Activity Coefficient Calculator

Ions in company behave as though there were fewer of them — and past 0.1 molar no simple formula follows it.

Activity coefficient, charge 10.92552extended Debye-Huckel, water at 25 °C

Ionic strength0.005 mol/L

Contribution of the first ion0.0025charge enters SQUARED, so a 2+ counts four times a 1+

Contribution of the second ion0.0025

Activity coefficient, charge 20.73374extended Debye-Huckel, water at 25 °C

Limiting law would give, charge 10.92047the simpler form, and it drifts low as strength rises

Below about 0.1 mol/L the extended form holds up; the limiting law alone is only good to a tenth of that.

The formula

I = 0.5 * sum(c * z^2) ; log10(gamma) = -0.509 * z^2 * sqrt(I) / (1 + sqrt(I))

Charge counts twice

The charge enters the sum squared, so a doubly charged ion contributes four times as much ionic strength as a singly charged one at the same concentration. That is why 0.1 M calcium chloride gives an ionic strength of 0.3 while 0.1 M sodium chloride gives 0.1 — the calcium alone accounts for two thirds of it.

Where the model stops

The limiting law is trustworthy only to about I = 0.01, and the extended form to roughly 0.1. Above that, measured activity coefficients stop falling, turn round and climb — in concentrated solutions they can exceed one. No simple expression follows that, so beyond 0.1 these pages report the direction rather than pretending to a value.

Which denominator?

Most of the confusion in solution work is not arithmetic but bookkeeping. Molarity divides by the volume of the finished solution; molality divides by the mass of the solvent; percent by mass divides by the mass of the solution again. The three agree closely in dilute water and diverge sharply in concentrated acid, which is why a bottle labelled 98 % is also labelled 18.4 M without contradiction.