Answer:
To determine the empirical formula of hexamethylenediamine, we need to calculate the mole ratios of carbon, hydrogen, and nitrogen in the compound.
1. Calculate the moles of carbon dioxide (CO2) produced:
Molar mass of CO2 = 12.01 g/mol (carbon) + 2 * 16.00 g/mol (oxygen) = 44.01 g/mol
Moles of CO2 = mass of CO2 / molar mass of CO2 = 14.36 g / 44.01 g/mol = 0.326 mol
2. Calculate the moles of water (H2O) produced:
Molar mass of H2O = 2 * 1.01 g/mol (hydrogen) + 16.00 g/mol (oxygen) = 18.02 g/mol
Moles of H2O = mass of H2O / molar mass of H2O = 7.832 g / 18.02 g/mol = 0.435 mol
3. Calculate the moles of carbon, hydrogen, and nitrogen in hexamethylenediamine:
Moles of carbon = moles of CO2 (since each CO2 molecule contains 1 carbon atom) = 0.326 mol
Moles of hydrogen = 2 * moles of H2O (since each H2O molecule contains 2 hydrogen atoms) = 2 * 0.435 mol = 0.870 mol
Moles of nitrogen = 0 (since there is no nitrogen in the products)
4. Divide the moles by the smallest number of moles to obtain the mole ratios:
Mole ratio of carbon : hydrogen : nitrogen = 0.326 mol : 0.870 mol : 0 mol
Since the mole ratio of nitrogen is zero, it means there is no nitrogen in the empirical formula.
Therefore, the empirical formula of hexamethylenediamine is CH3.
To determine the molecular formula, we need to know the molar mass of the compound. The molar mass of hexamethylenediamine is given as 116.2 g/mol.
5. Calculate the empirical formula mass:
Empirical formula mass = (molar mass of carbon) + (3 * molar mass of hydrogen) = 12.01 g/mol + 3 * 1.01 g/mol = 15.04 g/mol
6. Calculate the number of empirical formula units in the molecular formula:
Number of empirical formula units = molar mass of the compound / empirical formula mass = 116.2 g/mol / 15.04 g/mol ≈ 7.73
Since we cannot have a fractional number of empirical formula units, we need to multiply the empirical formula by an appropriate whole number to obtain a whole number of empirical formula units close to 7.73.
Multiplying the empirical formula CH3 by 2 gives C2H6, which has a molar mass of 30.08 g/mol. This is close to half of the given molar mass of hexamethylenediamine (116.2 g/mol).
Therefore, the molecular formula of hexamethylenediamine is (CH3)2, which can also be written as C2H6.