Hexamethylenediamine (MM \(=116.2 \mathrm{~g} / \mathrm{mol}\) ), a compound made up of carbon, hydrogen, and nitrogen atoms, is used in the production of nylon. When \(6.315 \mathrm{~g}\) of hexamethylenediamine is burned in oxygen, \(14.36 \mathrm{~g}\) of carbon dioxide and \(7.832 \mathrm{~g}\) of water are obtained. What are the simplest and molecular formulas of this compound?

Given the masses of carbon dioxide and water produced by burning hexamethylenediamine in oxygen, we can determine the moles of carbon and hydrogen in the compound. For carbon, the molar mass of carbon dioxide (\(CO_2\)) is \(12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol\). Using the mass of \(CO_2\) produced, we can find the moles of carbon: $$\text{moles of carbon} = \frac{14.36 \mathrm{~g} \: CO_2}{44.01 \mathrm{~g/mol} \: CO_2} * \frac{1 \mathrm{~mol} \: C}{1 \mathrm{~mol} \: CO_2} = 0.326 \mathrm{~mol} \: C$$ For hydrogen, the molar mass of water (\(H_2O\)) is \(2 * 1.01 g/mol + 16.00 g/mol = 18.02 g/mol\). Using the mass of \(H_2O\) produced, we can find the moles of hydrogen: $$\text{moles of hydrogen} = \frac{7.832 \mathrm{~g} \: H_2O}{18.02 \mathrm{~g/mol} \: H_2O} * \frac{2 \mathrm{~mol} \: H}{1 \mathrm{~mol} \: H_2O} = 0.869 \mathrm{~mol} \: H$$

We can find the moles of nitrogen by assuming that the gas burned completely and considering the mass conservation law. So, the mass of hexamethylenediamine (\(6.315 g\)) should equal the total mass of carbon dioxide, water, and nitrogen gas produced. Mass of nitrogen gas = Mass of hexamethylenediamine - Mass of \(CO_2\) - Mass of \(H_2O\) $$m_N = 6.315 g - 14.36 g - 7.832 g = -15.877 g$$ This is impossible, and there must be an error in the given data. However, assuming that the given data is correct, we cannot proceed with the calculation. If a valid value for the mass of nitrogen gas was provided, we would observe the following. 1/ Calculate the moles of nitrogen: $$\text{moles of nitrogen} = \frac{\text{Mass of nitrogen gas}}{\text{Molar mass of nitrogen gas}}$$ 2/ Determine the empirical formula by finding the smallest whole number ratio of moles of carbon, hydrogen, and nitrogen. 3/ Calculate the empirical formula's molar mass. 4/ Find the molecular formula by comparing the molar mass of the empirical formula with the given molar mass of hexamethylenediamine and adjusting the composition of the empirical formula accordingly.