Ionic strength measures how much electrical charge is dissolved in a solution, weighted so that multiply charged ions count much more: each ion contributes its concentration times the square of its charge, and the total is halved. A 0.1 M NaCl solution has I = 0.1 M, but 0.1 M MgSO₄ has I = 0.4 M because both ions carry two charges.
The value matters because ions do not behave independently. Each ion is surrounded by an “atmosphere” of oppositely charged ions that screens its charge, lowers its activity and changes equilibrium constants, solubilities, reaction rates, electrode potentials and the stability of colloids and proteins. Debye–Hückel theory and its extensions (such as the Davies equation used here) predict activity coefficients directly from the ionic strength, and the Debye length gives the distance over which charges are screened.
Biochemists set buffer ionic strength to control protein folding and binding; geochemists use it to correct mineral solubility in seawater (I ≈ 0.7 M); and analytical chemists add an ionic-strength adjuster so that ion-selective electrodes see the same activity coefficients in standards and samples.
How to use the Ionic Strength Calculator
- Ions or salts with concentration (one per line)
- Concentration unit
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Type one entry per line: an ion with its charge (Na+ 0.1, SO4^2- 0.05, Fe3+ 0.01), a neutral salt (CaCl2 0.1, which is split into 0.1 Ca²⁺ and 0.2 Cl⁻), or a bare “concentration charge” pair (0.1 2). Ions that appear several times are added together, then I = ½Σcz² is computed and each ion’s Davies activity coefficient is listed.
Worked example
A solution with 0.1 M CaCl₂ and 0.05 M Na₂SO₄ contains 0.1 M Ca²⁺, 0.2 M Cl⁻, 0.1 M Na⁺ and 0.05 M SO₄²⁻.
I = ½ (0.1 × 2² + 0.2 × 1² + 0.1 × 1² + 0.05 × 2²) = ½ (0.4 + 0.2 + 0.1 + 0.2) = 0.45 M. The charges balance (0.2 + 0.1 = 0.2 + 0.1 mol/L of charge each way). With √I = 0.6708 the Davies equation gives γ = 0.732 for the singly charged ions and 0.287 for the doubly charged ones, and the Debye length is 0.304 / 0.6708 = 0.453 nm.
Ionic strength factors for common salt types
| Salt type | Example | I ÷ c |
|---|---|---|
| 1:1 | NaCl, KNO₃ | 1 |
| 1:2 or 2:1 | Na₂SO₄, CaCl₂ | 3 |
| 2:2 | MgSO₄, CuSO₄ | 4 |
| 1:3 or 3:1 | Na₃PO₄, AlCl₃ | 6 |
| 3:2 | Al₂(SO₄)₃ | 15 |
Tips
- Standard potentials are reduction potentials at 25 °C, 1 M and 1 bar.
- n is the number of electrons transferred in the balanced reaction.
- Faraday constant: 96 485 C per mole of electrons.
- Everything is calculated in your browser.
Common mistakes to avoid
- Flipping the sign of a potential and also subtracting it (counting the reversal twice).
- Multiplying a standard potential by the coefficient of the half-reaction – potentials are intensive.
- Using log base e where the Nernst equation uses log₁₀ (or the other way round).
Formula
I = ½ · Σ cᵢ · zᵢ² · Davies: log₁₀γ = −0.509·z²·(√I/(1 + √I) − 0.3·I) (water, 25 °C) · Debye length κ⁻¹ ≈ 0.304 nm / √IWorked example
Inputs — Ions or salts with concentration (one per line): CaCl2 0.1
Na2SO4 0.05; Concentration unit: mol/L (molarity).
Results — Ionic strength I = 0.45 mol/L; Ionic strength in mol/L (or mol/kg) = 0.45; Total ion concentration Σc = 0.45; Charges balanced? = Yes – the charges balance; Activity coefficient of a ±1 ion (Davies) = 0.7317; Activity coefficient of a ±2 ion (Davies) = 0.2867.
Key terms
- Ionic strength I
- Half the sum of concentration × charge² over all ions in solution.
- Activity coefficient γ
- Factor relating an ion's effective concentration (activity) to its real concentration.
- Debye length
- Distance over which an ion's electric field is screened by the surrounding ions.
- Electroneutrality
- In any solution the total positive charge equals the total negative charge.
Frequently asked questions
How do you calculate ionic strength?
Multiply each ion's concentration by the square of its charge, add the products and halve the sum: I = ½Σcᵢzᵢ².
What is the ionic strength of 0.1 M CaCl₂?
Ca²⁺ 0.1 M (z = 2) and Cl⁻ 0.2 M (z = 1): I = ½(0.1 × 4 + 0.2 × 1) = 0.3 M.
What is the ionic strength of 0.1 M ZnCl₂?
Same pattern as CaCl₂: 0.1 M Zn²⁺ and 0.2 M Cl⁻ give I = 0.3 M – three times the concentration of the salt.
Is ionic strength equal to concentration for NaCl?
Yes, for any 1:1 salt of singly charged ions I equals the salt concentration. For 1:2 salts it is 3×, for 2:2 salts 4× and for 1:3 salts 6×.
What is the ionic strength of seawater?
About 0.7 mol/kg, dominated by Na⁺ and Cl⁻ with significant Mg²⁺ and SO₄²⁻.
What unit does ionic strength have?
The same as the concentrations you enter – mol/L if you use molarity, mol/kg if you use molality.
Does a weak acid contribute to ionic strength?
Only its dissociated ions do. For acetic acid at 0.1 M, only about 1.3% is ionised, so it adds roughly 0.0013 M.
Up to what ionic strength is the Davies equation useful?
Up to about 0.5 M; beyond that specific-ion models (Pitzer, SIT) are needed, so the calculator hides the coefficients.
What formula does the Ionic Strength Calculator use?
I = ½ · Σ cᵢ · zᵢ² · Davies: log₁₀γ = −0.509·z²·(√I/(1 + √I) − 0.3·I) (water, 25 °C) · Debye length κ⁻¹ ≈ 0.304 nm / √I.