Solubility Product (Ksp) Calculator
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
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.
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
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?
Common-ion effect — what’s the intuition?
pH effect — when does it matter?
Activity vs concentration?
Q vs Ksp — practical use?
Temperature effect on Ksp?
How do I find solubility from Ksp?
Why is hydroxyapatite Ksp so low?
Polymorphs — does Ksp differ?
Can Ksp predict whether a salt is "soluble"?
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.