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Problem 107

One of the compounds used to increase the octane rating of gasoline is toluene (right). Suppose 20.0 $\mathrm{mL}$ of toluene $(d=$ 0.867 $\mathrm{g} / \mathrm{mL}$ ) is consumed when a sample of gasoline burns in air.

(a) How many grams of oxygen are needed for complete combustion of the toluene? (b) How many total moles of gaseous products form? (c) How many molecules of water vapor form?

Answer

a)

$\mathrm{m}\left(\mathrm{O}_{2}\right)=54,24 \mathrm{g}$

b)

$\mathrm{n}($ total $)=\mathrm{n}\left(\mathrm{CO}_{2}\right)+\mathrm{n}\left(\mathrm{H}_{2} \mathrm{O}\right)=2,068 \mathrm{mol}$

c)

$\mathrm{N}\left(\mathrm{H}_{2} \mathrm{O}\right)=4,53^{*} 10^{23} \mathrm{molecules}$

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## Discussion

## Video Transcript

So we're looking at the conditions are told in So assume we have 20 million abilities foretold in and ah cost 20 dancers in Sioux 200.7 grand per monitor for women. And he is the molecular Are the condoms I Molecular formula. Okay, So, party. What would be the massive also require full complete combustion for party will be the number of mo off catches Port of Spain produce and also a prophecy. What would be the number of Marquis? What away from him for? Okay, so first of all, um, we have to weigh out the chemical reaction. So we have C six h five safely. You can write as Ah, normal, huh? Um, Mark a phoner. It's up to us now. We have everything off the atom with the same number, and then we should be good. Okay, So you know that to simplify it? Because I I show you the molecule form in there. So I woo after I mean the contents formula. So I will show you the ah, the molecular formula. Yes, that So I just combine All of this could have been together and also the, um how did you together? So you were mixing. Sees here. Okay, so we have C seven, um, h eight, and then we're going toe really fostering. And then because we're going through Ah, compassion, reaction. So we have water. So, too, is a complete combustion. Okay, so we have the guns of bounds of chemical reaction. Um, so we have 74 cabins, and then we have 44 waters over eight hide regions. Okay, so for oxygen, we were half Ah, 14 over here. And then we have full over here. So there were 18 so Ah, we will need nine off the oxygen market. All right, So, um, yeah, we have the bonds Camco reaction. The Dixie Chicks That we're going to do is we're going to cover off the information that we have in order to find out. Ah, um, the actual massive ocean and every need. Okay, first of all, we have to find the mass off the tourney. And so we have a 20 mil, and also ah, we will have the dance is a super 0.7867 So where you're going to modify them? Volume and the density off the, um Tony. And then we would have a mass, so we would have Ah, 20 mule. Ah, Move, Flight, Sirrah. Point a seven grand. Permal. Sorry. Gram per minute. A sedan city. And we should people find as physical to 17.3434 grand. So we're 17 4 feet, four grand. Well, far, Tony. So how about the Lambo? Moe's? So we're going to divide the modem ass off to our needs, and then we can found in the bottom or so were 17.34 d white by the moment more than muscle to warn you. So we have seven. Um, comment. And then we ate, um, hydrogen. So at the end, we should be able to find a serial point. Ah, 114 should be 15 You know that to force of configures to run up. So when five. I should be What? Um most Okay. So this will be the limbo most off our, um Tournant. Okay. Herbert the lumber. Most off our Hodgins. From here, we can see that's the more away show for 20 into high Also genius. 129129 So when we have soup on when a five syllable most oxygen will be nine times off that. So your records went into 1.6 96 most for oxygen. Okay, so we can forward to convert back to ah, massive postures. So we just the mobile Mobile Mobile Mobile the Mass. And then we should be able to find, as he was just 34.28 gram and this week with a mass for oxygen and is therefore before part, eh? Okay, so party we have found the most off guess Ridge Holdings. So we have. See what? You Ah, each d'oh! Okay, again we go back to our ah, compassionate with reaction equation. So we see that the limbo most off water I did the motorway show off our Tony into water is 1 to 4124 So I'm going to your job. Nice 1 to 4 and then four carbon will be coming down side B 1 to 7, 1 to 7. So the number of most of water you'll be equals to our number. Moose off. Atone in some point. Ah, one a five. Most time for So you're going to your style coma later. Two times four and then we we have soup on 75 Foremost for water. Okay for coming down side. Same thing again. We have Ah, lung. Bone was off. Ah, Tonin, times seven. So a soup on way five time seven. And there we have one point for you. 19 boats. Okay, so the total the more total number moves on average points we were adding coming down side of water. So we just need to add this tube number together. And then we we have the answers, so ah, it will be because the serial point 2.73 e mails okay, possible would be the lumber off water vapor. More watermark in what a waiver. So we know that Ah, limbo most of water syrup on 75 most. Which is you multiply that by our regard. Your number. And then we were just We were filed a lumber off molecule, so the abbey got your number. It says it's for no two time. Tend to power 23 then we should be able to find that secret. This 4.5 for you, nine times 10 to the power off 23 molecules of waters. And this is that he has a process

## Recommended Questions

Butane gas is compressed and used as a liquid fuel in dis- posable cigarette lighters and lightweight camping stoves. Suppose a lighter contains 5.50 $\mathrm{mL}$ of butane $(d=0.579 \mathrm{g} / \mathrm{mL})$

(a) How many grams of oxygen are needed to burn the butane completely?

