Common-Ion Effect - AP Chemistry Study Guide

Getting Started

We will investigate the equilibrium of sparingly soluble ionic compounds, focusing on how their solubility changes at the macroscopic level. The core problem is to understand and predict what happens when we try to dissolve a salt not in pure water, but in a solution that already contains one of the salt's constituent ions. This phenomenon, known as the common-ion effect, is a direct application of equilibrium principles.

What You Should Be Able to Do

After completing this section, you will be able to:

• Explain why the solubility of a sparingly soluble salt decreases in the presence of a common ion, using Le Châtelier's principle.

• Set up and solve equilibrium problems to calculate the molar solubility of a salt in a solution containing a common ion.

• Compare the molar solubility of a salt in pure water to its solubility in a solution containing a common ion.

• Calculate the concentration of ions in a saturated solution when a common ion is present.

Key Concepts & Analysis

This topic is best understood through the lens of Dynamics & Change, where we analyze how an established equilibrium system responds to a specific stress.

Baseline Condition: A Saturated Solution in Pure Water

When a sparingly soluble salt, such as lead(II) chloride (PbCl₂), is added to pure water, it dissolves until the solution is saturated. At this point, a dynamic equilibrium is established between the undissolved solid and its dissolved ions.

• The Equilibrium Reaction:

  PbCl₂(s) ⇌ Pb²⁺(aq) + 2Cl⁻(aq)

• The Equilibrium Expression: The concentration of the solid, PbCl₂(s), is constant and is incorporated into the equilibrium constant. The resulting expression is for the solubility product constant, Ksp.

  Ksp = [Pb²⁺][Cl⁻]²

At a given temperature, the value of Ksp is constant. The molar solubility (s) is defined as the moles of the solid that dissolve per liter of solution to reach saturation. In pure water, [Pb²⁺] = s and [Cl⁻] = 2s, so the Ksp expression becomes Ksp = (s)(2s)² = 4s³. We can solve for s to find the salt's solubility in pure water.

The Process or Stress: Introducing a Common Ion

The "stress" is the addition of a common ion—an ion that is already part of the salt's equilibrium. For our PbCl₂ system, a common ion could be Pb²⁺ (from a soluble salt like Pb(NO₃)₂) or Cl⁻ (from a soluble salt like NaCl or HCl).

Let's consider dissolving PbCl₂ in a 0.10 M NaCl solution instead of pure water.

• The Initial State: Before any PbCl₂ dissolves, the solution already contains Cl⁻ ions. The initial concentration of Cl⁻ is 0.10 M. The initial concentration of Pb²⁺ is 0 M.

The Resulting Change: A Shift in Equilibrium

According to Le Châtelier’s principle, if a stress (an increase in the concentration of a product, Cl⁻) is applied to a system at equilibrium, the system will shift to counteract the stress.

• Qualitative Analysis: The dissolution equilibrium is PbCl₂(s) ⇌ Pb²⁺(aq) + 2Cl⁻(aq). Adding Cl⁻ ions increases the concentration of a product. To relieve this stress, the equilibrium will shift to the left, favoring the formation of the reactant, solid PbCl₂(s). This means less PbCl₂ will dissolve than in pure water. The solubility of the salt is reduced.

• Quantitative Analysis: We can calculate the new, lower molar solubility using an ICE (Initial, Change, Equilibrium) table and the Ksp value. Let's assume Ksp for PbCl₂ is 1.7 x 10⁻⁵.

Now, substitute the equilibrium concentrations into the Ksp expression:

Ksp = [Pb²⁺][Cl⁻]²

1.7 x 10⁻⁵ = (s)(0.10 + 2s)²

Because Ksp is very small, we know that s (the molar solubility) will also be very small. Therefore, the change 2s will be negligible compared to the initial concentration of the common ion, 0.10 M. We can make a simplifying assumption:

0.10 + 2s ≈ 0.10

The equation simplifies to:

1.7 x 10⁻⁵ ≈ (s)(0.10)²

1.7 x 10⁻⁵ ≈ s(0.010)

s ≈ 1.7 x 10⁻³ M

The molar solubility of PbCl₂ in 0.10 M NaCl is 1.7 x 10⁻³ M. For comparison, its solubility in pure water would be s = ³√(Ksp/4) = ³√(1.7x10⁻⁵/4) ≈ 1.6 x 10⁻² M. The presence of the common ion reduced the solubility by a factor of about 10.

