Activity Coefficient γ
Debye-Hückel theory
In real electrolyte solutions, ions are not ideal. The activity coefficient γ corrects the deviation between concentration and activity.
log γ = -0.5 × z² × √I
As ionic strength increases, γ decreases. Multivalent ions are affected much more strongly due to the z² term.
- z = 1: moderate correction
- z = 2: much stronger correction
- crucial for equilibria and pH in salt-rich media
Formulas
log γ = -0.5 × z² × √I
γ = 10^(-0.5 × z² × √I)
I = ( log γ / (-0.5×z²) )²
Detailed examples
Example 1 (monovalent)
I = 0.10; z = 1
log γ = -0.5×1×√0.10 = -0.1581
γ ≈ 0.695
I = 0.10; z = 1
log γ = -0.5×1×√0.10 = -0.1581
γ ≈ 0.695
Example 2 (divalent)
I = 0.10; z = 2
log γ = -0.5×4×√0.10 = -0.6325
γ ≈ 0.233
I = 0.10; z = 2
log γ = -0.5×4×√0.10 = -0.6325
γ ≈ 0.233
Interpretation
At the same I, γ for z=2 drops much more than for z=1, strongly changing effective concentrations.
At the same I, γ for z=2 drops much more than for z=1, strongly changing effective concentrations.
Use case
In buffers with added salts and in geochemical systems, activity corrections are often essential for accurate equilibrium predictions.
In buffers with added salts and in geochemical systems, activity corrections are often essential for accurate equilibrium predictions.
Technical Background
Limits of the simple model
The simplified Debye-Hückel relation is most suitable at low to moderate ionic strength. At high ionic strength, extended models (e.g., Davies, Pitzer) are more accurate.
Why γ matters
Reaction quotients and equilibrium constants are based on activities. Without γ, electrolyte calculations can produce systematic errors in pH, redox, and complexation systems.
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