Question

The nitrogen content of organic compounds can be determined by the Dumas method. The compound in question is first reacted by passage over hot \(\mathrm{CuO}(s)\) : $$ \text { Compound } \stackrel{\mathrm{Hot}}{\longrightarrow} \mathrm{N}_{2}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ The product gas is then passed through a concentrated solution of \(\mathrm{KOH}\) to remove the \(\mathrm{CO}_{2}\). After passage through the KOH solution, the gas contains \(\mathrm{N}_{2}\) and is saturated with water vapor. In a given experiment a \(0.253-\mathrm{g}\) sample of a compound produced \(31.8 \mathrm{~mL} \mathrm{~N}_{2}\) saturated with water vapor at \(25^{\circ} \mathrm{C}\) and 726 torr. What is the mass percent of nitrogen in the compound? (The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is \(23.8\) torr.)

Short answer

The mass percent of nitrogen in the compound can be calculated by first finding the moles of nitrogen gas produced, converting it to mass, and then finding the mass percent using the given mass of the sample. The moles of nitrogen gas can be found using the ideal gas equation, which shows that 0.00134 moles of nitrogen gas were produced. The mass of nitrogen gas produced is 0.0188 g. Finally, the mass percent of nitrogen in the compound is 7.43%.

Step-by-step solution

Calculate moles of nitrogen gas

To calculate moles of nitrogen gas produced, first, we need to determine the pressure of nitrogen gas in the mixture. The total pressure of the mixture is 726 torr, and we know the vapor pressure of water at 25 degrees Celsius is 23.8 torr. We can calculate the pressure of nitrogen gas (P_N2) by subtracting the vapor pressure of water from the total pressure: \(P_{N2} = P_{total} - P_{H2O} = 726\,\text{torr} - 23.8\,\text{torr} = 702.2\,\text{torr}\) Now, we use the ideal gas equation to determine the moles of nitrogen gas produced: \(n_{N2} = \dfrac{P_{N2}\,V_{N2}}{RT}\) where \(n_{N2}\) is the moles of nitrogen gas, \(P_{N2}\) is the pressure of nitrogen gas, \(V_{N2}\) is the volume of nitrogen gas, R is the ideal gas constant and T is the temperature. Using the values given in the problem, we can calculate the moles of nitrogen gas.

Use the ideal gas equation to calculate the moles of nitrogen gas

First, it is important to convert the volume of nitrogen gas from milliliters to liters: \(V_{N2} = 31.8\,\text{mL} \times \dfrac{1\,\text{L}}{1000\,\text{mL}} = 0.0318\,\text{L}\) Additionally, we need to convert the pressure of nitrogen gas from torr to atmospheres: \(P_{N2} = 702.2\,\text{torr} \times \dfrac{1\,\text{atm}}{760\,\text{torr}} = 0.924\,\text{atm}\) Now, we can plug these values into the ideal gas equation using the gas constant R = 0.08206 L*atm/mol*K and the temperature T = 25 degrees Celsius + 273.15 = 298.15 K: \(n_{N2} = \dfrac{0.924\,\text{atm} \times 0.0318\,\text{L}}{0.08206\,\text{L}\cdot\text{atm/mol}\cdot\text{K} \times 298.15\,\text{K}}\) \(n_{N2} = 0.00134\,\text{moles}\)

Convert moles of nitrogen to mass

Now, we will convert moles of nitrogen to mass using the molar mass of nitrogen, which is 14.01 g/mol: mass_N2 = moles_N2 x molar_mass_N2 mass_N2 = 0.00134 moles × 14.01 g/mole = 0.0188 g

Calculate mass percent of nitrogen

Finally, we will calculate the mass percent of nitrogen in the compound: mass_percent_N = (mass_N2 / mass_sample) × 100% mass_percent_N = (0.0188 g / 0.253 g) × 100% = 7.43% The mass percent of nitrogen in the compound is 7.43%.

Key concepts

Nitrogen Content Determination

The Dumas method is a valuable technique used to determine the nitrogen content in organic compounds. This method involves heating the organic compound, resulting in its decomposition. The nitrogen present in the compound is transformed into nitrogen gas, which can then be measured to calculate its amount in the original compound.

The general reaction involves the compound passing over hot copper(II) oxide (\( \text{CuO} \)), leading to the production of nitrogen gas (\( \text{N}_2 \)) along with water vapor and carbon dioxide. The gases are then treated with a potassium hydroxide (\( \text{KOH} \)) solution to absorb carbon dioxide, leaving only nitrogen gas and water vapor.

• The nitrogen gas collected is often mixed with water vapor due to the conditions of the experiment.
• It is crucial to subtract the pressure contributed by water vapor to isolate the true pressure due to nitrogen gas alone.

Determining the nitrogen content helps in understanding the composition and nature of the organic compound.

Organic Compounds

Organic compounds are primarily made up of carbon atoms connected through covalent bonds, often accompanied by hydrogen, oxygen, and nitrogen atoms. These compounds form the basis of life and include substances like proteins, carbohydrates, and many industrial chemicals.

In the context of nitrogen determination, organic compounds are analyzed to identify their nitrogen content because nitrogen is an essential element in many biological molecules, like amino acids and nucleotides.

• First, the compound is decomposed through a chemical reaction which reveals the nitrogen contents.
• Recognizing these compounds helps chemists understand reactivity, physical properties, and potential uses or applications.

Therefore, accurately determining their nitrogen content is essential for applications in chemistry, biology, and material science.

Ideal Gas Law

The ideal gas law is a key equation in chemistry that relates the pressure, volume, and temperature of a gas to the number of moles. This relationship is expressed as \( PV = nRT \), where:

• \( P \) is the pressure of the gas.
• \( V \) is the volume it occupies.
• \( n \) is the amount of substance in moles.
• \( R \) is the ideal gas constant (approximately 0.08206 L·atm/mol·K).
• \( T \) is the temperature in Kelvin.

This equation is incredibly useful for converting between these properties when dealing with ideal gases, like nitrogen.

In the Dumas method, after collecting data on pressure, volume, and temperature, the ideal gas law allows us to determine the moles of nitrogen gas produced. it is necessary to convert volume and pressure to appropriate units (liters and atmospheres) before performing the calculations.

Calculating these moles is pivotal for determining the nitrogen's mass within the sample.

Mass Percent Calculation

Mass percent is a way of expressing the concentration of a component (in this case, nitrogen) in a mixture or compound. It is calculated as the ratio of the mass of the component to the total mass of the compound, multiplied by 100%:\[\text{Mass Percent} = \left( \frac{\text{Mass of Nitrogen}}{\text{Total Mass of Sample}} \right) \times 100%\]

In our case, after finding the mass of nitrogen from its moles using its molar mass (14.01 g/mol for nitrogen), we use the initial mass of the organic sample to calculate its mass percent.

• This calculation tells us what percentage of the compound's total mass is due to nitrogen.
• It quantifies how much of the sample consists of nitrogen, which helps verify the compound's molecular formula and structure.

Such percentage calculations are particularly useful in chemistry for understanding compositions and ensuring balance in chemical equations or reactions.