Complex Formation Solubility Helper

This tool estimates how complex formation affects the solubility of a metal salt in aqueous solution. It's designed for students, researchers, and lab technicians studying coordination chemistry or designing analytical separations. It handles scientific notation (e.g., 1.23e-5), decimal commas, and unit conversions. All calculations run offline in your browser.

Educational only. Follow your lab SOPs and SDS.

Solubility Calculator

Metal Salt K_sp (solubility product)

(unitless)

Enter the K_sp value for the metal salt (e.g., AgCl).

Complex Formation Constant (K_f or β)

(M^-n)

Enter the overall formation constant for the metal complex.

Free Ligand Concentration

µM

Concentration of the free (unbound) ligand in solution.

Ligands per Metal (Stoichiometry, n)

Number of ligand molecules bound per metal ion in the complex.

Results

Total Solubility (S_total)

0.0949 M

Total concentration of metal in solution.

Intermediate Values

[Mⁿ⁺] free: 1.89e-9 M
[ML_n] complex: 0.0949 M
Solubility enhancement factor: ~5.3e5

Export for Lab Notebook

K_sp = 1.80e-10, K_f = 1.00e+07, [L] = 0.100 M, n = 2.
Total solubility (S_total) = 9.49e-02 M.
Free [M^{2+}] = 1.89e-09 M, [ML2] = 9.49e-02 M.
Enhancement factor ≈ 5.27e+05.
Calculation based on S_total ≈ (K_sp * K_f * [L]^n)^(1/2).

Understanding Solubility Enhancement by Complexation

In aqueous chemistry, an insoluble metal salt can dissolve much more readily if a ligand is present that forms a stable soluble complex with the metal ion. This principle is used in analytical chemistry (e.g., using cyanide to dissolve gold), in medicine (chelating agents), and in environmental remediation.

How to Use This Tool

Enter the K_sp of your metal salt (e.g., from a reference table).
Enter the overall formation constant (K_f or β) for the metal-ligand complex.
Provide the concentration of free ligand in solution. Use the unit toggle if needed.
Specify the ligand-to-metal stoichiometry (n) of the dominant complex.
Click "Calculate Solubility". The total solubility, free metal concentration, and enhancement factor are displayed.

Realistic Examples

System	K_sp	K_f	[L] (M)	n	S_total (M)
AgCl in NH₃ (→ Ag(NH₃)₂⁺)	1.8e-10	1.0e7	0.1	2	~0.095
HgS in CN^- (→ Hg(CN)₄^2-)	4e-54	1.0e41	0.01	4	~2.5e-4
CaC₂O₄ in EDTA (→ CaEDTA^2-)	2.3e-9	5.0e10	0.001	1	~0.011

Common Mistakes & Pitfalls

Using the stepwise formation constant instead of the overall constant (β_n).
Assuming [L] remains constant when ligand is not in large excess.
Ignoring other competing equilibria (pH, competing ligands, ionic strength).
Applying a 1:1 approximation for systems with higher stoichiometry.

Quick Log K ↔ K Converter

Convert between formation constants (K) and their logarithmic form (log K) for easier comparison.

Constant K (unitless)

Enter a positive number. Scientific notation accepted.

log K (logarithmic)

Enter log₁₀ K (can be positive or negative).

Result

K = 1.00e+07 ↔ log K = 7.00

Frequently Asked Questions

What are the main assumptions of this calculation?

It assumes a single dominant complex forms (ML_n), ligand concentration is in large excess and remains approximately constant, no competing side reactions (like protonation of ligand), and ideal dilute solution behavior (activity coefficients = 1).

When does the approximation fail?

When ligand concentration is not in large excess relative to the dissolved metal, when multiple complexes exist (ML, ML₂, etc.), when pH affects ligand speciation, or when ionic strength is very high (>0.1 M).

How should I measure free ligand concentration in the lab?

Use analytical techniques like potentiometry (ion-selective electrode), spectrophotometry (if ligand absorbs), or calculate it from mass balance if you know total ligand added and the amount complexed (requires separate metal analysis).

Are there safety concerns with complexing agents?

Yes. Some ligands (cyanide, strong chelators like EDTA) can be toxic, increase metal bioavailability, or create hazardous waste. Always review SDS, use appropriate PPE, and follow waste disposal protocols.

Formulas & Assumptions

Main formula (approximation): S_total ≈ (K_sp × K_f × [L]ⁿ)^1/2

Free metal: [Mⁿ⁺] = K_sp / S_total

Complex concentration: [ML_n] = S_total − [Mⁿ⁺] ≈ S_total

Enhancement factor: S_total / √K_sp

Constants used: None beyond user inputs.

Rounding policy: Results shown to 3 significant figures; intermediate values use full precision.

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Complex Formation Solubility Helper

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