Final answer:
To determine the average molar mass of a mixture of CH4 and C2H4 that produced 35.2 grams of CO2 on complete oxidation, use the law of conservation of mass and stoichiometry. Calculate the moles of CO2 produced and assume they equal the moles of carbon in the original sample. The average molar mass is 12 grams divided by 0.8 moles, resulting in 15 g/mol.
Step-by-step explanation:
The question involves determining the average molar mass of a hydrocarbon mixture based on the mass of carbon dioxide (CO₂) produced from the complete oxidation of the mixture. Given a 12-gram sample of a mixture of CH₄ (methane) and C₂H₄ (ethylene) producing 35.2 grams of CO₂ when completely oxidized, one can apply the law of conservation of mass and stoichiometry to calculate the average molar mass.
To solve the problem, consider that each carbon atom in the hydrocarbons will produce one CO₂ molecule upon complete oxidation. Therefore, the moles of CO₂ produced can be found from the mass of CO₂:
Number of moles of CO₂ = Mass of CO₂ / Molar mass of CO₂
Number of moles of CO₂ = 35.2 g / 44 g/mol = 0.8 moles
Because the mixture contains only one carbon in CH₄ and two carbons in C₂H₄, the total moles of carbons in the original sample equal the moles of CO₂ produced. Therefore, the total moles of carbons in the original sample is 0.8 moles.
The original mass of the hydrocarbons (12 grams) divided by the total moles of carbons gives the average molar mass of the original sample.
Average molar mass = Original mass of hydrocarbons / Total moles of carbons
Average molar mass = 12 g / 0.8 moles = 15 g/mol