Final answer:
Silver nitrate is the most soluble in a polar solvent among the listed compounds because all nitrates are soluble in water, while silver chloride and silver carbonate are generally insoluble.
Step-by-step explanation:
The solubility of a compound in a polar solvent such as water depends on the general solubility rules. Among the compounds listed, silver nitrate (AgNO3), silver chloride (AgCl), and silver carbonate (Ag2CO3), the one that is most soluble in a polar solvent is silver nitrate.
This is because all nitrates are soluble in water, making silver nitrate highly soluble. Silver chloride, on the other hand, is generally considered insoluble in water due to the low solubility product constant (Ksp), which indicates a very small amount of the substance can dissolve. Silver carbonate also falls under the general rule that most carbonates are insoluble in water, with the exception of carbonates of the ammonium ion and the alkali metals.