Chemical Composition and Atomic Mass

Ionic Compounds and Formula Mass

Ionic compounds consist of ions held together by electrostatic forces. To find the formula mass (FM), we simply sum the average atomic masses of every atom present in the chemical formula.

Worked Example: Magnesium Bromide ($\text{MgBr}_2$) To find the formula mass of $\text{MgBr}_2$:

$$\begin{aligned} \text{FM of MgBr}_2 &= 1 \times (\text{mass of Mg}) + 2 \times (\text{mass of Br}) \\ &= 24.305\text{ amu} + 2(79.904\text{ amu}) \\ &= 184.113\text{ amu} \end{aligned}$$

Covalent Compounds and Molecular Mass

In the case of covalent compounds (substances where atoms share electrons), the formula mass is specifically referred to as the molecular mass (Mm). The calculation method is identical: sum the masses of all atoms in the molecule.

Worked Example: Water ($\text{H}_2\text{O}$)

$$\begin{aligned} \text{Mm of H}_2\text{O} &= 2(1.0079\text{ amu}) + 1(15.999\text{ amu}) \\ &= 18.015\text{ amu} \end{aligned}$$

The Mole and Avogadro’s Number

Because atoms are so small, chemists do not count them one by one. Instead, we use a unit called the mole. One mole represents a specific quantity of particles—whether they are atoms, molecules, or ions—equal to Avogadro’s number ($N_A$).

$$1\text{ mole} = 6.02214 \times 10^{23}\text{ particles}$$

To visualize how massive this number is, consider that a mole of milliliters of water is roughly equivalent to the volume of the Pacific Ocean.

Connecting Moles and Grams

The most critical connection in stoichiometry is the relationship between the atomic mass (in amu) and the molar mass (in g/mol). The molar mass of an element is numerically equal to its average atomic mass, but the units change from amu to grams per mole.

For example:

• Carbon: $12.01\text{ amu} \rightarrow 12.01\text{ g/mol}$
• Aluminum: $26.98\text{ amu} \rightarrow 26.98\text{ g/mol}$

This allows us to perform conversions using the following logic:

1. Grams to Moles: Divide the mass by the molar mass.
2. Moles to Atoms: Multiply the number of moles by Avogadro's number ($6.022 \times 10^{23}$).

Determining Chemical Formulas

Finally, we use these mass concepts to work backward to find the identity of a substance through two types of formulas:

1. Empirical Formula: The simplest whole-number ratio of elements in a compound.
2. Molecular Formula: The actual, true number of atoms of each element in a molecule.

The molecular formula is always a whole-number multiple ($n$) of the empirical formula:

$$\text{Molecular Formula} = (\text{Empirical Formula}) \times n$$

To find $n$, you divide the given molar mass of the compound by the molar mass of the empirical formula:

$$n = \frac{\text{Molar Mass of Compound}}{\text{Molar Mass of Empirical Formula}}$$

By mastering these conversions between amu, grams, moles, and particles, you gain the ability to navigate the entire scale of chemical composition.