Most Effective Coagulating Agent for Antimony Trisulfide Sol

To determine the most effective coagulating agent, we apply the Hardy-Schulze rule:

1. Charge on the Colloidal Sol:
   $\text{Sb}_2\text{S}_3$ (antimony trisulfide) is a metal sulfide sol. Metal sulfide sols are negatively charged colloidal sols due to the preferential adsorption of sulfide ions ($\text{S}^{2-}$).

2. Flocculating (Coagulating) Ion:
   According to the Hardy-Schulze rule:

   • Coagulation of a negatively charged sol is brought about by positively charged ions (cations).
   • The coagulating power of an electrolyte increases rapidly with an increase in the valency of the effective ion (flocculating ion).

3. Comparison of Cation Valencies:
   The cations provided by each electrolyte are:

   • From $\text{Na}_2\text{SO}_4$: $\text{Na}^+$ (charge $= +1$)
   • From $\text{CaCl}_2$: $\text{Ca}^{2+}$ (charge $= +2$)
   • From $\text{Al}_2(\text{SO}_4)_3$: $\text{Al}^{3+}$ (charge $= +3$)
   • From $\text{NH}_4\text{Cl}$: $\text{NH}_4^+$ (charge $= +1$)

   The valency order of the cations is:
   $\text{Al}^{3+} > \text{Ca}^{2+} > \text{Na}^+ \approx \text{NH}_4^+$

Since $\text{Al}^{3+}$ has the highest positive charge ($+3$), it has the maximum coagulating power (or the lowest flocculation/coagulation value) for the negatively charged $\text{Sb}_2\text{S}_3$ sol.

Therefore, $\text{Al}_2(\text{SO}_4)_3$ is the most effective coagulating agent.

Correct Option: C