Problem 21 - Chemistry A Molecular Approach

Question

How does a common ion affect the solubility of a compound? More specifically, how is the solubility of a compound with the general formula AX different in a solution containing one of the common ions \(\left(\mathrm{A}^{+}\right.\) or \(\left.\mathrm{X}^{-}\right)\) than it is in pure water? Explain.

Step-by-Step Solution

Answer

The addition of a common ion (either \(A^{+}\) or \(X^{-}\)) to a solution containing the compound AX will decrease its solubility by shifting the solubility equilibrium to the left, which causes more AX to precipitate until a new equilibrium is established.

Step 1: Understanding the Common Ion Effect

The common ion effect refers to the decrease in solubility of an ionic compound when a solution already contains one of the ions present in that compound. This is because increasing the concentration of one of the ions shifts the equilibrium to the left according to Le Chatelier's principle, reducing the amount of the compound that can be dissolved.

Step 2: Describing the Equilibrium Shift

For a compound AX that dissociates into \(A^{+}\) and \(X^{-}\) in solution, the solubility equilibrium can be represented as \(AX(s) \rightleftharpoons A^{+}(aq) + X^{-}(aq)\). Adding more of either \(A^{+}\) or \(X^{-}\) will shift this equilibrium towards the left, leading to the formation of more undissolved AX(s), in accordance with Le Chatelier's principle.

Step 3: Quantitative Expression of Solubility Changes

The solubility product constant (\(K_{sp}\)) of AX dictates the equilibrium concentrations of the ions. If one of the ions (\(A^{+}\) or \(X^{-}\)) is added to the solution, the product of the concentrations of these ions will exceed the \(K_{sp}\), forcing some of the ions to combine and precipitate out as AX until the system is back at equilibrium where the product of the ions’ concentration is equal to the \(K_{sp}\) once again.

Key Concepts

Solubility Equilibrium

When we talk about solubility equilibrium, we are referring to the balance point where a chemical compound in the solid state is dissolving in a solvent at the same rate that the dissolved particles are recombining to form the solid. This is a dynamic process, meaning it continually occurs without any net change in the amount of solid or dissolved particles once equilibrium has been reached.

For instance, when the compound AX is placed in water, it dissociates into its ions, represented by the equation:
\[AX(s) \rightleftharpoons A^{+}(aq) + X^{-}(aq)\].
This equilibrium is crucial because it dictates how much of the compound can be dissolved in a given volume of water at a particular temperature.

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept in chemistry that predicts how a system at equilibrium responds to external changes. If a stress is applied to a system, the equilibrium will shift to counteract the imposed change and restore a new equilibrium position.

For example, if you add more of ion A⁺ to the solution containing AX, Le Chatelier's principle suggests that the equilibrium will shift to the left, decreasing the solubility of AX. This shift helps reduce the change caused by the added common ion, aiming to maintain the system's balance.

Solubility Product Constant

The solubility product constant, or K_sp, is the equilibrium constant specific to the solubility of an ionic compound. It represents the highest possible product of the molar concentrations of ions in a saturated solution, each raised to the power of their stoichiometric coefficients in the equilibrium equation.

In mathematical terms, if the equilibrium for AX is \[AX(s) \rightleftharpoons A^{+}(aq) + X^{-}(aq)\],then the K_sp is defined by the expression:
\[K_{sp} = [A^{+}] \times [X^{-}]\].
When a common ion is added to the system, if the product of concentrations [A⁺][X^–] surpasses K_sp, then AX will precipitate until the product of ion concentrations equals K_sp again.

Ionic Compound Solubility

Ionic compound solubility refers to how much of an ionic compound can be dissolved in a solvent at a certain temperature to form a homogeneous mixture. This solubility is affected by various factors, including temperature, pressure (for gases), and the presence of other ions in the solution.

When a common ion is present, the solubility of an ionic compound decreases because the system works to lessen the effects of the added ion, which is a manifestation of Le Chatelier's principle. This solubility change is critical to understand, especially in processes such as crystallization, precipitation reactions, and maintaining the biological balance in living organisms.