Final answer:
The given data in the question is inconsistent with the provided answer choices, as none of them meet the calculated amount of hydrogen atoms derived from the given hydrocarbon's mass and molecular mass after combustion.
Step-by-step explanation:
The question involves determining the molecular formula of a hydrocarbon based on its combustion product and molecular mass. The hydrocarbon, when burned, produces 4.05 g of H2O, and its molecular mass is given as 138 g/mol. The student has provided a list of possible hydrocarbons with different molecular formulas as options. To determine the correct formula, it is essential to perform stoichiometric calculations, taking into account that each mole of water produced comes from two moles of hydrogen atoms in the hydrocarbon. Considering that the molar mass of water is 18 g/mol, the 4.05 g of water produced corresponds to 4.05 g / 18 g/mol = 0.225 moles. This means the hydrocarbon provided 0.225 moles * 2 = 0.45 moles of hydrogen atoms. Given the mass of the sample and its molar mass, the moles of hydrocarbon burned are 3.45 g / 138 g/mol = 0.025 moles. Each mole of hydrocarbon must contain 0.45 moles of hydrogen since this is the amount of hydrogen that fully reacted to form water. Thus, we need to find a formula wherein 0.025 moles of hydrocarbon contain 0.45 moles of hydrogen. This implies that each mole of hydrocarbon contains 0.45 / 0.025 = 18 moles of hydrogen atoms. However, none of the given options (C2H6, C3H8, C4H10, or C5H) has 18 hydrogen atoms per molecule. Therefore, the data provided seems to be inconsistent, or there may be a typo in the question or the answer choices. As a result, we cannot definitively provide an answer based on the provided information.