Coagulation and Hardy-Schulze rule — how electrolytes precipitate colloids

Question

What is coagulation of colloids? State the Hardy-Schulze rule. Arrange the following in increasing order of their coagulating power for a negatively charged colloid: NaCl, BaCl $_2$ , AlCl $_3$ .

(JEE Main 2022, similar pattern)

Solution — Step by Step

Coagulation (or flocculation) is the process of settling down of colloidal particles by the addition of an electrolyte. The electrolyte neutralises the charge on the colloidal particles, causing them to aggregate and precipitate.

The minimum amount of electrolyte required to cause coagulation is called the coagulation value or flocculation value.

The Hardy-Schulze rule states:

The coagulating power of an ion is directly proportional to the valence (charge) of the coagulating ion. The ion that causes coagulation is the one with the opposite charge to the colloidal particles.

Higher the valency of the coagulating ion → lower the coagulation value → greater the coagulating power.

The colloid is negatively charged, so the coagulating ion is the cation (positive ion).

Electrolyte	Coagulating ion	Valency
NaCl	Na $^+$	+1
BaCl $_2$	Ba $^{2+}$	+2
AlCl $_3$	Al $^{3+}$	+3

By Hardy-Schulze rule: higher valency → greater coagulating power.

Increasing order of coagulating power:

\mathbf{NaCl < BaCl_2 < AlCl_3}

Al $^{3+}$ is the most effective coagulant — you need the least amount of AlCl $_3$ .

Why This Works

Colloidal particles carry electric charge, which creates a repulsive barrier preventing them from clumping. When we add an electrolyte, the oppositely charged ions cluster around the colloidal particles, neutralising the charge. Once the charge is neutralised, Van der Waals forces take over and particles aggregate.

A trivalent ion ( $\text{Al}^{3+}$ ) neutralises the charge much more effectively than a monovalent ion ( $\text{Na}^+$ ) because it carries three times the charge, compressing the electrical double layer more efficiently.

Alternative Method — Using Coagulation Values

Experimentally, coagulation values (in mmol/L) confirm the Hardy-Schulze rule. For a typical negatively charged sol like As $_2$ S $_3$ :

NaCl: ~50 mmol/L
BaCl $_2$ : ~0.7 mmol/L
AlCl $_3$ : ~0.09 mmol/L

The ratio is roughly $1 : 1/64 : 1/500$ , approximately following $1/z^6$ (Schulze’s empirical observation).

JEE loves asking: “Which is the most effective coagulant for [positively/negatively] charged sol?” Identify the charge, then pick the ion with the highest opposite charge. For positive sol (e.g., Fe(OH) $_3$ ), use the anion: $[\text{Fe(CN)}_6]^{4-} > \text{PO}_4^{3-} > \text{SO}_4^{2-} > \text{Cl}^-$ .

Common Mistake

Students pick the wrong ion. For a negatively charged colloid, the cation (positive ion) causes coagulation — not the anion. For a positively charged colloid, it is the anion. Always first identify the charge on the colloid, then look at the counter-ion in the electrolyte.

Question

Solution — Step by Step

Why This Works

Alternative Method — Using Coagulation Values

Common Mistake

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