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Solubility Product (Ksp) Calculator

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How it Works

01Solubility

Molar solubility s of the salt in mol/L.

02Stoichiometry

1:1 (AgCl), 1:2 (CaF₂), 2:1 (Ag₂CrO₄), 2:3 (Ca₃(PO₄)₂).

03Calculate

Returns Ksp = [A]^a × [B]^b.

04Apply

Compare Q vs Ksp to predict precipitation or dissolution.

What is a Ksp Calculator?

The Solubility Product (Ksp) Calculator computes the equilibrium constant for dissolution of a sparingly soluble ionic compound. Ksp expresses how much of a salt actually dissolves in pure water at saturation: a tiny number (10⁻¹⁰ for AgCl, 10⁻²⁸ for PbS) means very little dissolves; a relatively large Ksp (10⁻⁵ for CaSO₄) means appreciable dissolution. Ksp is the foundation for predicting precipitation, designing separations, modeling natural water chemistry, and explaining why some salts dissolve readily while others stay rock-hard.


The math depends on the dissolution stoichiometry. For a 1:1 salt like AgCl: AgCl(s) ⇌ Ag⁺ + Cl⁻, with Ksp = [Ag⁺][Cl⁻]. From molar solubility s, both ion concentrations equal s, so Ksp = s². For a 1:2 salt like CaF₂: CaF₂(s) ⇌ Ca²⁺ + 2F⁻, where [Ca²⁺] = s but [F⁻] = 2s, giving Ksp = (s)(2s)² = 4s³. For a 2:3 salt like Ca₃(PO₄)₂: Ksp = (3s)³(2s)² = 108s⁵. The general formula for A_aB_b: Ksp = a^a × b^b × s^(a+b).


This calculator handles arbitrary stoichiometries — enter the molar solubility and the cation/anion subscripts, get back Ksp, individual ion concentrations, and the pKsp (negative log) for easy comparison with reference tables. Use it to convert measured solubility to tabulated Ksp values, predict whether a precipitate will form when two solutions mix, or check homework problems in general chemistry.


The common-ion effect is one of the most important applications: adding a counter-ion (e.g., NaCl to a saturated AgCl solution) shifts the equilibrium back toward solid, dramatically reducing the salt’s effective solubility. This is why hard-water scale forms only at certain concentrations, why selective precipitation works in qualitative analysis, and why kidney stones precipitate from supersaturated urine. The reverse — pH effects, where acid dissolves carbonates and hydroxides by protonating the anion — explains everything from acid rain dissolving limestone to the body’s use of acidic stomach fluid for mineral absorption.


Used by analytical chemists predicting precipitation thresholds, pharmaceutical formulators dealing with solubility-limited drug bioavailability (the BCS classification system relies on Ksp-like calculations), water treatment engineers managing scale formation, geochemists modeling mineral solubility in natural waters, and general chemistry students working through equilibrium homework, this is a foundational equilibrium tool. Once you have Ksp values, you can predict precipitation in any ion mixture by comparing the ion product Q to Ksp: Q < Ksp means more salt dissolves; Q = Ksp means saturation; Q > Ksp means precipitate forms.

How to Use the Calculator

Identify the Salt and Stoichiometry: Determine the chemical formula and the ratio of cations to anions. AgCl is 1:1, CaF₂ is 1:2, Ag₂CrO₄ is 2:1, Ca₃(PO₄)₂ is 3:2.
Enter Molar Solubility (s): In moles per liter (M). Convert from mass solubility (g/L) using molecular weight if needed.
Enter Cation Subscript (a) and Anion Subscript (b): For AgCl (a=1, b=1); for CaF₂ (a=1, b=2); for Ag₂CrO₄ (a=2, b=1); for Ca₃(PO₄)₂ (a=3, b=2).
Calculate: Returns Ksp value, individual ion concentrations [cation] = a×s and [anion] = b×s, and pKsp = −log(Ksp).
Compare to Reference Tables: Look up the published Ksp for your salt and verify your solubility measurement is consistent.
Apply to Real Problems: Use Ksp to predict precipitation in mixed solutions (compare Q to Ksp), calculate solubility under common-ion conditions, or design separations.

The Math Behind It

General formula: For A_aB_b(s) ⇌ a A^(b+) + b B^(a−):

Ksp = (a·s)^a × (b·s)^b = a^a × b^b × s^(a+b)

Where s is the molar solubility (mol/L) of the salt.

