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Ch.7 - Thermochemistry
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Tro 6th EditionCh.7 - Thermochemistry문제 124
7장, 문제 124

A gaseous fuel mixture stored at 745 mmHg and 298 K contains only methane (CH4) and propane (C3H8). When 11.7 L of this fuel mixture is burned, it produces 769 kJ of heat. What is the mole fraction of methane in the mixture? (Assume that the water produced by the combustion is in the gaseous state.)

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1
Identify the balanced chemical equations for the combustion of methane and propane: \( \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \) and \( \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \).
Determine the enthalpy change (\( \Delta H \)) for the combustion of each component: \( \Delta H_{\text{CH}_4} = -890.3 \text{ kJ/mol} \) and \( \Delta H_{\text{C}_3\text{H}_8} = -2220.1 \text{ kJ/mol} \).
Use the ideal gas law \( PV = nRT \) to calculate the total moles of the gas mixture: \( n = \frac{PV}{RT} \), where \( P = 745 \text{ mmHg} \), \( V = 11.7 \text{ L} \), \( R = 0.0821 \text{ L atm/mol K} \), and \( T = 298 \text{ K} \).
Set up an equation based on the total heat produced: \( 769 \text{ kJ} = n_{\text{CH}_4} \times (-890.3 \text{ kJ/mol}) + n_{\text{C}_3\text{H}_8} \times (-2220.1 \text{ kJ/mol}) \), where \( n_{\text{CH}_4} + n_{\text{C}_3\text{H}_8} = n_{\text{total}} \).
Solve the system of equations to find the mole fraction of methane: \( \text{Mole fraction of CH}_4 = \frac{n_{\text{CH}_4}}{n_{\text{total}}} \).

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주요 개념

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the number of moles of gases in a mixture, which is necessary for determining the mole fraction of each component in the fuel mixture.
추천 영상:
가이드 코스
01:15
Ideal Gas Law Formula

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of that component to the total number of moles of all components. It is crucial for understanding the composition of the fuel mixture and how it relates to the combustion process.
추천 영상:
가이드 코스
00:36
Mole Fraction Formula

Combustion Reaction

A combustion reaction involves the reaction of a fuel with oxygen to produce heat, carbon dioxide, and water. The heat produced during combustion can be quantified, and the stoichiometry of the reaction helps in determining the moles of reactants consumed, which is necessary for calculating the mole fraction of methane in the mixture.
추천 영상:
가이드 코스
02:24
Combustion Apparatus
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