Question

Which of the following is most soluble in water? (a) \(\mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2}\left(K_{s p}=6 \times 10^{-39}\right)\) (b) \(\operatorname{ZnS}\left(K_{s p}=7 \times 10^{-16}\right)\) (c) \(\mathrm{Fe}(\mathrm{OH})_{3}\left(K_{s p}=6 \times 10^{-38}\right)\) (d) \(\mathrm{Ag}_{3}\left(\mathrm{PO}_{4}\right)\left(K_{s p}=1.8 \times 10^{-18}\right)\)

Short answer

\(Ag_3(PO_4)\) is the most soluble in water since it has the highest Ksp value of \(1.8 \times 10^{-18}\).

Step-by-step solution

Understanding Solubility Product (Ksp)

The solubility product constant (Ksp) indicates the extent to which a compound will dissolve in water. A higher Ksp value means the compound is more soluble.

Comparing Ksp Values

To determine which compound is most soluble, compare their Ksp values directly. The compound with the highest Ksp will be the most soluble in water.

Determining the Most Soluble Compound

After comparing the Ksp values, we find that \(Ag_3(PO_4)\) has the highest Ksp value of \(1.8 \times 10^{-18}\), which indicates it is the most soluble among the given compounds.

Key concepts

Solubility in Water

Solubility is a measure of how much of a substance can dissolve in water to form a homogenous mixture or solution. The solubility of an ionic compound in water is governed by a delicate balance between forces of attraction within the ionic lattice of the solid and the solvation, which is the interaction of the ions with water molecules.

When an ionic compound dissolves in water, it dissociates into its constituent ions, a process that is influenced by the temperature, the pressure, and the nature of the solute and solvent involved. The solubility product constant, or Ksp, is a special equilibrium constant used to describe the solubility of sparingly soluble salts. It represents the maximum amount of a substance that can dissolve in water at a given temperature and pressure. Substances with higher Ksp values are generally more soluble in water, as they have a greater tendency to form ions in solution.

Comparing Ksp Values

To predict which compound is more soluble in water from a set of sparingly soluble compounds, you can compare their solubility product constants (Ksp). Ksp values offer a direct clue about the solubility of compounds under similar conditions. The higher the Ksp, the higher the solubility.

It's important to consider that a straightforward comparison only holds true when the number of ions produced during the dissociation process is the same for each compound. For dissimilar ionic compounds, the comparison becomes more complex, necessitating additional calculations involving the molar solubility and the ions' stoichiometry. Nevertheless, for our purpose concerning straightforward comparisons, a higher Ksp indicates a more soluble compound, meaning it can achieve a higher concentration of ions in solution before reaching equilibrium.

Solubility Calculations

Computing the solubility of a compound from its Ksp involves stoichiometric considerations based on the compound's dissolution equation. For instance, if a compound dissolves and separates into two ions, the Ksp expression is written in terms of the concentrations of these ions. The molar solubility, which is the number of moles of the compound that can dissolve per liter of solution, can be calculated from the Ksp value and the stoichiometry of the dissolution reaction.

For a compound with formula AaBb, which dissolves to form aA+ ions and bB- ions, the Ksp expression is given as: \[ K_{\text{sp}} = [A^{+}]^{a}[B^{-}]^{b} \]Here, [A+] and [B-] are the molar concentrations of the ions in the saturated solution. The solubility calculation is an important step in many chemical applications, including predicting precipitation results and purifying compounds by recrystallization.