Activity Coefficient Calculator
Explore ionic strength, non-ideal solutions and the models behind ionic activity.
Solution & ion parameters
Activity coefficient & ionic strength
Ca²⁺ · Davies equation · water at 25 °C · molality basis
Compare the three activity models
Davies selectedSolid: inside illustrative use range. Dashed: extrapolation. Range limits are guides, not accuracy guarantees.
Inside an ionic atmosphere
Conceptual viewNearby ions are not independent
A positive ion has a statistical excess of negative counter-ions nearby.
This changes the relation between composition and chemical potential.
Not a bonded shell, orbital path, or a quantitative particle snapshot.
From amount to thermodynamic activity
Selected Ca²⁺ molality: 0.0100 mol/kg
Standard state m° = 1 mol/kg. The scaled amount carries units; thermodynamic activity does not.
It does not measure ionization, binding or the free-ion fraction. Single-ion activity coefficients also depend on a convention.
Model comparison at your selected conditions
Same I · same charge| Model | γᵢ | log₁₀ γᵢ | Illustrative range | At selected I |
|---|---|---|---|---|
| Debye–Hückel limiting | 0.3505 | -0.4553 | I < 0.01 mol/kg | Extrapolated |
| Extended Debye–Hückel | 0.4829 | -0.3161 | I < 0.1 mol/kg | Within guide |
| Davies equation | 0.4555 | -0.3415 | I ≤ 0.5 mol/kg | Within guide |
Davies is not a concentrated-brine model. Even inside these guide ranges, ion-specific interactions may require a more appropriate model.
Formula & worked example
For Ca²⁺, I = 0.050 mol/kg and A = 0.509:
log₁₀ γᵢ ≈ −0.341527
γᵢ = 10−0.341527 ≈ 0.4555
The extended equation additionally uses a compatible ion-size parameter. Neither a charge number nor an ion-size preset establishes solution speciation.
Frequently asked questions
Is activity the same as concentration?
No. Activity is a dimensionless thermodynamic quantity referenced to a defined standard state; concentration and molality have units.
Can I convert mol/L to mol/kg with one switch?
No. A composition conversion requires additional solution information. Model constants and standard states must match the selected basis.
Why do charge and ion size matter?
These models use the squared charge number. The extended model also uses an effective ion-size parameter, not simply a bare-ion radius.
Is Davies suitable for every concentrated solution?
No. Its customary ionic-strength range is only an approximate guide and does not guarantee accuracy for a particular ion or electrolyte.
Is the ionic atmosphere a bound shell?
No. It describes a statistical excess of counter-charge, not fixed bonds or orbiting particles.
How does changing temperature affect A and B?
Reference-water mode applies an approximate temperature scaling anchored at A = 0.509 and B = 0.328 at 25 °C. It uses pure-water density and dielectric correlations from 0 to 100 °C. Custom coefficients are held as entered and must match the chosen temperature and concentration basis.
Sources & Reference Guides
Model reference: USGS PHREEQC documentation
Independent references, no institutional endorsement.
Explore ionic strength, non-ideal solutions and the models behind ionic activity.