(b) How many moles of $\mathrm{H}_{2} \mathrm{O}$ form when all the butane burns?

(c) How many total molecules of gas form when the butane burns completely?

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?

Isooctane, $\mathrm{C}_{8} \mathrm{H}_{18,}$ is the component of gasoline from which the term octane rating derives.

(a) Write a balanced equation for the combustion of isooctane to yield $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ .

(b) Assuming that gasoline is 100$\%$ isooctane, that isooctane burns to produce only $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ , and that the density of isooctane is 0.792 $\mathrm{g} / \mathrm{mL}$ , what mass of $\mathrm{CO}_{2}$ in kilograms is produced each year by the annual U.S. gasoline consumption of $4.6 \times 10^{10} \mathrm{L} ?$

(c) What is the volume in liters of this $\mathrm{CO}_{2}$ at STP?

(d) How many moles of air are necessary for the combustion of 1 $\mathrm{mol}$ of isooctane, assuming that air is 21.0$\% \mathrm{O}_{2} \mathrm{by}$ volume? What is the volume in liters of this air at STP?

The hydrocarbon octane $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ burns to give $\mathrm{CO}_{2}$ and water vapor:

$$

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

$$

If a 0.048 -g sample of octane burns completely in

$\mathrm{O}_{2},$ what will be the pressure of water vapor in a $4.75-\mathrm{L}$ flask at $30.0^{\circ} \mathrm{C} ?$ If the $\mathrm{O}_{2}$ gas needed for complete combustion was contained in a $4.75-\mathrm{L}$ flask at $22^{\circ} \mathrm{C},$ what would its pressure be?

The hydrocarbon octane $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ burns to give $\mathrm{CO}_{2}$ and water vapor:

$$

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

$$

If a $0.095-\mathrm{g}$ sample of octane burns completely in $\mathrm{O}_{2},$ what will be the pressure of water vapor in a $4.75-\mathrm{L}$. Thask at $30.0^{\circ} \mathrm{C} ?$ If the $\mathrm{O}_{2}$ gas needed for complete combustion was contained in a $4.75-\mathrm{L}$. flask at $22^{\circ} \mathrm{C},$ what would its pressure be?

(a) Combustion analysis of toluene, a common organic solvent, gives 5.86 $\mathrm{mg}$ of $\mathrm{CO}_{2}$ and 1.37 $\mathrm{mg}$ of $\mathrm{H}_{2} \mathrm{O}$ . If the compound contains only carbon and hydrogen, what is its empirical formula? (b) Menthol, the substance can smell in mentholated cough drops, is composed of $\mathrm{C}, \mathrm{H},$ and $\mathrm{O} . \mathrm{A}$ 0.1005 -gsample of mentholis combusted, producing 0.2829 $\mathrm{g}$ of $\mathrm{CO}_{2}$ and 0.1159 $\mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O} .$ What is the empirical formula for menthol? If menthol has a molar mass of 156 $\mathrm{g} / \mathrm{mol}$ what is its molecular formula?

Hydrocarbon mixtures are used as fuels. (a) How many grams of $\mathrm{CO}_{2}(g)$ are produced by the combustion of $200 . \mathrm{g}$ of a mixture that is 25.0$\% \mathrm{CH}_{4}$ and 75.0$\% \mathrm{C}_{3} \mathrm{H}_{8}$ by mass? (b) $\mathrm{A} 252-\mathrm{g}$

gaseous mixture of $\mathrm{CH}_{4}$ and $\mathrm{C}_{3} \mathrm{H}_{8}$ burns in excess $\mathrm{O}_{2},$ and 748 $\mathrm{g}$ of $\mathrm{CO}_{2}$ gas is collected. What is the mass $\%$ of $\mathrm{CH}_{4}$ in the mixture?

Consider the following reaction for the combustion of octane, $\mathrm{C}_{8} \mathrm{H}_{18} :$

$$2 \mathrm{C}_{8} \mathrm{H}_{18}(l)+25 \mathrm{O}_{2}(g) \rightarrow 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} 0(l)$$

What volume of oxygen gas at STP would be needed for the complete combustion of 10.0 g of octane?

High-Octane Gasoline Gasoline is a complex mixture of hydrocarbons. It is sold with a variety of octane ratings that are based on the comparison of the gasoline with the combustion propertics of isooctanc, a compound with the molecular formula $\mathrm{C}_{8} \mathrm{H}_{18} .$ The Lewis structures of isooctane and another compound with molecular formula $\mathrm{C}_{8} \mathrm{H}_{18}$ are shown in Figure $\mathrm{P} 11.41,$ along with their

(FIGURE CANNOT COPY)

normal boiling points and heats of vaporization. Determine the vapor pressure of each isomer on a day when the temperature is $38^{\circ} \mathrm{C}$.

When hydrocarbons are burned in a limited amount of air, both CO and $\mathrm{CO}_{2}$ form. When 0.450 g of a particular hydrocarbon was burned in air, 0.467 $\mathrm{g}$ of $\mathrm{CO}, 0.733 \mathrm{g}$ of $\mathrm{CO}_{2},$ and 0.450 $\mathrm{g}$ of $\mathrm{H}_{2} \mathrm{O}$ were formed. (a) What is the empirical formula of the compound? (b) How many grams of O $_{2}$ were used in the reaction? (c) How many grams would have been required for complete combustion?