Conditional Stability Constant Calculator

Calculator Inputs

Complex Name

Example: CdY2-, CaY2-, FeL.

Metal Label

Used in the result summary only.

Ligand Label

Use EDTA or your ligand name.

Ligand Fraction Mode

Auto mode estimates αY4- for EDTA.

Overall log Kf

Enter the literature formation constant as log10(Kf).

Solution pH

Used directly in auto EDTA mode and in graph highlighting.

Manual Ligand Fraction αL

Use for non-EDTA systems or known active ligand fraction.

Free Metal Fraction αM

Set to 1 when no auxiliary complexing agent is present.

Total Metal Concentration (M)

Used for the 1:1 equilibrium concentration estimate.

Total Ligand Concentration (M)

Used with the metal total for equilibrium speciation.

EDTA pKa1

EDTA pKa2

EDTA pKa3

EDTA pKa4

EDTA pKa5

EDTA pKa6

Reset

Plotly Graph

The chart shows how the conditional constant changes with pH. In auto mode, αY4- is recalculated across the full pH range using the EDTA pKa set.

Example Data Table

This example mirrors a common EDTA-style conditional calculation and shows how pH and auxiliary complexation reduce the apparent stability.

Item	Example Value	Interpretation
Complex	CdY2-	Representative 1:1 metal-ligand complex
log Kf	16.50	Overall stability constant input
pH	10.00	Buffered working condition
αY4-	0.3670	Fraction of free EDTA present as Y4-
αM	0.0881	Free metal fraction after auxiliary complexation
Conditional Constant	9.49E14	Effective stability under actual conditions
Total Metal	0.0050 M	Analytical metal concentration
Total Ligand	0.0050 M	Analytical ligand concentration

Formula Used

Overall stability constant
For a 1:1 complex, M + L ⇌ ML
Kf = [ML] / ([M][L])

Conditional stability constant
K′f = Kf × αL
Here αL is the fraction of free ligand present in the active binding form.

Double conditional stability constant
K″f = Kf × αL × αM
αM is the fraction of total free metal remaining as the uncomplexed active metal ion.

EDTA fraction in the Y4- form
αY4- = (K1K2K3K4K5K6) / (H⁶ + H⁵K1 + H⁴K1K2 + H³K1K2K3 + H²K1K2K3K4 + HK1K2K3K4K5 + K1K2K3K4K5K6)

1:1 concentration estimate
Kcond = [ML] / ((CM − [ML])(CL − [ML]))
The calculator solves this quadratic to estimate bound and free concentrations.

How to Use This Calculator

Enter the published log Kf for your metal-ligand pair.
Choose Auto if your ligand is EDTA and you want αY4- from pH and pKa values.
Choose Manual if you already know the active ligand fraction for another system.
Enter αM if an auxiliary ligand or buffer ties up part of the free metal. Use 1.0 when absent.
Provide total metal and total ligand concentrations to estimate complexed and free amounts at equilibrium.
Press Calculate to show the result block above the form.
Review the graph to see how pH changes the conditional constant.
Use the CSV or PDF buttons after calculation to export the result summary.

Frequently Asked Questions

1) What does a conditional stability constant represent?

It represents the effective binding strength under real solution conditions, not the idealized full-active-form case. It includes pH effects and, when needed, competing equilibria.

2) Why is the conditional constant smaller than Kf?

The active ligand form may be only a fraction of the total ligand. Auxiliary ligands can also reduce the free metal fraction. Both effects lower the apparent stability.

3) When should I use auto EDTA mode?

Use auto mode when the ligand is EDTA and the pH is known. The calculator then estimates αY4- from the pKa values and solution pH.

4) When is manual alpha more useful?

Use manual alpha when you already know the active ligand fraction from literature, software, or a different speciation model. It also helps for non-EDTA ligands.

5) What does αM mean in this page?

αM is the fraction of total free metal that remains in the active uncomplexed form. If buffers or auxiliary ligands bind the metal, αM becomes smaller than one.

6) Does this calculator assume a specific stoichiometry?

Yes. The equilibrium concentration estimate assumes a 1:1 metal-ligand complex. The conditional constant concept itself is broader, but the concentration solver here is 1:1.

7) Why do I see pM and pL values?

They give the negative logarithm of the active free metal and active free ligand forms. These values help compare residual free species across different conditions.

8) Can I use this for titration planning?

Yes. It is useful for screening pH windows, ligand activity, and competition effects. For full titration curves, combine it with dilution and volume-balance calculations.