Ionic Strength and Activity Coefficient Calculator (Debye–Hückel, Davies)
Ionic strength of a solution from its ions' concentrations and charges, the activity coefficient of an ion by the limiting law and the Davies equation, and the Debye length.
Results
What this tool does
Ions in solution feel one another, so their effective concentration, the activity, is less than the amount you weighed out; the activity coefficient γ measures that. Ionic strength I = ½ Σ c z² counts the charge twice over, so a 0.01 M calcium chloride has I = 0.03, three times its molarity. The Debye–Hückel limiting law only holds for very dilute solutions (below about 0.01 M); the Davies equation reaches roughly 0.5 M. Both use the constant 0.509 for water at 25 °C.
Formula
I = ½ Σ cᵢ zᵢ² · log γ = −0.509 z² √I (limiting law) · log γ = −0.509 z² (√I ÷ (1 + √I) − 0.3 I) (Davies, 25 °C, water)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
c1 | Concentration of ion 1 | mol/L |
z1 | Charge of ion 1 (without sign) | — |
c2 | Concentration of ion 2 | mol/L |
z2 | Charge of ion 2 (without sign) | — |
c3 | Concentration of ion 3 (0 if none) | mol/L |
z3 | Charge of ion 3 (without sign) | — |
zi | Charge of the ion whose activity coefficient you want | — |
IS | Ionic strength I | mol/L |
GD | Activity coefficient, Davies equation | — |
GL | Activity coefficient, Debye–Hückel limiting law | — |
DL | Debye length (screening distance) | nm |
Worked example
- Concentration of ion 10.01 mol/L
- Charge of ion 1 (without sign)2
- Concentration of ion 20.02 mol/L
- Charge of ion 2 (without sign)1
- Concentration of ion 3 (0 if none)0 mol/L
- Charge of ion 3 (without sign)1
- Charge of the ion whose activity coefficient you want2
- Ionic strength I0.0300 mol/L
- Activity coefficient, Davies equation0.522
- Activity coefficient, Debye–Hückel limiting law0.444
- Debye length (screening distance)1.76 nm
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.