All calculatorsKsp Solubility Product Calculator
Determine molar solubility (s) or Ksp for a salt with stoichiometry AxBy ⇌ x A + y B. Supports optional common ions ([A]₀ and/or [B]₀) and shows clear steps.
Background
For AxBy(s) ⇌ x Az+ + y Bz−, the solubility product is Ksp = [A]x[B]y. If no common ions are present, s can be found in closed form. With common ions, we solve Ksp = (x s + [A]₀)x(y s + [B]₀)y numerically.
How to use this calculator
- Solve for s: Enter x, y, and Ksp. Optionally add [A]₀/[B]₀ for common ions.
- Solve for Ksp: Enter x, y, and s. Optionally add [A]₀/[B]₀; we compute equilibrium concentrations and Ksp.
- Equilibrium expressions: [A] = x·s + [A]₀; [B] = y·s + [B]₀; Ksp = [A]x[B]y.
Assumes activity ≈ concentration (dilute solutions). Solids and pure liquids do not appear in Ksp.
Example Problems & Step-by-Step Solutions
Example 1 (No common ions)
AgCl(s) ⇌ Ag⁺ + Cl⁻; Ksp = 1.8×10⁻¹⁰. With x = y = 1: s = √Ksp = 1.34×10⁻⁵ M.
Example 2 (1:2 salt)
CaF₂(s) ⇌ Ca²⁺ + 2F⁻; Ksp = 3.9×10⁻¹¹. With x=1, y=2: Ksp = (s)(2s)² = 4s³ ⇒ s ≈ 2.1×10⁻⁴ M.
Example 3 (Common-ion effect)
PbCl₂(s) with [Cl⁻]₀ = 0.100 M: solve Ksp = ([Pb²⁺])([Cl⁻])² with [Pb²⁺] = s and [Cl⁻] = 2s + 0.100 numerically (bisection).
Frequently Asked Questions
Q: When can I use a direct formula for s?
If no common ions are present, s has a closed form, e.g., for A₁B₁: s = √Ksp; for A₁B₂: s = (Ksp/4)^(1/3). With common ions, solve numerically.
Q: Do solids or pure liquids appear in Ksp?
No. Their activity is ~1; they are omitted in the equilibrium expression.
Q: Are activities the same as concentrations?
In dilute solutions, activity ≈ concentration. At higher ionic strength, activity coefficients matter and Ksp calculations may deviate.
