Final answer:
The empirical formula of the organic compound, calculate the mole ratios of carbon and hydrogen based on the masses of CO₂ and H₂O. Scale up the mole ratios to whole numbers to get the empirical formula. Use the molar mass to determine the scaling factor and multiply the subscripts in the empirical formula by the scaling factor to obtain the molecular formula.
Step-by-step explanation:
To determine the empirical formula of the organic compound, we need to calculate the molar amounts of carbon and hydrogen in the sample. First, we convert the masses of CO₂ and H₂O to grams. The molar mass of carbon dioxide (CO₂) is 44.01 g/mol, so we divide the mass of CO₂ (20.65 g) by 44.01 g/mol to find the number of moles of carbon. Similarly, the molar mass of water (H₂O) is 18.015 g/mol, so we divide the mass of H₂O (5.638 g) by 18.015 g/mol to find the number of moles of hydrogen.
We then divide each of these mole amounts by the smallest of the two mole amounts to find the mole ratio of carbon to hydrogen. The empirical formula is determined by scaling up the smallest mole ratio to whole numbers. Finally, to find the molecular formula of the organic compound, we need to know the molar mass. In this case, the molar mass is given as 104.1 g/mol. We divide the molar mass of the molecular formula by the molar mass of the empirical formula to find the scaling factor. Multiplying the subscripts in the empirical formula by the scaling factor gives us the molecular formula.