Library / Solution chemistry, equilibria and kinetics / SCH-31
Solution chemistry, equilibria and kinetics
Fraction of metal bound at a fixed free ligand level
Fraction of the metal present as the 1:1 complex ML at a given free ligand concentration L, with formation constant Kf in L/mol.
- Ref
- SCH-31
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- fML
For M + L ⇌ ML with formation constant Kf = [ML]/([M][L]), the fraction of the metal as the complex is f = Kf L/(1 + Kf L), where L is the free ligand concentration. It is one half when L = 1/Kf. This form needs only M and ML to be present and L to be fixed, so total ligand can replace L only if binding depletes it negligibly.
Fraction of the metal present as the 1:1 complex ML at a given free ligand concentration L, with formation constant Kf in L/mol. Only M and ML are present. Use total ligand in place of L only if binding barely depletes it.
Calculator
- Fraction of free metal, 1 − f0.3333
- Ratio [ML]/[M], Kf L2
- Free ligand giving half binding, 1/Kf0.001 mol/L
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 0.002 mol/L of free ligand, 66.67 % of the metal is bound and 33.33 % is free.
- Half of the metal is bound at L = 0.001 mol/L, and going from 10 % to 90 % bound needs an 81-fold change in L.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| L Free ligand concentration | 1e-8 to 1 mol/L | 1e-5 | 0.999 | 0.999 | +10% | +3.13 % |
| Kf Formation constant | 1 to 1e12 L/mol | 0.001996 | 1 | 0.998 | +10% | +3.13 % |
Sweep of Free ligand concentration
| Free ligand concentration (mol/L) | Fraction as ML |
|---|---|
| 1e-8 | 1e-5 |
| 1e-7 | 9.999e-5 |
| 1e-6 | 9.99e-4 |
| 1e-5 | 0.009901 |
| 1e-4 | 0.09091 |
| 0.001 | 0.5 |
| 0.01 | 0.9091 |
| 0.1 | 0.9901 |
| 1 | 0.999 |
Sweep one variable
Variables and how each one contributes
Fraction as ML
What the equation gives you. Everything else feeds it.
Formation constant
The formation constant of the 1:1 complex, in L/mol. A larger Kf raises the bound fraction, saturating at 1. Raising it by 10 % (to 1,100) moves the result by +3.13 %, from 0.6667 to 0.6875.
Free ligand concentration
The free ligand concentration, in mol/L. More free ligand raises the bound fraction, saturating at 1. Raising it by 10 % (to 0.0022) moves the result by +3.13 %, from 0.6667 to 0.6875.
Worked example with the values above
- Product: Kf L = 1,000 × 0.002 = 2.
- Denominator: 1 + 2 = 3.
- f = 2 / 3 = 0.66667.
Assumptions and limits
- A 1:1 complex, or a single neutral species partitioning, with constants in concentration units.
- Equilibrium reached in each step, and no side reactions unless the conditional constant includes them.
Common mistakes
- Using the total ligand concentration for the free ligand when binding depletes it.
- Using the absolute EDTA constant at a pH where much of the EDTA is protonated.
- Mixing the units of the two phase volumes.
Statistics and uncertainty
Formation constants depend on the medium and the temperature, and a quoted constant for a different ionic strength can be off by a factor of two or more. Extraction results are sensitive to pH near the pKa.
Where it is used
- Designing complexometric titrations and metal-binding experiments.
- Planning solvent extractions and pH-controlled separations.
Maths you need
- Formation constant: Kf = [ML]/([M][L])
- Partition coefficient: the ratio of a species in two phases
- Mass balance: total equals free plus bound