EDTA Titrations and Water Hardness

If you live in an area with hard water, you’ll know the signs: a white crust inside the kettle, soap that won’t lather, and cloudy marks on glasses. That hardness is caused by dissolved calcium and magnesium ions, and water companies measure it precisely with a technique called complexometric titration, using a remarkable molecule called EDTA.

What makes water hard

Water becomes hard when it flows through rocks such as limestone (calcium carbonate) and dolomite (calcium magnesium carbonate), picking up Ca²⁺ and Mg²⁺ ions.

• Temporary hardness is caused by dissolved calcium and magnesium hydrogencarbonates. Boiling removes it by precipitating calcium carbonate: Ca(HCO₃)₂ → CaCO₃ + H₂O + CO₂. That’s the limescale in kettles.
• Permanent hardness is caused by calcium and magnesium sulfates and chlorides. Boiling doesn’t remove it.

Hard water causes scale in pipes, boilers and appliances, reducing efficiency, and it forms scum with soap. (It’s not harmful to drink; the minerals can even contribute to dietary calcium.)

EDTA: the claw molecule

EDTA is ethylenediaminetetraacetic acid. Its fully deprotonated form, EDTA⁴⁻ (often written Y⁴⁻), has six atoms that can each donate a pair of electrons to a metal ion: two nitrogen atoms and four oxygen atoms from carboxylate groups.

It wraps around a metal ion like a claw, forming a very stable complex in a 1 : 1 ratio, whatever the metal ion’s charge:

Ca²⁺ + Y⁴⁻ → [CaY]²⁻ Mg²⁺ + Y⁴⁻ → [MgY]²⁻

A ligand that binds through several atoms like this is called a chelating agent (from the Greek chele, a crab’s claw), and EDTA is a hexadentate ligand. The complexes are especially stable because of the chelate effect: replacing six separate water molecules around the metal with one EDTA molecule increases the number of free particles in solution, which increases entropy and favours complex formation. See Lewis acids and bases: the metal ion is the Lewis acid, EDTA the Lewis base.

The 1 : 1 ratio makes calculations simple: moles of EDTA = moles of metal ions.

In practice, the titrant is usually the more soluble disodium salt, Na₂H₂Y·2H₂O.

Why a pH 10 buffer?

EDTA is a weak acid with four acidic protons. At low pH, it’s mostly protonated and binds metal ions poorly. As pH rises, more of it is in the fully deprotonated Y⁴⁻ form, which binds strongly.

For calcium and magnesium, the titration is carried out at about pH 10, using an ammonia–ammonium chloride buffer. At this pH:

• EDTA binds Ca²⁺ and Mg²⁺ strongly enough for a sharp end point
• magnesium hydroxide doesn’t yet precipitate
• the indicator gives a clear colour change

See buffer capacity for why a buffer is needed: the reaction releases H⁺ ions from H₂Y²⁻, which would otherwise lower the pH.

The indicator: Eriochrome Black T

Eriochrome Black T (EBT, also called Solochrome Black) is itself a weaker complexing agent that changes colour when it binds metal ions:

• Free indicator at pH 10: blue
• Indicator bound to Mg²⁺ (or Ca²⁺): wine red

How the end point works:

1. At the start, a little indicator binds to metal ions, making the solution wine red.
2. As EDTA is added, it binds the free Ca²⁺ and Mg²⁺ first.
3. Near the end point, EDTA, which binds metals much more strongly than the indicator does, pulls the last metal ions away from the indicator.
4. The indicator is released as its free form, and the solution turns blue.

The end point is the change from wine red through purple to pure blue, with no trace of red.

EBT gives a sharper end point with magnesium than with calcium. If a sample contains very little magnesium, a small, known amount of Mg–EDTA complex is often added to sharpen the change.

Method: measuring total hardness

Equipment: burette, 50.00 cm³ pipette, conical flasks, measuring cylinder, 0.0100 mol/dm³ EDTA solution, pH 10 ammonia buffer, Eriochrome Black T indicator.

