Ionic strength, activity coefficients and solubility

1. Enter your water analysis

Use a decimal point or comma; do not use thousands separators. For dilute water, ppm is approximated as mg/L; this assumes a density close to 1 kg/L. g/m³ and mg/L are equivalent.

2. Read your results

Ionic-strength and activity-coefficient results are shown to four significant figures, with full internal calculation precision. The divalent coefficient is copied automatically into the example below. The retained solubility routine reports approximately three significant figures.

How the calculation works

I = ½ Σ c_iz_i², where c_i is the molar concentration in mol/L and z_i is the ion charge number. For example, Ca²⁺ has z = +2, so z² = 4.

log₁₀ γ = −0.5 z² √I / (1 + √I), with γ = 10^{log₁₀ γ}.

This simplified Debye–Hückel expression uses a fixed coefficient of 0.5, approximately representing water near 25 °C. It is a dilute-water estimate, not the full Davies equation or a complete speciation model. It assigns the same coefficient to ions of the same charge magnitude. The temperature entered below does not change these activity coefficients.

Only the eight listed ions contribute to the calculated ionic strength. Unlisted charged species, including fluoride, carbonate and charged silicate species, may also contribute. Neutral dissolved substances do not contribute directly. Analytical totals and free-ion concentrations can differ where complexation or acid–base speciation is significant.

3. Simplified calcium-carbonate equilibrium example

For CaCO₃(s) ⇌ Ca²⁺ + CO₃²⁻, the solubility product is K_sp = a_Ca²⁺ × a_CO₃²⁻. Under the equal-concentration approximation, c = √K_sp / γ, with concentrations expressed relative to the 1 mol/L standard state.

Temperature changes the solubility constant in this example; it does not update the activity model above. The mg/L output is expressed as calcium (Ca), not as CaCO₃.