Bauxite, the principal ore used in the production of aluminum, has a molecular formula of \(\mathrm{Al}_{2} \mathrm{O}_{3} \cdot 2 \mathrm{H}_{2} \mathrm{O}\). The \(\cdot \mathrm{H}_{2} \mathrm{O}\) in the formula are called waters of hydration. Each formula unit of the compound contains two water molecules. a. What is the molar mass of bauxite? b. What is the mass of aluminum in \(0.58\) mole of bauxite? c. How many atoms of aluminum are in \(0.58\) mole of bauxite? d. What is the mass of \(2.1 \times 10^{24}\) formula units of bauxite?

Understanding waters of hydration is essential when studying compounds like bauxite, the primary ore of aluminum.
Most students are taught that salts can contain water molecules that are an integral part of their crystal structure. These water molecules are known as waters of hydration or water of crystallization.

In the case of bauxite, with the molecular formula \(\mathrm{Al}_{2} \mathrm{O}_{3} \cdot 2 \mathrm{H}_{2} \mathrm{O}\), the dot (\cdot) indicates that two molecules of water are bound to the compound. Therefore, for each unit of bauxite, there are two water molecules incorporated into its structure. This knowledge is crucial when calculating the molar mass of a hydrated compound, as it involves counting the mass of the waters of hydration along with the anhydrous salt.

The process of molecular formula calculation involves determining the composition of a chemical compound in terms of the elements present and their respective numbers.
To calculate the molar mass of a compound like bauxite, one must consider the atomic masses of each element and their quantity within the formula. For bauxite, the molar mass accounts for aluminum (Al), oxygen (O), and the waters of hydration, each involving their own molar mass multiplied by the number of atoms present in the formula. Adding these values gives the total molar mass of the compound.

This is crucial for subsequent calculations, such as finding the mass of a certain element within a given number of moles of the compound or converting between moles and mass for the entire compound. Problem-solving in chemistry frequently entails such computations, reinforcing the importance of accurately determining the molecular formula of substances.

A key concept in chemistry is Avogadro's number, which helps students transition between the microscopic world of atoms and the macroscopic world we can measure.
Avogadro's number, approximately \(6.022 \times 10^{23}\), represents the number of units (be they atoms, molecules, or formula units) in one mole of a substance.

In the example of bauxite, understanding Avogadro's number allows us to calculate the actual number of aluminum atoms in a given sample by multiplying the number of moles by Avogadro's number. Similarly, the opposite is true when we have a specific number of formula units and wish to calculate the mass of the sample; we simply convert the number of units to moles using Avogadro's number, then use the molar mass to transition to grams. Being able to manipulate these quantities is fundamental in chemistry, as it bridges the gap between theoretical concepts and practical measurements.