Final answer:
The molecular formula of the compound with a molar mass of 78.1 g/mol is C6H6.
Step-by-step explanation:
To determine the molecular formula of a compound, we need to know its empirical formula and its molar mass. The empirical formula represents the simplest whole-number ratio of atoms in a compound. In this case, the compound contains 92.3% carbon, which corresponds to approximately 92.3 g of carbon in a 100 g sample. The remaining mass is due to hydrogen. We can assume 100 g of the compound.
We can convert the mass of each element to moles using their molar masses. The molar mass of carbon is 12.01 g/mol, and the molar mass of hydrogen is 1.008 g/mol. The number of moles of carbon can be calculated by dividing the mass by the molar mass:
moles of carbon (C) = mass of carbon / molar mass of carbon = 92.3 g / 12.01 g/mol = 7.688 mol C
We can do the same calculation for hydrogen:
moles of hydrogen (H) = mass of hydrogen / molar mass of hydrogen = (100 g - 92.3 g) / 1.008 g/mol = 7.618 mol H
The empirical formula is determined by dividing the number of moles of each element by the lowest number of moles. In this case, both the number of moles of carbon and hydrogen are very similar. Therefore, the empirical formula is CH.
To determine the molecular formula, we divide the molar mass of the compound by the molar mass of the empirical formula:
molecular formula = molar mass of compound / molar mass of empirical formula
In this case, the molar mass of the compound is given as 78.1 g/mol. The molar mass of the empirical formula CH is:
molar mass of CH = (12.01 g/mol × 1) + (1.008 g/mol × 1) = 13.018 g/mol
Dividing the molar mass of the compound by the molar mass of the empirical formula gives:
molecular formula = 78.1 g/mol / 13.018 g/mol ≈ 5.999
Since the result is close to 6, the molecular formula is approximately 6 times the empirical formula. Therefore, the molecular formula of the compound with a molar mass of 78.1 g/mol is C6H6.