Problem 104 - General Chemistry: Principles and Modern Applications

Question

Which of the following has the highest molar solubility? (a) \(\mathrm{MgF}_{2}, K_{\mathrm{sp}}=3.7 \times 10^{-8}\) \(\mathrm{MgCO}_{3}\), \(K_{\mathrm{sp}}=3.5 \times 10^{-8} ;(\mathrm{c}) \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}, K_{\mathrm{sp}}=1 \times 10^{-25}\); (d) \(\mathrm{Li}_{3} \mathrm{PO}_{4}, K_{\mathrm{sp}}=3.2 \times 10^{-9}\).

Step-by-Step Solution

Answer

The substance with the highest molar solubility among the given substances is MgF2.

Step 1: Understand the Concept of Molar Solubility

Molar solubility is the number of moles of a substance (solute) that can be dissolved per liter of solution before the solution becomes saturated. It essentially determines the quantity of the solute that can be dissolved in a solution.

Step 2: Understand the Concept of Solubility Product constant (Ksp)

The solubility product constant (Ksp) is the equilibrium constant for a solid that is in equilibrium with its ions in a solution. It represents the level at which a solute dissolves in solution. The higher the Ksp, the higher the molar solubility, because a larger amount of the solute can dissolve in the solution before it becomes saturated.

Step 3: Compare the Ksp Values

From the given data, compare the solubility product constants (Ksp) of the salts. Their values are as follows: \(MgF_{2}, K_{sp} = 3.7 \times 10^{-8}\), \(MgCO_{3}, K_{sp} = 3.5 \times 10^{-8}\), \(Mg_{3}(PO_{4})_{2}, K_{sp} = 1 \times 10^{-25}\), and \(Li_{3}PO_{4}, K_{sp} = 3.2 \times 10^{-9}\). The substance with the highest Ksp value will have the highest molar solubility.

Step 4: Identify the Substance with Highest Molar Solubility

From comparison, it can be seen that MgF2 has the highest solubility product constant (Ksp). Therefore, it has the highest molar solubility among the given substances.

Key Concepts

Solubility Product Constant

Understanding the solubility product constant, often denoted as Ksp, is fundamental to characterizing the solubility of compounds in aqueous solutions. The Ksp is a type of equilibrium constant specifically for the dissolution of sparingly soluble ionic compounds. When a solid ionic compound is in dynamic equilibrium with its dissolved ions, the Ksp represents the maximum product of the ion concentrations at saturation, each raised to the power of its stoichiometric coefficient.

For instance, the Ksp of magnesium fluoride (\( MgF_{2} \) ) suggests the maximum product of magnesium and fluoride ion concentrations in a saturated solution. A simple formula to depict this for a generic compound AB₂ would be:
\[\[\begin{align*} AB_2 &\leftrightarrows A^{2+} + 2B^{-} \K_{sp} &= [A^{2+}][B^{-}]^2\end{align*}\]\]
Factors Influencing Ksp

• Temperature: The solubility of solids generally increases with temperature, so the Ksp typically increases as well.
• Common Ion Effect: Presence of a common ion in solution can affect the solubility of a compound, decreasing the Ksp value.
• pH of the Solution: For some compounds, the solubility and hence Ksp can be influenced by the acidity or basicity of the solution.

By examining the Ksp values, one can theoretically determine which compound has the highest molar solubility, assuming all other factors such as temperature and pH are constant. In the given exercise, MgF₂ with the highest Ksp value would typically have the highest molar solubility.

Aqueous Solution Saturation

The concept of aqueous solution saturation is akin to reaching the capacity limit of a solution to dissolve more solute. At the point of saturation, any additional solute will remain undissolved, creating a state of dynamic equilibrium where the rate of substance dissolving and the rate of crystal formation (precipitate forming) are equal. Saturation is a condition crucial for determining solubility, especially in the case of sparingly soluble salts.

For practical applications and laboratory conditions, once a solution has reached saturation, the Ksp becomes a valuable tool. It helps us predict whether a precipitate will form when two solutions are mixed. If the product of the ion concentrations in the mixed solution exceeds the Ksp, the excess ions will form a precipitate.

Understanding saturation is also critical for various industrial and biological processes, as it can influence reaction yields, the formation of scale in pipes and boilers, as well as the bioavailability of minerals for nutrition in biological systems.

Equilibrium Constant

Moving further into chemical equilibria, the equilibrium constant, often represented as K, is a number that expresses the ratio of products to reactants at equilibrium for a reversible chemical reaction. The value of K provides a quantitative measure of how far a reaction will proceed before reaching equilibrium under a given set of conditions, typically at a constant temperature.

In the context of solubility, the equilibrium constant specifically refers to the Ksp (solubility product constant), which is a specific version of the equilibrium constant. It's important to note that the value of an equilibrium constant is dimensionless and is a reflection of the inherent tendency of the compound to dissolve or precipitate under equilibrium conditions.

Equilibrium constants also provide insight into the favorability of reactions:

• A large K (or Ksp) value indicates a reaction that favors the formation of products (e.g., higher solubility).
• A small K (or Ksp) value implies a reaction that favors the reactants (e.g., lower solubility).

For students who are delving into these concepts for perhaps the first time, recognizing the role of equilibrium constants in predicting the behavior of reactions is essential to understanding chemical processes.