Solubility (Ksp)

How much of a sparingly soluble salt dissolves in water? From the solubility product Ksp, find the molar solubility and the grams per litre — or work out Ksp from a measured solubility. Add an ion that is already in the water to see the common-ion effect.

EquilibriumSolubilityPrecipitation

Inputs

Input examples

Type the salt (_ gives a subscript: PbI_2); it is used for the molar mass. Enter how many cations and anions one formula unit gives: PbI₂ gives 1 Pb²⁺ and 2 I⁻, Ca₃(PO₄)₂ gives 3 and 2. Then click Solve next to Ksp or the solubility. The ion already present is optional: for example the Cl⁻ of a salt solution.

Salt

AgCl

Cations per formula unit a

Anions per formula unit b

Solubility product K_sp

Molar solubility s — mol/L of the salt that dissolves

Ion already in the water

Its concentration — mol/L

What is a Solubility Product?

A “insoluble” salt such as silver chloride still dissolves a tiny bit. In a saturated solution the solid is in equilibrium with its ions, and the product of the ion concentrations, each raised to its coefficient, is a constant: the solubility product K_sp. The solid itself does not appear in it.

If s mol/L of M_aX_b dissolves, the solution holds a·s of the cation and b·s of the anion, so K_sp = (as)^a(bs)^b. A salt with a smaller K_sp is not always less soluble: compare the molar solubilities instead. Adding one of the ions from elsewhere pushes the equilibrium back: the salt dissolves even less. This common-ion effect is used to precipitate ions almost completely.

ABK_sp = s²

AB₂K_sp = 4s³

A₃B₂K_sp = 108 s⁵

common ionsolubility drops

Solubility with an Ion Already Present

solubility with that much of the anion already present

with that much of the cation

your result

Result

Enter the values above

Worked Techniques

From Ksp to Solubility

Write each ion concentration in terms of s, multiply them with their powers and solve for s.

Example: times the molar mass (461 g/mol): 0.62 g per litre.

From Solubility to Ksp

Measure how much dissolves, convert to mol/L and put it back into the Ksp expression.

Example: grams per litre ÷ molar mass gives s.

Common-Ion Effect

With chloride already present, silver chloride dissolves about 7500 times less than in pure water.

Example: the reason a salt solution keeps silver out of solution.

Sources & Verification

References

S. S. Zumdahl & S. A. Zumdahl, Chemistry, 10th ed., Cengage Learning, 2018 — Ch. 15 (Solubility Equilibria: Ksp, relative solubilities, the common-ion effect).
D. C. Harris, Quantitative Chemical Analysis, 9th ed., W. H. Freeman, 2015 — Ch. 6 (Chemical Equilibrium: solubility product and common-ion effect).

The Ksp values in the examples are typical values at 25 °C; published tables differ slightly. Activity effects at higher ion strengths are not included.