Concept:
According to the Hardy–Schulze rule, the coagulating power of an electrolyte depends on the valency of the ion having charge opposite to that of the colloidal particles.
• For a negative sol, the cation is responsible for coagulation.
• Higher the valency of the cation, greater will be its coagulating power.
Step 1: Identify the charge on the sol.
The sol \(As_2S_3\) is a negatively charged sol.
Therefore, the coagulating ion must be a cation.
Step 2: Compare the valency of cations in the given electrolytes.
\[
NaCl \rightarrow Na^+ \quad (\text{valency } = 1)
\]
\[
MgCl_2 \rightarrow Mg^{2+} \quad (\text{valency } = 2)
\]
\[
AlCl_3 \rightarrow Al^{3+} \quad (\text{valency } = 3)
\]
Step 3: Apply Hardy–Schulze rule.
\[
Al^{3+} > Mg^{2+} > Na^+
\]
Thus, \(Al^{3+}\) has the highest coagulating power.
\[
\boxed{AlCl_3}
\]