Ionic Strength Calculator

Ionic strength (I) measures the total concentration of ions in a solution, weighted by the square of their charges:

I = (1/2) × Σ(cᵢ × zᵢ²)

Where cᵢ is the molar concentration of ion i (in mol/L) and zᵢ is its charge (e.g., +2 for Ca²⁺, −1 for Cl⁻).

The charge is squared, so multiply-charged ions contribute much more than singly charged ones. A 0.1 M MgSO₄ solution (Mg²⁺ at charge +2, SO₄²⁻ at charge −2):

I = (1/2) × [0.1 × 4 + 0.1 × 4] = (1/2) × 0.8 = 0.4 mol/L

Compare to 0.1 M NaCl (Na⁺ at +1, Cl⁻ at −1):

I = (1/2) × [0.1 × 1 + 0.1 × 1] = 0.1 mol/L

Same concentration, four times the ionic strength for the divalent salt.

Why ionic strength matters: in any solution containing ions, electrostatic interactions between ions reduce the effective concentration of each species — this is captured by the activity coefficient γ. The Debye-Hückel limiting law approximates:

log(γ) ≈ −A × z² × √I

At low ionic strength, activities can deviate significantly from concentrations. Biochemical assays, pH measurements, and equilibrium calculations in electrolyte solutions all need activity corrections at higher ionic strengths.

Seawater has an ionic strength of about 0.7 M, dominated by Na⁺ and Cl⁻. Blood plasma sits around 0.15 M. These differences affect how drugs behave in different physiological environments.

Where the idea comes from. Ionic strength was introduced by Gilbert N. Lewis and Merle Randall in 1921 to give Debye-Hückel theory the right input variable — they noticed that activity coefficients of dilute electrolytes depended not just on total concentration but on charges weighted as z². The half-factor in the definition is what makes a simple 1:1 electrolyte like NaCl give I equal to its molar concentration, which is convenient enough that it has stuck for a century.