Knowledge of basic solubility rules is enough to answer this question. Nitrates and salts of alkali metals are always soluble, as are salts of ammonium. Acetates are also always soluble. Acid-base reactions, such as with hydrofluoric acid, produce a soluble salt and water. Sulfates are commonly soluble, with certain exceptions (mostly alkaline earth metals).

The only reaction that produces an insoluble product is that between silver nitrate and potassium chloride. Silver chloride is a common precipitate obtained in double replacement reactions.

A colloid is a suspension of particles larger than molecules, but too small to be individually distinguished by the naked eye. Only colloids disperse light by the Tyndall effect. Milk is an example of a colloid.

Knowing some of the general solubility trends will greatly facilitate your understanding of solubility in chemistry. Here are a couple guidelines you can follow in order to predict which compounds are soluble.

1. Compounds containing alkali metals, ammonium cations, or nitrate anions are soluble.

2. Compounds containing halogen anions are soluble. Key exceptions are halogens attached to silver, mercury, and lead.

3. Sulfates are soluble, except when attached to heavier alkaline metals, like barium (thus the correct answer).

4. Carbonates, phosphates, and hydroxides are generally insoluble; however, if they are attached to one of the ions mentioned in one of the above points, they are soluble.

These solubility rules should be known for the MCAT and are presented as a hierarchy.

1. All group 1 salts and ammonium salts are soluble

2. All nitrates, perchlorates, and acetates are soluble

3. All mercury, lead, and silver salts are NOT soluble

Understanding these solubility rules as a hierarchy, we can understand why Mg(NO₃)₂ and AgNO₃ are soluble and why AgCl is not soluble. 

Molecules are most soluble in solvents that possess similar properties and intermolecular forces to the solute.

Pentane is a non-polar compound, which interacts predominately through london dispersion forces. Ammonia, silver chloride, and phosphorus trichloride are all polar molecules. Ammonia has a lone pair on the nitrogen; silver is an ionic compound; phosphorus trichloride has lone pairs on both the phosphorus and chlorine atoms.

In contrast, carbon dioxide has lone pairs only on the oxygen atoms and has a linear geometry. This creates a line of symmetry in the molecule such that the net polarities of the carbon-oxygen bonds cancel each other. Even though carbon dioxide has polar bonds, it is not a polar molecule and would likely dissolve in pentane.

Compounds that contain sulfate groups (  )are soluble in water, unless they are bound to mercury, strontium, lead, calcium, or barium. Hence, barium sulfate, , is insoluble in water.

Compounds that contain nitrates ( ), ammonium (  ), and alkali metals are generally soluble in water. Compounds containing halogens are soluble in water unless they are bound to mercury, lead, or silver.

When  is dissolved in water, it forms  and . Both of these are basic compounds.

Each of the other answer options will result in at least one acidic compound when dissolved in solution.

Since water is polar, it dissolves substances that have electrostatic charge due to electron arrangement. All of the answer choices describe molecules that would have positive and negative components except those with evenly dispersed electrons. This describes a nonpolar molecule, which would not dissolve in water.