Final answer:
The molecular formula of a compound containing 92.3% carbon with a molar mass of 78.1 g/mol is determined to be C₆H₆, by calculating the empirical formula as CH and then using the molar mass to find that it is six times the empirical formula.
Step-by-step explanation:
A compound of carbon and hydrogen contains 92.3% carbon and has a molar mass of 78.1 g/mol. To determine its molecular formula, we need to find the empirical formula first using the percent composition, and then use the molar mass to find the actual molecular formula.
The empirical formula is based on the lowest whole number ratio of elements in the compound. Since we have 92.3% carbon, let's assume we have 100 g of the compound so we would have 92.3 g of C and the remainder (7.7 g) as H. We can calculate the moles of C and H:
- Moles of C = 92.3 g / 12.01 g/mol = 7.687 moles
- Moles of H = 7.7 g / 1.008 g/mol = 7.638 moles
We then divide by the smallest number of moles to get the simplest whole number ratio:
- Ratio of C:H = 7.687 moles C / 7.638 moles H ≈ 1:1
Therefore, the empirical formula is CH, with a molar mass of 13.018 g/mol. To find the molecular formula, we use the ratio of the molar mass of the molecular formula to the empirical formula: Molecular Formula Mass / Empirical Formula Mass = 78.1 g/mol / 13.018 g/mol ≈ 6. Therefore, the molecular formula is C6H6, which is option (a) C6H6.