Question

How does the common ion effect influence solubility equilibria? Use Le Châtelier's principle to explain the decrease in solubility of \(\mathrm{CaCO}_{3}\) in an \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) solution.

Short answer

The common ion effect reduces the solubility of \( \text{CaCO}_3 \) in \( \text{Na}_2\text{CO}_3 \) by shifting the equilibrium to favor more solid \( \text{CaCO}_3 \), according to Le Châtelier's principle.

Step-by-step solution

Identify the Equilibrium Reaction

First, recognize the solubility equilibrium of calcium carbonate, represented as: \( \text{CaCO}_3(s) \rightleftharpoons \text{Ca}^{2+}(aq) + \text{CO}_3^{2-}(aq) \). This equation describes the dissolution of solid calcium carbonate into its constituent ions in solution.

Introduce the Common Ion

When \( \text{Na}_2\text{CO}_3 \) is added to the solution, it dissociates completely into \( 2\text{Na}^+ \) and \( \text{CO}_3^{2-} \). Here, \( \text{CO}_3^{2-} \) is the common ion because it is already part of the equilibrium of \( \text{CaCO}_3 \).

Apply Le Châtelier's Principle

According to Le Châtelier's principle, if a system at equilibrium experiences a change in concentration, temperature, volume, or pressure, the equilibrium shifts to counteract the imposed change. Adding \( \text{CO}_3^{2-} \) from \( \text{Na}_2\text{CO}_3 \) increases the concentration of one of the products in the \( \text{CaCO}_3 \) equilibrium.

Predict the Shift in Equilibrium

With an increased concentration of \( \text{CO}_3^{2-} \), the equilibrium will shift to the left, favoring the formation of solid \( \text{CaCO}_3 \) to reduce the disturbance. This shift results in a decrease in the concentration of \( \text{Ca}^{2+} \) and \( \text{CO}_3^{2-} \) ions in solution.

Conclude the Impact on Solubility

As a result of the leftward shift and the formation of more solid \( \text{CaCO}_3 \), the solubility of calcium carbonate decreases in the presence of additional \( \text{CO}_3^{2-} \) ions from \( \text{Na}_2\text{CO}_3 \), demonstrating the common ion effect's influence on solubility equilibria.

Key concepts

Le Châtelier's Principle

Le Châtelier's Principle is a core concept in chemistry that describes how a system at equilibrium responds to changes. When a change is introduced, such as modifications in concentration, temperature, or pressure, the system will adjust itself to counteract that change.
In simpler terms, if you disturb a chemical equilibrium, the system will shift in a direction that minimizes the disturbance. For example, if the concentration of a reactant is increased, the equilibrium will shift to convert the excess reactant into products.
This principle is often applied to understand and predict how changes affect a chemical reaction or an equilibrium, making it an invaluable tool for chemists.

Solubility Equilibria

Solubility equilibria refer to the balance established between the dissolved ions and the undissolved solid in a saturated solution. When a solid salt dissolves in water, it disintegrates into its respective ions, which move freely in the solution.
The equation representing solubility equilibrium of a salt generally looks like: \[ \text{AB(s)} \rightleftharpoons \text{A}^+(aq) + \text{B}^-(aq) \].
In these reactions, the concentration of the solid remains constant while the ionic concentrations attain a state of balance, or equilibrium. Understanding solubility equilibrium is crucial as it aids in predicting how changes in conditions can affect the amount of solute that can dissolve in the solution.

Calcium Carbonate Solubility

Calcium carbonate (\(\text{CaCO}_3\)) exhibits specific solubility behavior in water. It dissolves to produce calcium ions (\(\text{Ca}^{2+}\)) and carbonate ions (\(\text{CO}_3^{2-}\)). However, it is sparingly soluble, meaning only a small amount actually dissolves at equilibrium.
When additional carbonate ions are introduced to the solution from another source, such as sodium carbonate (\(\text{Na}_2\text{CO}_3\)), the concentration of (\(\text{CO}_3^{2-}\)) increases. This increase leads to the common ion effect, where the presence of a common ion suppresses the dissolution of the compound, reducing calcium carbonate's solubility.
The understanding of calcium carbonate's solubility is essential as it is commonly found in natural settings, waste treatment processes, and even daily products.

Equilibrium Shift

An equilibrium shift occurs when a system at equilibrium adjusts due to a disturbance such as the addition of a reactant or product. This shift restores a new equilibrium state, which can be predicted using Le Châtelier’s Principle.
In the case of calcium carbonate (\(\text{CaCO}_3\)), when the concentration of carbonate ions (\(\text{CO}_3^{2-}\)) is increased by adding sodium carbonate, the equilibrium shifts towards forming more solid calcium carbonate. Consequently, this shift lowers the concentrations of dissolved ions.

• The shift is leftward, signifying more precipitation (solid formation).
• It results in a decreased solubility of \(\text{CaCO}_3\).

Understanding equilibrium shifts helps predict how changes affect the solute concentration in reversible reactions and is a fundamental aspect in chemical reaction management.