A \(7.63 \mathrm{~g}\) sample of hydrated magnesium sulphate \(\mathrm{MgSO}_{4} \cdot \mathrm{xH}_{2} \mathrm{O}\) is heated until all of the water is driven off. If \(3.72\) grams of anhydrous \(\mathrm{MgSO}_{4}\) is obtained, how many water molecules combined with each formula unit of magnesium sulphate in the hydrate? (a) 6 (b) 7 (c) 8 (d) 9

Stoichiometry is the aspect of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is a central concept in chemistry that allows us to predict how much product will form from a given amount of reactants, or conversely, how much reactant is needed to produce a certain amount of product. The principles of stoichiometry are founded on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction.

In the context of our exercise, stoichiometry is used to relate the mass of the hydrated magnesium sulphate before heating to the mass of the anhydrous magnesium sulphate and water after heating. By calculating and comparing the amount of substance in moles, we can deduce the ratio of water to magnesium sulphate, which yields the number of water molecules associated with each formula unit of magnesium sulphate in the hydrate. Mastery of stoichiometry is essential for understanding the composition of hydrates and executing the hydration and dehydration processes in the lab.

The mole concept is a fundamental principle in chemistry that provides a bridge between the atomic or molecular scale and the macroscopic world we observe. One mole is defined as the amount of substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of pure carbon-12. This number, known as Avogadro's number, is approximately 6.022 x 10^23.

When we talk about the mole concept in our exercise, we focus on how to convert the mass of a substance to moles using its molar mass, which is the mass of one mole of that substance. In the solution steps, this concept is applied by dividing the mass of anhydrous magnesium sulphate by its molar mass to find the moles of MgSO4, and similarly for water. Understanding the mole concept is critical as it allows us to quantify substances and interpret chemical equations in a meaningful way for laboratory and practical applications.

The empirical formula of a compound provides the simplest whole-number ratio of the elements present in the compound. Unlike the molecular formula, the empirical formula does not necessarily represent the actual number of atoms but rather the smallest ratio in which the atoms combine. To determine the empirical formula, we first measure the moles of each element in a sample and then express these quantities as a ratio of small whole numbers.

In our hydration problem, after determining the moles of water and anhydrous magnesium sulphate, we compare the ratio of moles of water to moles of MgSO4. This ratio helps us to infer the empirical formula of the hydrate, which includes the number of water molecules per formula unit of MgSO4, denoted as MgSO4 ⋅ xH2O. The empirical formula is vital for chemists and other scientists as it is used to understand and describe the composition of chemical compounds, especially in cases like hydrates where the number of associated water molecules needs to be determined precisely.