Textbook Question
The ΔH for the oxidation of sulfur in the gas phase to SO3 is –204 kJ/mol and for the oxidation of SO2 to SO3 is 89.5 kJ/mol. Find the enthalpy of formation of SO2 under these conditions.
Ch.7 - Thermochemistry
Chapter 7, Problem 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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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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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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.
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Related Practice
Textbook Question
The ΔH°f of TiI3(s) is –328 kJ/mol and the ΔH ° for the reaction 2 Ti(s) + 3 I2(g) → 2 TiI3(s) is –839 kJ. Calculate the ΔH of sublimation of I2(s), which is a solid at 25 °C.
Textbook Question
A gaseous fuel mixture contains 25.3% methane (CH4), 38.2% ethane (C2H6), and the rest propane (C3H8) by volume. When the fuel mixture contained in a 1.55 L tank, stored at 755 mmHg and 298 K, undergoes complete combustion, how much heat is emitted? (Assume that the water produced by the combustion is in the gaseous state.)
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