Question

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?

Short answer

Answer: To find the simplest and molecular formulas of a compound, follow these steps: 1. Calculate the moles of each element in the compound using the masses of the products formed. 2. Calculate the moles of any remaining elements by considering the mass conservation law. 3. Determine the empirical formula by finding the smallest whole number ratio of moles of each element. 4. Calculate the molar mass of the empirical formula. 5. Find the molecular formula by comparing the molar mass of the empirical formula with the given molar mass of the compound and adjusting the composition of the empirical formula accordingly.

Step-by-step solution

Calculate the moles of carbon and hydrogen

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: $$\text{moles of hydrogen} = \frac{7.832 \mathrm{~g} \: H_2O}{18.02 \mathrm{~g/mol} \: H_2O} * \frac{2 \mathrm{~mol} \: H}{1 \mathrm{~mol} \: H_2O} = 0.869 \mathrm{~mol} \: H$$

Calculate the moles of nitrogen

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.

Key concepts

Molecular Formula

Molecular formulas represent the actual number of atoms of each element in a molecule of a compound. It is crucial in understanding the true composition of a compound rather than just the basic ratio of elements. For hexamethylenediamine, we are given its molar mass as 116.2 g/mol. After calculating the moles of each element involved and determining their ratios, we can arrive at the empirical formula. However, to find the molecular formula, we need to ensure that the molar mass of the empirical formula corresponds fractions or multiples to the given molar mass. This involves dividing the compound's molar mass by the empirical formula's molar mass, providing a factor by which each subscript in the empirical formula should be multiplied to produce the molecular formula.

Mass Conservation

The Law of Mass Conservation is fundamental in chemical reactions. This law states that mass is neither created nor destroyed in a chemical reaction. When hexamethylenediamine combusts, the total mass of the reactants must equal the total mass of the products. In this case, you mix hexamethylenediamine with oxygen to produce carbon dioxide and water, along with nitrogen-containing products.

• The total initial mass is calculated as the sum of the reactant masses: here, just the mass of hexamethylenediamine, which is 6.315 g.
• Then, the products are weighed. In this exercise, the combined masses of CO2 and H2O give us an idea of the result, leading to a discrepancy as the expected product nitrogen is not considered properly due to wrong data.

This highlights the importance of correct and complete data in verifying the law during chemistry exercises.

Moles Calculation

Calculating moles is a cornerstone of understanding chemistry, as it allows us to work with amounts of substances in chemical reactions. In the context of hexamethylenediamine combustion, here's how you approach mole calculations:

Given the amount of CO2 produced, along with its molar mass (44.01 g/mol), you calculate the moles of carbon by dividing the mass of CO2 by its molar mass. Each mole of CO2 contains one mole of carbon, making it straightforward to find that there are 0.326 moles of carbon.

Similarly, using the molar mass of H2O (18.02 g/mol), calculate the moles of hydrogen found in the water produced. Since each molecule of water contains two hydrogen atoms, the number of moles of hydrogen is double the moles of water, resulting in 0.869 moles of hydrogen.
Understanding how to step through these calculations opens up deeper insights into balancing chemical equations and finding stoichiometric relationships.

Hexamethylenediamine Combustion

The combustion of hexamethylenediamine is a classic representation of how organic compounds can be decomposed into simpler molecules like carbon dioxide and water through burning. This type of reaction typically requires oxygen and results in a complete breakdown of the compound, releasing energy in the process.

• Combustion gives insight into the structural composition of hexamethylenediamine, emphasizing its carbon, hydrogen, and inevitable nitrogen content.
• The analysis of products such as CO2 and H2O helps to retrieve empirical data about the combustion process, showcasing real-world applications of theoretical chemistry concepts.
• Unfortunately, the given exercise data hinted at an inconsistency, particularly regarding nitrogen calculation, demonstrating that combustion analyses can sometimes be challenged by data irradiation or errors.

This understanding helps reinforce the principles of chemical reactions, mass conservation, and analytical methods within chemistry.