When ionic compounds dissolve in a solvent (tipically water), the ionic bonds between the component ions break, generating free ions, usually solvated by solvent molecules (hydrogen bonding and ion-dipole bonding).
This is a reversible chemical reaction. As ionic bonds break and the compound dissolves, ions in the solution collide, creating new ionic bonds and basically forming a solid precipitate (that can instantaneously redisolve). This is a dynamic equilibrium just like any other equilbirum.
If the equilibrium of the dissolution process is shifted to the right (to the products side), the compound is highly soluble, and if it's shifted to the left the compound has a low solubility.
Consider the ionic compound \(M_{m}N_{n}\)
The dissolution equilibrium equation can be written as:
\(M_{m}N_{n (s)}\rightarrow mM^{n+}_{ (aq)} + nN^{m+}_{ (aq)}\)
The equilibrium constant for this reaction is \(K = \frac{[M^{n+}]^m[N^{m+}]^n}{[M_{m}N_{n}]}\)
However, in chemical equilibra, the activity of solid substances is considered to be equal to 1. So, we can write \(K=[M^{n+}]^m[N^{m+}]^n\)
We denote this equilbirum constant by \(K_{s}\) or \(K_{sp}\) and we call it the substance's solubility product.
As for other equilibrium constants, we also define the solubility product \(pK_{sp}=-log(K_{sp})\)
The condition for a precipiatte to not form is \([M^{n+}]^m[N^{m+}]^n\leq K_{sp}\) (1)
We call the maximum molar concentration of a substance in a certain solvent (the concentration of a saturated solution) the solubility of the substance and we denote it by S.
If the compound completely dissolves, the concentrations of the two ions are \([M^{n+}]=mS\) and \([N^{m+}] = nS\)
Writing the limit case of equation (1) (for a saturated solution) we get \([M^{n+}]^m[N^{m+}]^n = K_{sp}\)
Substituting the two concentrations, \((mS)^m\cdot (nS)^n=K_{sp}\)
This is equivalent to \(m^m\cdot n^n \cdot S^{m+n}=K_{sp}\)
For the solubility, we get the final expression:
\(S = \sqrt[m+n]{\frac{K_{sp}}{m^m\cdot n^n}}\)
Because solvated species are stabilised by intermolecular interactions with the solvent, the most important factor in determing the solubility is the solvent.
As a general rule, highly polarized sollutes (ionic or polar substances) dissolve in highly polarized solvents (usually polar), while weakly polarized sollutes (non-polar substances) dissolve in weakly polarized solvents (non-polar substances).
Examples of polar solvents are water, ethanol or methanol, while example of non-polar solvents are hydrocarbons (n-hexane, benzene) or carbon tetrachloride.
This also explain why NaCl is way more soluble in water than AgCl. Na has a strong electropositive character, making the Na-Cl bond higly polarized (strong ionic character), while Ag is not that electropositive and doesn't have the power to polarize the Ag-Cl bond that much. That results in a partial covalent character of AgCl resulting in a relatively low solubility in polar water.
Another factor influencing solubility is temperature. In general, the solubility of solids and liquids increases with temperature, while that of gases decreases.
The solubility of gases only is also affected by pressure. Higher pressures result in higher solubilities. This is described quantitatively by Henry's law:
\(S=K_{H}\cdot p\)
where S is the solubility of the gas, p is its partial pressure and \(K_{H}\) is called Henry's constant and its value changes for each substance and temperature.
Written by Alex Jicu