Why ionic strength is the number that matters

Molar concentration tells you how much salt is in your beaker. Ionic strength tells you how much electrostatic chaos those dissolved ions create — and that’s what actually controls activity coefficients, solubility products in real solutions, the speed of ionic reactions, and protein stability in a buffer. Two solutions can have identical molar concentration of dissolved salt and behave completely differently if one of them carries multiply-charged ions.

The defining formula:

I = ½ · Σ (cᵢ · zᵢ²)

cᵢ is the molar concentration of each ion, zᵢ is its charge number. The square is the part that bites — a 2+ ion contributes four times what a 1+ ion does at the same concentration. A 3+ ion contributes nine times.

The four-step workflow

Step 1 — write every dissociation explicitly

Don’t trust your memory of the salt’s formula. Write the dissociation reaction.

NaCl → Na⁺(aq) + Cl⁻(aq) — gives 0.10 M Na⁺ and 0.10 M Cl⁻ from 0.10 M NaCl CaCl₂ → Ca²⁺(aq) + 2 Cl⁻(aq) — gives 0.10 M Ca²⁺ and 0.20 M Cl⁻ from 0.10 M CaCl₂

That second case is where students lose half the chloride contribution by typing 0.10 instead of 0.20.

Step 2 — table every ion with c and z

Ion	cᵢ (M)	zᵢ	cᵢ·zᵢ²
Na⁺	0.10	+1	0.10
Cl⁻	0.10	−1	0.10

Step 3 — sum the cᵢ·zᵢ² column

Σ = 0.10 + 0.10 = 0.20

Step 4 — multiply by ½

I = ½ × 0.20 = 0.10 M

So 1:1 electrolytes have I = c. That shortcut is worth memorizing alongside the others below.

Worked example — mixed electrolytes

Solution: 0.050 M Na₂SO₄ + 0.030 M NaCl. Find I.

Dissociation:

Na₂SO₄ → 2 Na⁺ + SO₄²⁻
NaCl → Na⁺ + Cl⁻

Pool the ion concentrations across both salts:

[Na⁺] = 2(0.050) + 0.030 = 0.130 M
[SO₄²⁻] = 0.050 M
[Cl⁻] = 0.030 M

Sum of cᵢ·zᵢ²:

Na⁺: 0.130 × 1² = 0.130
SO₄²⁻: 0.050 × 2² = 0.200
Cl⁻: 0.030 × 1² = 0.030
Σ = 0.360

I = ½ × 0.360 = 0.180 M

Look at how the sulfate ion — present at only 0.050 M — contributes more (0.200) than all the singly-charged ions combined. That z² weighting is the whole point of using ionic strength rather than total ion concentration.

Worked example — MgCl₂ (the 2:1 case)

0.020 M MgCl₂.

[Mg²⁺] = 0.020 M, [Cl⁻] = 0.040 M Σ = 0.020(2²) + 0.040(1²) = 0.080 + 0.040 = 0.120 I = ½ × 0.120 = 0.060 M

For a 2:1 salt like MgCl₂ or CaCl₂, I = 3c. For a 1:1 salt (NaCl, KNO₃), I = c. For a 2:2 salt (MgSO₄), I = 4c. For a 3:1 salt (AlCl₃, K₃PO₄), I = 6c. Memorize these factors and you can sanity-check any calculation in five seconds.

Where ionic strength shows up

The Debye-Hückel equation uses √I to estimate activity coefficients:

log γ = −A · z² · √I / (1 + B · a · √I)

with A = 0.509 at 25 °C in water. Activity coefficients correct equilibrium expressions, solubility calculations, electrochemistry, and pH measurements for the non-ideality that emerges when ions interact at non-trivial concentrations. Pure dilute Debye-Hückel works up to about I = 0.01 M; the extended version stretches to roughly 0.1 M; above that you need empirical models like Pitzer.

In practice this is why a pH 7 phosphate buffer at low ionic strength reads slightly differently from the same buffer at physiological I = 0.15 M, and why ion-selective electrodes need to be calibrated at the ionic strength of the samples they’ll measure.

Traps that catch students

Ignoring stoichiometry. A mole of CaCl₂ produces two moles of Cl⁻. Write the dissociation before the table — every time.

Forgetting to square z. The single most expensive arithmetic error in this calculation. A 2+ ion contributes 4× per mole of concentration, not 2×.

Double-counting or under-counting shared ions. When Na⁺ comes from both NaCl and Na₂SO₄, you add the contributions before squaring or multiplying. The total [Na⁺] enters once, raised to z² once.

Confusing I with total ion concentration. Total ion concentration is just Σcᵢ. Ionic strength weights every ion by the square of its charge, then halves the sum. The two numbers can be very different in solutions with multivalent ions.

Practice

Check with the Solution Concentration Calculator:

I for 0.15 M KNO₃.
I for 0.10 M Al₂(SO₄)₃.
I for a mixture of 0.020 M CaCl₂ and 0.050 M NaCl.
I for 0.25 M K₃PO₄.
What concentration of NaCl matches the ionic strength of 0.050 M MgSO₄?

How to Calculate Ionic Strength