Final answer:
To determine the empirical formula, we calculate the moles of carbon and hydrogen from the produced CO2 and H2O, then find the simplest mole ratio. The calculation yields an empirical formula of C4H7 for the hydrocarbon, which is option D.
Step-by-step explanation:
Determining the Empirical Formula of a Hydrocarbon
To find the empirical formula of the hydrocarbon, it is necessary to convert the masses of CO₂ and H₂O to moles, then find the ratio of these to infer the ratio of carbon to hydrogen in the original hydrocarbon.
From the mass of CO₂ (27.8 g), we can find the moles of carbon, since every mole of CO₂ contains one mole of carbon atoms. Similarly, from the mass of H₂O (9.96 g), we can calculate the moles of hydrogen. The formula to convert mass to moles is:
moles = mass (g) / molar mass (g/mol)
Carbon's molar mass is approximately 12.01 g/mol and hydrogen's is about 1.01 g/mol. Therefore:
- For CO₂: moles of C = 27.8 g / 44.01 g/mol (molar mass of CO₂) ≈ 0.6315 mol C
- For H₂O: moles of H = 9.96 g / 18.02 g/mol (molar mass of H₂O) ≈ 0.5528 mol H
However, since each water molecule has two hydrogen atoms, we need to multiply the moles of H by 2 to get the total moles of hydrogen atoms.
The simplest whole number ratio of moles of carbon to hydrogen can be found by dividing both by the smallest one:
Moles of carbon to hydrogen = 0.6315 mol C : (2 * 0.5528 mol H)
The empirical formula thus becomes C4H7, which matches option D from the provided choices.