Example: 0.10 M NaCl plus 0.005 M CaSO4 contributes multiple charge terms.
| Ion | Concentration (mol/L) | z | ci·z² |
|---|---|---|---|
| Na+ | 0.10 | +1 | 0.10 |
| Cl− | 0.10 | −1 | 0.10 |
| Ca2+ | 0.005 | +2 | 0.020 |
| SO42− | 0.005 | −2 | 0.020 |
| Σ(ci·z²) | 0.240 | ||
| I = 0.5 × Σ(ci·z²) | 0.120 mol/L | ||
Ionic strength measures the total electrical effect of dissolved ions: I = ½ × Σ(ci × zi²)
- ci is the molar concentration of ion i (mol/L).
- zi is the ionic charge (e.g., −1, +2).
- Squaring zi makes multivalent ions dominate ionic strength.
- Enter a solution label so exports are easy to identify.
- Add ions with their concentration and charge, or use Quick add salt.
- Choose units (mol/L, mM, or µM). The tool converts to mol/L.
- Press Submit to view ionic strength and contributions.
- Use charge-balance feedback to catch missing ions or wrong signs.
- Download CSV or PDF to save and share your calculation.
Why ionic strength matters in real solutions
Ionic strength summarizes how strongly ions interact in a mixture. Two solutions with the same total salt can behave differently if charges differ. As ionic strength increases, electrostatic screening grows and activity coefficients (γ) move away from 1, so equilibrium and kinetics trends can change with salt level. Higher ionic strength also compresses electrical double layers, affects colloid stability, and shifts solubility behavior. Reporting I (mol/L) alongside pH and temperature improves comparability. Many analytical methods, like titrations, benefit from consistent I across standards and samples during calibration and validation.
Interpreting results across common concentration ranges
As a practical guide, ultrapure water is near zero, while many biochemical buffers sit around 0.05–0.20 mol/L. Physiological saline is commonly near 0.15 mol/L, and concentrated brines can exceed 1.0 mol/L. Natural waters vary widely; seawater is typically much higher than lab buffers. When I rises, simple “use concentration” assumptions weaken, and activities can better represent effective availability.
How multivalent ions dominate the calculation
Because the formula squares charge, a small amount of a 2+ or 3− ion can contribute disproportionately. For example, 5 mM Ca2+ contributes the same ci·z² term as 20 mM of a monovalent ion. This calculator shows each ion’s percentage contribution so you can identify which components drive I and prioritize tighter measurement control where it matters most.
Quality control with charge balance and unit hygiene
Accurate inputs matter: select the correct unit, include counter‑ions, and keep charge signs consistent. The charge-balance check computes Σ(ci·zi); values close to zero indicate a plausible electroneutral mixture. Large deviations often mean a missing partner ion, an incorrect salt split, or a concentration entered in the wrong unit. Use the tolerance field to match your workflow.
Reporting and exporting for reproducible lab notes
For documentation, record the ion list, units, and rounding rule used for display. The CSV export supports spreadsheet auditing and batch comparisons, while the PDF report is convenient for notebooks and sharing. Each export includes a timestamp, helping you keep a clear trail from recipe to ionic-strength value when formulations evolve.
What does the ionic strength value represent?
It is half the sum of each ion’s molar concentration times charge squared. The result reflects total electrostatic influence, not just total dissolved solids.
Which unit should I enter for concentration?
Use any provided unit. The calculator converts mmol/L and µmol/L to mol/L internally, then applies the ionic strength formula using molar concentrations.
Why do multivalent ions change results so much?
Charge is squared in the equation, so 2+ ions count four times and 3+ ions count nine times versus monovalent ions at the same concentration.
What does the charge-balance check tell me?
It reports Σ(ci·zi). Values near zero suggest an electroneutral mixture. Large offsets usually indicate a missing counter‑ion, wrong sign, or unit mismatch.
Do neutral molecules affect ionic strength?
No. Species with z = 0 contribute zero to ionic strength. You can omit neutrals like glucose unless you are tracking them for another reason.
When should I consider activity corrections?
At moderate to high ionic strength, activity coefficients can differ from 1. If you compare equilibria across different salt levels, activity-based models often behave better.