Question

Hexamethylenediamine \((\mathrm{MM}=116.2 \mathrm{~g} / \mathrm{mol}),\) 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?

Short answer

Answer: The molecular formula of hexamethylenediamine is C6H16N2.

Step-by-step solution

Convert the mass of CO2 and H2O to moles.

Use the molar masses of CO2 (44.01 g/mol) and H2O (18.02 g/mol) to convert the masses of CO2 and H2O produced into moles. Moles of CO2 = \(\frac{14.36 \mathrm{~g} \mathrm{~CO}_2}{44.01 \mathrm{~g/mol} \mathrm{~CO}_2}\) = 0.326 moles of CO2. Moles of H2O = \(\frac{7.832 \mathrm{~g} \mathrm{~H}_2\mathrm{O}}{18.02 \mathrm{~g/mol} \mathrm{~H}_2\mathrm{O}}\) = 0.435 moles of H2O.

Determine the moles of C and H from the moles of CO2 and H2O.

There is one mole of carbon in one mole of CO2, and there are two moles of hydrogen in one mole of H2O. Therefore, we can directly use the moles of CO2 as moles of C and twice the moles of H2O as moles of H present in the compound. Moles of C = 0.326 moles. Moles of H = 2 * 0.435 moles = 0.870 moles.

Find the mass of C and H in the compound. Then, find the mass of N.

Using the molar masses of C (12.01 g/mol) and H (1.008 g/mol), find the mass of C and H in the given compound. Then, subtract these from the initial mass of the compound to find the mass of N. Mass of C = 0.326 moles * 12.01 g/mol = 3.914 g C. Mass of H = 0.870 moles * 1.008 g/mol = 0.877 g H. Mass of N = 6.315 g (initial mass) – 3.914 g C – 0.877 g H = 1.524 g N.

Convert the mass of N to moles and determine the empirical formula.

Use the molar mass of N (14.01 g/mol) to convert the mass of N to moles. Then, find the mole ratio of C, H, and N to determine the empirical formula. Moles of N = \(\frac{1.524 \mathrm{~g} \mathrm{~N}}{14.01 \mathrm{~g/mol} \mathrm{~N}}\) = 0.109 moles of N. The mole ratio of C:H:N is approximately 3:8:1 (0.326:0.870:0.109). So, the empirical formula is C3H8N.

Determine the molecular formula.

Find the molecular mass of the empirical formula and compare it to the given molar mass (116.2 g/mol). Find the multiple needed to reach the correct molecular mass, and apply that multiple to the empirical formula to find the molecular formula. Molar mass of empirical formula = (3 * 12.01 g/mol C) + (8 * 1.008 g/mol H) + (1 * 14.01 g/mol N) = 58.1 g/mol. Multiple needed = \(\frac{116.2 \mathrm{~g/mol}}{58.1 \mathrm{~g/mol}}\) = 2. Molecular formula = 2 * (C3H8N) = C6H16N2, which is the molecular formula of hexamethylenediamine.

Key concepts

Stoichiometry

Stoichiometry, at its core, serves as a bridge between the microscale world of atoms and molecules and the macroscale world of grams and liters that we interact with. It is the area of chemistry that quantifies the relationships between reactants and products in a chemical reaction using the mole concept.

For example, in the combustion of hexamethylenediamine, stoichiometry helps us understand how many moles of carbon dioxide and water are produced when a known amount of hexamethylenediamine reacts with oxygen.

From the textbook exercise, while solving for the empirical and molecular formulas, stoichiometry plays a pivotal role in determining the amount of each element that makes up the compound. The ratios of moles of carbon, hydrogen, and nitrogen derived from the combustion products give us the empirical formula. To convert to a molecular formula, stoichiometry allows us to scale up from the empirical formula using the molar mass, ensuring we have a formula that represents the actual number of atoms in a molecule of hexamethylenediamine.

Mole Concept

The mole concept is akin to a bridge uniting the subatomic world with one that we can measure and observe. In chemistry, the mole is a fundamental unit that represents a specific quantity of particles, usually atoms, molecules, or ions. One mole is defined as the amount of substance that contains as many particles as there are atoms in 12 grams of carbon-12, which is approximately 6.022 x 10^23 particles (Avogadro's number).

This concept lets us convert between mass, moles, and the number of atoms or molecules. For instance, in the calculation for hexamethylenediamine, moles were used as an intermediary to convert the mass of carbon dioxide and water to the mass of carbon, hydrogen, and nitrogen atoms in the compound. By knowing the molar masses of these substances, we can make these conversions and eventually apply them to find the empirical and molecular formulas.

Combustion Analysis

Combustion analysis is an experimental method used to determine the elemental composition of a compound, particularly for substances with carbon and hydrogen. By burning a known mass of the compound in pure oxygen, carbon and hydrogen are converted entirely to carbon dioxide (CO2) and water (H2O), respectively.

In combustion analysis, the masses of CO2 and H2O are measured. These masses can be converted into moles, as shown in the step-by-step solution, and used to deduce the moles and, subsequently, the mass of carbon and hydrogen present in the original compound. If the compound also contains other elements, such as nitrogen in hexamethylenediamine, their mass can be determined by subtracting the mass of carbon and hydrogen from the total mass of the compound. After all components are quantified, the empirical formula is found by determining the simplest whole-number ratio of moles of elements in the compound.