The complete combustion of octane, C 8 H 18 , a component of gasoline, proceeds as follows: 2 C 8 H 18 (l) + 25 O 2 (g) → 16 CO 2 (g) + 18 H 2 O(g). (d) How many grams of CO 2 are produced when 15.0 gal of C 8 H 18 are combusted? (d) How many grams of CO 2 are produced when 15.0 gal of C 8 H 18 are combusted?

Hi everyone here, we have a question telling us that lighters commonly used Beauty and gas C four H 10 for fuel. And our goal is to calculate the mass of carbon dioxide in grams produced upon the complete combustion of 56.0 mL of butane fuel fluid, approximate contents of a refill bottle. And we're going to assume that the density of the fluid is 0.573 g per milliliter. So first we're going to calculate the mass of beating and we're gonna do that by taking our amount 56 mL Times our density, which is 0. g per mil leader. And our ml will cancel out and that gives us 32. g a butane. Next, we need to write our balanced combustion reaction. So we have butane and because it's a combustion reaction, we're going to add oxygen and it is a di atomic adam. So there's two of them and that is going to form carbon dioxide plus water as a byproduct. So to balance this, let's ride out what we have on each side. So for carbon We have eight or we have four for hydrogen, we have 10 and oxygen, we have to and on our product side we have one carbon, two hydrogen and three oxygen. So we're gonna start this by putting a four in front of our carbon dioxide and that's going to change our carbon to four And our oxygen to nine. And next we're going to change our Hydrogen to five. So we have 10 hydrogen And we have 13 oxygen And as we can see with oxygen on our react inside there is a two. So we can't get 13. So we're going to have to multiply everything by two. So we're gonna change this to eight and this to 10, which gives us eight carbons, 20 hydrogen And oxygen's. And now we can balance the react inside by putting a two in front of our butane and a 13 in front of our oxygen. So we have eight carbon, 20 hydrogen And 26 oxygen. Now we have a balanced combustion reaction. So now we want to calculate the mass of carbon dioxide produced. And to do that, we first have to calculate the molar mass of butane and carbon dioxide. So our molar mass of butane, we have carbon, Which is 12.01 times four Equals 48.04. We have hydrogen which is 1. times 10 Which is 10.1 For a total of 58.14 g per mole. And all of these numbers are taken off the periodic table. And now we're going to do the same for carbon dioxide. So we have carbon which is 12. And we have oxygen which is 16 and we have two of them, Which is For a total of 44.01 g per mole. And now we're going to do our dimensional analysis. So we have .09 g a butane times one mole a butane over the molar mass of butane. And that's going to convert it into moles. So over 58. g of butane times eight moles of carbon dioxide over two moles of butane. And that is from our balanced combustion reaction times .01g of carbon dioxide. That's its molar mass Over one mole of carbon dioxide. And our grams of butane are going to cancel out. Our moles of butane are going to cancel out and our moles of carbon dioxide are going to cancel out, giving us 97.2 g of carbon dioxide. And that is our final answer. Thank you for watching. Bye.

Ch.3 - Chemical Reactions and Reaction Stoichiometry

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Brown 14th Edition

Ch.3 - Chemical Reactions and Reaction Stoichiometry

Problem 68d

Chapter 3, Problem 68d

The complete combustion of octane, C₈H₁₈, a component of gasoline, proceeds as follows: 2 C₈H₁₈(l) + 25 O₂(g) → 16 CO₂(g) + 18 H₂O(g). (d) How many grams of CO₂ are produced when 15.0 gal of C₈H₁₈ are combusted? (d) How many grams of CO₂ are produced when 15.0 gal of C₈H₁₈are combusted?

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First, convert the volume of octane from gallons to liters using the conversion factor: 1 gallon = 3.78541 liters.

Next, calculate the mass of octane in grams. Use the density of octane, which is approximately 0.703 g/mL, to convert the volume in liters to mass in grams.

Determine the number of moles of octane (C8H18) using its molar mass. The molar mass of C8H18 is calculated by adding the atomic masses of carbon and hydrogen: (8 * 12.01 g/mol for C) + (18 * 1.008 g/mol for H).

Use the stoichiometry of the balanced chemical equation to find the moles of CO2 produced. According to the equation, 2 moles of C8H18 produce 16 moles of CO2. Use this ratio to calculate the moles of CO2 from the moles of C8H18.

Finally, convert the moles of CO2 to grams using the molar mass of CO2, which is 44.01 g/mol. Multiply the moles of CO2 by this molar mass to find the mass of CO2 produced.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows us to calculate the amounts of substances consumed and produced in a reaction based on balanced chemical equations. In this case, stoichiometry will help determine how many grams of CO2 are produced from a given volume of octane.

Molar Volume of a Gas

The molar volume of a gas at standard temperature and pressure (STP) is approximately 22.4 liters per mole. This concept is essential for converting between the volume of gaseous reactants or products and the number of moles, which can then be used in stoichiometric calculations. Understanding this relationship is crucial for determining how many moles of CO2 are produced from the combustion of octane.

Density and Conversion Factors

Density is the mass per unit volume of a substance, typically expressed in grams per milliliter (g/mL) for liquids. To convert the volume of octane (in gallons) to grams, one must use the density of octane, which allows for the calculation of mass from volume. This conversion is necessary to find out how many grams of CO2 are produced from the combustion of the specified volume of octane.

The complete combustion of octane, C8H18, a component of gasoline, proceeds as follows: 2 C8H18(l) + 25 O2(g) → 16 CO2(g) + 18 H2O(g). (d) How many grams of CO2 are produced when 15.0 gal of C8H18 are combusted? (d) How many grams of CO2 are produced when 15.0 gal of C8H18 are combusted?

Verified video answer for a similar problem:

Key Concepts

Stoichiometry

Molar Volume of a Gas

Density and Conversion Factors