Solubility Product (Ksp) Calculator

Solubility Product Guide

What Is the Solubility Product?

For a sparingly soluble salt AB dissolving: AB(s) ⇌ A⁺(aq) + B⁻(aq). Ksp = [A⁺][B⁻]. If molar solubility = s mol/L, then [A⁺] = s and [B⁻] = s, so Ksp = s². For AB₂: PbCl₂ ⇌ Pb²⁺ + 2Cl⁻. [Pb²⁺] = s, [Cl⁻] = 2s. Ksp = s × (2s)² = 4s³. Large Ksp = relatively more soluble. Ksp only applies to saturated solutions of sparingly soluble salts — it does not apply to freely soluble salts like NaCl.

What should I know about Common Ksp Values?

Very sparingly soluble (Ksp < 10⁻¹⁵): AgI (8.5×10⁻¹⁷), PbS (3.0×10⁻²⁸). Sparingly soluble (Ksp 10⁻⁸ to 10⁻¹²): AgCl (1.8×10⁻¹⁰), Ag₂CrO₄ (1.1×10⁻¹²), CaF₂ (3.9×10⁻¹¹), BaSO₄ (1.1×10⁻¹⁰). Slightly soluble (Ksp 10⁻⁴ to 10⁻⁸): PbCl₂ (1.6×10⁻⁵), CaSO₄ (4.9×10⁻⁵). Applications: Ksp controls the precipitation of sparingly soluble salts in qualitative analysis and water treatment.

What should I know about The Common Ion Effect?

Adding a common ion reduces solubility — Le Chatelier's principle. If AgCl is dissolved in 0.1 mol/L NaCl instead of pure water: [Cl⁻] = 0.1 + s ≈ 0.1 (s is tiny). Ksp = [Ag⁺] × 0.1 = 1.8×10⁻¹⁰. [Ag⁺] = 1.8×10⁻⁹ mol/L (compared to 1.34×10⁻⁵ mol/L in pure water). The common ion suppresses solubility by a factor of approximately 7,000 in this example. Applications: water softening adds calcium hydroxide to precipitate calcium carbonate; qualitative analysis exploits the common ion effect.

Will Precipitation Occur?

Compare the ion product Q to Ksp: Q = [A⁺]initial × [B⁻]initial. If Q > Ksp: solution is supersaturated — precipitation will occur until Q = Ksp. If Q = Ksp: solution is exactly saturated — at equilibrium. If Q < Ksp: solution is unsaturated — no precipitation, dissolving can continue. Example: mix 50 mL of 2×10⁻⁴ mol/L AgNO₃ with 50 mL of 2×10⁻⁴ mol/L NaCl. After mixing (both halved): [Ag⁺] = [Cl⁻] = 10⁻⁴. Q = 10⁻⁸. Ksp(AgCl) = 1.8×10⁻¹⁰. Q > Ksp → precipitation occurs.

What should I know about Ksp and Temperature?

Like all equilibrium constants, Ksp varies with temperature — it is not a universal constant for a compound at all conditions. Dissolution of most ionic solids is endothermic, so Ksp generally increases with temperature, meaning solubility rises as the solution is heated. This is why recrystallisation purification works: dissolve impure solid in hot solvent (high solubility), then cool (Ksp falls, solution becomes saturated, pure crystals form as the solute re-precipitates while impurities, present in smaller amounts, stay dissolved). A few compounds show the opposite behaviour, with solubility decreasing as temperature rises, because their dissolution is exothermic. Published Ksp values are only valid at the stated temperature (almost always 298 K in data tables) — using a 25 degree C Ksp value to calculate solubility at a very different temperature can give a significantly wrong answer, especially for compounds with a large enthalpy of solution.

What's the key thing to understand about Fractional (Selective) Precipitation?

When a solution contains two or more ions that could each form a precipitate with the same reagent, the one with the lower Ksp (relative to the stoichiometry) precipitates first as the reagent is added gradually — fractional or selective precipitation. Example: a solution containing both Cl- and I- ions is treated dropwise with AgNO3. Ksp(AgI) = 8.5x10^-17 is far smaller than Ksp(AgCl) = 1.8x10^-10, so AgI (pale yellow) precipitates almost completely before AgCl (white) begins to form. The concentration of Ag+ needed to start precipitating Cl- can be calculated from Ksp(AgCl)/[Cl-], and compared with the Ag+ concentration remaining once [I-] has dropped to a negligible level — in practice over 99.9% of the iodide precipitates before any chloride does. This principle underlies qualitative analysis schemes for identifying halide ions and is used industrially in selective recovery of metals from mixed-ion solutions, such as refining silver from photographic waste.

What should I know about Finding Molar Solubility from Ksp?

