Question

. Describe how the presence of a common ion reduces the solubility of an ionic compound

Short answer

The presence of a common ion reduces the solubility of an ionic compound due to the common ion effect. When a salt containing a common ion is added to a solution of a slightly soluble ionic compound, the equilibrium of the dissolution reaction shifts to favor the solid, undissolved form of the compound, as predicted by Le Châtelier’s Principle. In the example of AgCl and NaCl, the addition of NaCl introduces more Cl- ions, causing the equilibrium of AgCl to shift left and decrease its solubility. The new solubility can be calculated using the solubility product constant (Ksp), and we find that the solubility of AgCl is significantly reduced in the presence of the common ion.

Step-by-step solution

Define the Common Ion Effect

The common ion effect is a phenomenon that occurs when the addition of a salt containing a common ion to a solution containing a slightly soluble ionic compound reduces the solubility of the ionic compound. This effect is due to the shift in the equilibrium of the dissolution reaction caused by the presence of the common ion as predicted by Le Châtelier’s Principle.

Choose an Example Compound to Analyze

To illustrate the common ion effect, let's consider the slightly soluble ionic compound, silver chloride (AgCl). Its dissolution equilibrium in water can be represented by the following chemical equation: AgCl(s) ⇌ Ag+ (aq) + Cl- (aq)

Introduce the Common Ion

Now suppose we add an aqueous solution of sodium chloride (NaCl), which contains a common ion (Cl-), to the AgCl solution. The presence of additional Cl- ions will shift the equilibrium to the left, as predicted by Le Châtelier's Principle, which states that if a stress (in this case, additional Cl- ions) is applied to a system at equilibrium, the system will shift to oppose the stress and restore equilibrium.

Calculate the Reduction in Solubility

To quantify the reduction in solubility due to the common ion effect, we can use the solubility product constant, Ksp. For AgCl, Ksp = 1.8 × 10^-10. In the absence of a common ion, let the solubility of AgCl be x mol/L. In this case: Ksp = [Ag+][Cl-] 1.8 × 10^-10 = x^2 Now let's say we add 0.1 mol/L of NaCl solution to the AgCl solution. The NaCl will completely dissociate into Na+ and Cl- ions, so the concentration of Cl- ions due to NaCl is 0.1 mol/L. Since the equilibrium will shift to the left, the solubility of AgCl will decrease. Let the decrease in solubility be y mol/L. Therefore, the final concentration of Ag+ and Cl- ions will be x-y and 0.1+y, respectively. The new Ksp expression is: 1.8 × 10^-10 = (x-y)(0.1+y)

Solve for the New Solubility

Since the concentration of the common ion is much larger than that of the AgCl, we can assume that y is very small compared to 0.1, so the terms containing y can be neglected. Therefore: 1.8 × 10^-10 = (x-y)(0.1) To find the new solubility of AgCl (x-y), divide the Ksp value by 0.1: (x-y) = 1.8 × 10^-10 / 0.1 = 1.8 × 10^-9

Compare the Original Solubility and the New Solubility

From Step 4, we found the original solubility of AgCl to be x. Now we found the solubility in the presence of the common ion to be (x-y) = 1.8 × 10^-9. Comparing these solubilities, we can clearly see that the presence of the common ion (Cl-) has significantly reduced the solubility of AgCl. This demonstrates the common ion effect in reducing the solubility of an ionic compound.

Key concepts

Le Châtelier’s principle

Le Châtelier’s principle is a fundamental concept in equilibrium chemistry that helps us predict how a system at equilibrium responds to changes or 'stresses'. This principle states that if an external stress is applied to a system in equilibrium, the system adjusts to minimize that stress and re-establish equilibrium.

Consider an example where we have a sealed container with a mixture of nitrogen, hydrogen, and ammonia gases in equilibrium. If we add more nitrogen to the container, Le Châtelier’s principle suggests that the system will react to reduce the effect of this added nitrogen by forming more ammonia.

This principle is crucial for understanding the common ion effect because it explains why the solubility of an ionic compound decreases when a common ion is added to the solution. The system reacts to the added common ion by shifting the equilibrium to reduce its concentration, as we see with our silver chloride example.

Solubility product constant

The solubility product constant, known as Ksp, is a special type of equilibrium constant used for sparingly soluble ionic compounds. Ksp is defined for the equilibrium that involves the dissolution of solids into their constituent ions. For any ionic compound with a general formula of AbBc iton, Ksp is given by: Ksp = [A^+]^b[B^-]^cWhere [A+] and [B-] are the molar concentrations of the dissolved ions at equilibrium, and b and c are the stoichiometric coefficients in the balanced dissolution equation.

Ksp is a critical tool in predicting whether a precipitate will form in a solution. A solution is said to be saturated when the product of the concentrations of the ions in solution is equal to the Ksp. If this product exceeds the Ksp, the excess ions will precipitate out of the solution until equilibrium is re-established.

Equilibrium chemistry

Equilibrium chemistry centers on the understanding of how reversible chemical reactions occur and the conditions under which the reactants and products are in a state of balance. At equilibrium, the rates of the forward and reverse reactions are equal, and the concentrations of the reactants and products remain constant over time.

When working with equilibrium systems, it's essential to know how to apply Le Châtelier’s principle and calculate constants like Ksp to predict the behavior of a system. The common ion effect is a perfect example of equilibrium chemistry at play. It's the alteration in solubility of an ionic compound when other compounds providing the same ions are present in the solution. Understanding equilibrium allows chemists to manipulate conditions to favor the formation or removal of certain products in industrial processes, medicine, and environmental science.

Ionic compounds

Ionic compounds are made up of positively and negatively charged ions held together by strong electrostatic forces known as ionic bonds. These compounds generally have high melting and boiling points and are soluble in water due to their charged nature, which interacts favorably with the polar water molecules.

In the context of the common ion effect, the solubility of an ionic compound in water can be influenced by the presence of other compounds that share a common ion. For example, adding sodium chloride to an aqueous solution of silver chloride introduces more chloride ions (the common ion), which affects the solubility of silver chloride. These relationships are crucial for predicting precipitation, understanding biological systems, and designing products in various industries.