A sample of a hydrocarbon is combusted completely in O21g2 to produce 21.83 g CO21g2, 4.47 g H2O1g2, and 311 kJ of heat. (a) What is the mass of the hydrocarbon sample that was combusted?

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Identify the chemical reaction involved: The complete combustion of a hydrocarbon (CxHy) in oxygen (O2) produces carbon dioxide (CO2) and water (H2O).

Use the given masses of CO2 and H2O to determine the moles of each product formed. Use the molar mass of CO2 (44.01 g/mol) and H2O (18.02 g/mol) for these calculations.

Determine the moles of carbon and hydrogen in the hydrocarbon by using the stoichiometry of the combustion reaction. Each mole of CO2 corresponds to one mole of carbon, and each mole of H2O corresponds to two moles of hydrogen.

Calculate the mass of carbon and hydrogen in the hydrocarbon sample using their respective atomic masses (C: 12.01 g/mol, H: 1.008 g/mol).

Add the masses of carbon and hydrogen to find the total mass of the hydrocarbon sample that was combusted.

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Key Concepts

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

Combustion Reaction

A combustion reaction is a chemical process in which a substance (usually a hydrocarbon) reacts with oxygen to produce carbon dioxide and water, releasing energy in the form of heat. In this case, the complete combustion of the hydrocarbon generates specific amounts of CO2 and H2O, which can be used to determine the mass of the original hydrocarbon.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the conservation of mass. It involves using molar ratios derived from balanced chemical equations to relate the amounts of substances consumed and produced. In this question, stoichiometry will help relate the masses of CO2 and H2O produced to the mass of the hydrocarbon that was combusted.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between the mass of a substance and the number of moles, which is crucial in stoichiometric calculations. To find the mass of the hydrocarbon, the molar masses of CO2 and H2O will be used to determine the moles produced, which can then be related back to the original hydrocarbon sample.

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One of the best-selling light, or low-calorie, beers is 4.2% alcohol by volume and a 355-mL serving contains 110 Calories; remember: 1 Calorie = 1000 cal = 1 kcal. To estimate the percentage of Calories that comes from the alcohol, consider the following questions. (a) Write a balanced chemical equation for the reaction of ethanol, C2H5OH, with oxygen to make carbon dioxide and water. (b) Use enthalpies of formation in Appendix C to determine ΔH for this reaction. (c) If 4.2% of the total volume is ethanol and the density of ethanol is 0.789 g/mL, what mass of ethanol does a 355-mL serving of light beer contain? (d) How many Calories are released by the metabolism of ethanol, the reaction from part (a)? (e) What percentage of the 110 Calories comes from the ethanol?

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