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 \((A^{+}\) or \(X^{-})\) than it is in pure water? Explain.

Short answer

The solubility of a compound AX is reduced in a solution containing a common ion (either \(A^+\) or \(X^-\)) due to the common ion effect. This is aligned with Le Chatelier's Principle, where the presence of the common ion shifts the dissolution equilibrium, reducing the solubility of the compound.

Step-by-step solution

Understanding Common Ion Effect

The common ion effect refers to the phenomenon where the solubility of a salt (compound) is reduced when one of its constituent ions is added to the solution. This occurs because the added common ion shifts the equilibrium of the dissolution process.

Applying Le Chatelier's Principle

According to Le Chatelier's Principle, if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust itself to counteract the change and a new equilibrium will be established. In this case, adding a common ion to the solution will shift the dissolution equilibrium to the left, reducing the solubility of the AX compound.

Examining the Solubility Product

The solubility product (\(K_{sp}\) for the compound AX can be written as \[K_{sp} = [A^+][X^-]\] Adding a common ion (either \(A^+\) or \(X^-\)) increases the concentration of that ion in the solution, which means the product \([A^+][X^-]\) would exceed the \(K_{sp}\), thus driving the reaction to form more solid AX to restore equilibrium. This results in a decrease in the concentration of the other ion, ultimately reducing the solubility of compound AX.

Key concepts

Solubility Product

The solubility product, commonly abbreviated as (K_{sp}), is a key concept in understanding the solubility of compounds in a solution. It is a specialized form of equilibrium constant that applies to the dissolution of sparingly soluble ionic compounds. The K_{sp} value is determined by the concentrations of the ions at equilibrium and can be represented by an equation such as

(K_{sp} = [A^+][X^-])

for a compound with the formula AX.

This equilibrium constant is specific to a particular compound at a given temperature and indicates how much of the compound can dissolve to form a saturated solution. If additional ion A or X is introduced into the solution, for AX in this case, the product of

([A^+][X^-])

will increase. If this product exceeds the K_{sp}, additional AX will precipitate out until the concentrations again match the value of the K_{sp}. The presence of a common ion thus reduces the solubility of the compound by effectively lowering the concentration of the other ion that's not added, till the equilibrium is re-established.

Le Chatelier's Principle

Le Chatelier's Principle offers a way to predict how a system at chemical equilibrium responds to changes in concentration, temperature, or pressure. When a stress is applied to the system, it reacts in a way to counteract the applied change. In terms of solubility, adding an ion that is already present in the compound (common ion effect) constitutes such a stress.

To visualize this, imagine an equilibrium between solid AX and its ions in solution:

AX(s) ↔ A^+(aq) + X^-(aq).

When additional A+ or X- is introduced into the solution, Le Chatelier's Principle suggests that the equilibrium will shift to oppose this increase in concentration. As a result, the reaction will proceed in the direction that produces more of the solid AX (to the left in the above equation), leading to a decrease in the solubility of the compound in the solution.

Chemical Equilibrium

Chemical equilibrium is a state wherein the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time. It is a dynamic process where the reactions continue to occur, but they do so in a way that doesn't affect the overall system's balance.

In the context of solubility, an ionic solid in a solution is in equilibrium with its ions. When a system is at equilibrium, it can be described by an equation that represents the balance between the undissolved solid and the dissolved ions. Any change in conditions, such as the addition of a common ion, will alter the position of the equilibrium. The system will then adjust according to the principles of Le Chatelier to return to a new state of equilibrium where the K_{sp} is respected, even if it means that less of the ionic compound remains in solution. This adjustment may involve changing the solubility of the compound to accommodate the change in ion concentration, resulting in either more solid precipitating out or more ions dissolving, depending on the nature of the change imposed on the system.