Final answer:
The molecular formula of the unknown hydrocarbon, composed of 85.7% carbon with a molar mass of 84.0 g/mol, is C6H12, corresponding to option d) C6H12.
Step-by-step explanation:
To determine the molecular formula of an unknown hydrocarbon composed of 85.7% carbon with an atomic mass of 84.0 g/mol, we can follow these steps:
- Calculate the mass of carbon and hydrogen in 100 g of the compound. Since hydrogen and carbon are the only elements in a hydrocarbon, if we have 85.7 g of carbon, we have 14.3 g of hydrogen (100 g - 85.7 g).
- Divide the mass of each element by its respective atomic mass to find the mole ratio. The atomic mass of carbon (C) is 12.01 g/mol, and that of hydrogen (H) is 1.008 g/mol.
- For carbon: 85.7 g ÷ 12.01 g/mol = approximately 7.14 mol. For hydrogen: 14.3 g ÷ 1.008 g/mol = approximately 14.19 mol.
- To find the simplest mole ratio, divide each amount by the smallest number of moles calculated: 7.14 mol ÷ 7.14 = 1 for carbon, and 14.19 mol ÷ 7.14 = approximately 2 for hydrogen. This gives us an empirical formula of CH2.
- Calculate the molar mass of the empirical formula: (12.01 g/mol × 1) + (1.008 g/mol × 2) = 14.026 g/mol.
- Determine how many empirical units are in the molecular formula by dividing the given molecular mass by the mass of the empirical formula: 84.0 g/mol ÷ 14.026 g/mol = 5.99, which is approximately 6.
- Multiply the empirical formula by this number to get the molecular formula: C6H12.
Therefore, the molecular formula of the unknown hydrocarbon is C6H12, which corresponds to option d) C6H12.