The solubility of \(\mathrm{KNO}_{3}\) is \(155 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water at \(75^{\circ} \mathrm{C}\) and \(38.0 \mathrm{~g}\) at \(25^{\circ} \mathrm{C}\). What mass (in grams) of \(\mathrm{KNO}_{3}\) will crystallize out of solution if exactly \(100 \mathrm{~g}\) of its saturated solution at \(75^{\circ} \mathrm{C}\) are cooled to \(25^{\circ} \mathrm{C} ?\)

Chemical solubility refers to the maximum amount of a solute that can be dissolved in a solvent at a specific condition, usually measured as mass of solute per volume of solvent. It's a fundamental concept in chemistry that enables us to understand how substances interact with each other in solutions. For example, \textbf{potassium nitrate (KNO\(_3\))} has a solubility of \textbf{155 grams in 100 grams of water} at \textbf{75°C}.

This property of solubility is crucial not just in scientific laboratories, but also in everyday applications like medicine, where the solubility of drugs affects their efficiency, and in cooking, where solubility determines how spices can flavor a dish. By understanding the chemical solubility, students can anticipate how a substance will behave in a mixture, predict possible reactions, and calculate concentrations of solutions.

A saturated solution represents a point of equilibrium where the solvent contains the maximum concentration of solute and cannot dissolve any more at a given temperature and pressure. In the case of our exercise, \textbf{a saturated solution of KNO\(_3\) at 75°C} would hold \textbf{155 grams of the salt} in \textbf{100 grams of water}.

Why does this matter? When working in a chemistry lab or studying geological formations, knowing a substance's saturation point helps when trying to grow crystals or avoid the formation of a precipitate. If you're making rock candy, for instance, creating a saturated sugar solution is exactly what you need to start growing those tasty crystals. Understanding the concept of saturated solutions also assists in applications such as salt removal from seawater, where the saturation limit determines the efficiency of the desalination process.

Temperature has a significant effect on the solubility of substances. Generally, for most solids, an \textbf{increase in temperature results in increased solubility}, and vice versa. In our exercise, \textbf{KNO\(_3\) is more soluble} in water at \textbf{75°C than at 25°C}. This implies that when the temperature drops, the excess solute will crystallize out.

When students grasp this concept, they can predict and explain occurrences such as the formation of sugar crystals at the bottom of a cup of tea as it cools. In industrial processes like metallurgy, temperature control is vital for extracting metals from ores by utilizing their solubility differences at varying temperatures. In environmental science, concepts of solubility are at play when assessing the impact of temperature changes on the distribution of chemicals in bodies of water.