Ionic strength of an electrolyte solution
Ionic strength weights each ionic concentration by the square of its charge number, so multivalent ions contribute strongly. The concentration-basis result is Ic = ½Σcizi².
A bulk macroscopic solution should be electrically neutral. The calculator therefore also evaluates Σcizi and warns when the entered list may omit counterions or contain inconsistent analytical concentrations.
How to calculate ionic strength
- List every ion: Enter each cation and anion separately at its solution concentration.
- Enter signed charge: Use values such as +1, −1, +2, or −3; sign does not alter ionic strength but is needed for the balance warning.
- Calculate: Review ionic strength and any electroneutrality warning.
- Select an activity model separately: Confirm the resulting range is valid for the intended activity-coefficient equation.
Formula and variables
The sum must include every ionic species present at its actual molar concentration. Neutral solutes do not contribute.
Ic = ½ Σ(cizi²)- Ic — Concentration ionic strength
- Charge-weighted ion concentration (mol/L)
- ci — Ion concentration
- Molar concentration of ionic species i (mol/L)
- zi — Charge number
- Signed nonzero integer charge on species i (dimensionless)
0.1 M sodium chloride
Ideal complete dissociation gives 0.1 M Na+ and 0.1 M Cl−.
- Na+
- 0.1 mol/L, z = +1
- Cl−
- 0.1 mol/L, z = −1
- Ic = ½[(0.1)(1²) + (0.1)(−1)²]
Result: Ionic strength is 0.1 mol/L and the listed charges balance.
For a 1:1 electrolyte under complete dissociation, ionic strength equals the formula-unit molarity.
Understanding your results
Ionic strength is not total ion concentration
Charge is squared in the ionic-strength sum, while sign is retained only in the separate electroneutrality check.
- A divalent ion contributes four times its concentration before the one-half factor.
- Analytical salt concentration must be expanded into actual ionic concentrations.
- Speciation, association, complexation, and acid–base equilibria can change the ion list.
- A balance warning is diagnostic, not an automatic correction.
Assumptions
- Entered concentrations represent all ionic species after relevant dissociation and speciation.
- Concentrations are in mol/L and charge numbers are nonzero integers.
- The concentration-based rather than molality-based definition is intended.
Limitations
- Does not solve chemical speciation, activity coefficients, ion pairing, complex formation, or electroneutrality corrections.
- Concentration and molality ionic strength are not interchangeable in every solution.
- Does not determine whether a selected activity model is valid at the calculated strength.
Common mistakes
- Entering salt molarity once instead of listing its individual ions.
- Forgetting to multiply ionic concentration by stoichiometric dissociation count.
- Using charge magnitude as concentration.
- Ignoring an unbalanced ion list.
Practical use cases
Electrolyte coursework
Compare contributions from monovalent and multivalent ions.
Activity-model preparation
Calculate an input quantity after solution speciation has been established independently.
Frequently asked questions
Why is charge squared?
The ionic-strength definition weights both positive and negative ions by the square of charge magnitude, making multivalent ions more influential.
Does the sign of charge matter?
Not in zi², but it matters for checking whether the entered cations and anions are electrically balanced.
Should water or neutral molecules be entered?
No. Species with zero net charge do not contribute to the ionic-strength sum.
Sources and review
- Ionic Strength — IUPAC Compendium of Chemical Terminology. Accessed 2026-07-13.
Reviewed 2026-07-13.