A compound is 85.6% carbon by mass. The rest is hydrogen. When 10.0 g of the compound is evaporated at 50.0 ∘C, the vapor occupies 6.30 L at 1.00 atm pressure. What is the molecular formula of the compound?
To find the molecular formula of the compound, we need to determine the empirical formula and the molar mass.
1. Calculating the empirical formula:
To find the empirical formula, we need the masses of carbon and hydrogen in the compound. We are given that the compound is 85.6% carbon by mass, which means the remaining 14.4% is hydrogen.
Assuming we have 100g of the compound, 85.6g would be carbon and 14.4g would be hydrogen.
Next, we need to convert these masses to moles. We can use the molar mass of carbon and hydrogen to do this.
The molar mass of carbon (C) is 12.01 g/mol.
The molar mass of hydrogen (H) is 1.01 g/mol.
For carbon:
Moles of C = Mass of C / Molar mass of C
Moles of C = 85.6g / 12.01 g/mol
For hydrogen:
Moles of H = Mass of H / Molar mass of H
Moles of H = 14.4g / 1.01 g/mol
Now, we need to calculate the mole ratio between carbon and hydrogen.
Dividing the moles of each element by the smallest number of moles (in this case, hydrogen), we get:
Moles of C = (85.6g / 12.01 g/mol) / (14.4g / 1.01 g/mol)
Moles of C = 7.877
Moles of H = (14.4g / 1.01 g/mol) / (14.4g / 1.01 g/mol)
Moles of H = 14.256
To obtain the simplest whole number ratio, we divide both values by the smallest mole value, which is approximately 7.88:
Moles of C = 7.877 / 7.88 = 1
Moles of H = 14.256 / 7.88 ≈ 1.81
The empirical formula is CH.
2. Calculating the molar mass:
To determine the molar mass of the compound, we need to know the molar mass of the empirical formula CH.
Molar mass of CH = (Molar mass of C) + (Molar mass of H)
Molar mass of CH = (12.01 g/mol) + (1.01 g/mol)
Molar mass of CH ≈ 13.02 g/mol
Now that we have the molar mass of the empirical formula, we can proceed to the next step.
3. Calculating the molecular formula:
To find the molecular formula, we need the molar mass of the compound. We are given that 10.0 g of the compound was used.
Moles of compound = Mass of compound / Molar mass of the empirical formula
Moles of compound = 10.0g / 13.02 g/mol ≈ 0.77
To determine the ratio between the empirical formula and the molecular formula, we divide the moles of the compound by the moles of the empirical formula:
Moles of compound / Moles of CH ≈ 0.77 / 1 ≈ 0.77
Since the ratio is less than 1, it suggests that the empirical formula (CH) contains only one unit.
Therefore, the molecular formula of the compound is also CH.