Enter your Calculation Model, Ion Charge (z), Ionic Strength (I), and supporting parameters like Ion Size Parameter (aᵢ) and Temperature to calculate the Activity Coefficient (γᵢ) for your ion — along with log₁₀ γᵢ, the Mean Activity Coefficient (γ±), and the Debye-Hückel Constant (A).
Activity Coefficient (γᵢ)
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log₁₀ γᵢ
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Mean Activity Coefficient (γ±)
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Debye-Hückel Constant (A)
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The activity coefficient (γ) measures deviations of a solution from ideal behavior. It relates chemical activity to concentration: activity = γ × concentration. A value of 1 indicates ideal behavior, less than 1 shows attractive interactions, and greater than 1 indicates repulsive interactions.
The Debye-Hückel limiting law calculates activity coefficient using: log₁₀γᵢ = -A × zᵢ² × √I, where A is the Debye-Hückel constant (0.509 at 25°C), zᵢ is the ion charge, and I is the ionic strength. This equation is valid for very dilute solutions (I < 0.01 M).
Yes, ionic strength is crucial for activity coefficient calculations. It represents the total concentration of all ions in solution and directly affects the electrostatic interactions between ions. Higher ionic strength generally leads to greater deviations from ideal behavior.
Use Debye-Hückel for very dilute solutions (I < 0.01 M), Davies equation for moderate ionic strengths up to 0.5 M, and Extended Debye-Hückel when you have ion size data and need accuracy at higher concentrations. Davies is the most versatile for general use.
Activity coefficient depends on ionic strength, ion charge (z²), temperature, ion size, and the specific interactions between ions in solution. The charge has a particularly strong effect due to the z² term in the equations.
An activity coefficient greater than 1 indicates that the ions experience repulsive interactions or excluded volume effects, making the solution behave as if it were more concentrated than it actually is. This often occurs in concentrated solutions or with large, highly charged ions.
For a typical monovalent ion (z = ±1) at I = 0.1 mol/kg, the Davies equation gives γ ≈ 0.78, while the limiting Debye-Hückel law gives γ ≈ 0.67. The exact value depends on the specific ion and model used.
The mean activity coefficient γ± accounts for both cations and anions in an electrolyte: γ± = (γ₊^ν₊ × γ₋^ν₋)^(1/(ν₊+ν₋)), where ν₊ and ν₋ are the stoichiometric coefficients of cations and anions, respectively. This provides a single value representing the overall electrolyte behavior.