For a salt that dissociates as AB₂ → A²⁺ + 2B⁻, letting molar solubility be s gives [A²⁺] = s and [B⁻] = 2s, so Ksp = [A²⁺][B⁻]² = s(2s)² = 4s³. Solving for s = ³√(Ksp/4) gives the molar solubility directly. The stoichiometry matters enormously here: a simple 1:1 salt (AB) gives Ksp = s², while a 1:2 salt like this one introduces the extra factor of 4 — forgetting that coefficient is one of the most common errors students make converting between Ksp and molar solubility.

What should I know about Units of Ksp?

Unlike most equilibrium constants, Ksp is conventionally written and used without units, even though dimensionally it isn't actually dimensionless — this is a common source of confusion. The underlying reason is that Ksp values are calculated from concentrations expressed in mol/dm³ relative to a standard reference concentration of 1 mol/dm³, which cancels out the units algebraically, so by convention the resulting number is quoted as unitless. However, the actual dimensions of Ksp do vary with the stoichiometry of the dissolution equation: for a 1:1 salt like AgCl (Ksp = [Ag⁺][Cl⁻]), the implied units would be (mol/dm³)², whereas for a 1:2 salt like PbCl₂ (Ksp = [Pb²⁺][Cl⁻]²), they would be (mol/dm³)³. This matters practically when comparing Ksp values across different salts: a numerically larger Ksp does not automatically mean a more soluble compound unless the salts have the same stoichiometry, because the exponents differ. Converting Ksp values to molar solubility first is the reliable way to compare how soluble different ionic compounds genuinely are on a like-for-like basis.

Worked Example: Calculating Molar Solubility from Ksp

For silver chloride (AgCl), which dissociates as AgCl ⇌ Ag⁺ + Cl⁻, the Ksp at 25°C is 1.8 × 10⁻¹⁰. Since each mole of AgCl that dissolves produces one mole of Ag⁺ and one mole of Cl⁻, if 's' is the molar solubility: Ksp = [Ag⁺][Cl⁻] = s × s = s². Solving: s = √(1.8 × 10⁻¹⁰) = 1.34 × 10⁻⁵ mol/L. This means essentially no AgCl dissolves — confirming why silver chloride is used as a classic 'insoluble' precipitate in qualitative analysis tests for chloride ions. For a compound with a 1:2 dissociation ratio, such as calcium fluoride (CaF2 ⇌ Ca²⁺ + 2F⁻, Ksp = 3.9 × 10⁻¹¹), the relationship changes because two moles of fluoride form per mole dissolved: Ksp = [Ca²⁺][F⁻]² = (s)(2s)² = 4s³. Solving: s³ = 3.9 × 10⁻¹¹ / 4 = 9.75 × 10⁻¹², so s = 2.13 × 10⁻⁴ mol/L — illustrating why the stoichiometric ratio, not just the Ksp value itself, must always be accounted for when converting between Ksp and molar solubility.

Why Ksp Values Span Such a Huge Range

Published Ksp values range from relatively soluble salts (around 10⁻² to 10⁻⁴) to extraordinarily insoluble ones (10⁻³⁰ or smaller for some heavy metal sulfides), a span of over 25 orders of magnitude, which reflects just how differently ionic lattice energy and hydration energy balance out between different salts. A Ksp this small essentially means 'for all practical laboratory purposes, insoluble' — even a Ksp of 10⁻¹⁰, as with silver chloride, corresponds to a solution so dilute (around 10⁻⁵ mol/L) that it's often simply described as insoluble in introductory chemistry, even though technically a vanishingly small amount is always present at equilibrium.

Qsp vs Ksp: Predicting Whether a Precipitate Forms

Comparing the reaction quotient (Qsp, calculated from current, possibly non-equilibrium ion concentrations) against Ksp tells you which direction a mixture will move: if Qsp exceeds Ksp, the solution is supersaturated and a precipitate will form until equilibrium is restored; if Qsp is less than Ksp, the solution is unsaturated and no precipitate forms, and if it already exists it will continue to dissolve. This Qsp-vs-Ksp comparison is the standard method taught for predicting precipitation reactions before they're observed experimentally.

Ksp and Everyday Water Chemistry

Solubility product calculations underpin practical water chemistry problems such as predicting limescale (calcium carbonate, CaCO3, Ksp ≈ 3.3 × 10⁻⁹) formation in hard-water areas — as water evaporates or is heated, the concentration of calcium and carbonate ions rises until the reaction quotient exceeds Ksp, at which point CaCO3 begins precipitating out as the visible scale seen inside kettles and on shower heads. This is why hard-water areas (where dissolved calcium and bicarbonate levels are naturally higher) see limescale form faster and more heavily than naturally soft-water areas, for exactly the same appliance and usage pattern.

Ksp Is Temperature-Specific

Every published Ksp value is only valid at the specific temperature it was measured at (almost always 25°C/298K in standard reference tables), since solubility — and therefore Ksp — generally increases with temperature for most ionic solids, following the same logic as any other equilibrium constant shifting with temperature; using a 25°C Ksp value to predict solubility behaviour at a notably different temperature, such as a hot water system or an industrial process, will give a misleading answer unless a temperature-specific Ksp value is used instead.