Solubility Product Calculator

The solubility product constant (Ksp) is the equilibrium constant for the dissolution of a sparingly soluble ionic compound in water. It expresses the maximum product of ion concentrations that can exist in solution before precipitation begins. For a generic salt MₘAₙ that dissolves as mM^(n+) + nA^(m-), the Ksp expression is Ksp = [M^(n+)]^m × [A^(m-)]^n, where the brackets denote molar concentrations at equilibrium.

Ksp values are temperature-dependent and are typically tabulated at 25°C. They range over many orders of magnitude—from approximately 10⁵ for highly soluble salts to less than 10⁻⁵⁰ for extremely insoluble compounds. A larger Ksp indicates greater solubility for salts with the same stoichiometry, though direct comparison between salts with different formulas requires converting Ksp to molar solubility.

The Ksp concept is essential for predicting whether precipitation will occur when two solutions are mixed. If the ion product Q (calculated from the actual concentrations) exceeds Ksp, the solution is supersaturated and precipitation will occur until Q = Ksp. If Q < Ksp, the solution is unsaturated and no precipitate forms. This principle underlies qualitative analysis schemes, water treatment processes, and the formation of mineral deposits in geological systems.

The common ion effect describes the decrease in solubility when a soluble salt containing one of the ions is already present in solution. For example, the solubility of AgCl decreases dramatically in a solution containing NaCl because the additional Cl⁻ ions shift the dissolution equilibrium toward the solid. This effect is quantitatively described by the Ksp expression and is widely exploited in analytical chemistry and industrial processes.

The relationship between Ksp and molar solubility depends on the stoichiometry of the salt. For a 1:1 salt like AgCl, Ksp = s² where s is the molar solubility. For a 1:2 salt like PbCl₂, Ksp = 4s³. For a 2:3 salt like Ca₃(PO₄)₂, Ksp = 108s⁵. The general formula for MₘAₙ is Ksp = m^m × n^n × s^(m+n).

This relationship can be inverted to calculate molar solubility from Ksp: s = (Ksp / (m^m × n^n))^(1/(m+n)). This calculation is essential for predicting how much of a sparingly soluble compound will dissolve in pure water.

When a common ion is present, the solubility decreases. For a 1:1 salt with common ion concentration C, the simplified expression becomes Ksp = s(s + C), which can be solved for s. For more complex stoichiometries, the relationship requires solving a polynomial equation, though approximations are often valid when C >> s.

The pKsp (negative logarithm of Ksp) provides a more convenient scale for comparing very small Ksp values. A compound with pKsp = 10 has Ksp = 10⁻¹⁰, while one with pKsp = 50 has Ksp = 10⁻⁵⁰. Higher pKsp values indicate lower solubility.

This solubility product calculator works in two modes: converting molar solubility to Ksp, and converting Ksp to molar solubility. Follow these steps:

1. Choose Calculation Mode: Select "Ksp from Solubility" if you know the molar solubility and want to find Ksp. Select "Solubility from Ksp" if you have a Ksp value and want to find the molar solubility.
2. Set Stoichiometric Coefficients: Enter the cation coefficient (m) and anion coefficient (n) for your salt. For AgCl, both are 1. For CaF₂, m = 1 and n = 2. For Fe(OH)₃, m = 1 and n = 3.
3. Enter Your Known Value: In "Ksp from Solubility" mode, enter the molar solubility in mol/L. In "Solubility from Ksp" mode, enter the Ksp value.
4. Optional: Common Ion Effect: If you want to account for a common ion already in solution, enter its concentration. This will calculate the reduced solubility in the presence of the common ion.
5. Review Results: Examine the calculated Ksp (or molar solubility), pKsp, ion concentrations, and the Ksp expression for your compound.

Quick-select buttons are provided for common Ksp values including AgCl, AgBr, AgI, BaSO₄, CaF₂, and PbCl₂ to speed up calculations.

The calculator provides the Ksp value (or molar solubility), the pKsp, equilibrium concentrations of both ions, and the Ksp expression. The ion concentrations are calculated from the molar solubility using the stoichiometric coefficients: [cation] = m × s and [anion] = n × s.

The pKsp is a convenient way to express very small Ksp values. A pKsp of 10 corresponds to Ksp = 10⁻¹⁰, while a pKsp of 50 corresponds to Ksp = 10⁻⁵⁰. Higher pKsp values indicate lower solubility.

When a common ion is present, the solubility is significantly reduced. For example, the solubility of AgCl (Ksp = 1.8 × 10⁻¹⁰) in pure water is 1.34 × 10⁻⁵ M, but in 0.1 M NaCl it drops to 1.8 × 10⁻⁹ M—a reduction of nearly 10,000-fold. This dramatic effect is the basis for common-ion precipitation in analytical chemistry.

The Ksp expression shown in the results confirms the equilibrium relationship for your compound. The ion product Q is calculated from the actual concentrations and compared to Ksp to determine whether precipitation would occur in a given situation.

Ksp calculations are fundamental to many areas of chemistry and geology. In analytical chemistry, controlled precipitation using Ksp data allows selective separation of metal ions. By adjusting pH and adding specific reagents, chemists can precipitate one ion while keeping others in solution, enabling qualitative and quantitative analysis.

In water treatment, Ksp values guide the removal of heavy metals, fluoride, and hardness ions. Calcium carbonate precipitation (scale formation) in pipes and boilers is predicted using Ksp calculations. Water softening exploits the Ksp difference between calcium carbonate and calcium EDTA complexes.

Geochemistry uses Ksp to explain mineral formation, cave formation, and the transport of dissolved minerals in groundwater. The dissolution and precipitation of calcium carbonate, governed by its Ksp, controls the formation of limestone caves, stalactites, and stalagmites.

In pharmaceutical chemistry, drug solubility and Ksp values determine formulation strategies for poorly soluble compounds. Salt form selection, co-crystal design, and amorphous formulations all rely on understanding the dissolution equilibrium of drug substances.

Environmental science applies Ksp to predict the mobility of heavy metals and metalloids in soil and groundwater. The Ksp of metal sulfides, hydroxides, and carbonates determines whether these toxic elements remain immobilized or dissolve into drinking water supplies.