To determine which compound is most likely to exist based on the periodic table, we can examine the elements involved and their typical bonding behavior.
Barium (Ba) is an alkaline earth metal that typically forms +2 cations. Chlorine (Cl), a nonmetal, commonly forms -1 anions. The combination of Ba as a +2 ion and Cl as -1 ions allows for the formation of BaCl2, where two chloride ions bond with one barium ion to achieve a stable compound. This makes BaCl2 a very stable and commonly occurring compound.
In contrast, potassium (K) is an alkali metal that usually forms +1 cations, while it is unlikely for it to form KCl2 because the one K+ ion would only be able to balance one Cl- ion, leading to the existence of KCl instead.
Aluminum (Al) normally forms +3 cations, and forming AlCl2 would imply that it is bonding with two chloride ions, leading to an unbalanced charge scenario, as three Cl- ions would be necessary to balance a +3 aluminum ion in a stable compound.
Carbon dichloride (CCl2) occurs in some contexts, but free carbon does not commonly form stable