Step-by-step Solution

1. Identify the nature of the colloidal sol: The given sol is Antimony(III) sulfide, Sb₂S₃. Sulfide sols, such as As₂S₃ and Sb₂S₃, are classic examples of negatively charged colloids. This is because during their preparation, sulfide ions (S²⁻) are preferentially adsorbed onto the surface of the colloidal particles, giving them an overall negative charge.

2. Understand the principle of coagulation: Coagulation (or flocculation) is the process of aggregating colloidal particles to form a precipitate. This is achieved by adding an electrolyte. According to the Hardy-Schulze rule, the ion carrying a charge opposite to that of the colloidal particle is responsible for coagulation. This ion is called the flocculating or coagulating ion.

3. Apply the Hardy-Schulze Rule: The rule states that the coagulating power of an ion increases significantly with an increase in its valency (charge). For a negatively charged sol like Sb₂S₃, the cations from the added electrolytes will act as the coagulating ions. The effectiveness of these cations will depend on the magnitude of their positive charge.

4. Analyze the given electrolytes and their cations: Let's dissociate the given electrolytes to identify their cations and their respective valencies:

   • A: Na₂SO₄ dissociates into 2Na⁺ and SO₄²⁻. The coagulating ion is Na⁺, with a valency of +1.
   • B: CaCl₂ dissociates into Ca²⁺ and 2Cl⁻. The coagulating ion is Ca²⁺, with a valency of +2.
   • C: Al₂(SO₄)₃ dissociates into 2Al³⁺ and 3SO₄²⁻. The coagulating ion is Al³⁺, with a valency of +3.
   • D: NH₄Cl dissociates into NH₄⁺ and Cl⁻. The coagulating ion is NH₄⁺, with a valency of +1.

5. Compare the coagulating power: Based on the Hardy-Schulze rule, the coagulating power of the cations will be in the order of their valencies: $\text{Al}^{3+} > \text{Ca}^{2+} > \text{Na}^{+} = \text{NH}_4^{+}$
   Since Al³⁺ has the highest positive charge (+3), it will be the most effective in neutralizing the negative charge of the Sb₂S₃ sol particles and causing coagulation.

6. Conclusion: The electrolyte that provides the most effective coagulating ion (Al³⁺) is Al₂(SO₄)₃. Therefore, Al₂(SO₄)₃ is the most effective coagulating agent for Sb₂S₃ sol among the given options.

Final Answer is option C.