Key Models & Representations

This flowchart outlines the quantitative problem-solving process for common-ion effect calculations.

Problem-Solving Flowchart: Calculating Solubility with a Common Ion

Key Terms, Quantities, & Concepts

• Sparingly Soluble Salt: An ionic compound that dissolves to only a very small extent in a solvent, establishing a dissolution equilibrium.

• Solubility Product Constant (Ksp): The equilibrium constant for the dissolution of a sparingly soluble salt. Its value is constant for a given salt at a specific temperature.

• Molar Solubility (s): The number of moles of a salt that can dissolve in one liter of solution to form a saturated solution. Its unit is mol/L (or M).

• Common Ion: An ion that is present in the solution and is also a product of the dissolution of the sparingly soluble salt.

• Common-Ion Effect: The decrease in the solubility of an ionic compound when it is dissolved in a solution that already contains an ion common to the compound.

• Le Châtelier’s Principle: States that if a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress.

• ICE Table: A tool used to organize concentrations for an equilibrium system, tracking Initial, Change, and Equilibrium values.

Skill Snapshots

• Causation:

  1. The presence of a common ion in a solution causes the dissolution equilibrium of a sparingly soluble salt to shift to the left.

  2. A leftward shift in the dissolution equilibrium results in a decrease in the molar solubility of the salt.

  3. The small value of Ksp justifies the simplifying assumption that the change in concentration, s, is negligible compared to the initial concentration of the common ion.

• Comparison:

  1. The molar solubility of a salt is always lower in a solution containing a common ion than it is in pure water.

  2. The value of Ksp for a salt is a constant at a given temperature, whereas the molar solubility (s) changes depending on the composition of the solution.

  3. In pure water, the initial concentration of product ions is zero, unlike in a common-ion problem, where one ion has a non-zero initial concentration.

• Change and Continuity Over Time (CCOT):

  • Baseline: A saturated solution of AgCl in pure water is at equilibrium, with [Ag⁺] = [Cl⁻].

  • Change 1: Upon adding NaCl, the [Cl⁻] increases, stressing the equilibrium.

  • Change 2: The equilibrium shifts left, causing AgCl to precipitate and reducing the [Ag⁺] until a new equilibrium is established where [Ag⁺] < [Cl⁻].

  • Continuity: Throughout this process, the value of the solubility product constant, Ksp = [Ag⁺][Cl⁻], remains unchanged as long as the temperature is constant.

Common Misconceptions & Clarifications

1. Misconception: Adding a common ion changes the value of Ksp.

   • Clarification: Ksp is an equilibrium constant and is only dependent on temperature. The common-ion effect changes the molar solubility (s) and the individual ion concentrations at equilibrium, but the Ksp value itself remains constant.

2. Misconception: In an ICE table for a common-ion problem, the initial concentration of both ions is zero.

   • Clarification: The defining feature of a common-ion problem is that the solution already contains one of the ions. The initial concentration of that specific ion must be included in the "I" row of the ICE table.

3. Misconception: For a salt like CaF₂, the change in the common ion F⁻ is +s.

   • Clarification: The change must always reflect the stoichiometry of the dissolution reaction: CaF₂(s) ⇌ Ca²⁺(aq) + 2F⁻(aq). The change for Ca²⁺ is +s, but the change for F⁻ is +2s. This is a frequent source of error in calculations.

4. Misconception: The common-ion effect only applies to anions.

   • Clarification: The effect works for common cations as well. Dissolving AgCl in a silver nitrate (AgNO₃) solution will also reduce the solubility of AgCl because Ag⁺ is the common ion.

One-Paragraph Summary

The common-ion effect describes the reduction in the solubility of a sparingly soluble salt when it is dissolved in a solution that already contains one of its constituent ions. This phenomenon is a direct consequence of Le Châtelier's principle: the presence of the common ion, a product in the dissolution equilibrium, causes the equilibrium to shift to the left, favoring the solid reactant and thus decreasing the amount of salt that can dissolve. While the molar solubility of the salt decreases significantly, the solubility product constant, Ksp, remains unchanged at a constant temperature. We can quantitatively determine this new, lower solubility by setting up an ICE table that includes the initial concentration of the common ion and solving the Ksp expression.