When \(5.60 \mathrm{~g}\) of anhydrous copper (II) sulphate is exposed to moist air, it absorbs water. If the hydrated copper compound has a mass of \(8.13 \mathrm{~g}\), what is the chemical formula of the hydrate? (a) \(\mathrm{CuSO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) (c) \(\mathrm{CuSO}_{4} \cdot 4 \mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{CuSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\)

Understanding the transition from an anhydrous to a hydrated compound is essential when working with chemical reactions that involve water absorption. An anhydrous compound is one that does not contain water, while a hydrated compound includes water molecules incorporated into its structure. When anhydrous copper sulfate is exposed to moisture, it absorbs water and forms a hydrated compound. The amount of water absorbed can be determined by calculating the difference in mass before and after hydration.

This transition is not only a physical change (the intake of water) but also a chemical one, as the water molecules become part of the crystalline structure of the hydrated compound. In the case of copper sulfate, this hydration process results in a color change from white (anhydrous) to blue (hydrated), providing a visual clue of the chemical alteration.

The step-by-step process of determining the chemical formula of a compound is a fundamental skill in chemistry. For hydrated compounds, the formula reflects not only the ratio of the original ions but also the number of water molecules associated with each formula unit of the salt. In our example with copper sulfate, we're aiming to find out how many moles of water (H_2O) are incorporated per mole of anhydrous copper sulfate (CuSO_4).

To do this accurately, comparing the mass of the anhydrous compound with the mass of the hydrated compound is vital. The increase in mass corresponds to the mass of the water absorbed. Understanding the concept of molar mass is key to converting this mass into moles, thus enabling the stoichiometric determination of the hydrate's formula.

Molar mass is the mass of a given substance (chemical element or chemical compound) divided by its amount of substance. The molar mass calculation provides a bridge between the weight of a material and the number of molecules or atoms it contains. In practical terms, to find the number of moles of a substance, you divide the substance's mass by its molar mass.

For example, to determine the number of moles of anhydrous copper sulfate (CuSO_4), one would take the mass of the sample and divide it by the molar mass of copper sulfate, which is approximately 159.61 g/mol. A similar calculation is done with water, using its molar mass of 18.015 g/mol. These calculations are critical in quantifying the components in a chemical reaction.

Stoichiometry is the section of chemistry that pertains to measuring the quantities of reactants and products in chemical reactions. In the context of hydrates, stoichiometry involves determining the fixed ratio between the anhydrous compound and the water molecules within the hydrate's structure.

Once the moles of the anhydrous compound and the moles of water are calculated, the stoichiometric ratio can be found. This ratio reveals how many moles of water are associated with each mole of the anhydrous compound. With this information, one can deduce the correct formula of the hydrate, applying stoichiometric principles to understand and predict how substances will interact and change during a chemical reaction. Being accurate in these calculations ensures the determination of the correct chemical formula for a hydrated compound, such as hydrated copper sulfate.