Common cases:

  • 1:1 salts (AgCl, BaSO₄, AgBr): Ksp = s²
  • 1:2 salts (CaF₂, Mg(OH)₂, PbI₂): Ksp = 4s³
  • 2:1 salts (Ag₂CrO₄, Ag₂S): Ksp = 4s³
  • 1:3 salts (Fe(OH)₃, Cr(OH)₃): Ksp = 27s⁴
  • 3:1 salts (Ag₃PO₄): Ksp = 27s⁴
  • 2:3 salts (Ca₃(PO₄)₂): Ksp = 108s⁵

Reaction quotient Q: same formula but using current ion concentrations instead of equilibrium values. Compare Q to Ksp:

  • Q < Ksp → unsaturated, more solid dissolves
  • Q = Ksp → equilibrium (saturated)
  • Q > Ksp → supersaturated, precipitate forms

Common-ion effect: If you add a salt providing one of the same ions, the new equilibrium has [common ion]_total = added + dissolved-from-salt. Calculate the new effective solubility by setting Ksp = (added + a·s)^a × (b·s)^b and solving for s.

Real-World Example

Worked Example

Silver chloride solubility: AgCl is sparingly soluble in water with measured molar solubility s = 1.3 × 10⁻⁵ M at 25°C.

  • Stoichiometry: 1:1 → Ksp = s²
  • Ksp = (1.3 × 10⁻⁵)² = 1.69 × 10⁻¹⁰
  • Compares well to tabulated value of 1.8 × 10⁻¹⁰
  • pKsp = −log(1.69 × 10⁻¹⁰) = 9.77

Calcium fluoride: CaF₂ has measured s ≈ 2.1 × 10⁻⁴ M.

  • Stoichiometry: 1:2 → Ksp = 4s³
  • Ksp = 4 × (2.1 × 10⁻⁴)³ = 4 × 9.26 × 10⁻¹² = 3.7 × 10⁻¹¹
  • [Ca²⁺] = s = 2.1 × 10⁻⁴ M, [F⁻] = 2s = 4.2 × 10⁻⁴ M

Common-ion problem: What’s the solubility of AgCl in 0.1 M NaCl? Without NaCl, [Cl⁻] from AgCl alone = 1.3 × 10⁻⁵ M. With 0.1 M NaCl added, [Cl⁻]_total ≈ 0.1 M (the AgCl contribution is negligible). Solving Ksp = [Ag⁺] × 0.1 = 1.69 × 10⁻¹⁰: [Ag⁺] = 1.69 × 10⁻⁹ M. The solubility dropped from 1.3 × 10⁻⁵ M to 1.69 × 10⁻⁹ M — a 10,000-fold decrease just from the common-ion effect. This is why qualitative analysis textbooks specify saturated NaCl solutions for separations.

Who Uses It

1
Analytical Chemists: Predict precipitation thresholds in qualitative and quantitative separations.
2
Pharmaceutical Formulators: Solubility-limited drug bioavailability (BCS class II and IV drugs).
3
Water Treatment Engineers: Manage scale formation (CaCO₃, CaSO₄, BaSO₄) in pipes, boilers, and membranes.
4
Geochemists: Mineral solubility and weathering in natural waters.
5
General Chemistry Students: Solve Ksp problems on homework and exams.
6
Dental Researchers: Hydroxyapatite (tooth enamel) Ksp drives demineralization and remineralization studies.
7
Forensic Chemists: Selective precipitation for identification of trace metals.

Technical Reference

Selected Ksp Values at 25°C:

  • AgCl: 1.8 × 10⁻¹⁰
  • AgBr: 5.0 × 10⁻¹³
  • AgI: 8.5 × 10⁻¹⁷
  • BaSO₄: 1.1 × 10⁻¹⁰
  • CaCO₃ (calcite): 3.4 × 10⁻⁹
  • CaCO₃ (aragonite): 6.0 × 10⁻⁹
  • CaF₂: 3.9 × 10⁻¹¹
  • CaSO₄: 4.9 × 10⁻⁵
  • Mg(OH)₂: 5.6 × 10⁻¹²
  • MgCO₃: 6.8 × 10⁻⁶
  • Fe(OH)₂: 4.9 × 10⁻¹⁷
  • Fe(OH)₃: 2.8 × 10⁻³⁹
  • PbCl₂: 1.7 × 10⁻⁵
  • PbS: 8 × 10⁻²⁸
  • HgS: 4 × 10⁻⁵³ (one of the lowest known)
  • Ca₃(PO₄)₂: 2.1 × 10⁻³³
  • Hydroxyapatite Ca₅(PO₄)₃OH: 1 × 10⁻⁵⁹

pH Effects: Salts of weak acids (CO₃²⁻, S²⁻, PO₄³⁻) and bases (OH⁻) become much more soluble at low pH because protonation removes the anion from solution: e.g., CaCO₃ dissolves in dilute acid via CO₃²⁻ + 2H⁺ → H₂O + CO₂↑. This is why acid rain dissolves limestone and why stomach acid liberates calcium and magnesium for absorption.

