Final answer:
To determine the molecular formula of the gaseous hydrocarbon, first find the empirical formula by calculating the mole ratio of carbon to hydrogen. Then compare the molar mass of the empirical formula with the given molar mass to find the molecular formula.
Step-by-step explanation:
The empirical formula for the gaseous hydrocarbon can be determined using the percent composition of carbon. Since the hydrocarbon sample contains 82.66% carbon, assuming a 100 g sample would result in 82.66 g of carbon. The number of moles of carbon can be calculated by dividing the mass by the molar mass of carbon (12.01 g/mol). Similarly, the number of moles of hydrogen can be calculated using the same method.
Next, determine the mole ratio of carbon to hydrogen by dividing the number of moles of each element by the smallest number of moles. This ratio gives the empirical formula of the compound.
Finally, to determine the molecular formula, compare the molar mass of the empirical formula with the given molar mass of the compound. If the molar mass of the empirical formula is less than the given molar mass, multiply the subscripts in the empirical formula by a whole number until the molar mass of the compound matches the given molar mass.