Question

In the estimation by Duma's method, \(0.59 \mathrm{~g}\). of an organic compound gave \(112 \mathrm{~mL}\) nitrogen at NTP. The percentage of nitrogen in the compound is about: (a) \(23.7\) (b) \(16.8\) (c) \(33.07\) (d) \(27.5\)

Short answer

The percentage of nitrogen in the compound is approximately 23.7%, option (a).

Step-by-step solution

Identify Given and Required

We are given the mass of the organic compound as \(0.59 \text{ g}\) and the volume of nitrogen gas at NTP as \(112 \text{ mL}\). We need to calculate the percentage of nitrogen in the compound.

Convert Volume to Moles

Using the molar volume of a gas at NTP, which is \(22.4 \text{ L/mol}\) or \(22400 \text{ mL/mol}\), we convert the volume of nitrogen gas to moles. \[ \text{Moles of } N_2 = \frac{112 \text{ mL}}{22400 \text{ mL/mol}} = 0.005 \text{ mol}\]

Calculate the Mass of Nitrogen Gas

The molecular mass of nitrogen gas \(N_2\) is \(28 \text{ g/mol}\). Using the moles calculated, we find the mass of nitrogen. \[\text{Mass of } N_2 = 0.005 \text{ mol} \times 28 \text{ g/mol} = 0.14 \text{ g}\]

Calculate the Percentage of Nitrogen

Using the mass of nitrogen and the total mass of the compound, we calculate the percentage of nitrogen. \[\text{Percentage of } N = \left( \frac{0.14 \text{ g}}{0.59 \text{ g}} \right) \times 100 = 23.7\%\]

Select the Correct Answer

The calculated percentage of nitrogen is approximately \(23.7\%\), which corresponds to option (a).

Key concepts

Nitrogen Estimation

Nitrogen estimation refers to the process of determining the nitrogen content in a substance, commonly practiced in the field of organic chemistry. One popular method for nitrogen estimation is the Dumas Method, which involves combusting a sample in the presence of oxygen to convert all nitrogen to nitrogen gas \(N_2\).

In our example, the Dumas method is used to determine the percentage of nitrogen in an organic compound. We start by taking a small quantity of the compound and precisely measuring the nitrogen gas produced upon complete combustion.

The percentage of nitrogen is calculated by dividing the mass of nitrogen by the total mass of the organic compound, then multiplying by 100. Accurately determining the nitrogen content is important for various applications, including pharmaceutical calculations, agricultural fertilizer requirements, and nutritional analysis.

Molar Volume at NTP

NTP stands for Normal Temperature and Pressure, which refers to a condition of 0°C (273.15 K) temperature and 1 atm (101.3 kPa) pressure. At NTP, the molar volume of an ideal gas is approximately 22.4 liters per mol.

The concept of molar volume is crucial in stoichiometry because it allows us to convert between the volume of gas and the number of moles. This property assists in the direct calculation of moles from the given volume.

For the problem at hand, knowing the molar volume at NTP helped us convert the volume of nitrogen gas (112 mL) into moles. By using the molar volume, students can apply this in solving exercises related to gas chemical reactions and predicting gas behavior under standard conditions.

Organic Compound Analysis

Organic compound analysis involves identifying the components of organic compounds through various testing methods. Understanding what makes up a compound is integral for chemists, as it enables them to determine molecular structures and compositions.

The Dumas method is just one approach used in organic compound analysis, particularly in quantifying nitrogen. There are many other elements and molecule assessments like carbon, hydrogen, and oxygen estimation methods that are part of understanding organic compounds.

The goal of organic compound analysis is to thoroughly understand a compound's molecular makeup, which helps in applications ranging from pharmaceuticals to petrochemicals. A thorough analysis provides information needed to synthesize new compounds or enhance the properties of existing ones.