Activity Coefficient Calculator

The activity coefficient (γ) accounts for non-ideal behavior in solutions. Activity a = γ · concentration. In an ideal (infinitely dilute) solution, γ = 1.0 and activity equals concentration. As ionic strength increases, γ deviates from 1.0 due to electrostatic interactions between ions. For most ions at physiological ionic strength (~0.15 M), γ is about 0.7-0.8.

The DHLL is: log₁₀(γ) = -A · z² · √I, where A = 0.5115 at 25°C in water, z is the ion charge, and I is ionic strength in mol/kg. It is accurate for I < 0.01 mol/kg. The extended form adds a denominator term (1 + B · a · √I) to account for the finite size of ions, improving accuracy up to I ~ 0.1 mol/kg.

Activity coefficients deviate significantly from 1.0 when ionic strength exceeds 0.01 mol/kg. For a divalent ion (z=2) at I=0.1 mol/kg, the extended Debye-Huckel equation with an ion size a = 3.0 angstroms gives γ about 0.32, meaning the effective concentration is only about a third of the actual concentration (the limiting law is harsher, giving about 0.22 at this ionic strength). This matters in precise equilibrium calculations, potentiometry (pH electrodes), and biophysical measurements at physiological salt concentrations.

The Davies equation drops the adjustable ion-size term for a fixed empirical correction: log₁₀(γ) = -A · z² · (√I / (1 + √I) - 0.3 · I), which works reasonably up to I ≈ 0.5 mol/kg without needing a per-ion size. For the extended Debye-Huckel mode you instead supply an effective ion size a in angstroms; common Kielland values are about 9 for H⁺, 6 for Li⁺, Ca²⁺, and Mg²⁺, 4 to 4.5 for Na⁺ and HCO₃⁻, and 3 for K⁺, Cl⁻, and NO₃⁻ (larger, less-hydrated ions take smaller a). Above roughly 0.5 mol/kg, or for seawater and brines, the Pitzer equations and the specific ion interaction theory (SIT) add ion-specific interaction terms and are the accepted models.