Solubility is the measure of the maximum amount of solute that can be dissolved in a given quantity of solvent at a given temperature and pressure. Solubility is usually measured in molarity (M) or moles per liter (mol/L). A compound is termed soluble if it dissolves in water.

When soluble salts dissolve in water, the ions in the solid separate and disperse uniformly throughout the solution; this process represents a physical change known as dissociation. Potassium chloride (KCl) is an example of a soluble salt. When solid KCl is added to water, the positive (hydrogen) end of the polar water molecules is attracted to the negative chloride ions, and the negative (oxygen) ends of water are attracted to the positive potassium ions. The water molecules surround individual K⁺ and Cl⁻ ions, reducing the strong forces that bind the ions together and letting them move off into solution as solvated ions. 

Another example of a soluble salt is silver nitrate, AgNO₃, which dissolves in water as Ag⁺ and NO₃^- ions. Nitrate, NO₃^-, is a polyatomic ion, and in solution, it stays intact as a single whole unit. Unlike monatomic ions (K⁺, Cl^-, Ag⁺), which contain only one atom, polyatomic ions are a group of atoms that carry a charge (NO₃^-, SO₄^2-, NH₄⁺). They remain such in solution and do not split into individual atoms. 

A compound is termed insoluble if it does not dissolve in water. However, in reality, “insoluble” compounds dissolve to some extent, that is, less than 0.01 M.

In the case of insoluble salts, the strong interionic forces that bind the ions in the solid are stronger than the ion-dipole forces between individual ions and water molecules. As a result, the ions stay intact and do not separate. Thus, most of the compound remains undissolved in water. Silver chloride (AgCl) is an example of an insoluble salt. The water molecules cannot overcome the strong interionic forces that bind the Ag⁺ and Cl^-  ions together; hence, the solid remains undissolved.

Solubility Rules

The solubility of ionic compounds in water depends on the type of ions (cation and anion) that form the compounds. For example, AgNO₃ is water-soluble, but AgCl is water-insoluble. The solubility of a salt can be predicted by following a set of empirical rules (listed below), developed based on the observations on many ionic compounds.

i) Compounds containing ammonium ions (NH₄⁺) and alkali metal cations are soluble
ii) All nitrates and acetates are always soluble.
iii) Chloride, bromide, and iodide compounds are soluble with the exception of those of silver, lead, and mercury(I)
iv) All sulfate salts are soluble except their salts with silver, lead, mercury(I), barium, strontium, and calcium
v) All carbonates, sulfites, and phosphates are insoluble except their salts with ammonium and alkali metal cations.
vi) Sulfides and hydroxides of all salts are insoluble, with the exception of their salts with alkali metal cations, ammonium ion, and calcium, strontium, and barium ions.
vii) All oxide-containing compounds are insoluble except their compounds with calcium, barium, and alkali metal cations.

This text is adapted from OpenStax Chemistry 2e, Section 11.2: Electrolytes.