Final answer:
The molecular formula of the gaseous hydrocarbon X is C4H10, as 15.0 cm³ of X produces 60.0 cm³ of CO2 and 75.0 cm³ of H2O, indicating 4 moles of carbon and 10 moles of hydrogen are present in the molecular formula.
Step-by-step explanation:
To determine the molecular formula of a gaseous hydrocarbon X, first, consider that the volumes of gases in a reaction measured at the same temperature and pressure are in the ratio of their mole numbers, according to Avogadro's law. Since the complete combustion of 15.0 cm³ of X produces 60.0 cm³ of carbon dioxide and 75.0 cm³ of water vapor, we can infer the stoichiometry of the reaction. For every 1 mole of X, 4 moles of CO₂ and 5 moles of H₂O are produced. The molecular formula of X can be deduced from the number of moles of carbon (C) and hydrogen (H) atoms present in the combustion products.
Since there are 4 moles of CO₂ for each mole of X, there must be 4 moles of carbon in X. Similarly, because there are 5 moles of H₂O and each molecule of water contains 2 hydrogen atoms, there are 10 moles of hydrogen in X. Therefore, the molecular formula of the hydrocarbon X is C4H10, which matches option A from the multiple choice answers provided.
The balanced equation for the combustion of X (C4H10) can be written as follows:
2C4H10 (g) + 13O2 (g) → 8CO2 (g) + 10H2O (g)