Final answer:
Among MgO, CaO, and BaO, BaO will be the most soluble in water because it has the lowest lattice energy due to the increase in ionic size down the Group 2 metals from Mg to Ba.
Step-by-step explanation:
The solubility of ionic compounds in water often depends on the attraction between the ions and the energy required to separate them, which is known as lattice energy. A high lattice energy indicates a strong attraction between the ions and typically translates to lower solubility in water. Comparing MgO, CaO, and BaO, we can infer that the solubility will be highest for the compound with the lowest lattice energy.
Considering the trend on the periodic table, as you move down the Group 2 metals from Mg to Ba, the ionic size increases, which leads to a decrease in lattice energy. Thus, among MgO, CaO, and BaO, BaO is expected to have the lowest lattice energy and consequently, the highest solubility in water. Therefore, BaO will be the most soluble in water out of the three options given.