Predict whether each of the following compounds is soluble in water: (a) \(\mathrm{AgI},\) (b) \(\mathrm{Na}_{2} \mathrm{CO}_{3},\) (c) \(\mathrm{BaCl}_{2},\) (d) \(\mathrm{Al}(\mathrm{OH})_{3}\), (e) \(\mathrm{Zn}\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{2}\).

Here are some key solubility rules that will help us in determining the solubility of the compounds: 1. Most alkali metal compounds, i.e., those from Group 1 such as sodium (Na) and potassium (K), are soluble in water. 2. Most nitrates (NO3-), bicarbonates (HCO3-), and chlorides (Cl-), bromides (Br-), and iodides (I-) salts are soluble, except for silver (Ag), lead (Pb), and mercury (Hg) compounds. 3. Sulfates (SO4 2-) are usually soluble, except for barium (Ba), calcium (Ca), and strontium (Sr) sulfates. 4. Most carbonates (CO3 2-), phosphates (PO4 3-), and chromates (CrO4 2-) are insoluble, except when combined with alkali metals. 5. Most hydroxides (OH-) and sulfides (S2-) are insoluble, except when combined with alkali metals or ammonium (NH4+). 6. Some carboxylates (such as acetates CH3COO-) are soluble like sodium and potassium salts. Now, let's use these rules to determine the solubility of the given compounds.

Using rule 2, most iodide salts are soluble, except for silver (Ag) compounds. So, AgI is insoluble in water.

According to rule 4, most carbonates are insoluble, except when combined with alkali metals. Since this compound is formed with sodium (Na), an alkali metal, Na2CO3 is soluble in water.

Considering rule 2, most chloride salts are soluble. Thus, BaCl2 is soluble in water.

Using rule 5, most hydroxides are insoluble, except when combined with alkali metals or ammonium. Since this compound has aluminum (not an alkali metal), Al(OH)3 is insoluble in water.

According to rule 6, some carboxylates, such as acetates, are soluble, specifically when they are combined with sodium and potassium salts. Zinc acetate (Zn(CH3COO)2) is soluble in water because acetates are generally soluble in water. In conclusion,: a) AgI - Insoluble b) Na2CO3 - Soluble c) BaCl2 - Soluble d) Al(OH)3 - Insoluble e) Zn(CH3COO)2 - Soluble