The reaction of potassium dichromate (K₂Cr₂O₇) and ammonium phosphate ((NH₄)₃PO₄) is a double displacement reaction that produces potassium phosphate (K₃PO₄), ammonium dichromate ((NH₄)₂Cr₂O₇), and water (H₂O). However, ammonium dichromate is unstable and decomposes into nitrogen gas (N₂), chromium(III) oxide (Cr₂O₃), and water (H₂O).

Here's the breakdown of the reaction:

1. The initial double displacement reaction:

3K₂Cr₂O₇ (aq) + 2(NH₄)₃PO₄ (aq) → 2K₃PO₄ (aq) + 3(NH₄)₂Cr₂O₇ (aq)

2. The decomposition of ammonium dichromate:

3(NH₄)₂Cr₂O₇ (aq) → N₂ (g) + Cr₂O₃ (s) + 4H₂O (l)

3. Combining the reactions and simplifying:

3K₂Cr₂O₇ (aq) + 2(NH₄)₃PO₄ (aq) → 2K₃PO₄ (aq) + N₂ (g) + Cr₂O₃ (s) + 4H₂O (l)

Therefore, the balanced equation for the reaction of potassium dichromate and ammonium phosphate is:

3K₂Cr₂O₇ (aq) + 2(NH₄)₃PO₄ (aq) → 2K₃PO₄ (aq) + N₂ (g) + Cr₂O₃ (s) + 4H₂O (l)