Activity Coefficient Calculator — Debye–Hückel & Davies
Compute the mean ionic activity coefficient γ± for an electrolyte at 25 °C in aqueous solution. Choose between the Debye–Hückel limiting law (very dilute solutions) and the Davies equation (up to ~0.5 mol/L). The chart shows how γ± changes across a range of concentrations.
mol/L
Model
Dimensionless correction for ion–ion interactions in solution (1 = ideal)
- 1
Ionic strength I = ½c(z₊² + z₋²)
½ × 0.1 × (1² + 1²) = 0.1 mol/L - 2
√I
√0.1 = 0.3162 - 3
log₁₀(γ±) — Davies equation
−0.5085 × 1 × 1 × (0.3162 ÷ (1 + 0.3162) − 0.3 × 0.1) = -0.1069 - 4
Mean activity coefficient γ± = 10^log₁₀(γ±)
10^(-0.1069) = 0.7818
How does this calculator work?
At 25 °C in water, γ± is given by the Davies equation: log₁₀(γ±) = −0.5085|z₊z₋|(√I/(1+√I) − 0.3I) or the simpler DHLL: −0.5085|z₊z₋|√I. Ionic strength I = ½(cz₊² + cz₋²). Valid up to ~0.5 mol/L (Davies) or ~0.01 mol/L (DHLL). γ± = 1 at infinite dilution.
Formula
How this is calculated
In real electrolyte solutions, ions interact electrostatically and their effective concentration (activity) differs from the stoichiometric concentration. The mean activity coefficient γ± captures this non-ideality: a± = γ± × c, where a± is the mean ionic activity. At infinite dilution γ± → 1 (ideal behaviour); it falls below 1 as concentration increases, reflecting attraction between oppositely charged ions.
The Debye–Hückel limiting law (DHLL) is the simplest model, valid for I < ~0.01 mol/L: log₁₀(γ±) = −A|z₊z₋|√I, where I = ½Σcᵢzᵢ² is the ionic strength and A ≈ 0.5085 at 25 °C in water. For higher concentrations the Davies equation adds an empirical correction term (−0.3I) that extends accuracy to I ≈ 0.5 mol/L. Both apply only at 25 °C in water — A changes with temperature and solvent.
The ionic strength is calculated assuming a single symmetric electrolyte at the entered concentration; in mixed-electrolyte solutions you would sum contributions from every ion species separately. Activity coefficients are essential in equilibrium calculations (solubility products, pH of buffers, electrode potentials via the Nernst equation) whenever concentrations exceed a few millimolar.
Frequently asked questions
The Debye–Hückel limiting law (DHLL) is most accurate below ~0.01 mol/L ionic strength. Above that, DHLL overestimates deviations — use the Davies equation, which is reliable up to about 0.5 mol/L. Beyond 0.5 mol/L neither model is adequate; Pitzer equations or specific-ion-interaction theory are needed.
Opposite-charge ions attract each other, lowering their free energy relative to an ideal solution. This makes their effective concentration (activity) lower than the analytical concentration, so γ± < 1. Only at infinite dilution, where interactions vanish, does γ± approach 1.
Yes. The Debye–Hückel constant A equals 0.5085 specifically at 25 °C in water. At other temperatures A changes (e.g. 0.488 at 15 °C, 0.535 at 45 °C). This calculator assumes 25 °C; for other temperatures you would need the temperature-dependent value of A.
Also known as
TG we-Calculate Editorial Team. (2026). Activity Coefficient Calculator — Debye–Hückel & Davies [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/activity-coefficient-calculator
TG we-Calculate Editorial Team. "Activity Coefficient Calculator — Debye–Hückel & Davies." TG we-Calculate. 2026. https://we-calculate.com/calculator/activity-coefficient-calculator.
TG we-Calculate Editorial Team, "Activity Coefficient Calculator — Debye–Hückel & Davies," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/activity-coefficient-calculator
@misc{wecalculate_activity_coefficient_calculator, title = {Activity Coefficient Calculator — Debye–Hückel & Davies}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/activity-coefficient-calculator}}, year = {2026}, note = {TG we-Calculate} }
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