Question

In Dumas method, \(0.2 \mathrm{~g}\) of an organic nitrogenous compound gave \(28 \mathrm{ml}\) of \(\mathrm{N}_{2}\) (volume reduced to \(0^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) ). What is the percentage of nitrogen, by mass, in the compound? (a) \(17.5\) (b) \(8.75\) (c) \(35.0\) (d) \(14.0\)

Short answer

Question: Calculate the percentage of nitrogen by mass in an organic nitrogenous compound if 0.2 g of the compound produced 28 ml of N2 gas at 0°C and 1 atm through the Dumas method. Answer: 17.5%

Step-by-step solution

Understand the Dumas Method and Given Information

In the Dumas method, nitrogen in the organic compound is converted to nitrogen gas (N2). We are given that 0.2 g of the organic nitrogenous compound produced 28 ml of N2 gas at 0°C and 1 atm. Keep these given values in mind for further calculations.

Convert the volume of N2 gas to moles using the Ideal Gas Law

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the amount of gas in moles, R is the ideal gas constant, and T is the temperature in Kelvin. In this case, we have P = 1 atm, V = 28 ml (or 0.028 L), R = 0.0821 L atm/mol K, and T = 273 K (0°C). To find the moles of N2 gas (n), we can rearrange the ideal gas law: n = PV / RT n = (1 atm * 0.028 L) / (0.0821 L atm/mol K * 273 K) n ≈ 0.00125 moles

Calculate the mass of nitrogen gas (N2) using its molar mass

To find the mass of N2 gas, multiply the moles of N2 by its molar mass: m_N2 = n_N2 * M_N2. The molar mass of nitrogen gas (N2) is 28 g/mol. m_N2 = 0.00125 moles * 28 g/mol m_N2 ≈ 0.035 g

Calculate the percentage of nitrogen by mass in the organic compound

Now that we have the mass of N2 gas (which is solely comprised of nitrogen), we can calculate the percentage of nitrogen in the organic compound using the following formula: Percentage of Nitrogen = (Mass of Nitrogen in the compound / Total mass of the compound) * 100 Percentage of Nitrogen = (0.035 g / 0.2 g) * 100 Percentage of Nitrogen = 17.5% The correct answer is (a) 17.5%.

Key concepts

Nitrogen Gas Determination

The Dumas method is a classic technique employed to determine the nitrogen content present within an organic compound. In this method, the organic compound is combusted, leading to the release of nitrogen gas (\(\mathrm{N}_{2}\)). This gas is then measured to ascertain how much nitrogen was originally in the compound.

To carry out this process accurately, it is crucial that the sample and experimental setup ensure complete conversion of all nitrogen present in the compound into nitrogen gas. Once the nitrogen gas is collected, its volume is used in further calculations to determine the nitrogen content.

This methodology is particularly useful due to its straightforwardness and ability to handle a variety of organic nitrogenous compounds, allowing chemists and researchers to gather significant insights into the molecular composition of these substances.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry represented as \(PV = nRT\), where:

• \(P\) stands for pressure,
• \(V\) is the volume,
• \(n\) is the number of moles,
• \(R\) is the gas constant (0.0821 L atm/mol K),
• \(T\) represents temperature in Kelvin.

This equation allows scientists to relate various physical properties of gases and is essential when determining the moles of gas in an experiment.

For instance, in the context of the problem relying on the Dumas method, it's applied to convert the measured volume of nitrogen gas collected at a standardized temperature and pressure into moles. By rearranging the formula to solve for \(n\), we obtain the number of moles of \(\mathrm{N}_{2}\), which is crucial for knowing nitrogen's mass in the sample.

The accuracy of such calculations can greatly impact the determination of nitrogen contents in organic compounds, reflecting the importance of understanding and applying this law correctly.

Organic Nitrogenous Compounds

Organic nitrogenous compounds are rich in nitrogen and play a significant role in both chemistry and biology. These compounds are varied and include proteins, amino acids, nucleic acids, and certain alkaloids and amines.

Understanding the nitrogen content in these substances is crucial since it affects their functions and characteristics. The nitrogen determination in the Dumas method provides insight into the purity and molecular structure of such compounds.

Knowing how much nitrogen is present can reveal the proportion of the sample that consists of nitrogen-containing functional groups or the degree of nitrogen saturation. This is pivotal when analyzing biological samples, food items, pharmaceuticals, and various chemical formulations.

Molar Mass Calculation

Calculating molar mass is a core concept in chemistry that helps determine the mass of a given substance per mole. For a molecule like nitrogen gas (\(\mathrm{N}_{2}\)), the molar mass is computed by adding the atomic masses of the nitrogen atoms involved. Since nitrogen has an atomic mass of 14 g/mol, the molar mass of nitrogen gas is calculated as 27 g/mol.

In the solution of the problem, this molar mass is used to find the actual mass of the nitrogen gas produced, via multiplying the number of moles calculated from the ideal gas law application by the molar mass of nitrogen gas.

Mastering this calculation ensures that chemists can link moles to actual quantities, enabling practical application of theoretical knowledge. It is beneficial for anyone studying stoichiometry, chemical reactions, and compound analysis, providing a tangible measure of the amounts involved.