The solubility of barium hydroxide in water at \(20^{\circ} \mathrm{C}\) is \(1.85 \mathrm{~g} / 100 \mathrm{~g}\) water. A solution is made up of \(256 \mathrm{mg}\) in \(35.0 \mathrm{~g}\) of water. Is the solution saturated? If not, how much more barium hydroxide needs to be added to make a saturated solution?

Understanding the chemical solubility of a substance is crucial when working with solutions in chemistry. Solubility refers to the maximum amount of a solute, like barium hydroxide, that can be dissolved in a solvent, such as water, at a specific temperature and pressure to form a homogeneous solution. It is usually expressed in units of grams of solute per 100 grams of solvent.

The concept of solubility becomes particularly interesting because it varies for different substances and it can change with temperature and the presence of other chemicals in the solution. In the case of barium hydroxide, knowing its solubility at a specific temperature allows us to predict how much of it can be dissolved in a given amount of water before the solution becomes saturated.

This knowledge is not only essential for creating a solution of desired concentration but also for understanding the outcomes of a chemical reaction where barium hydroxide is a reactant. When we add barium hydroxide to water, the ionic compound dissociates into barium and hydroxide ions until the point of saturation is reached.

A saturated solution is a mixture where the maximum amount of solute has been dissolved in the solvent at a given temperature. Beyond this point, any additional solute will not dissolve and will instead remain as a separate phase, such as a solid precipitate or an additional liquid layer, depending on the system.

Identifying if a solution is saturated or not is crucial, as this impacts the solution's properties and potential applications. For instance, if more solute is added to a saturated solution, it will not increase the concentration of the solution but can lead to the formation of a precipitate, which is a solid that settles out of the solution. This can be seen in industries such as pharmaceuticals or food science, where the solubility limits are critical for the desired product's stability and effectiveness.

The barium hydroxide solution in the exercise was found to be unsaturated, meaning that there was still capacity for more barium hydroxide to dissolve without forming a precipitate. By calculating the difference between the current amount of solute and the solubility limit, we can determine exactly how much more solute can be added to reach saturation.

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves calculations that allow us to predict the amounts of substances needed and formed in a reaction. Stoichiometric calculations are based on the conservation of mass and the concept of the mole, which is a unit for a specific number of particles.

In practice, stoichiometry can answer questions like 'How much product will be formed from a certain amount of reactant?' or 'How much of one reactant is required to completely react with another?'. For the exercise at hand, stoichiometry isn’t directly applied to a chemical reaction but rather to the process of dissolving a substance until a saturated solution is achieved, a concept that shares the rationale of quantitative relationships.

By applying stoichiometric principles, we calculate the amount of barium hydroxide that can be dissolved in a given weight of water (in this instance, 35.0 grams), taking into account the solubility ratio. Stoichiometry helps us to understand that even though we talk about dissolving a substance, there remain consistent and calculable relationships that govern how much solute can be held in a solution.