Common-Ion Effect on Solubility

Introduction

A salt generally dissolves less when its solution already contains one of its ions. The added common ion raises the current ion product, so less additional solid must dissolve to reach Ksp. This is a change in molar solubility and equilibrium composition; the salt's Ksp remains fixed at the same temperature under the same standard-state definition.

Core explanation

For AgCl(s) ⇌ Ag⁺ + Cl⁻, Ksp ≈ [Ag⁺][Cl⁻]. In pure water with no side reactions, the simple molar solubility is s ≈ √Ksp. If a soluble chloride salt supplies initial chloride concentration c, dissolution adds approximately s to chloride and s to silver, so Ksp ≈ s(c+s). If c greatly exceeds s, Ksp ≈ sc and s ≈ Ksp/c. The common chloride reduces the amount of AgCl that can dissolve. The estimate must be checked: computed s should indeed be much smaller than c.

The same idea applies to a 1:2 salt, but stoichiometric coefficients matter. For CaF₂(s) ⇌ Ca²⁺ + 2F⁻, adding fluoride raises Qsp = [Ca²⁺][F⁻]². If free fluoride is approximately a large imposed concentration c and dissolved calcium is s, Ksp ≈ sc². Adding calcium instead gives approximately Ksp ≈ c(2s)² under suitable conditions. These two additions do not produce identical algebra, even though both suppress dissolution.

An immediate increase in common-ion activity can make Qsp exceed Ksp, causing precipitation if solid formation proceeds. At the new equilibrium, free-ion product returns to Ksp while dissolved amount changes. If there is no solid available in an undersaturated system, adding a common ion may simply move the solution closer to saturation. Always specify whether solid is present and whether the added ion comes from a fully soluble source.

Real solutions complicate the simple prediction. Ionic strength can change activity coefficients, and added ions may form complexes with dissolved metal ions or participate in acid-base chemistry. A ligand that binds a metal ion could increase total dissolved metal even while the free-ion Ksp condition remains satisfied. Therefore “common ion always lowers measured total solubility” is too broad without considering all chemical reactions. In standard introductory problems, assume no important side reactions unless stated.

Step-by-step reasoning

1. Write the salt dissolution equation and Ksp expression. 2. Identify the concentration supplied independently by the soluble common-ion source. 3. Add the dissolution contribution using correct stoichiometry. 4. Solve for s, then check any approximation against the result.

Visual explanation

Draw a beaker already containing chloride ions before AgCl enters. Its initial chloride level fills part of the Ksp product, leaving only a smaller allowable silver concentration at saturation.

Real-world analogy

If one side of a balance is already loaded, less additional weight is needed to reach a fixed product-like target. The analogy concerns equilibrium amounts, not a change in the target itself.

Real-world example

Adding sodium chloride to a saturated silver-chloride system supplies chloride ions and can reduce dissolved silver ion concentration. The visible effect depends on amounts and experimental conditions.

Why?

Why does a chloride source suppress AgCl dissolution? A higher chloride concentration lets the fixed Ksp product be satisfied with a lower free silver concentration, so less solid dissolves.

Common misconception

“The common ion decreases Ksp.” Ksp is temperature dependent; the common ion instead changes the concentrations needed to satisfy the same equilibrium value.

Worked example

An idealized 1:1 MX salt has Ksp = 1.0 × 10⁻¹⁰. In pure water, s ≈ 1.0 × 10⁻⁵ M. In a solution initially containing 0.010 M free X⁻, Ksp ≈ s(0.010+s). Assuming s ≪ 0.010 gives s ≈ 1.0 × 10⁻⁸ M. The ratio s/0.010 = 10⁻⁶ confirms the approximation. Solubility is about one thousand times lower than in pure water in this simplified model.

Quick check

1. Does adding chloride to AgCl at fixed temperature change Ksp? Answer: No. It changes the equilibrium free-ion concentrations and molar solubility.

Exam focus

Keep initial common-ion concentration separate from the amount produced by dissolving solid. State and check a large-common-ion approximation rather than silently dropping s.

Advanced insight

Thermodynamic Ksp uses activities, so adding an electrolyte may alter activity coefficients. In highly ionic solutions, a concentration-only calculation can misestimate the degree of common-ion suppression.

Summary

A shared dissolved ion usually suppresses simple salt dissolution by increasing Qsp at fixed Ksp. Quantitative work uses initial ion concentration plus stoichiometric dissolution contributions and checks approximations.

Practice questions

1. In AgCl equilibrium, which ion is common when NaCl is added? Answer: Cl⁻. 2. If initial chloride is c and AgCl solubility is s, what is its simple Ksp equation? Answer: Ksp ≈ s(c+s). 3. Why can complex formation alter a naive common-ion prediction? Answer: Complexes remove free ions, changing total dissolved amount while the free-ion Ksp condition still holds.