 Solution

The product is 1,3,4-Oxadiazole. Protonation or phosphorylation activates one formyl carbonyl of the diacylhydrazine. The oxygen of the other carbonyl attacks intramolecularly, closing a five-membered ring containing the atom sequence O–C–N–N–C. Proton transfers and loss of water produce the conjugated ring; deprotonation restores the neutral aromatic heterocycle.

The overall transformation is ${\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{N}}_2{\mathrm{O}}_2\to {\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{N}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{O}$. Polyphosphoric acid provides carbonyl activation and an acidic medium. P${}_4$O${}_{10}$ acts as a strong dehydrating agent, consuming water and maintaining the condensation-driving environment. Neither nitrogen is expelled, and the oxygen retained in the heterocycle originates from a carbonyl rather than an inserted reagent oxygen.