Activity Coefficient Calculator
Apply the Debye-Hückel limiting law to approximate ionic activity coefficients for dilute electrolyte solutions.
Valid for dilute solutions where I ≲ 0.1 mol/L.
Use the absolute value of the ionic charge.
A ≈ 0.509 for water at 25 °C.
log₁₀ γ
-0.0509
Activity coefficient, γ
0.889406
For ionic strength 0.01, ion charge |z| = 1, and Debye-Hückel constant 0.509, the activity coefficient is 0.889406.
How to Use This Calculator
Measure ionic strength
Estimate the ionic strength of your solution (I = 0.5 Σ cᵢ zᵢ²). The Debye-Hückel limiting law is accurate when I is below about 0.1 mol/L.
Enter ion charge
Provide the absolute value of the ionic charge for the ion of interest. Multivalent ions (e.g., z = 2) have stronger interactions.
Specify the Debye-Hückel constant
Use A = 0.509 for water at 25 °C. Adjust A for other solvents or temperatures if data is available.
Review log γ and γ
The tool reports log₁₀ γ and γ directly. Multiply analytical concentrations by γ to obtain activities.
Formula
log₁₀ γ = -A z² √I
γ is the activity coefficient, A is the Debye-Hückel constant for the solvent, z is the ionic charge, and I is the ionic strength (mol/L).
Example
A 1:1 electrolyte (z = 1) in water at 25 °C with ionic strength 0.01 has log₁₀ γ = -0.509 × 1² × √0.01 = -0.0509, so γ ≈ 0.89.
Full Description
The Debye-Hückel limiting law describes how ionic interactions lower the effective concentration (activity) of ions in dilute electrolyte solutions. It shows that activity coefficients decrease as charge magnitude increases or as ionic strength grows.
This calculator focuses on the limiting law, which is most accurate when ionic strength is low (typically below 0.1 mol/L). For more concentrated systems, extended Debye-Hückel or Pitzer models provide improved accuracy.
Use this tool to correct analytical concentrations, interpret electrochemical measurements, or estimate deviations from ideality in aqueous media.
Frequently Asked Questions
When is the limiting law valid?
It is reliable for ionic strengths below about 0.1 mol/L. At higher ionic strength, apply extended models that include ion-size parameters.
How do I calculate ionic strength?
Use I = 0.5 Σ cᵢ zᵢ², summing over all ions in solution. Concentrations (cᵢ) should be molar units and zᵢ the ionic charges.
Can I adjust for temperature?
Yes. Replace A with the appropriate Debye-Hückel constant for your solvent and temperature. For water, A decreases slightly as temperature rises.
Does this handle multivalent ions?
Yes. Enter the absolute charge (e.g., z = 2 for Ca²⁺). Note that activity coefficients drop quickly as charge increases.
What if my solution is concentrated?
Use more advanced models such as the Davies equation, extended Debye-Hückel, or Pitzer equations to capture non-ideal behavior at higher ionic strengths.