Concept:
According to the Hardy–Schulze rule:
The greater the valency of the ion responsible for neutralizing the charge of a colloidal particle, the greater its coagulating power.
For a negatively charged sol, the coagulating ions are positive ions (cations).
Step 1: Identify the nature of the sol.
The sol \(As_2S_3\) is a negative sol.
Thus, cations will cause coagulation.
Step 2: Compare the valencies of the cations.
\[
NaCl \rightarrow Na^+ \quad (\text{valency } 1)
\]
\[
MgCl_2 \rightarrow Mg^{2+} \quad (\text{valency } 2)
\]
\[
AlCl_3 \rightarrow Al^{3+} \quad (\text{valency } 3)
\]
\[
KCl \rightarrow K^+ \quad (\text{valency } 1)
\]
Step 3: Apply Hardy–Schulze rule.
Since the coagulating power increases with valency:
\[
Al^{3+} > Mg^{2+} > Na^+ = K^+
\]
Step 4: Identify the most effective electrolyte.
Thus the most effective coagulating electrolyte is:
\[
AlCl_3
\]