Question

Potassium chloride has a solubility of \(43 \mathrm{~g}\) of \(\mathrm{KCl}\) in \(100 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) at \(50{ }^{\circ} \mathrm{C}\). State if each of the following forms an unsaturated or saturated solution at \(50^{\circ} \mathrm{C}\) : a. adding \(25 \mathrm{~g}\) of \(\mathrm{KCl}\) to \(100 . \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) b. adding \(25 \mathrm{~g}\) of \(\mathrm{KCl}\) to \(50 . \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) c. adding \(86 \mathrm{~g}\) of \(\mathrm{KCl}\) to \(150 . \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\)

Short answer

a. Unsaturated, b. Saturated, c. Saturated.

Step-by-step solution

Understanding Solubility

The solubility of potassium chloride (KCl) at 50°C is 43 g in 100 g of water. This means that a maximum of 43 g of KCl can dissolve in 100 g of water at this temperature. Any amount less than 43 g in 100 g of water forms an unsaturated solution, while 43 g or more forms a saturated solution.

Calculating for Case (a): 25 g of KCl in 100 g of Water

For part (a), 25 g of KCl is added to 100 g of water. Since 25 g is less than the maximum solubility of 43 g in 100 g of water, the solution is unsaturated.

Calculating for Case (b): 25 g of KCl in 50 g of Water

For part (b), calculate the equivalent solubility of KCl in 50 g of water. Since the solubility is 43 g per 100 g of water, in 50 g of water: \[ \text{Solubility} = \frac{43 \text{ g}}{100 \text{ g}} \times 50 \text{ g} = 21.5 \text{ g} \] Adding 25 g of KCl, which is more than 21.5 g, forms a saturated solution.

Calculating for Case (c): 86 g of KCl in 150 g of Water

For part (c), calculate the equivalent solubility of KCl in 150 g of water. Since the solubility is 43 g per 100 g of water, in 150 g of water: \[ \text{Solubility} = \frac{43 \text{ g}}{100 \text{ g}} \times 150 \text{ g} = 64.5 \text{ g} \] Adding 86 g of KCl, which is more than 64.5 g, forms a saturated solution.

Key concepts

solubility

Solubility is a key concept in solution chemistry. It refers to the maximum amount of a substance (solute) that can dissolve in a given amount of solvent at a specific temperature, forming a stable solution.
The solubility of potassium chloride (KCl) at 50°C is 43 g per 100 g of water. This means that at this temperature, 43 g of KCl can completely dissolve in 100 g of water. If more than 43 g of KCl is added to 100 g of water, the excess will remain undissolved, leading to a saturated solution.
Different factors affect solubility, such as temperature and the nature of the solute and solvent. For most solid solutes, solubility increases with temperature, while for gases, solubility generally decreases.
This concept is crucial for understanding the behavior of solutes in solvents and predicting whether a solution will be unsaturated or saturated under given conditions.

unsaturated solution

An unsaturated solution is one that contains less solute than the maximum amount that can dissolve in a solvent at a particular temperature. In an unsaturated solution, there is still room for more solute to dissolve.
For instance, if 25 g of KCl is added to 100 g of water at 50°C, the solution is unsaturated. This is because 25 g is less than the solubility limit of 43 g at this temperature. Thus, more KCl could be dissolved if needed.
Unsaturated solutions are quite flexible. They can absorb more solute without any undissolved particles. This property is important in various chemical processes and applications, such as in making mixtures that require specific concentrations of solutes.

saturated solution

A saturated solution occurs when the solvent holds the maximum amount of solute it can dissolve at a specific temperature. In this state, any additional solute will remain undissolved.
For example, if 86 g of potassium chloride is added to 150 g of water at 50°C, we can calculate the maximum amount that can dissolve as follows:
Solubility: \(\frac{43 \text{ g}}{100 \text{ g}} \times 150 \text{ g} = 64.5 \text{ g}\)
Since 86 g exceeds 64.5 g, the solution is saturated, and the excess KCl will not dissolve.
Understanding saturated solutions is vital for practical applications like formulating pharmaceuticals, where the precise concentration of solutes is crucial.

potassium chloride

Potassium chloride (KCl) is a common ionic compound used in various applications, including fertilizers, medicine, and as a salt substitute. Its solubility properties make it an important example in solution chemistry.
Potassium chloride dissolves in water to form potassium (K⁺) and chloride (Cl⁻) ions, which are free to move and conduct electricity. This dissolution process is heavily dependent on temperature, with higher temperatures generally increasing solubility.
For learning purposes, KCl's behavior in water serves as a good model to understand solubility limits, saturation points, and factors affecting solubility. By mastering these concepts with KCl, students can apply similar principles to other solutes and solvents in their studies and real-world applications.