Introduction to Solubility Equilibria - AP Chemistry Study Guide

Getting Started

When we mix an "insoluble" ionic compound like silver chloride with water, it appears that nothing happens. On a macroscopic level, the white solid sits at the bottom of the beaker. At the atomic level, however, a dynamic process is occurring: a small number of ions break away from the crystal lattice and enter the solution, while dissolved ions simultaneously return to the solid state. This chapter explores the chemical equilibrium established in a saturated solution, introducing a way to quantify the very limited solubility of these so-called insoluble salts.

What You Should Be Able to Do

After completing this section, you will be able to:

• Write the balanced chemical equation for the dissolution of a sparingly soluble salt and its corresponding solubility-product expression (Ksp).

• Calculate the molar solubility of a salt in pure water using its Ksp value.

• Determine the Ksp value for a salt from its experimentally measured solubility.

• Compare the relative solubilities of different salts by analyzing their Ksp values and chemical formulas.

Key Concepts & Analysis

The dissolution of a sparingly soluble salt is a reversible process that reaches equilibrium. We can analyze this system by examining the inputs, the calculation steps that connect them, and the resulting outputs. This process-oriented view allows us to quantify and predict solubility.

Inputs & Preconditions

• Reactant: A sparingly soluble ionic solid (e.g., PbI₂(s)).

• Solvent: Typically pure water.

• Precondition: The system must be a saturated solution. This is a state of dynamic equilibrium where the solid salt is in contact with its maximum concentration of dissolved ions. In this state, the rate of dissolution equals the rate of precipitation.

Key Steps / Mechanism

The central task in solubility equilibria is to relate the equilibrium constant (Ksp) to the salt's solubility. This involves two primary calculation pathways.

Process 1: Calculating Molar Solubility (s) from Ksp

The molar solubility (s) is defined as the number of moles of the salt that can dissolve in one liter of solution to reach saturation.

• Step 1: Write the Dissolution Equation and Ksp Expression.

  Write the balanced equation showing the solid salt dissociating into its constituent aqueous ions. The solubility-product constant (Ksp) expression is written from this equation, excluding the solid reactant.

  Example: Silver Chloride (AgCl)

  AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq)

  Ksp = [Ag⁺][Cl⁻]

• Step 2: Define Equilibrium Concentrations in Terms of 's'.

  Use the stoichiometry of the dissolution reaction to express the equilibrium concentration of each ion in terms of the molar solubility, s. An "ICE" (Initial, Change, Equilibrium) table is useful here.

  Example: AgCl

  	AgCl(s)	Ag⁺(aq)	Cl⁻(aq)
  Initial	Solid	0 M	0 M
  Change	-s	+s	+s
  Equilibrium	Solid	s	s

  At equilibrium, [Ag⁺] = s and [Cl⁻] = s.

• Step 3: Substitute and Solve for 's'.

  Substitute the equilibrium concentration expressions into the Ksp expression and solve for s.

  Example: AgCl (Ksp = 1.8 x 10⁻¹⁰)

  Ksp = [Ag⁺][Cl⁻]

  1.8 x 10⁻¹⁰ = (s)(s) = s²

  s = √(1.8 x 10⁻¹⁰) = 1.3 x 10⁻⁵ M

  The molar solubility of AgCl is 1.3 x 10⁻⁵ mol/L.

Process 2: Calculating Ksp from Molar Solubility (s)

This process is the reverse of the first. You are given the solubility and asked to find the equilibrium constant.

• Step 1: Use 's' and Stoichiometry to Find Ion Concentrations.

  From the given molar solubility, s, use the balanced dissolution equation to determine the equilibrium concentration of each ion.

  Example: Calcium Fluoride (CaF₂)

  The molar solubility of CaF₂ is found to be 2.1 x 10⁻⁴ M.

  CaF₂(s) ⇌ Ca²⁺(aq) + 2F⁻(aq)

  Based on the 1:1:2 stoichiometry:

  [Ca²⁺] = s = 2.1 x 10⁻⁴ M

  [F⁻] = 2s = 2 * (2.1 x 10⁻⁴ M) = 4.2 x 10⁻⁴ M

• Step 2: Write the Ksp Expression.

  Ksp = [Ca²⁺][F⁻]²

• Step 3: Substitute Concentrations and Calculate Ksp.

  Plug the calculated ion concentrations into the Ksp expression to find its value.

  Ksp = (2.1 x 10⁻⁴)(4.2 x 10⁻⁴)²

  Ksp = (2.1 x 10⁻⁴)(1.76 x 10⁻⁷)

  Ksp = 3.7 x 10⁻¹¹

Outputs & Effects

• Quantitative Output: The calculation yields either the molar solubility (s) or the solubility-product constant (Ksp).

• Qualitative Effect: These values allow for the prediction and comparison of salt solubilities. A very small Ksp value (e.g., 10⁻⁵⁰) indicates extremely low solubility, while a Ksp value greater than 1 indicates a soluble salt, where the concept of a saturated solution is not practically limiting.

Controls & Limiting Factors

• Temperature: Ksp values are constant only at a specific temperature. Dissolution can be endothermic or exothermic, so temperature changes will shift the equilibrium and change the Ksp value.

