The propane fuel (C₃H₈) used in gas barbeques burns according to the thermochemical equation: C₃H₈(g) + 5 O₂(g) → 3 CO₂(g) + 4 H₂O(g) ΔH°_rxn = –2044 kJ If a pork roast must absorb 1.6×10³ kJ to fully cook, and if only 10% of the heat produced by the barbeque is actually absorbed by the roast, what mass of CO₂ is emitted into the atmosphere during the grilling of the pork roast?

검증된 단계별 안내

Calculate the total amount of heat required to cook the pork roast considering only 10% efficiency. This is done by dividing the heat needed by the roast (1.6 * 10^3 kJ) by 0.10.

Determine the amount of propane (C3H8) needed to produce the calculated total heat. Use the given ΔH°rxn (-2044 kJ per mole of C3H8) and calculate the moles of C3H8 required by dividing the total heat by -2044 kJ/mol.

Using the stoichiometry of the balanced chemical equation, calculate the moles of CO2 produced. For every mole of C3H8 burned, 3 moles of CO2 are produced.

Convert the moles of CO2 to mass. Use the molar mass of CO2 (approximately 44.01 g/mol) and multiply it by the number of moles of CO2 calculated in the previous step.

The result from the previous step gives the mass of CO2 emitted into the atmosphere during the grilling of the pork roast.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

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

Thermochemical Equations

Thermochemical equations represent the heat changes associated with chemical reactions. They include the enthalpy change (ΔH) which indicates whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). In this case, the combustion of propane releases -2044 kJ of energy, which is crucial for calculating how much energy is available for cooking the pork roast.

Heat Transfer Efficiency

Heat transfer efficiency refers to the percentage of heat produced that is effectively utilized for a specific purpose. In this scenario, only 10% of the heat generated by the barbeque is absorbed by the pork roast. This efficiency is vital for determining the actual amount of energy available for cooking, which influences the calculations for the mass of CO2 produced.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. It allows us to relate the amount of propane burned to the amount of carbon dioxide produced. By using the stoichiometric coefficients from the combustion reaction, we can determine how much CO2 is emitted based on the energy absorbed by the roast.