1. Pipette 50.00 cm³ of the water sample into a conical flask.
2. Add about 2 cm³ of pH 10 buffer (in a fume cupboard, because of the ammonia).
3. Add a small amount of Eriochrome Black T until the solution is a clear wine red.
4. Titrate with 0.0100 mol/dm³ EDTA from the burette, swirling, until the colour changes from wine red to pure blue.
5. Repeat to obtain concordant titres.

Worked example 1: total hardness

50.00 cm³ of tap water needs 12.40 cm³ of 0.0100 mol/dm³ EDTA. Calculate the total hardness as mg/dm³ of CaCO₃.

Hardness is conventionally reported as if all the calcium and magnesium were calcium carbonate.

• n(EDTA) = 0.0100 × 0.01240 = 1.240 × 10⁻⁴ mol
• n(Ca²⁺ + Mg²⁺) = 1.240 × 10⁻⁴ mol (1 : 1)
• As CaCO₃: mass = 1.240 × 10⁻⁴ × 100.09 = 0.01241 g in 50.00 cm³
• Per dm³: 0.01241 × (1000 ÷ 50.00) = 0.2482 g/dm³ = 248 mg/dm³ as CaCO₃

How hard is that?

One widely used classification:

mg/dm³ as CaCO₃	Description
0–60	soft
61–120	moderately hard
121–180	hard
above 180	very hard

So 248 mg/dm³ is very hard water.

Worked example 2: calcium and magnesium separately

To measure calcium alone, the titration is done at pH 12–13 (using sodium hydroxide). At this pH, magnesium precipitates as Mg(OH)₂ and doesn’t react with EDTA. A different indicator (such as murexide or calconcarboxylic acid) is used.

A second 50.00 cm³ sample at pH 12 needs 8.60 cm³ of 0.0100 mol/dm³ EDTA.

• n(Ca²⁺) = 0.0100 × 0.00860 = 8.60 × 10⁻⁵ mol
• n(Mg²⁺) = total − Ca = 1.240 × 10⁻⁴ − 8.60 × 10⁻⁵ = 3.80 × 10⁻⁵ mol

Concentrations in the water:

• [Ca²⁺] = 8.60 × 10⁻⁵ ÷ 0.05000 = 1.72 × 10⁻³ mol/dm³ = 68.9 mg/dm³ of Ca²⁺ (× 40.08 × 1000)
• [Mg²⁺] = 3.80 × 10⁻⁵ ÷ 0.05000 = 7.60 × 10⁻⁴ mol/dm³ = 18.5 mg/dm³ of Mg²⁺ (× 24.31 × 1000)

Temporary and permanent hardness

1. Titrate an unboiled sample → total hardness.
2. Boil another sample for about 15 minutes, cool, filter off the precipitated CaCO₃, make up to the original volume with distilled water, and titrate → permanent hardness.
3. Temporary hardness = total − permanent.

Other uses of EDTA

EDTA titrations measure many metal ions, including zinc, nickel, copper, lead and aluminium, with appropriate pH and indicators. Beyond titrations, EDTA’s metal-binding power is widely used:

• Medicine: chelation therapy for lead poisoning (as calcium disodium EDTA).
• Food: as a preservative (E385), binding metal ions that would catalyse spoilage and rancidity.
• Cosmetics and detergents: preventing metal ions from interfering with soaps and fragrances.
• Blood samples: EDTA tubes stop blood clotting by binding calcium.
• Industry: preventing scale in boilers and cleaning metal surfaces.

Key takeaways

• Water hardness is caused by dissolved Ca²⁺ and Mg²⁺; it’s measured by titration with EDTA.
• EDTA is a hexadentate chelating ligand that forms very stable 1 : 1 complexes with metal ions.
• A pH 10 ammonia buffer and Eriochrome Black T (wine red to blue) are used for total hardness.
• Hardness is reported as mg/dm³ of CaCO₃; above 180 is very hard.
• Titrating at pH 12, where Mg(OH)₂ precipitates, gives calcium alone; magnesium is found by difference.