Identify the condensed formula: H4P2O7 corresponds to which form of phosphoric acid?

Introduction / Context:
Phosphoric acids can polymerize or condense, producing a family that includes ortho-, pyro- (di-), and meta- acids. Recognizing the empirical formula helps in identifying the correct member, which is commonly referenced in phosphate processing and fertilizer chemistry.

Given Data / Assumptions:

• The formula provided is H4P2O7.
• We compare it to typical forms: H3PO4 (ortho), (HPO3)n (meta), and H4P2O7 (pyro).
• No structural drawing tools are used; identification is by formula pattern.

Concept / Approach:
Pyrophosphoric (diphosphoric) acid results from the condensation of two molecules of orthophosphoric acid with loss of one molecule of water: 2 H3PO4 → H4P2O7 + H2O. Thus, the characteristic formula H4P2O7 uniquely points to the “pyro” species among common phosphoric acids.

Step-by-Step Solution:
Recall: orthophosphoric acid is H3PO4.Condense two orthos: 2 H3PO4 → H4P2O7 + H2O.Therefore, H4P2O7 is pyrophosphoric acid.

Verification / Alternative check:
Textbook tables list H3PO4 (ortho), H4P2O7 (pyro), and (HPO3)n (meta). The given formula matches the pyro entry exactly.

Why Other Options Are Wrong:
Orthophosphoric acid would be H3PO4; metaphosphoric acid is typically represented as a linear or cyclic polymer, (HPO3)n; “perphosphoric acid” is not a standard acid form used in fertilizer practice.

Common Pitfalls:
Confusing “pyro” with “meta”—remember that meta has the repeating HPO3 unit, whereas pyro has H4P2O7 from dehydrating two orthos.

Final Answer:
Pyrophosphoric acid