The most effective coagulating agent among the options for ${\mathrm{Sb}}_2{\mathrm{S}}_3$ sol is

${\mathrm{Sb}}_2{\mathrm{S}}_3$ sol is negatively charged sol. 

Hardy schulze rule states that greater is the valency of of oppositely charged ion of the electrolyte being added, Faster is coagulation. The principle is electrostatic forces of attraction. Greater the valency of flocculating ion, greater is the coagulation power.

Coagulation power:

${\mathrm{Al}}^{3+}>{\mathrm{Ca}}^{2+}>{\mathrm{Na}}^{+}>{\mathrm{NH}}_4^{+}$

So, ${\mathrm{Al}}_2{\left({\mathrm{SO}}_4\right)}_3$ is the most effective coagulating agent.