Enter Equilibrium Data
Use the form below to estimate cumulative complex formation behavior for a reaction of the form M + nL ⇌ MLn.
Plotly Graph
The graph tracks how predicted complex concentration and percent complexed vary as free ligand concentration changes around your current equilibrium point.
Formula Used
βn = [MLn] / ([M][L]n)
log βn = log10(βn)
Kd = 1 / βn
ΔG° = -RT ln(βn)
Kn = βn / βn-1
α = βn[L]n / (1 + βn[L]n)
How to Use This Calculator
- Enter the equilibrium free metal concentration.
- Enter the equilibrium free ligand concentration.
- Provide the measured complex concentration.
- Set the stoichiometric coefficient n for your complex.
- Add total metal and total ligand values when available.
- Optionally enter βn-1 to estimate a stepwise constant.
- Click Calculate Constant to show results above the form.
- Review the table, graph, and mass-balance indicators.
- Export the results using the CSV or PDF buttons.
Example Data Table
This example uses the default values included in the form.
| Sample | n | [M] (mol/L) | [L] (mol/L) | [MLn] (mol/L) | βn | log βn | Kd |
|---|---|---|---|---|---|---|---|
| Sample A | 2 | 0.0010 | 0.0100 | 0.0008 | 8.000000e+3 | 3.903090 | 1.250000e-4 |
| Sample B | 1 | 0.0020 | 0.0150 | 0.0036 | 1.200000e+2 | 2.079181 | 8.333333e-3 |
| Sample C | 3 | 0.0004 | 0.0200 | 0.0010 | 3.125000e+5 | 5.494155 | 3.200000e-6 |
Interpretation Notes
A larger β value usually indicates stronger complex stability under the specified equilibrium conditions. A positive mass-balance residual suggests missing species, rounding error, or mismatched measurements. A negative residual often indicates that one or more entered values are physically inconsistent with the stated total concentration.
This tool assumes one dominant complex of the form MLn. Systems with competing complexes, protonation, hydrolysis, or ionic-strength corrections may require more advanced speciation models.
FAQs
1) What does the formation constant represent?
It describes how strongly a metal ion and ligand combine at equilibrium. Higher values usually mean the complex is more stable under the tested conditions.
2) Why do I need free concentrations instead of starting amounts?
The equilibrium expression uses free species concentrations, not initial charges. Initial values can differ greatly after binding occurs, especially in strong complexes.
3) What is the difference between βn and Kn?
βn is the cumulative constant for forming MLn directly from free metal and free ligand. Kn is the stepwise constant for adding the nth ligand.
4) Why is log β often reported instead of β?
Formation constants can span many orders of magnitude. The logarithmic form is easier to compare, report, and interpret across different systems.
5) What does a negative ΔG° mean here?
A negative value suggests the complex formation is thermodynamically favorable under the chosen temperature and equilibrium assumptions.
6) Can this calculator handle multiple competing complexes?
No. It is designed for one dominant complex species only. Multi-species systems need a broader equilibrium and speciation treatment.
7) Why might the mass-balance residual not be zero?
Residuals can appear because of measurement uncertainty, rounding, missing side reactions, or entered totals that do not match the measured equilibrium species.
8) Does ionic strength affect the reported constant?
Yes. Apparent constants can shift with ionic strength, solvent, and temperature. Use activity-corrected data when rigorous comparison is necessary.