Potassium chloride is widely used in the manufacture of fertilizers. Its solubility is \(37.0 \mathrm{~g} / 100 \mathrm{~g}\) water at \(30^{\circ} \mathrm{C}\). At \(70^{\circ} \mathrm{C}\) its solubility is \(48.3 \mathrm{~g} / 100 \mathrm{~g}\) water. (a) Calculate the mass of potassium chloride that dissolves in \(44.5 \mathrm{~g}\) of water at \(30^{\circ} \mathrm{C}\). (b) Calculate the mass of water required to dissolve \(39.6 \mathrm{~g}\) of potassium chloride at \(70^{\circ} \mathrm{C}\). (c) If \(40.0 \mathrm{~g}\) of potassium chloride are added to \(75.0 \mathrm{~g}\) of water at \(30^{\circ} \mathrm{C}\), will it all dissolve? If the temperature is increased to \(70^{\circ} \mathrm{C}\), will it all dissolve? How many grams (if any) are undissolved at \(30^{\circ} \mathrm{C} ?\) at \(70^{\circ} \mathrm{C} ?\)

Understanding the mass of solute in a solution is vital in fields ranging from cooking to chemical manufacturing. The mass of solute is simply the weight of the single type of particle, typically a solid, that is dissolved in a liquid. In chemistry, this concept allows us to precisely calculate how much of a substance will dissolve in a given amount of solvent at a specific temperature.

Let's consider the fertilizer industry, where potassium chloride, a common ingredient, is dissolved in water. Knowing how much of this solute can be dissolved is critical for creating the right concentrations. For instance, if a recipe calls for a saturated solution of potassium chloride at a certain temperature, calculating the correct mass of potassium chloride to add to a defined amount of water is key. The textbook exercise you’re tackling demonstrates this calculation by showing that, at a temperature of 30°C, 37.0 grams of potassium chloride can dissolve in 100 grams of water. Thus, for any mass of water, this solubility ratio helps to calculate the corresponding soluble amount of potassium chloride.

Remember, the mass of solute that can be dissolved changes with the mass of the solvent and the temperature, both of which can be calculated using simple proportional relationships as shown in the textbook solutions.

Temperature dramatically affects the solubility of substances. As temperature rises, most solid solutes become more soluble in water, meaning a larger amount can be dissolved. This phenomenon is illustrated in our exercise by comparing the solubility of potassium chloride at two different temperatures: 30°C and 70°C.

Why Does This Happen?

Increased temperature usually leads to increased kinetic energy, meaning the water molecules move faster, thereby more effectively breaking apart the solute molecules and integrating them into the solution.

However, do note that this trend is not universal. For some compounds, increased heat can decrease solubility, but for our potassium chloride example, a hotter temperature means more can dissolve — as reflected in going from 37.0 g at 30°C to 48.3 g at 70°C per 100 g of water. This temperature-related change will guide many industrial processes, like those in the exercise, where heating a solution could enable more solute to dissolve and thus streamline manufacturing efficiency.

The concept of solubility in water is fundamental to understanding many scientific and cooking processes. Solubility is defined as the maximum amount of solute that can be dissolved in a solvent before the solution becomes saturated. This quantity is commonly expressed in units of mass of solute per volume or mass of solvent at a specific temperature.

In our exercise, the solubility of potassium chloride in water varies with temperature, but at any given temperature it has a specific maximum value. It's crucial to note that not all substances have the same solubility. For example, sodium chloride (table salt) is more soluble in water than potassium chloride, which is reflected in the different solubility values that can be found for these two substances under the same conditions.

Understanding these differences is important for many applications. For instance, in health sciences, the solubility of drugs determines how they can be administered and absorbed by the body. In environmental sciences, solubility influences the behavior of pollutants in groundwater. Always bear in mind that solubility in water is a unique property of each substance and it dictates how substances can be mixed, used, and disposed of.