Ionic strength calculator

Prepare the solution you want —one or several salts, strong acids or bases, in molarity, moles or grams and in the volume you choose— and get its ionic strength with every step.

What you can do

Over 40 electrolytes (NaCl, CaCl₂, MgSO₄, Na₂SO₄, Al₂(SO₄)₃, K₄[Fe(CN)₆]…), electrolytes you type and single ions.
Concentration of each ion, I = ½ Σ cᵢ zᵢ² with the numbers and an electroneutrality check.
Activity coefficients with the Debye–Hückel limiting law, the Güntelberg equation and the Davies equation, and which one fits for your I.
Ionic strength of mixtures with weak acids and bases, from the equilibrium of «Solutions (pH)».

Guide: ionic strength and activity coefficients

In a solution with ions, each ion is surrounded by an "atmosphere" of oppositely charged ions that screens it. That is why, in equilibria, solubilities or electrode potentials, an ion behaves as if its concentration were lower than it really is. Ionic strength measures how much charge there is in the solution, and activity coefficients quantify the effect. This guide explains both concepts and works an example.

Definition of ionic strength

I = ½ Σ c_i · z_i²

The sum runs over every ion in the solution, each with its concentration c_i (mol/L) and its charge z_i. Because the charge is squared, an ion of charge 2 counts four times as much as one of charge 1 at the same concentration, and one of charge 3, nine times as much.

The shortcut by electrolyte type

For a single strong salt of concentration c that dissociates completely:

1:1 (NaCl, KNO₃): I = c.
1:2 or 2:1 (Na₂SO₄, MgCl₂, CaCl₂): I = 3c.
2:2 (MgSO₄, CuSO₄): I = 4c.
1:3 or 3:1 (AlCl₃, Na₃PO₄): I = 6c.

With several salts, the contributions of all the ions are added; if two salts share an ion, its concentrations are added first.

Activity and activity coefficient

The activity of an ion is a = γ · c, where γ is its activity coefficient (γ = 1 in an infinitely dilute solution). The most common expressions to estimate γ in water at 25 °C, with A = 0.509 (mol/L)^−1/2, are:

Debye–Hückel limiting law: log γ = −A z² √I, only for very dilute solutions.
Güntelberg: log γ = −A z² √I / (1 + √I), useful up to moderate ionic strengths.
Davies: log γ = −A z² [√I / (1 + √I) − 0.3 I], used up to somewhat higher ionic strengths.

All of them predict the same trend: γ drops as the ionic strength grows, much more so for highly charged ions.

Worked example: 0.010 M MgCl₂

Dissociation: MgCl₂ → Mg²⁺ + 2 Cl⁻, so [Mg²⁺] = 0.010 M and [Cl⁻] = 0.020 M.
Ionic strength: I = ½ (0.010 · 2² + 0.020 · 1²) = ½ (0.040 + 0.020) = 0.030 M, which matches the 3c shortcut.
Electroneutrality: Σ c·z = 0.010·(+2) + 0.020·(−1) = 0. The charges balance.
Activity coefficients (Davies): √I = 0.1732; √I/(1 + √I) − 0.3·I = 0.1476 − 0.0090 = 0.1386.
- Mg²⁺: log γ = −0.509 · 4 · 0.1386 ≈ −0.282, so γ ≈ 0.522 and a ≈ 0.0052 M.
- Cl⁻: log γ = −0.509 · 1 · 0.1386 ≈ −0.0706, so γ ≈ 0.850 and a ≈ 0.0170 M.

At this concentration magnesium already "acts" as if there were about half as much. The calculator gives these same values, plus those of the other two equations (Güntelberg gives γ ≈ 0.50 for Mg²⁺), and tells you which one suits the computed ionic strength.

What it is used for

Salt effect: adding an inert salt raises the ionic strength, lowers the activity coefficients and increases the solubility of sparingly soluble salts.
Equilibrium constants: thermodynamic constants are written with activities; with concentrations they are only approximate.
Electrochemistry and buffers: the pH measured with an electrode is a measure of activity, not concentration.

How to use the calculator

Add solutes from the list (or type the ions of another electrolyte, or single ions) with their amount in M, mM, mol or g; with mol or g it is divided by the volume of the solution.
Read the ionic strength, the electroneutrality check, the table of ions with their contributions and the activity coefficients from the three equations.

The tool assumes complete dissociation. For weak acids and bases, or salts that hydrolyze such as Na₂CO₃, use the acid–base equilibrium tool and its "Ionic strength →" button.

Common mistakes

Forgetting the factor ½ or not squaring the charge.
Counting the salt instead of its ions: MgCl₂ gives twice as much Cl⁻ as Mg²⁺.
Using the Debye–Hückel limiting law at high ionic strength, where it no longer holds.

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