Activity Coefficient Calculator
The Activity Coefficient Calculator estimates the activity coefficient (γ) of an ion in solution using the Debye-Hückel limiting-law form. It corrects for how electrostatic interactions in an electrolyte make an ion's effective (active) concentration differ from its actual concentration. Enter the ionic strength and the ion's charge to get γ.
Formula
log γ = -A × z² × √I / (1 + √I), where γ = 10^(log γ)
- Activity Coefficient Calculator gives you a fast estimate using your inputs and updates instantly when you change any value.
- Formula: log γ = -A × z² × √I / (1 + √I), where γ = 10^(log γ)
- Input definitions: • Ionic strength (I): the numeric ionic strength (i) used in the calculation • Ion charge (|z|): the numeric ion charge (|z|) used in the calculation
- Manual method: write down each input, apply the formula step by step, then compare your manual result with the calculator output.
- Uses standard SI and chemistry units (mol, L, g/mol, M, Pa, K) unless otherwise stated.
- Based on standard stoichiometric and thermodynamic equations. Results may vary with temperature, pressure, and substance purity.
- Cross-check results against known standards or reference tables to confirm they are physically reasonable.
- Practical tip: test a low, medium, and high scenario to understand sensitivity before making decisions.
Example Calculation
Inputs
- Ionic strength (I): 0.1 mol/L
- Ion charge (|z|): 1
For a singly charged ion (z = 1) at ionic strength I = 0.1 mol/L: log γ = −0.51 × 1 × √0.1 / (1 + √0.1) ≈ −0.122, so γ ≈ 0.75 — the ion behaves as if about 75% of its concentration is active.
Frequently asked questions
What is an activity coefficient?
It is a factor (γ) that relates an ion's effective concentration (activity) to its actual concentration. In dilute solutions γ approaches 1; as ionic strength rises, γ typically falls below 1.
What is the Debye-Hückel equation?
This calculator uses the extended limiting form log γ = −A·z²·√I / (1 + √I), with A = 0.51 for water at 25 °C. It models how ionic atmosphere screening reduces ion activity.
When is this valid?
The Debye-Hückel limiting law is most accurate for dilute solutions, roughly I < 0.1 mol/L. At higher ionic strengths, extended models (such as Davies or Pitzer) are needed.
Why does charge matter so much?
The charge appears squared in the formula, so a 2+ ion deviates from ideal behaviour far more than a 1+ ion at the same ionic strength.
What is ionic strength?
Ionic strength I = ½ Σ cᵢ zᵢ² sums the concentration of every ion weighted by the square of its charge. It captures the total electrostatic environment of the solution.