Question

What is meant by the solubility product for a sparingly soluble salt? Choose a sparingly soluble salt and show how the salt ionizes when dissolved in water, and write the expression for its solubility product.

Short answer

The solubility product (K_sp) is a measure of the equilibrium between a solid and its dissolved ions in a saturated solution, helping to predict the solubility of a sparingly soluble salt in water. As an example, consider Silver Chloride (AgCl), which dissociates in water as follows: \[AgCl(s) \rightleftharpoons Ag^+(aq) + Cl^-(aq)\] The solubility product expression for AgCl is given by: \[K_{sp} = [Ag^+][Cl^-]\] Here, K_sp is approximately \(1.8 \times 10^{-10}\) at 25°C, indicating that AgCl is sparingly soluble in water.

Step-by-step solution

1. Understanding solubility product

Solubility product, also known as the solubility product constant (K_sp), is a measure of the equilibrium between a solid and its dissolved ions in a saturated solution. It is used to predict the solubility of a sparingly soluble salt in water. The solubility product is represented by the mathematical product of the concentrations of the ions of the salt, each raised to the power of their stoichiometric coefficient in the balanced chemical equation.

2. Choosing a sparingly soluble salt

For this illustration, let's choose Silver Chloride (AgCl) as a sparingly soluble salt. AgCl is a white crystalline solid which is not very soluble in water (meaning that only a small amount of it dissolves in a given amount of water).

3. Ionization of the chosen salt in water

When AgCl is added to water, it dissociates into its constituent ions in a limited extent, since it is a sparingly soluble salt. The balanced chemical equation for the dissociation of AgCl in water is as follows: \[AgCl(s) \rightleftharpoons Ag^+(aq) + Cl^-(aq)\] Here, (s) denotes solid, and (aq) denotes the ions in aqueous solution.

4. Writing the expression for the solubility product

To write the expression for the solubility product (K_sp) of AgCl, we can express it as follows: \[K_{sp} = [Ag^+][Cl^-]\] In this expression, [Ag^+] represents the concentration of silver ions (Ag+) and [Cl^-] represents the concentration of chloride ions (Cl-) at equilibrium. The solubility product constant is obtained from experimental data or available tables. For AgCl, the value of K_sp is approximately \(1.8 \times 10^{-10}\) at 25°C. The small magnitude of K_sp shows that the salt is sparingly soluble in water.

Key concepts

Sparingly Soluble Salt

A sparingly soluble salt is a salt whose solubility in water is very limited. This means that only a small amount of the salt will dissolve in water to form ions. While some salts dissolve completely and form a large number of ions in solution, sparingly soluble salts only partially dissolve.
This characteristic is important for understanding the behavior of these salts in various chemical processes, such as precipitation reactions and equilibrium studies.

• Example: Silver Chloride (AgCl) is a common example of a sparingly soluble salt.
• Its limited dissolution is due to the strong ionic bonds in the crystal lattice of the solid.

Being sparingly soluble usually means a very low value of solubility product, denoting low ionic concentrations in solution at equilibrium.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction and its reverse proceed at the same rate, resulting in no net change in the concentration of reactants and products. For a sparingly soluble salt like silver chloride, equilibrium is reached when a solution contains the maximum amount of dissolved ions while the rest remains undissolved.

• At equilibrium, the rates of the dissolving and precipitating of the salt are equal.
• This balance is dynamic, meaning ions are continuously being exchanged between the solid and aqueous states.

Understanding chemical equilibrium helps predict how substances will behave in different chemical environments.

Ion Concentration

Ion concentration in a solution determines how much a solute has dissolved to form ions. In the case of sparingly soluble salts, these concentrations are typically very low, reflecting the minimal amount that dissolves in water.

• For AgCl, when equilibrium is reached, the concentrations of Ag⁺ and Cl^- ions are equal.
• The ion concentration is generally measured in moles per liter (M).

In precipitation, equilibrium, and solubility studies, knowing the ion concentration is crucial for making predictions about reactions and their feasibility under various conditions.

Equilibrium Expression

The equilibrium expression for a sparingly soluble salt is defined in terms of its solubility product (K_{sp}). This expression relates the concentrations of the dissolved ions to each other when equilibrium is reached.
The formula for the equilibrium expression of a generic sparingly soluble salt, AB, that dissociates into A⁺(aq) and B^-(aq) is:
\[K_{sp} = [A^+][B^-]\]This means that the product of the concentrations of the ions is a constant for a particular salt at a given temperature. For specific salts like AgCl, the equilibrium expression becomes:

• \( K_{sp} = [Ag^+][Cl^-] \)

The low numerical value of K_{sp} confirms that AgCl is sparingly soluble. Understanding and using equilibrium expressions allows chemists to predict the solubility of salts and their tendencies to either dissolve or precipitate under different conditions.