• Stoichiometry: The ion ratio in the salt's formula is a critical factor that controls the relationship between s and Ksp. As seen with CaF₂, the fluoride ion concentration was 2s and was squared in the Ksp expression, significantly impacting the calculation.

Key Models & Representations

The relationship between Ksp and molar solubility (s) can be modeled as a two-way calculation pathway.

Key Terms, Quantities, & Concepts

• Solubility: A measure of the maximum amount of a substance (solute) that can dissolve in a given amount of solvent at a specific temperature to form a saturated solution.

• Molar Solubility (s): The solubility expressed in units of moles per liter (mol/L). It represents the moles of salt that dissolve to form one liter of saturated solution.

• Saturated Solution: A solution in which the maximum amount of solute has been dissolved. In this state, the dissolved solute is in dynamic equilibrium with any undissolved solid solute.

• Dissolution: The process in which a solid ionic compound breaks apart into its constituent ions as it dissolves in a solvent.

• Precipitation: The reverse of dissolution, where dissolved ions come together to form a solid ionic compound.

• Solubility-Product Constant (Ksp): The equilibrium constant for the dissolution of a sparingly soluble ionic compound. It is calculated from the product of the equilibrium concentrations of the dissolved ions, each raised to the power of its stoichiometric coefficient.

• Sparingly Soluble Salt: An ionic compound that has a very low solubility in water. These are the compounds for which Ksp values are most relevant.

Skill Snapshots

Causation

• A salt's specific stoichiometric ratio of cations to anions causes a unique mathematical relationship between its molar solubility (s) and its Ksp.

• The establishment of a dynamic equilibrium between dissolution and precipitation causes the ion concentrations in a saturated solution to remain constant over time.

• A very small Ksp value (e.g., 10⁻²⁵) causes a substance to have a very low molar solubility, meaning very little of it will dissolve.

Comparison

• For salts with the same ion ratio (e.g., AgCl and AgBr, both 1:1), the salt with the larger Ksp is more soluble than the salt with the smaller Ksp.

• The molar solubility of CaF₂ (a 1:2 salt) is not directly comparable to the molar solubility of AgCl (a 1:1 salt) simply by looking at their Ksp values; a full calculation of s is required.

• Soluble salts (like NaCl) have Ksp values much greater than 1, whereas sparingly soluble salts (like PbSO₄) have Ksp values much less than 1.

Change and Continuity Over Time (CCOT)

• Baseline: A saturated solution of silver chromate (Ag₂CrO₄) is at equilibrium, with solid Ag₂CrO₄ on the bottom of the beaker. The concentrations of Ag⁺(aq) and CrO₄²⁻(aq) are constant.

• Change 1: If some water is allowed to evaporate from the solution, the ion concentrations will increase, causing the rate of precipitation to temporarily exceed the rate of dissolution. The equilibrium will shift left, forming more solid Ag₂CrO₄ until the ion product equals Ksp again.

• Change 2: If pure water is added to the beaker, the solution becomes unsaturated. The rate of dissolution will exceed the rate of precipitation, and more solid will dissolve until the solution becomes saturated again or all the solid is gone.

• Continuity: As long as the temperature remains constant, the value of Ksp for silver chromate does not change, regardless of how much solid is present or how much water is added or removed.

Common Misconceptions & Clarifications

1. Misconception: "Insoluble" salts do not dissolve at all.

   Clarification: "Insoluble" is a relative term. Sparingly soluble salts dissolve to a small but measurable extent, establishing an equilibrium that is described by Ksp.

2. Misconception: The salt with the bigger Ksp is always more soluble.

   Clarification: This is only a reliable shortcut when comparing salts with the same ion stoichiometry (e.g., comparing two 1:1 salts like AgCl and BaSO₄). To compare salts with different stoichiometries (e.g., AgCl [1:1] vs. MgF₂ [1:2]), you must calculate the molar solubility (s) for each salt to make an accurate comparison.

3. Misconception: The concentration of the solid salt, [AgCl], should be included in the Ksp expression.

   Clarification: The concentration or activity of a pure solid is considered constant. This constant value is incorporated into the equilibrium constant, Ksp. For this reason, pure solids (and pure liquids) are always omitted from equilibrium constant expressions.

4. Misconception: Ksp is just a generic product of ion concentrations.

   Clarification: Ksp is the solubility product, which is the specific value of the ion-concentration product when the solution is saturated and at equilibrium. At other concentrations (unsaturated or supersaturated), the product of the ion concentrations is called the ion product (Q), not Ksp.

One-Paragraph Summary

The dissolution of sparingly soluble ionic compounds in water is a reversible process that establishes a dynamic equilibrium in a saturated solution. This equilibrium is quantitatively described by the solubility-product constant, Ksp, which is the product of the dissolved ion concentrations raised to their stoichiometric powers. There is a direct mathematical relationship between Ksp and a salt's molar solubility (s), allowing for the calculation of one from the other. The stoichiometry of the salt is critical in defining this relationship. By understanding and calculating Ksp and molar solubility, we can precisely predict the extent to which a compound will dissolve and compare the relative solubilities of different substances.