Which of the following salt solutions would coagulate the colloid solution formed when FeCl$$_3$$ is added to NaOH solution, at the fastest rate?

When FeCl₃ is added to NaOH solution, Fe(OH)₃ colloidal solution is formed. Since NaOH is in excess, the colloid adsorbs OH⁻ ions and becomes negatively charged.

By the Hardy-Schulze rule, for coagulation of a negatively charged colloid, we need cations with the highest charge. Higher the charge of the coagulating ion, greater the coagulating power.

Examining the options:

Option A: AlCl₃ → provides Al³⁺ (charge +3) — highest coagulating power

Option B: Na₂SO₄ → provides Na⁺ (charge +1) — lowest coagulating power

Option C: Ca₃(PO₄)₂ → provides Ca²⁺ (charge +2)

Option D: CaCl₂ → provides Ca²⁺ (charge +2)

Al³⁺ has the highest charge (+3), so it will coagulate the negatively charged colloid at the fastest rate, even considering the concentration differences.

The answer is Option A: 10 mL of 0.2 mol dm⁻³ AlCl₃.