 121102.8016 $\mathrm{g}$ of $\mathrm{CO} 2$

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## Discussion

## Video Transcript

So in this problem, we're given way and compassionate nation off often junkers like thiss. So you're writing the balance to question off the compassion off Ogden. Okay. C eight h eighteen in liquid form will react Going to find oxygen molecule in gas form and will produce sixteen carbon dioxide and eighteen water whipper. Now, first question here is how many mall so fort were needed to burn one point five mole off, See eight, age eighteen. So from here, you can see that true matloff. Oh, Captain's Since we have a coefficient off to here, we can see that drool off octane is burned by twenty five full of oxygen so we can write two more ch eighteen this barn by twenty five more photo that men's one point five mole are fucked in. We learn by you five over two times one point five more, which will give us a fellow off eighteen point seven five more total eighteen point seven five more photo is required to burn one down five more often. Now, in this second part of this problem, we're asked how many grams off auto are needed to burn ten gram off talked it So as you know that from the reaction in relation, we have to deal with the number of malls off each react under product. That means if we're given any react under protecting mass than we have, first thing we have to do is tow. We could have too convert the mass in the number of most. So you're given Ah, Dean Graham off oct in. That means we have to find out the number of moles off ten. Remove auction. So and you know that the number of bowls is massive or more massage. Ten Grandma and means ten grams over the Moler. Massive fork and which is one hundred forty Ingram, Grandpa, our mall. And this will give us a value off zero point zero eight eight mall. So this is the number of moral function for pain, Grandma Fokin. And now we have to find out how many malls off oxygen is needed to burn this much moral foxton. And from the number of Mall of Oxygen, we can find out how many grams of oxygen we need to burn Ingraham off. Doctor. Now again. Ah, we have seen that to Matloff. Stockton is burned by twenty five more. Okay, Oxygen net means zero point zero eight eight more often will be burned away. Going to find a way to times zero point zero eight eight more, which will give us a fellow off. Oh, one burn zero nine six more auto. So one point zero nine say small boat is required to burn Seo eighty eight more Stockton. And again we can find out the mass off oxygen forthis number of mall of Oxygen, which is simply my way of We have to multiply this number of more by a molar mass of oxygen. So mass off oxygen and one burned zero nine, six more times The more massive oxygen which is thirty two. Since we have oxygen molecule here. Thank you. And this will give us avello off started five point one gram. Right. So this is the mass of oxygen which is required to burn. No, Denver, come off Stockton on the tart bird were given the density of foxton and we have to find out how many grams of oxygen required to burn fifteen Galan off walked in the same thing. We have to first convert this gallant A number of malls and Then we have to find out how many moles off oxygen we need the barn and that animals are locked in and from there from the number of most of oxygen we confined a gram of oxygen required to learn in the fifteen Galan and fucked it. So first we can convert The gallant to the militar says the density is given Ingraham Parmelee. Later we have to find out how many milliliters starting fifteen gallons. So fifteen galan Um, so one gallon is three seven eight five mil Later, that makes fifteen governments fifteen gallon times three, seven, eight, five, fifteen times crucified five ml It'LL give us a value off Ah, five point six eight times to the bar before, maybe later. So this is the Corrigan writing ml par in Cologne and fifteen Galan. So Seiple cease. This time in the world for ML is the volume for fifteen gallons. Now, as you know that we're given the density of oxygen and now we have find out the volume ofthe Ogden and if we just multiply dance city by volume we confined the mass off fifteen get knocked in. So the masses volume times density Volunteer is five point six eight times ten to the bar for ml. And the density is given, as is there a persistent program, Bremen. And from here, the value will be three point nine three times during the war for in from Stockton. So this is the massive forked and for fifteen gala knocked. And now we know the mess so from the massive and find out the number of malls all fucked in. So the number of most of Vulcan is now use mass or molar mass. So, Trooper, ninety three times ten of the war for Graham over the Moler massive fork in which is on one hundred for Ingram Cramp our mall and this will give us a value off three. Forty five Mall three. Forty five Matloff Acton. So you have to find out how many more of oxygen we need to burn to forty five mole off Stockton. Now, I have already seen that two more of Upton is barred by into five more oxygen. That means through forty five more often for the barn by twenty five over two times two forty five more, which is equal to forty one toe point five more off oxygen. And now we can this convert this mortal mass, get them massive oxygen. So for two, three, one, two point five mall times the molar mass if oxygen Monica, which is thirty two, cramp our mall and this will give us a bell off one point three eight times Tin cube from oxygen. So this is the massive oxygen, which is required to burn our fifteen gallon off often. Now, in the last part of this problem, we have to find out how many grams of see Oto are produced when fifteen gallon off, see eight inch eighteen or come buster. So, as I've already said whatever quantity were given, we have to first toe convert everything in a number of malls to find out how many, most ofthe other reactant or product is required. Our bodies posed. So once again, we have to find out the number of Moors for fifteen Callen off walked in and what we have already done. So here we have find out. But this is the number of moral fifteen gallons Ogden. So we know that three forty five more of walked in. So we have to find out how many more of carbon dioxide is produced. Fire three. Forty five mole off Oakton. And from there we can find out how many grams off sealed was produced from fortify Model Walked on. We go backto the main re actually question again. So here you can say that. For true Matloff Oct in we can have sixteen Melo Seo too. That means weaken right two more often can produce sixteen more. Toto, that means through forty five mall och ten will propose sixteen over too. Times two. Forty five mole. See, you're too. Which will give us. Yeah. Two, seven, six serum. All photo. And if we just multiplied these by the Moler Massive theater, which is forty four point or one cramp our mall. It could give us the massive theater, which is one point two one times going to deploy five Graham photo. So one point one times ten to the world. Five grandma sealed. Who is required? Our is produced when ar fifteen galan off often are combust. It

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