Final answer:
To determine the molecular formula of a hydrocarbon with an empirical formula CH₂ and a density of 1.84 g/L at STP, you calculate the molar mass and then use it to find the multiple of the empirical mass. The molecular formula of the hydrocarbon is C₃H₆, option (a).
Step-by-step explanation:
Determining the Molecular Formula of a Hydrocarbon Gas
To find the molecular formula of a hydrocarbon gas with the empirical formula CH₂ and a density of 1.84 g/L at STP, we first need to calculate the gas's molar mass. Using the ideal gas law and the given density, we can find the molar mass by the formula:
Molar mass = (Density at STP) × (Molar volume at STP)
The molar volume of any gas at STP (standard temperature and pressure) is 22.4 L/mol. Thus, the molar mass of the gas is:
Molar mass = 1.84 g/L × 22.4 L/mol = 41.22 g/mol.
The empirical mass (EM) for CH₂ is 14.03 g/mol (12.01 g/mol for carbon + 2 × 1.01 g/mol for hydrogen). To find the molecular formula, we divide the molar mass by the empirical mass:
Molecular formula multiplier = Molar mass / EM = 41.22 g/mol / 14.03 g/mol ≈ 3
Since the molecular formula is a whole-number multiple of the empirical formula, we multiply CH₂ by 3 to get:
Molecular formula = C₃H₆.
Therefore, the correct molecular formula of the gas is C₃H₆, which corresponds to option (a) C₃H₆.