In a colloidal state the particle size of the dispersed phase range between \(10^3\) to \(10^6\) pm and colloidal sol is heterogenous in nature. Based on the nature of interaction between the dispersed phase and dispersion medium colloidal sol are classified as lyophilic and lyophobic. Stability of sol is due to presence of charge on the sol particles and the neutralization of the same is known as coagulation or precipitation.

Based on this answer the following:

The Arseneous sulphide, \(As_2S_3\) sol has negative charge. The maximum precipitate is of:

\(AlCl_3\)

The correct answer is option 3. \(AlCl_3\).

When an arsenious sulfide (\(As_2S_3\)) sol, which contains negatively charged sulfide ions (\(S^{2-}\)), is treated with a cation, a less soluble compound can form if the cation forms a strong bond with the sulfide ions. In this context, aluminum chloride (\(AlCl_3\)) is a suitable candidate.

When aluminum chloride (\(AlCl_3\)) is added to the \(As_2S_3\) sol, the aluminum cations (\(Al^{3+}\)) can react with the sulfide ions to form aluminum sulfide (\(Al_2S_3\)), which is insoluble in water. This precipitation reaction reduces the concentration of sulfide ions in solution, effectively removing them and forming a precipitate.

The other options mentioned, such as \(H_2SO_4\), \(Na_3PO_4\), and \(CaCl_2\), may not form precipitates as effectively with the sulfide ions present in the \(As_2S_3\) sol. Therefore, \(AlCl_3\) is the most likely candidate to cause precipitation in this scenario.