Question

What number of atoms of nitrogen are present in \(5.00 \mathrm{~g}\) of each of the following? a. glycine, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}_{2} \mathrm{~N}\) b. magnesium nitride c. calcium nitrate d. dinitrogen tetroxide

Short answer

The number of nitrogen atoms in 5.00 g of each compound are as follows: a. Glycine: \(4.01\times10^{22}\) N atoms b. Magnesium Nitride: \(5.96\times10^{22}\) N atoms c. Calcium Nitrate: \(3.67\times10^{22}\) N atoms d. Dinitrogen Tetroxide: \(6.54\times10^{22}\) N atoms

Step-by-step solution

Determine the molar mass of each compound

We will use the periodic table to find the molar mass of each element in the compound, then add them together to find the total molar mass of each compound. a. Glycine: C₂H₅O₂N Molar Mass = (2 × C) + (5 × H) + (2 × O) + N Molar Mass = (2 × 12.01) + (5 × 1.01) + (2 × 16.00) + 14.01 Molar Mass = 75.07 g/mol b. Magnesium Nitride: Mg₃N₂ Molar Mass = (3 × Mg) + (2 × N) Molar Mass = (3 × 24.31) + (2 × 14.01) Molar Mass = 100.95 g/mol c. Calcium Nitrate: Ca(NO₃)₂ Molar Mass = Ca + (2 × (N + (3 × O))) Molar Mass = 40.08 + (2 × (14.01 + (3 × 16.00))) Molar Mass = 164.10 g/mol d. Dinitrogen Tetroxide: N₂O₄ Molar Mass = (2 × N) + (4 × O) Molar Mass = (2 × 14.01) + (4 × 16.00) Molar Mass = 92.02 g/mol

Determine the molar mass of nitrogen

From the periodic table, the molar mass of nitrogen (N) is 14.01 g/mol.

Determine the moles of each compound

We will now use the 5.00 g of each compound and divide it by their respective molar masses to find the moles of each compound. a. Glycine: Moles = 5.00 g / 75.07 g/mol = 0.06664 mol b. Magnesium Nitride: Moles = 5.00 g / 100.95 g/mol = 0.04953 mol c. Calcium Nitrate: Moles = 5.00 g / 164.10 g/mol = 0.03046 mol d. Dinitrogen Tetroxide: Moles = 5.00 g / 92.02 g/mol = 0.05433 mol

Determine the number of nitrogen atoms in each mole of the compound

a. Glycine: 1 nitrogen atom per mole b. Magnesium Nitride: 2 nitrogen atoms per mole c. Calcium Nitrate: 2 nitrogen atoms per mole d. Dinitrogen Tetroxide: 2 nitrogen atoms per mole

Calculate the total number of nitrogen atoms in 5.00 g of each compound

We will multiply the moles of each compound by the number of nitrogen atoms in each mole of the compound, and then by Avogadro's number (6.022 x 10²³) to find the total number of nitrogen atoms. a. Glycine: \(0.06664\text{ mol } \times 1 \times 6.022\times10^{23}\) atoms = \(4.01\times10^{22}\) N atoms b. Magnesium Nitride: \(0.04953\text{ mol } \times 2 \times 6.022\times10^{23}\) atoms = \(5.96\times10^{22}\) N atoms c. Calcium Nitrate: \(0.03046\text{ mol } \times 2 \times 6.022\times10^{23}\) atoms = \(3.67\times10^{22}\) N atoms d. Dinitrogen Tetroxide: \(0.05433\text{ mol } \times 2 \times 6.022\times10^{23}\) atoms = \(6.54\times10^{22}\) N atoms

Key concepts

Molar Mass

The concept of molar mass is crucial in chemistry because it allows you to relate mass to moles, which in turn helps you determine the number of atoms or molecules present in a sample. The molar mass of a compound is the mass of one mole of that compound, expressed in grams per mole (g/mol). To find the molar mass, simply add up the masses of all the atoms in a single molecule of the compound using the periodic table.

Here's a simple breakdown of how calculating the molar mass works:

• Identify the elements in the compound.
• Determine the molar mass of each element (typically listed in atomic mass units on the periodic table).
• Multiply the molar mass of each element by the number of times that element appears in the compound.
• Sum up these values to get the total molar mass of the compound.

For example, the molar mass of glycine (\(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{O}_{2}\mathrm{N}\)) is found by adding 2 carbon atoms, 5 hydrogen atoms, 2 oxygen atoms, and 1 nitrogen atom, leading to a molar mass of 75.07 g/mol.

Understanding molar mass is essential for transitioning between the mass of a substance and the amount in moles, a critical step in many chemical calculations.

Nitrogen Atoms

Nitrogen atoms are a vital part of many chemical compounds, especially in organic and biochemical reactions. When calculating the number of nitrogen atoms, it's important to recognize how many nitrogen atoms are present in the formula of a compound or molecule.

Here's how you can find out the number of nitrogen atoms in a compound:

• Look at the chemical formula of the compound to identify nitrogen atoms. For instance, in dinitrogen tetroxide (N₂O₄), there are 2 nitrogen atoms.
• Use this information in your calculations to find the total number of nitrogen atoms present in a given mass of the compound.

To determine the total number of nitrogen atoms in a sample, you need the number of moles of the compound and the number of nitrogen atoms per molecule. You then use Avogadro's number to convert moles to atoms.

This understanding lets you explore how nitrogen, as an essential element, interacts and binds with other atoms, forming a variety of compounds with unique properties beneficial in processes like protein synthesis in living organisms.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, representing the number of atoms, ions, or molecules in one mole of a substance. The value is approximately \(6.022 imes 10^{23}\),and it is named after the scientist Amedeo Avogadro. This constant is essential because it provides the conversion factor between moles and the count of atoms or molecules.

Using Avogadro's number in calculations:

• First, determine the number of moles of the substance you're working with.
• Identify the quantity of specific atoms or molecules per mole of the substance from its chemical formula.
• Multiply the number of moles by Avogadro's number to calculate the total number of such atoms or molecules.

For example, if you have 0.06664 moles of glycine and know there is 1 nitrogen atom per molecule, multiplying \(0.06664 imes 6.022 imes 10^{23}\) gives you the total nitrogen atoms. This calculation is crucial for quantitative chemical analysis, helping to translate the macro-world into the nano-world scale.

Chemical Compounds

Chemical compounds are substances formed by the chemical combination of two or more elements. In these compounds, elements are present in fixed ratios, governed by the principles of chemical bonding, which can be ionic or covalent. The properties of chemical compounds vary significantly, influenced by the types and arrangements of atoms within them.

Key points about chemical compounds:

• Chemical formulas represent the types and numbers of atoms in a compound—for example, calcium nitrate is Ca(NO₃)₂, containing calcium, nitrogen, and oxygen atoms.
• The properties of chemical compounds depend on their atomic arrangements and the types of bonds holding the atoms together.
• Compounds have unique molar masses which are critical for navigating reactions and producing the desired chemical quantity from a given amount of reactant or product.

Understanding chemical compounds allows you to predict reactions and behaviors of materials, making them central to the study of chemistry and applicable in disciplines ranging from material science to pharmacology.