Isooctane, C8H18, is the component of gasoline from which the term octane rating derives. (c) What is the volume in liters of CO2 produced at STP?

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Identify the balanced chemical equation for the combustion of isooctane (C8H18). The general form of a combustion reaction is: C8H18 + O2 -> CO2 + H2O. Balance this equation to find the stoichiometric coefficients.

Determine the number of moles of isooctane (C8H18) you are starting with. If not given, assume a certain amount or use a standard amount like 1 mole for calculation purposes.

Using the balanced equation, find the mole ratio between isooctane and carbon dioxide (CO2). This will allow you to calculate the moles of CO2 produced from the moles of C8H18 combusted.

Recall that at Standard Temperature and Pressure (STP), 1 mole of any ideal gas occupies 22.4 liters. Use this information to convert the moles of CO2 to volume in liters.

Multiply the moles of CO2 by 22.4 L/mol to find the volume of CO2 produced at STP. This will give you the final volume in liters.

Key Concepts

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

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the proportions of substances consumed and produced. In this case, understanding the stoichiometry of the combustion of isooctane will allow us to calculate the amount of CO2 produced from a given volume of isooctane.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 liters. This law is essential for converting the amount of CO2 produced from the combustion of isooctane into a volume measurement at STP.

Combustion Reaction

A combustion reaction is a chemical process in which a substance reacts with oxygen to produce heat and light, typically resulting in carbon dioxide and water as products. For isooctane, the balanced equation shows how many moles of CO2 are produced per mole of isooctane burned. Understanding this reaction is crucial for determining the volume of CO2 generated during the combustion process.

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Combustion Apparatus

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Textbook Question

An empty 4.00-L steel vessel is filled with 1.00 atm of CH₄(g) and 4.00 atm of O₂(g) at 300 °C. A spark causes the CH₄ to burn completely, according to the equation

CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(g) ΔH° = -802 kJ

Textbook Question

When a gaseous compound X containing only C, H, and O is burned in O₂, 1 volume of the unknown gas reacts with 3 volumes of O₂ to give 2 volumes of CO₂ and 3 volumes of gaseous H₂O. Assume all volumes are measured at the same temperature and pressure. (a) Calculate a formula for the unknown gas, and write a balanced equation for the combustion reaction.

Textbook Question

Isooctane, C₈H₁₈, is the component of gasoline from which the term octane rating derives. (a) Write a balanced equation for the combustion of isooctane to yield CO₂ and H₂O.

Textbook Question

Isooctane, C₈H₁₈, is the component of gasoline from which the term octane rating derives. (b) Assuming that gasoline is 100% isooctane, that isooctane burns to produce only CO₂ and H₂O, and that the density of isooctane is 0.792 g/mL, what mass of CO₂ in kilograms is produced each year by the annual U.S. gasoline consumption of 4.6⨉10¹⁰ L?

Textbook Question

Isooctane, C₈H₁₈, is the component of gasoline from which the term octane rating derives. (d) How many moles of air are necessary for the combustion of 1 mol of isooctane, assuming that air is 21.0% O₂ by volume? What is the volume in liters of this air at STP?