Question

Consider separate \(100.0-\mathrm{g}\) samples of each of the following: \(\mathrm{NH}_{3}, \mathrm{N}_{2} \mathrm{O}, \mathrm{N}_{2} \mathrm{H}_{4}, \mathrm{HCN}, \mathrm{HNO}_{3} .\) Arrange these samples from largest mass of nitrogen to smallest mass of nitrogen and prove/explain your order.

Short answer

The order of compounds from largest mass of nitrogen to smallest mass of nitrogen in 100 g samples is: \(\mathrm{N}_{2}\mathrm{H}_{4} (87.40\% \, \mathrm{N})\), \(\mathrm{NH}_{3} (82.23\% \, \mathrm{N})\), \(\mathrm{N}_{2}\mathrm{O} (63.63\% \, \mathrm{N})\), \(\mathrm{HCN} (51.83\% \, \mathrm{N})\), and \(\mathrm{HNO}_{3} (22.24\% \, \mathrm{N})\). This order is determined by calculating percent compositions of nitrogen in each compound using their respective molar masses.

Step-by-step solution

Calculate Percent Composition of Nitrogen in each compound.

First, we need to find the molar mass of each compound: Molar Mass of \(\mathrm{NH}_{3} = 14.01 (\mathrm{N}) + 3 \times 1.01 (\mathrm{H}) = 17.03\,\mathrm{g/mol}\) Molar Mass of \(\mathrm{N}_{2}\mathrm{O} = 2 \times 14.01 (\mathrm{N}) + 16.00 (\mathrm{O}) = 44.02\,\mathrm{g/mol}\) Molar Mass of \(\mathrm{N}_{2}\mathrm{H}_{4} = 2 \times 14.01 (\mathrm{N}) + 4 \times 1.01 (\mathrm{H}) = 32.05\,\mathrm{g/mol}\) Molar Mass of \(\mathrm{HCN} = 1.01 (\mathrm{H}) + 12.01 (\mathrm{C}) + 14.01 (\mathrm{N}) = 27.03\,\mathrm{g/mol}\) Molar Mass of \(\mathrm{HNO}_{3} = 1.01 (\mathrm{H}) + 14.01 (\mathrm{N}) + 3 \times 16.00 (\mathrm{O}) = 63.02\,\mathrm{g/mol}\) Now, we will calculate the percent composition of nitrogen in each compound: Percent Nitrogen in \(\mathrm{NH}_{3} = \frac{14.01}{17.03} \times 100\% = 82.23\%\) Percent Nitrogen in \(\mathrm{N}_{2}\mathrm{O} = \frac{2 \times 14.01}{44.02} \times 100\% = 63.63\%\) Percent Nitrogen in \(\mathrm{N}_{2}\mathrm{H}_{4} = \frac{2 \times 14.01}{32.05} \times 100\% = 87.40\%\) Percent Nitrogen in \(\mathrm{HCN} = \frac{14.01}{27.03} \times 100\% = 51.83\%\) Percent Nitrogen in \(\mathrm{HNO}_{3} = \frac{14.01}{63.02} \times 100\% = 22.24\%\)

Arrange the samples in descending order of Nitrogen percentage.

Using the percentages calculated in step 1, we can now arrange these samples from largest mass of nitrogen to the smallest mass of nitrogen: 1. \(\mathrm{N}_{2}\mathrm{H}_{4}\) (87.40% Nitrogen) 2. \(\mathrm{NH}_{3}\) (82.23% Nitrogen) 3. \(\mathrm{N}_{2}\mathrm{O}\) (63.63% Nitrogen) 4. \(\mathrm{HCN}\) (51.83% Nitrogen) 5. \(\mathrm{HNO}_{3}\) (22.24% Nitrogen) Thus, the order of compounds from largest mass of nitrogen to smallest mass of nitrogen is: \(\mathrm{N}_{2}\mathrm{H}_{4}\), \(\mathrm{NH}_{3}\), \(\mathrm{N}_{2}\mathrm{O}\), \(\mathrm{HCN}\), and \(\mathrm{HNO}_{3}\).

Key concepts

Molar Mass Calculation

Understanding molar mass is critical in determining the percent composition of nitrogen in any chemical compound. Molar mass is defined as the mass of one mole of a substance, and it is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, we sum the molar masses of each element present, multiplied by the number of atoms of that element in the compound. For example, for ammonia (\(NH_3\)), we add the molar mass of nitrogen (\(14.01g/mol\)) and three times the molar mass of hydrogen (\(1.01g/mol\)) as there are three hydrogen atoms.
Molar mass is fundamental as it serves as a conversion factor between the mass of a substance and the amount of substance (in moles). This concept is crucial in chemistry as it helps to quantify substances which then allows scientists and students to perform stoichiometric calculations and understand chemical reactions at a molecular level.

Chemical Compound Nitrogen Content

Determining the nitrogen content in a chemical compound involves calculating the percent composition of nitrogen. The percent composition is the percentage by mass of each element in a compound. To find the percent nitrogen, divide the total mass of nitrogen atoms by the molar mass of the compound and multiply the result by 100%. For example, the percent nitrogen in nitrogen gas (\(N_2O\)) is calculated by dividing the mass of nitrogen (which is two times its atomic mass since there are two nitrogen atoms) by the molar mass of \(N_2O\) and then multiplying by 100 to get the percentage.
This calculation tells us how much nitrogen, by mass, is present in a compound. It is particularly important for applications such as agriculture, where fertilizers' nitrogen content needs to be accurately known to ensure the proper growth of plants.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of the mole. Through stoichiometry, students learn to balance chemical equations and use proportional relationships to calculate the mass, moles, or volume of reactants and products involved.

• It enables the prediction of the outcomes of reactions, identifying limiting reactants and calculating theoretical yields.
• In this case, stoichiometry is applied to compare amounts of nitrogen across different compounds.
• Given the mass of each compound sample, we can use its percent nitrogen to find the amount of nitrogen present.

For comprehending chemical processes, both in academic problems and real-world applications, stoichiometry acts as a crucial tool, enabling the understanding and design of chemical reactions.