Activity Coefficient Calculator
Calculate the activity coefficient (γ) for ions and molecules in solution. The activity coefficient shows ratio of actual chemical activity to theoretical concentration based on non-ideal behavior. Use ionic strength and charge to estimate using Debye-Hückel theory.
Chemical activity of the species
Molar concentration in mol/L
Activity coefficient (1 for ideal solution)
Temperature in Celsius (for ionic strength)
Use Debye-Hückel if known
What is an activity coefficient?
The activity coefficient (γ) measures how much a real solution deviates from ideal behavior. In ideal solutions, γ = 1 and activity equals concentration. Real solutions have γ < 1 for solutes that interact more strongly than expected (attractive forces reduce activity), and γ > 1 for repulsion. Activity coefficients are essential for accurate equilibrium and rate calculations.
How do I calculate activity coefficient?
Activity coefficient is calculated from γ = Activity ÷ Concentration. For electrolyte solutions, use the Debye-Hückel equation: log γ = -A × |z+×z-| × √I / (1 + Ba × √I), where I is ionic strength, z are ion charges, and A, B are temperature-dependent constants. For dilute solutions (< 0.01 M), use the limiting law: log γ = -A × |z+×z-| × √I.
What affects activity coefficient?
Activity coefficient depends on: ionic strength (higher I → lower γ), ion charge magnitude (higher charges → more deviation), temperature (higher T → less deviation), solvent type, and solute type. At infinite dilution, γ → 1 (ideal behavior). As concentration increases, electrostatic interactions cause increasing deviation from ideality.
Why does activity matter instead of concentration?
Chemical potential and reaction equilibria depend on activity, not just concentration. Ions interact electrostatically, altering their "effective concentration" for reactions. Using concentration alone gives wrong equilibrium constants, especially for ionic species. Equilibrium expressions should use activities: K = a_products / a_reactants. Activity accounts for non-ideal behavior.
What is ionic strength?
Ionic strength (I) measures total ion concentration weighted by charge: I = 0.5 × Σ(cᵢ × zᵢ²). For 0.1 M NaCl: I = 0.5[(0.1×1²) + (0.1×1²)] = 0.1 M. For 0.1 M CaCl₂: I = 0.5[(0.1×2²) + (0.2×1²)] = 0.3 M. Higher ionic strength causes more deviation from ideal behavior.
When is activity approximately equal to concentration?
At very low ionic strengths (< 0.001 M), activity coefficients are close to 1, so activity ≈ concentration. This is the "infinite dilution" limit. For dilute solutions, especially 1:1 electrolytes like NaCl, the approximation is reasonable. For precise work or higher concentrations, you must use actual activity coefficients.
How is activity coefficient used in equilibria?
In equilibrium constants, activities replace concentrations: K = a₁a₂ / a₃a₄ = (γ₁[M₁])×(γ₂[M₂])/(γ₃[M₃])×(γ₄[M₄]). For example, Ka = ([H⁺]γ×[A⁻]γ)/([HA]γ). The "thermodynamic equilibrium constant" uses activities; the "concentration constant" uses concentrations but is only valid when γ ≈ 1.