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Ionic Strength Calculator

Calculate the ionic strength of a solution from the concentration and charge of each ion, with the contribution of each and the Davies activity coefficients up to 0.5 M.

Formula

I=12∑icizi2I = \dfrac{1}{2}\sum_i c_i z_i^{2}
log⁡10γ=−0.509 z2(I1+I−0.3 I)(Davies, 25 ∘C)\log_{10}\gamma = -0.509\,z^2\left(\dfrac{\sqrt{I}}{1 + \sqrt{I}} - 0.3\,I\right)\quad(\text{Davies, } 25\,^\circ\mathrm{C})
cic_i
molar concentration of ion i
ziz_i
charge number of ion i
γ\gamma
activity coefficient: effective concentration = γ × concentration

How it works

Ionic strength measures the total electrical environment of a solution. Each ion contributes its concentration times the square of its charge, so a divalent ion counts four times as much as a monovalent one and a trivalent ion nine times as much. That is why small amounts of magnesium or phosphate can dominate the ionic strength of a buffer.

It matters because ions are shielded by their neighbours: the effective concentration (activity) of an ion is less than its concentration, by an amount that depends on its charge and on the ionic strength. The Davies equation estimates the activity coefficient up to about 0.5 M. Activity shifts measured pH, pKa values and binding constants.

Worked example

150 mM NaCl with 2 mM MgSO₄, entered as four ions.

  1. ½ × (0.150 × 1 + 0.150 × 1 + 0.002 × 4 + 0.002 × 4) = ½ × 0.316 = 0.158 M.
  2. Davies: γ(Na⁺) = 0.757 and γ(Mg²⁺) = 0.329 at this ionic strength.

Ionic strength 0.158 M. The divalent Mg²⁺ has an activity less than a third of its concentration.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Every ion is entered. Uncharged species are left out.
  • The Davies equation at 25 °C, unreliable above about 0.5 M.
  • Complete dissociation, with no ion pairing, such as the association of Mg²⁺ with phosphate.

Common mistakes

  • Counting 150 mM NaCl as 150 mM rather than as two ions.
  • Ignoring the ionised part of a buffer, whose charged forms contribute.
  • Using Davies activity coefficients in a concentrated solution.

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