Understanding the Solubility Product (Ksp)

The Equilibrium of Sparingly Soluble Salts.

What is the Solubility Product (Ksp)?

The Solubility Product Constant (Ksp) is a type of equilibrium constant that measures the extent to which a sparingly soluble ionic compound dissolves in a solution.

When a slightly soluble solid is placed in water, a small amount of it dissolves, establishing a dynamic equilibrium between the undissolved solid and its dissociated ions in the solution.

The Ksp value represents the product of the ion concentrations at equilibrium in a saturated solution. A smaller Ksp value indicates a lower solubility.

Example: For a compound like silver chloride (AgCl), most of it remains as a solid, but a tiny amount dissolves into Ag⁺ and Cl⁻ ions. Ksp quantifies this very slight dissolution.

The Ksp Expression

For the dissolution of a generic ionic compound, AₐBₑ(s) ⇌ aA⁺(aq) + bB⁻(aq)

The solubility product expression is written as the product of the ion concentrations, with each concentration raised to the power of its stoichiometric coefficient from the balanced equation.

The formula is: Ksp = [A⁺]ᵃ[B⁻]ᵇ

A critical rule is that the concentration of the pure solid reactant is excluded from the expression because its concentration is considered constant.

Example:For the dissolution of lead(II) chloride, PbCl₂(s) ⇌ Pb²⁺(aq) + 2Cl⁻(aq), the expression is Ksp = [Pb²⁺][Cl⁻]².

Interpreting the Value of Ksp

The magnitude of Ksp is a direct indicator of a compound's solubility:

A very small Ksp (e.g., 10⁻³⁰): The compound is highly insoluble. The concentration of ions in the solution at equilibrium is extremely low.

A moderately small Ksp (e.g., 10⁻⁸): The compound is slightly soluble.

By comparing the Ksp values of two different salts, we can determine which one is more soluble (the one with the larger Ksp), provided they produce the same number of ions.

Example:Silver chloride (AgCl, Ksp = 1.8 x 10⁻¹⁰) is less soluble than silver phosphate (Ag₃PO₄, Ksp = 8.9 x 10⁻¹⁷) because a direct comparison is complex due to different numbers of ions. However, we can calculate their molar solubilities to compare.

The Common Ion Effect

The Common Ion Effect describes the decrease in solubility of a sparingly soluble salt when a solution already contains one of the ions from the salt (a 'common ion').

This is an application of Le Châtelier's Principle. If you add a common ion to a saturated solution at equilibrium, you are 'adding a product'. The equilibrium will shift to the left, causing more of the solid to precipitate out of the solution to re-establish equilibrium.

Example:If you try to dissolve silver chloride (AgCl) in a solution of sodium chloride (NaCl) instead of pure water, it will be even less soluble because the solution already contains chloride ions (the common ion).

Real-World Application: Kidney Stones and Water Treatment

The principles of Ksp and solubility are crucial in many natural and medical contexts.

Kidney Stones: Most kidney stones are composed of calcium oxalate (CaC₂O₄), a sparingly soluble salt. They form when the concentrations of calcium ions and oxalate ions in urine exceed the Ksp, causing the compound to precipitate as a solid in the kidneys.

Water Treatment: The common ion effect is used in water treatment facilities to remove unwanted heavy metal ions. For example, adding sodium carbonate to water containing lead ions will precipitate the lead as lead carbonate, which has a very low Ksp and can be easily filtered out.

Geology: The formation of caves, stalactites, and stalagmites is a slow process involving the dissolution and re-precipitation of calcium carbonate (limestone) based on the concentration of CO₂ in the water.

Example:Dietary advice for preventing kidney stones often involves avoiding foods high in oxalates to keep the ion concentrations below the Ksp threshold.

Key Summary

The **Solubility Product (Ksp)** is the equilibrium constant for the dissolution of a sparingly soluble ionic compound.
A smaller Ksp value indicates lower solubility.
The Ksp expression is **Ksp = [Products]**, with each ion concentration raised to the power of its coefficient. The solid is excluded.
The **Common Ion Effect** describes how the solubility of a salt decreases when it is dissolved in a solution containing one of its ions.

Practice Problems

Problem: The molar solubility of silver chromate (Ag₂CrO₄) in pure water is found to be 6.5 x 10⁻⁵ mol/L. What is the Ksp for silver chromate?

1. Write the dissolution equation. 2. Determine the equilibrium ion concentrations based on molar solubility 's'. 3. Plug these concentrations into the Ksp expression.

Solution: Ag₂CrO₄(s) ⇌ 2Ag⁺(aq) + CrO₄²⁻(aq). At equilibrium, [Ag⁺] = 2s = 2 * (6.5 x 10⁻⁵) = 1.3 x 10⁻⁴ M. [CrO₄²⁻] = s = 6.5 x 10⁻⁵ M. Ksp = [Ag⁺]²[CrO₄²⁻] = (1.3 x 10⁻⁴)² * (6.5 x 10⁻⁵) ≈ 1.1 x 10⁻¹².

Problem: Calculate the molar solubility of lead(II) iodide (PbI₂) in pure water. The Ksp for PbI₂ is 7.9 x 10⁻⁹.

1. Write the dissolution equation. 2. Set up the Ksp expression in terms of molar solubility 's'. 3. Solve for 's'.

Solution: PbI₂(s) ⇌ Pb²⁺(aq) + 2I⁻(aq). Ksp = [Pb²⁺][I⁻]². Let s = molar solubility. Then [Pb²⁺] = s and [I⁻] = 2s. 7.9 x 10⁻⁹ = (s)(2s)² = 4s³. s³ = (7.9 x 10⁻⁹) / 4 = 1.975 x 10⁻⁹. s = ∛(1.975 x 10⁻⁹) ≈ 1.25 x 10⁻³ mol/L.

Frequently Asked Questions

What is the difference between solubility and the solubility product (Ksp)?

Solubility is the maximum amount of a substance that can dissolve in a given amount of solvent at a specific temperature (often expressed in g/L or mol/L). Ksp is an equilibrium constant that represents the product of the ion concentrations in a saturated solution. While related, they are not the same thing, but you can calculate one from the other.

Why are pure solids not included in the Ksp expression?

The 'concentration' of a pure solid is its density divided by its molar mass, which is a constant value. Since it doesn't change during the reaction, it is incorporated into the equilibrium constant (Ksp) and omitted from the expression itself.

Does temperature affect Ksp?

Yes, significantly. The dissolution of most solids is an endothermic process, so according to Le Châtelier's principle, increasing the temperature will increase the solubility and therefore increase the value of Ksp. Ksp values are always reported at a specific temperature, usually 25°C.

Solubility Product (Ksp) Calculator

Solubility Product (Ksp) Calculator