A liquid fuel mixture contains 30.35% hexane (C6H14), 15.85%
hept...

Question

A liquid fuel mixture contains 30.35% hexane (C6H14), 15.85%
heptane (C7H16), and the rest octane (C8H18). What maximum
mass of carbon dioxide is produced by the complete combustion
of 10.0 kg of this fuel mixture?

Accepted Answer

Hey everyone. Our question here is asking us to calculate the maximum mass of carbon dioxide form in the sample containing hep dane, hexane and octane. Looking at what we have, let's go ahead and calculate the percent of each compound by kg. Starting off with our hep dane, we were told that we have 23.29%,, Converting that into decimal form. We have 0.2329 And we can multiply this by kg. This will get us to a value of 8.85 kilograms. Next looking at our hexane, We're told that we have 52.18%. So converting this into decimal form, we have 0.5-18 Times 38 kg, which will get us to a value of 19.828 kg. Lastly looking at our octane, we can go ahead and take our 38 kg and subtract Our 8.85 kg Plus our 19.828 kg. This will get us to a value of 9. kg. Next we want to determine our reactions, since we have a combustion reaction for each starting off with our hep dane, we have C seven H 16 and since this is a combustion reaction, we reacted with oxygen and this will get us to the products of carbon dioxide plus water. And when we balance this out, We end up with 11 of our oxygen seven of our carbon dioxide and eight of our water. Next looking at our hexane, we have C six H 14. Again, we react this with oxygen and we create carbon dioxide and water Balancing out our reaction, we end up with two of our hacks, Ain 19 of our oxygen 12 of our carbon dioxide and 14 of our water. Lastly looking at our octane, which is C eight H 18, we again react this with oxygen to form carbon dioxide plus water balancing this out, we end up with two of our octane, 25 of our oxygen 16 of our carbon dioxide and 18 of our water. Now that we have our reactions, let's go ahead and calculate the grams of carbon dioxide. Starting off with our 8.85 kg of hep dane. We first want to convert this into grams. So we know that one kg contains 10 to the third grams and obtaining the molar mass of hep dane, we know that we have 100.0 to 1 g of hep dane Per one Mole of Hep Dane. And since we want to convert this into grams of carbon dioxide, we're going to look at our multiple ratios by looking at our reaction. So as we can see from our reaction of top, we have one more of HeP Dean per seven mole of carbon dioxide. And looking at carbon dioxide solar mass, we know that per one mole We have .01 g of carbon dioxide. So when we calculate this out and cancel out our units, we end up with a value of 2.73 times 10 to the eight grams of carbon dioxide coming from our hep dane. Next looking at our hexane, we have 19.828 kg. And we want to convert this into g. So per one kg we have 10 to the 3rd g. Looking at hex eins molar mass, we know that we have 86.18 g of hexane Per one Mole of Hexane. And looking at our reaction, we can see that we have two moles of hexane Per 12 mole of carbon dioxide. And we know that carbon dioxide molar mass is 44. g per one mole. And when we calculate this out, we end up with a value of 4.51 times 10 to the eight grams of carbon dioxide coming from our hexane. And lastly looking at our octane, we have 9.32 kg of octane. And we're going to convert this into grams. So we know that one kg contains 10 to the third grams. Looking at the Mueller massive octane, we have 114.23 g of octane Per one Mole of Octane. And when we look at a reaction, we have two mole of octane Per mole of carbon dioxide. And lastly, we want to convert our carbon dioxide into grams of carbon dioxide by using its molar mass of 44.01 g per one mole. We end up with a total of 1.73 times 10 to the eight grams of carbon dioxide coming from our octane. Now, going back to our question, they want us to calculate the maximum mass of carbon dioxide. We're going to take our 2.73 times 10 to the 8th g And add our 4.51 times 10 to the 8th g. And lastly, at our 1.7, 3 times 10 to the 8th g. This will get us to a total of 8.97 Times 10 to the 8th g, which is going to be our final answer. So I hope this made sense. And let us know if you have any questions.

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