Final answer:
The compound from the options that is insoluble in water is AgCl. It does not dissolve in water because its solubility product constant is very low, and it tends to remain in solid form.
Step-by-step explanation:
The compound that is insoluble in water out of the options given is AgCl (silver chloride). According to solubility rules, salts containing carbonates (CO32-), phosphates (PO43-), and hydroxides (OH-) are generally insoluble in water. However, there are exceptions to these rules, and while compounds of alkali metal cations are typically soluble, AgCl does not fit this category and is known to be insoluble in water.
AgCl forms a precipitate when dissolved in water because its dissolution equilibrium constant (Ksp) is very low, indicating a higher tendency to remain in an insoluble solid form rather than dissociating into its ions.
On the other hand, the other mentioned compounds, such as K2CO3 (potassium carbonate), are soluble in water because they contain alkali metal cations, which are an exception to the rule stating that carbonates are insoluble. Potassium is an alkali metal, which makes its compounds, including carbonates, soluble in water.