Activity Coefficient Calculator
Debye-Hückel γ, and where it stops being reliable.
Work out Activity Coefficient. Debye-Hückel γ, and where it stops being reliable. Handles the awkward cases, not just the tidy ones.
Leave at 0 for the limiting law. H⁺ is about 9, Li⁺ and Mg²⁺ 6, K⁺ and Cl⁻ 3.
Optional — gives the effective (active) concentration.
Debye-Hückel is a limiting theory. Above roughly 0.1 M ionic strength it stops being quantitative.
Activity coefficient γ
0.8894
Debye-Hückel limiting law — within its valid range
Activity is what an ion behaves as, and it is always lower than its concentration in a real solution because the surrounding ions of opposite charge partly screen it. Equilibrium constants are strictly defined in terms of activities, which is why calculations using concentrations drift as solutions get more concentrated. The limiting law is good below about I = 0.01 M. The extended form with an ion-size parameter stretches that to roughly 0.1 M, and above that neither is reliable — the Davies equation or a specific ion-interaction model is needed.
How the Activity Coefficient Calculator works
Enter an ion's charge and the solution's ionic strength for the Debye-Hückel activity coefficient, with the extended form available if you supply an ion size. The page says explicitly whether the ionic strength falls inside the model's valid range.
Also known as: debye huckel calculator · ionic activity calculator · extended debye huckel equation · activity coefficient formula
Frequently asked questions
What is an activity coefficient?
The factor relating an ion's effective concentration to its actual one. It is always below 1 in a real solution, because surrounding ions of opposite charge partly screen each ion from participating.
What is the Debye-Hückel limiting law?
log γ = −0.509 z²√I at 25 °C in water. It is a limiting law in the strict sense — exact as concentration approaches zero, and reliable only up to about I = 0.01 M.
When do I need the extended equation?
Above roughly I = 0.01 M. The extended form adds an ion-size parameter in the denominator, which stretches usable accuracy to about I = 0.1 M. Beyond that, the Davies equation or a specific ion-interaction model is required.
Does this matter in practice?
Yes, at seawater or physiological ionic strengths. A divalent ion can have an activity coefficient near 0.4, meaning it behaves as under half its measured concentration — enough to shift a calculated solubility by a factor of several.
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