Key Takeaways

Ksp predicts whether a salt will precipitate from a given ion mixture. Compare ion product Q to Ksp: Q < Ksp means unsaturated; Q = Ksp means saturation; Q > Ksp means precipitate will form. The common-ion effect dramatically lowers solubility when a counter-ion is added in excess. pH affects salts of weak acids (carbonates, phosphates, sulfides) and bases (hydroxides) — lower pH usually increases their solubility.


Practical caveats: Ksp values are at 25°C unless noted. Temperature dependence is significant — most salts become more soluble in hot water (endothermic dissolution), but some (CaSO₄, Ca(OH)₂) become less soluble. Activity coefficients matter at high ionic strength (above 0.01 M) and can make published Ksp values 2–5× off from real solubility in concentrated salt solutions. For reef-tank chemistry, biological media, and seawater calculations, use activity-corrected models.

Frequently Asked Questions

Why are Ksp values so small?
They’re defined for sparingly soluble salts — by definition, ions are present in low concentration at saturation. Highly soluble salts (NaCl, KNO₃) don’t use Ksp because the high ionic concentrations make activity corrections too important; the simple [ion]^n product becomes meaningless.
Common-ion effect — what’s the intuition?
Adding a counter-ion shifts the dissolution equilibrium back toward solid by Le Chatelier’s principle. Excess Cl⁻ from added NaCl makes the AgCl-Cl⁻ "side" overloaded, so the system responds by precipitating AgCl out. Quantitatively, this is why selective precipitations work in qualitative analysis.
pH effect — when does it matter?
For salts containing the conjugate base of a weak acid (carbonates, phosphates, sulfides) or hydroxides. Acid protonates the anion (removing it from solution), driving more salt to dissolve. CaCO₃ solubility increases roughly 100× per 2 pH units lower. Salts of strong-acid anions (Cl⁻, NO₃⁻, SO₄²⁻) are largely pH-insensitive.
Activity vs concentration?
Strictly, Ksp uses activities, not concentrations. For dilute solutions (under 0.01 M ionic strength), activity ≈ concentration and the difference is negligible. For seawater, biological fluids, or concentrated salt solutions, use activity coefficients (Davies equation, Pitzer model) — Ksp predictions can be off by 2–5× without correction.
Q vs Ksp — practical use?
Calculate Q = ^a × ^b using current concentrations. If Q < Ksp, more dissolves. If Q = Ksp, saturated. If Q > Ksp, precipitation occurs (kinetics may delay it — supersaturation can persist for hours or days for some salts).
Temperature effect on Ksp?
Most salts: Ksp increases with temperature (endothermic dissolution, more soluble in hot water). Exceptions: CaSO₄ (gypsum), Ca(OH)₂ (lime), Li₂CO₃ — Ksp decreases with temperature (retrograde solubility). Always note temperature when quoting Ksp; published values are typically at 25°C.
How do I find solubility from Ksp?
Solve the Ksp expression for s. For 1:1 salts: s = √Ksp. For 1:2 salts: s = (Ksp/4)^(1/3). General: s = (Ksp / (a^a × b^b))^(1/(a+b)). Calculator does the algebra automatically.
Why is hydroxyapatite Ksp so low?
It’s a 5:3 stoichiometry plus an OH⁻, so the ion product s^9 is raised to a high power. Even modest concentrations multiplied together give vanishingly small products. This extremely low solubility is exactly why hydroxyapatite is the natural mineral framework of bones and teeth — it’s thermodynamically stable and resists dissolution under normal conditions.
Polymorphs — does Ksp differ?
Yes. CaCO₃ exists as calcite (Ksp = 3.4 × 10⁻⁹), aragonite (6 × 10⁻⁹), and vaterite (1 × 10⁻⁸). Calcite is the most stable polymorph at room conditions. Different polymorphs have different Ksp because they have different crystal lattice energies.
Can Ksp predict whether a salt is "soluble"?
Roughly: Ksp > 10⁻⁴ (or pKsp < 4) is considered "soluble" in qualitative analysis. Ksp 10⁻⁴ to 10⁻⁸ is "slightly soluble". Ksp < 10⁻⁸ is "insoluble". These are conventions, not bright lines — actual usability depends on context (pure water, common-ion solution, biological fluid, etc.).

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Disclaimer

Ksp values are temperature-dependent and assume dilute solutions where activity ≈ concentration. For high ionic strength (greater than 0.01 M), use activity coefficients. For polymorphs (calcite vs aragonite, anatase vs rutile), Ksp values differ — make sure your reference matches the crystal form you’re analyzing.