Problem 121 - General Chemistry: Principles and Modern Applications

Question

The greatest number of \(\mathrm{N}\) atoms is found in (a) \(50.0 \mathrm{g}\) \(\mathrm{N}_{2} \mathrm{O} ;\) (b) \(17.0 \mathrm{g} \mathrm{NH}_{3} ;\) (c) \(150 \mathrm{mL}\) of liquid pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{N}(d=0.983 \mathrm{g} / \mathrm{mL}) ;\) (d) \(1.0 \mathrm{mol} \mathrm{N}_{2}\)

Step-by-Step Solution

Answer

After calculating and comparing the number of Nitrogen atoms for each substance, the substance with the largest number of Nitrogen atoms can be identified. Remember, always carry out these calculations carefully and thoughtfully.

Step 1: Calculate the number of moles for each compound

For each compound, use its molar mass and given mass or volume to find the number of moles. For \(N_2O\), use the molar mass approximately 44 g/mol, for \(NH_3\) use the molar mass about 17 g/mol. For Pyridine \(C_5H_5N\) first, we need to convert the volume to mass using the density (0.983 g/mL), then use molar mass which is approximately 79 g/mol. For \(N_2\), it's already in moles, so no further calculation is needed.

Step 2: Calculate number of nitrogen atoms for each compound

For \(N_2O\), there are two nitrogen atoms, so double the number of moles. For \(NH_3\) there is one nitrogen atom, so the number of moles equals the number of Nitrogen atoms. For pyridine, there is one Nitrogen atom, so again, the number of moles equals the number of Nitrogen atoms. For \(N_2\), as there are 2 nitrogen atoms, double the number of moles.

Step 3: Compare the final numbers

After calculating the number of Nitrogen atoms for each compound, compare these numbers to identify which is the largest and thus answer the original question.

Key Concepts

Molar Mass

Chemistry often requires understanding how the mass of atoms and molecules relate to the larger scales we work with in lab settings. Molar mass is the mass of one mole of a substance. It’s expressed in grams per mole (g/mol).
When working with chemical calculations, knowing the molar masses of elements and compounds helps convert between mass and number of moles. For instance:

• The molar mass of nitrogen gas, \(N_2\), is approximately 28 g/mol, considering each nitrogen atom has a molar mass of about 14 g/mol.
• For nitrous oxide, \(N_2O\), the molar mass is roughly 44 g/mol (28 g/mol for \(N_2\) + 16 g/mol for one oxygen atom).
• Ammonia, \(NH_3\), have a molar mass of approximately 17 g/mol.

Understanding molar mass allows us to convert particle masses into usable, comparable mole units for calculations.

Nitrogen Atoms

The calculation of the number of nitrogen atoms in a substance involves determining how many moles of nitrogen there are and then using Avogadro’s number. Avogadro's number is\( 6.022 \times 10^{23} \) atoms/mol, which converts moles into atoms.
Different compounds have different numbers of nitrogen atoms:

• In \(N_2O\), there are 2 nitrogen atoms per molecule, meaning you double the number of moles when finding nitrogen atoms.
• \(NH_3\) contains 1 nitrogen atom per molecule, so the moles of \(NH_3\) equates directly to moles of nitrogen atoms.
• In pyridine \((C_5H_5N)\), there is 1 nitrogen atom in each molecule.
• For nitrogen gas \((N_2)\), each molecule has 2 nitrogen atoms, hence, you multiply the moles by 2.

This understanding helps in calculating the correct numbers of nitrogen atoms across different scenarios.

Chemical Compounds

Chemical compounds are substances produced when atoms of different elements bond together in a specific ratio. They are represented by chemical formulas which provide insight into their composition and the quantity of each constituent element.
A few examples include:

• \(N_2O\), commonly known as nitrous oxide, indicates the presence of nitrogen and oxygen in a 2:1 ratio.
• \(NH_3\), or ammonia, shows one nitrogen atom paired with three hydrogen atoms.
• Pyridine \((C_5H_5N)\) illustrates a compound where carbon, hydrogen, and nitrogen atoms are bonded in a precise structure, often used in industrial applications.

Understanding chemical compounds involves knowing their empirical and molecular formula, which guide the preparation and reactions in chemical processes.

Density Calculation

Density is a measure of how much mass exists in a given volume. It’s often expressed in grams per milliliter (g/mL) in chemistry.
For example, if you're given the volume and need to find the mass, use the formula:\[ \text{Mass} = \text{Density} \times \text{Volume} \]

For pyridine in our exercise, knowing its density is 0.983 g/mL allows us to multiply by the volume to convert it to mass:

• Using a volume of 150 mL, the mass becomes \(150 \, \text{mL} \times 0.983 \, \text{g/mL} = 147.45 \, \text{g}\).

This calculated mass information can then be utilized to find the number of moles, using its molar mass, leading to further chemical analyses like determining the number of atoms when calculating empirical formulas or conducting reactions.Density provides a critical link between the physical substance and standard chemical units.