Solubility of Solute When Complex Ions Form

General Chemistry • Solubility and Complex Ion Equilibria

Written by STEM Calculators Team Published April 18, 2026 Updated April 18, 2026

Solubility of a Solute When Complex Ions Form

This calculator estimates the molar solubility of a slightly soluble 1:1 salt MX(s) in the presence of a ligand L that forms the complex ML_a. It uses an exact equilibrium model with mass balances, not just the simplified overall-reaction approximation. The setup assumes a 1:1 salt, an initial ligand concentration [L]₀, and no initially added metal ion or common ion.

Quick data paste or CSV

Recognized keys: M, L, a, X, Ksp, Kf, L0, precision.

Import CSV

Metal–ligand system

Metal symbol

Ligand formula

Complex stoichiometry a in ML_a

a = 1 a = 2 a = 3

Salt and constants

Anion symbol X

K_sp for MX(s)

K_f for ML_a

Displayed significant figures

Ligand solution

Initial ligand concentration [L]₀ (mol·L⁻¹)

Ready

Rate this calculator

0.0 /5 (0 ratings)

Be the first to rate.

Your rating

Name (optional) Review (optional)

You can update your rating any time.

Solubility of a salt when complex ions form

A slightly soluble salt \(\mathrm{MX}(s)\) can dissolve much more in a solution containing a ligand \(\mathrm{L}\) that forms a stable complex \(\mathrm{ML_a}\) with the metal ion.

Competing equilibria

\[ \mathrm{MX}(s) \rightleftharpoons \mathrm{M^{n+}} + \mathrm{X^-} \quad K_{sp} = [\mathrm{M^{n+}}][\mathrm{X^-}] \] \[ \mathrm{M^{n+}} + a\,\mathrm{L} \rightleftharpoons \mathrm{ML_a} \quad K_f = \frac{[\mathrm{ML_a}]}{[\mathrm{M^{n+}}][\mathrm{L}]^{a}} \]

Adding these gives the overall reaction:

\[ \mathrm{MX}(s) + a\,\mathrm{L} \rightleftharpoons \mathrm{ML_a} + \mathrm{X^-} \] \[ K = K_{sp}K_f = \frac{[\mathrm{ML_a}][\mathrm{X^-}]}{[\mathrm{L}]^{a}}. \]

Relating \(K\) to molar solubility \(s\)

If solid \(\mathrm{MX}(s)\) is in equilibrium with a solution that initially contains only ligand at \([\mathrm{L}]_0\) (no metal or \(\mathrm{X^-}\)) and the molar solubility is \(s\):

\([\mathrm{ML_a}] = s\), \([\mathrm{X^-}] = s\)
\([\mathrm{L}] \approx [\mathrm{L}]_0 - a\,s\)

Substituting into \(K\):

\[ K = \frac{s^{2}}{\left([\mathrm{L}]_0 - a\,s\right)^{a}}. \]

The calculator uses your \(K_{sp}\), \(K_f\), \(a\) and \([\mathrm{L}]_0\) to find the value of \(s\) that satisfies this equation (typically solved numerically).

Comparison with solubility in pure water

In pure water (no ligand), for a 1:1 salt:

\[ K_{sp} = s_0^{2} \;\Rightarrow\; s_0 = \sqrt{K_{sp}}. \]

The tool reports both \(s_0\) (no ligand) and \(s\) (with complex formation) and the enhancement factor \(s/s_0\).

Assumes a single 1:1 salt \(\mathrm{MX}\), one dominant complex \(\mathrm{ML_a}\), activities ≈ concentrations, and no extra acid–base or competing equilibria.

Frequently Asked Questions

How does complex formation increase the solubility of MX(s)?

When M^n+ binds ligand L to form ML_a, the free metal-ion concentration decreases. Lower free [M^n+] allows more MX(s) to dissolve while still satisfying the solubility product equilibrium.

What constants does the calculator use for this solubility problem?

It uses the solubility product Ksp for MX(s) and the formation constant Kf for ML_a. The overall equilibrium constant is K = Ksp x Kf for MX(s) + aL ⇌ ML_a + X-.

What equation is solved to find the molar solubility with ligand present?

For a 1:1 salt and one dominant complex, the calculator uses K = s^2 / ([L]0 - a x s)^a and solves for s. This comes from [ML_a] = s, [X-] = s, and free ligand approximately equal to [L]0 - a x s.

How is solubility in pure water computed on this page?

For a 1:1 salt in pure water with no ligand, Ksp = s0^2, so s0 = sqrt(Ksp). The tool reports both s0 and the ligand-enhanced solubility s.

What limitations should be considered when using this calculator?

It assumes a single 1:1 salt MX, one dominant complex ML_a, and activities approximated by concentrations. Additional equilibria such as acid–base reactions, competing ligands, multiple complexes, or significant ionic strength can change the true solubility.