You are describing the ions barium (Ba²⁺) and nitride (N³⁻). To form a neutral compound, we need to find the lowest common multiple of the charges (2 and 3), which is 6.

Here's how to get the chemical formula:

* Barium: To get a +6 charge, we need 3 Ba²⁺ ions (3 x +2 = +6).

* Nitride: To get a -6 charge, we need 2 N³⁻ ions (2 x -3 = -6).

Therefore, the chemical formula for the compound formed by Ba²⁺ and N³⁻ is Ba₃N₂.

The balanced chemical equation for the reaction is:

3 Ba + N₂ → Ba₃N₂

This equation shows that 3 barium atoms react with 1 nitrogen molecule (N₂) to form 1 molecule of barium nitride (Ba₃N₂).