The balanced equation for the reaction between zirconium (Zr) and nitrogen (N₂) to form zirconium nitride (Zr₃N₄) is:

3 Zr + 2 N₂ → Zr₃N₄

Here's how we balance it:

* Zr: There are 3 Zr atoms on the left and 3 Zr atoms on the right.

* N: There are 4 N atoms on the right (2 x 2 = 4) and 4 N atoms on the left.

This equation represents the reaction of zirconium metal with nitrogen gas to produce zirconium nitride, a ceramic material with high melting point and hardness.