How this calculator works
The Debye-Huckel limiting law estimates electrostatic non-ideality at very low ionic strength. This page uses the molal scale, with A about 0.509 for water at 25 C. Ionic strength is one half the sum of each ion molality times squared charge. The inverse charge is a mathematical magnitude and may be non-integer. Single-ion activity coefficients rely on conventions; concentrated solutions require another model. Values above 0.01 mol/kg are explicitly labelled extrapolations.
Formula
log10(gamma) = -A z^2 sqrt(I). Thus I = [-log10(gamma)/(A z^2)]^2.
Worked example
With A = 0.5, z = 1 and I = 0.01 mol/kg, gamma = 10^-0.05 = 0.89125094. For gamma = 0.1, z = 2 and A = 0.5, the algebraic inverse gives I = 0.25 mol/kg, outside the limiting-law range.
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Frequently asked questions
Why does the sign of charge disappear?
The expression contains charge squared, so positive and negative ions of equal magnitude give the same estimate.
Can gamma be above one?
Real coefficients can exceed one, but this limiting-law model only produces values up to one.
Why not use molar concentration units?
This implementation uses molal ionic strength in mol/kg. It should not silently substitute mol/L.