Which of the following is soluble in water?

AgF

The correct answer is option 4. \(AgF\).

Let us delve into the solubility of each compound in water:

1. AgCl (Silver Chloride):

Silver chloride is sparingly soluble in water. While a small amount of silver chloride will dissolve in water to form a solution, it is considered insoluble for practical purposes. This limited solubility arises from the strong electrostatic attraction between the silver ions \((Ag^+)\) and chloride ions \((Cl^-)\) in the solid state, which makes it difficult for water molecules to separate and solvate these ions.

2. AgBr (Silver Bromide):

Similar to silver chloride, silver bromide is sparingly soluble in water. It exhibits slightly higher solubility than silver chloride but is still considered practically insoluble. The solubility of silver bromide is influenced by the strength of the electrostatic interactions between the silver ions \((Ag^+)\) and bromide ions \((Br^-)\) in the solid crystal lattice.

3. AgI (Silver Iodide):

Silver iodide is also sparingly soluble in water. It has slightly higher solubility compared to silver chloride and silver bromide but is still considered insoluble for practical purposes. The solubility of silver iodide is influenced by the weaker electrostatic interactions between the silver ions \((Ag^+)\) and iodide ions \((I^-)\) in the solid state, compared to silver chloride and silver bromide.

4. AgF (Silver Fluoride):

Silver fluoride is soluble in water. Unlike silver chloride, silver bromide, and silver iodide, silver fluoride exhibits significant solubility in water. This solubility arises from the strong hydrogen bonding interactions between fluoride ions \((F^-)\) and water molecules. Fluoride ions have a high charge density and strong hydrogen bonding ability, allowing them to form stable complexes with water molecules and remain in solution.

In summary, among the given options, only silver fluoride \((AgF)\) is soluble in water due to the strong hydrogen bonding interactions between fluoride ions and water molecules. Silver chloride \((AgCl)\), silver bromide \((AgBr)\), and silver iodide \((AgI)\) are sparingly soluble or practically insoluble in water due to the strong electrostatic interactions between silver ions and halide ions in their crystal lattices.