Question

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

Short answer

The common ion effect and Le Châtelier's principle explain the decrease in solubility of \( \mathrm{CaCO}_{3} \) in a \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) solution. The addition of the common ion \( \mathrm{CO}_{3}^{2-} \) to the system increases its concentration, leading the equilibrium to shift left, decreasing the solubility of \( \mathrm{CaCO}_{3} \).

Step-by-step solution

Understand the Common Ion Effect

Common ion effect refers to the decrease in solubility of a salt when a common ion is added. In the context of the exercise, \( \mathrm{CO}_{3}^{2-} \) ion is the common ion in both \( \mathrm{CaCO}_{3} \) and \( \mathrm{Na}_{2} \mathrm{CO}_{3} \). By adding \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) in a solution with \( \mathrm{CaCO}_{3} \), the concentration of \( \mathrm{CO}_{3}^{2-} \) ions increases.

Explanation Based on Le Châtelier's Principle

Le Châtelier's principle states that a system in equilibrium will respond in a way to counteract a change. If an equilibrium is disturbed by changing the conditions, the system responds to restore the equilibrium. In the context of the problem the equilibrium \(\mathrm{CaCO}_{3}(s) \leftrightharpoons \mathrm{Ca}^{2+} (aq) + \mathrm{CO}_{3}^{2-}(aq)\) is disturbed by adding \(\mathrm{Na}_{2} \mathrm{CO}_{3}\), which increases the concentration of \(\mathrm{CO}_{3}^{2-} \) ions. The system counteracts this by decreasing the solubility of \(\mathrm{CaCO}_{3}\), shifting the equilibrium to the left, which results in a decrease of \(\mathrm{CO}_{3}^{2-}\) ion concentration by converting more \(\mathrm{CaCO}_{3}\) into its solid form.

Summarize the Explanation.

The addition of a common ion \( \mathrm{CO}_{3}^{2-} \) from \( \mathrm{Na}_{2} \mathrm{CO}_{3} \) to a solution of \( \mathrm{CaCO}_{3} \) increases the concentration of \( \mathrm{CO}_{3}^{2-} \) ions. This disturbance to the equilibrium is counteracted by the system shifting the equilibrium to the left, reducing the solubility of \( \mathrm{CaCO}_{3} \) and thus restoring equilibrium.

Key concepts

Le Châtelier's principle

Understanding Le Châtelier's principle is essential when studying dynamic chemical processes. This principle helps us predict how a chemical system at equilibrium responds to changes in concentration, pressure, or temperature. When a system is in a state of equilibrium and is subjected to an external change, like addition of reactants or removal of products, it will shift to offset that change. This adjustment is what maintains balance within the system.

For instance, consider a sealed container where nitrogen and hydrogen gases are reacting to form ammonia. If we suddenly introduce additional nitrogen into the container, Le Châtelier's principle tells us that the system will react by producing more ammonia to reduce the excess nitrogen and restore equilibrium. This principle also applies to changes in pressure and temperature, each causing the equilibrium to shift in a direction that minimizes the effect of that change.

In the context of our exercise with calcium carbonate and sodium carbonate, the addition of a common ion causes the equilibrium to shift in such a way as to decrease the solubility of calcium carbonate, and this effect is perfectly described by Le Châtelier's principle.

Solubility Equilibrium

Solubility equilibrium is a specific type of chemical equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solubility product (\(K_{sp}\)) is a constant that provides the ratio of a solute’s concentration in a saturated solution at a given temperature.

When a solid compound dissolves in water, it breaks into its constituent ions until the rate at which it dissolves equals the rate at which it reforms into the solid. This point is where solubility equilibrium is reached. However, if more solute is added than the solvent can dissolve, or a common ion is introduced, the equilibrium will shift to re-establish balance by precipitating the excess ions in the form of solid.

For example, if we have a saturated solution of calcium carbonate, which is in equilibrium its ions in solution, and we add more carbonate ions by adding a compound such as sodium carbonate, the increased concentration of carbonate ions drives the reaction towards the formation of more solid calcium carbonate, thus decreasing its overall solubility.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction's forward and reverse reactions occur at the same rate, resulting in no net change in the amount of reactants and products. This does not mean that the reactants and products are equal in concentration, but rather that their concentrations have stabilized at a certain ratio and remain constant over time.

At equilibrium, the rates of the forward and reverse reactions are equal. However, it’s important to note that the reactions are still occurring on the molecular level; there is a dynamic exchange between reactants forming products and products re-forming reactants. The equilibrium constant (\(K_{eq}\)) quantifies the equilibrium position of a reaction, representing the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients.

In our textbook problem, when we dissolve calcium carbonate in water, it establishes an equilibrium between the solid and its ions in solution. The addition of a common ion, like carbonate from sodium carbonate, perturbs the equilibrium, leading to a shift to re-establish the balance, typically seen as a decrease in the solubility of the calcium carbonate because the reaction favors the formation of more solid to reduce the concentration of the common ion.