Question

The combustion method used to analyze for carbon and hydrogen can be adapted to give percentage \(\mathrm{N}\) by collecting the nitrogen from combustion of the eompound as \(\mathrm{N}_{2}\). A sample of a compound weighing \(8.75 \mathrm{mg}\) gave \(1.59 \mathrm{~mL} \mathrm{~N}_{2}\) at \(25^{\circ} \mathrm{C}\) and \(749 \mathrm{mmHg} .\) What is the percent- age \(\mathrm{N}\) in the compound?

Short answer

The percentage of nitrogen in the compound is approximately 20.8%.

Step-by-step solution

Convert Volume to Moles

First, we'll convert the volume of nitrogen gas (2) to moles using the ideal gas law, PV = nRT.Given: Pressure, P = 749 mmHg = 749/760 atmVolume, V = 1.59 mL = 0.00159 LTemperature, T = 25°C = 298 K (in Kelvin)R (ideal gas constant) = 0.0821 L·atm/(mol·K)The formula for the ideal gas law can be rearranged to find the number of moles (n):\[ n = \frac{PV}{RT} \]Substitute the values into the equation:\[ n = \frac{(749/760 \, \text{atm}) \times 0.00159 \, \text{L}}{0.0821 \, \text{L·atm/(mol·K)} \times 298 \, \text{K}} \] After calculation, moles of 2 = 6.5 \times 10^{-5} \text{ mol}.

Convert Moles of N2 to Mass of Nitrogen

Since nitrogen gas (2) is diatomic, each molecule of 2 contains two atoms of nitrogen.Therefore, moles of nitrogen atoms = 2 × moles of 2 = 2 × 6.5 \times 10^{-5} = 1.3 \times 10^{-4} \text{ mol N}. The atomic mass of nitrogen (N) is 14.01 g/mol, so the mass of nitrogen is given by:\[ \text{Mass of N} = (1.3 \times 10^{-4} \, \text{mol}) \times (14.01 \, \text{g/mol}) = 1.82 \times 10^{-3} \, \text{g} \] Thus, 1.82 mg N was collected.

Calculate Percentage of N

Finally, calculate the percentage of nitrogen in the sample using the formula:\[ \text{Percentage } N = \left(\frac{\text{Mass of N}}{\text{Mass of compound}}\right) \times 100 \]\[ \text{Percentage } N = \left(\frac{1.82 \, \text{mg}}{8.75 \, \text{mg}}\right) \times 100 \approx 20.8\% \] Thus, the percentage of nitrogen in the compound is approximately 20.8%.

Key concepts

Combustion Analysis

Combustion analysis is a common method used in chemistry to determine the elemental composition of a compound. In this method, the compound is completely burned in oxygen to yield gases like carbon dioxide (from carbon), water vapor (from hydrogen), and nitrogen gas (from nitrogen).
The gases are collected and measured, such as nitrogen being collected as \(\mathrm{N_2}\). By analyzing these gases, chemists can calculate the amounts of each element in the original sample.
Combustion analysis is particularly useful for organic compounds, which are primarily made up of carbon, hydrogen, and nitrogen.

• Carbon is determined as carbon dioxide (\(\mathrm{CO_2}\)).
• Hydrogen is measured as water (\(\mathrm{H_2O}\)).
• Nitrogen is collected as nitrogen gas (\(\mathrm{N_2}\)).

By using these measured volumes and the ideal gas law, chemists can work backward to find the percentage composition of each element within the compound.

Mole Calculation

In chemistry, the mole is a standard unit used to express amounts of a chemical substance. Knowing how to calculate moles is crucial for converting between different units.
The ideal gas law, represented as \(PV = nRT\), allows chemists to solve for the number of moles (\(n\)) of a gas, given its pressure (\(P\)), volume (\(V\)), and temperature (\(T\)). Here, R is the ideal gas constant.
In the context of this problem, the volume of the nitrogen gas produced from combustion was converted into moles using this formula: \[n = \frac{PV}{RT} \]
In this case:

• Convert the pressure from mmHg to atm to match the units of R, the gas constant.
• Convert volume from mL to L.
• Convert Celsius to Kelvin.

By plugging these values into the formula, you find the moles of nitrogen gas. Understanding mole calculations is foundational for stoichiometry and other chemistry applications.

Nitrogen Percentage

Calculating the nitrogen percentage in a compound is essential for understanding its composition. Once moles of nitrogen are known, they can be converted to grams using the atomic mass of nitrogen.
Using the equation: \[\text{Mass of } \mathrm{N} = (\text{moles of } \mathrm{N})(\text{molar mass of } \mathrm{N})\]
This value can then be used to find the percentage of nitrogen in the overall sample:

• Determine the total mass of nitrogen collected.
• Divide the mass of nitrogen by the total mass of the compound sample.
• Multiply by 100 to get a percentage.

In this problem, the percentage of nitrogen was calculated using the formula: \[\text{Percentage } \mathrm{N} = \left(\frac{\text{Mass of } \mathrm{N}}{\text{Mass of compound}}\right) \times 100\]
This provides insight into how much nitrogen is part of the compound, expressed as a percentage, which was approximately 20.8% in this scenario.

Chemical Stoichiometry

Chemical stoichiometry involves calculating the quantities of reactants and products in chemical reactions. It is an essential part of chemistry that helps predict the results of mixing substances.
Stoichiometry is based on the law of conservation of mass where the mass of the reactants equals the mass of the products.
For stoichiometry related to combustion analysis, one starts by understanding the balanced chemical equation for the reaction.

• Determine the volume of nitrogen collected and its conversion into moles.
• Convert moles of nitrogen into mass using its molar mass.
• Use the mass of nitrogen to calculate its percentage in the compound.

These steps show the practical application of stoichiometry, by converting analytical data into chemical quantities.
Understanding this concept helps chemists to analyze and design experiments efficiently, ensuring the correct proportions of elements or compounds are used.