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?

검증된 단계별 안내

Determine the balanced chemical equation for the combustion of isooctane: \[ \text{C}_8\text{H}_{18} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]. Balance the equation to find the stoichiometric coefficients.

Calculate the mass of isooctane consumed annually by using its density: \[ \text{mass} = \text{density} \times \text{volume} \]. Convert the volume from liters to milliliters to match the density units.

Convert the mass of isooctane to moles using its molar mass: \[ \text{moles of C}_8\text{H}_{18} = \frac{\text{mass of C}_8\text{H}_{18}}{\text{molar mass of C}_8\text{H}_{18}} \].

Use the balanced chemical equation to find the moles of \( \text{CO}_2 \) produced per mole of isooctane. Multiply the moles of isooctane by this ratio to find the moles of \( \text{CO}_2 \) produced.

Convert the moles of \( \text{CO}_2 \) to mass in kilograms using the molar mass of \( \text{CO}_2 \): \[ \text{mass of CO}_2 = \text{moles of CO}_2 \times \text{molar mass of CO}_2 \]. Convert grams to kilograms.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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, understanding the stoichiometric ratios between isooctane, CO2, and H2O is essential for determining the mass of CO2 produced from the combustion of isooctane.

Combustion Reaction

A combustion reaction is a chemical process in which a substance reacts rapidly with oxygen, releasing energy in the form of heat and light. For isooctane, the combustion reaction can be represented as C8H18 + O2 → CO2 + H2O. Knowing the products of this reaction, specifically CO2 and H2O, is crucial for calculating the total mass of CO2 generated from the complete combustion of isooctane.

Density and Mass Calculation

Density is defined as mass per unit volume and is a critical concept for converting between the volume of a substance and its mass. In this scenario, the density of isooctane (0.792 g/mL) allows us to convert the volume of gasoline consumed (4.6×10^10 L) into mass. This mass is then used in stoichiometric calculations to determine the mass of CO2 produced from the combustion of the isooctane.

관련 실천

교과서 질문

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.

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교과서 질문

The Rankine temperature scale used in engineering is to the Fahrenheit scale as the Kelvin scale is to the Celsius scale. That is, 1 Rankine degree is the same size as 1 Fahrenheit degree, and 0 °R = absolute zero. (b) What is the value of the gas constant R on the Rankine scale in 1L ~ atm2>1°R ~ mol2? (c) Use the van der Waals equation to determine the pressure inside a 400.0-mL vessel that contains 2.50 mol of CH4 at a temperature of 525 °R. For CH4, a = 2.253 1L2 ~ atm2>mol2 and b = 0.04278 L>mol.

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교과서 질문

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.

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교과서 질문

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?

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