Which of the following electrolytes will have maximum coagulating value for \(AgI/Ag^+\) sol?

\(Na_3PO_4\)

The correct answer is option 2. \(Na_3PO_4\).

In the case of the \(AgI/Ag^+\) sol, which contains negatively charged \(I^-\) ions, the electrolyte that can provide ions to neutralize these charges effectively will have the maximum coagulating value.

Let us reconsider each option:

1. \(Na_2S\) - This electrolyte dissociates into \(2Na^+\) ions and \(S^{2-}\) ions. The \(S^{2-}\) ions can potentially neutralize the \(I^-\) ions in the sol.

2. \(Na_3PO_4\) - This electrolyte dissociates into \(3Na^+\) ions and \(PO_4^{3-}\) ions. The \(PO_4^{3-}\) ions can provide three negative charges to neutralize the \(I^-\) ions in the sol, making it an effective coagulating agent.

3. \(Na_2SO_4\) - This electrolyte dissociates into \(2Na^+\) ions and \(SO_4^{2-}\) ions. The \(SO_4^{2-}\) ions are not likely to effectively neutralize the \(I^-\) ions in the sol.

4. \(NaCl\) - This electrolyte dissociates into \(Na^+\) ions and \(Cl^-\) ions. The \(Cl^-\) ions are not likely to effectively neutralize the \(I^-\) ions in the sol.

Based on this analysis, it appears that \(Na_3PO_4\) (option 2) is indeed the electrolyte that will have the maximum coagulating value for the \(AgI/Ag^+\) sol because it provides ions (\(PO_4^{3-}\)) that can effectively neutralize the negative charges on the sol particles. Therefore, the correct answer is indeed option 2, \(Na_3PO_4\).