Step 1: Understanding the Question:
We need to identify which of the given preparation methods results in a colloidal solution (sol) where the colloidal particles have a negative charge.
Step 2: Key Formula or Approach:
The charge on colloidal particles is due to the preferential adsorption of ions from the dispersion medium that are common to the crystal lattice of the colloidal particle. When a colloid is formed by a chemical reaction, the charge is determined by which reactant is in excess.
Step 3: Detailed Explanation:
The formation of silver iodide (AgI) sol occurs from the reaction: \( \text{AgNO}_3 + \text{KI} \rightarrow \text{AgI(s)} + \text{KNO}_3 \).
(A) KI added to AgNO\(_3\) solution: In this case, AgNO\(_3\) is the dispersion medium and is in excess. The AgI particles will be surrounded by excess Ag\(^+\) and NO\(_3^-\) ions. The Ag\(^+\) ion is common to the AgI lattice, so it will be preferentially adsorbed on the surface of the AgI particles. This results in a positively charged sol: [AgI]Ag\(^+\).
(B) AgNO\(_3\) added to KI solution: Here, KI is the dispersion medium and is in excess. The AgI particles will be surrounded by excess K\(^+\) and I\(^-\) ions. The I\(^-\) ion is common to the AgI lattice, so it will be preferentially adsorbed. This results in a negatively charged sol: [AgI]I\(^-\).
(C) FeCl\(_3\) added to hot water: This process involves the hydrolysis of FeCl\(_3\) to form a hydrated ferric oxide sol, Fe\(_2\)O\(_3\).xH\(_2\)O. This sol is positively charged due to the adsorption of Fe\(^{3+}\) ions from the solution: [Fe\(_2\)O\(_3\).xH\(_2\)O]Fe\(^{3+}\).
(D) Al\(_2\)O\(_3\).xH\(_2\)O in water: Hydrated alumina sol is also a positively charged sol.
Step 4: Final Answer:
The method that produces a negatively charged sol is adding silver nitrate solution to a potassium iodide solution. This corresponds to option (B).