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As given in pKa of H4P2O7 and H3PO4. The acidity of pyrophosphoric acid is clearly stronger than phosphoric acid. The two acid structures is given below.

Thought: Consider the pyrophosphoric acid dissociates first proton on the left, the stronger acidity might be attributed to the other phosphate group on the right. In other words, I think that the induction effect of the other P=O group results to O-H bond more polarized compared to H3PO4

Is it true in this case? enter image description here enter image description here

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  • $\begingroup$ Have you checked whether the effect is not simply statistical? One molecule has 4 x OH, the other 3 x OH (correction!) that can dissociate. That alone can explain why one has a higher acidity. To figure out if that is the case, assume you were determining the pKa of a substance but were mistakenly using 4/3 x the concentration that you thought you were. How would this affect the pKa determination? $\endgroup$
    – Buck Thorn ♦
    Commented Dec 26, 2023 at 8:02

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Yes, your thought process is on the right track.

Reason: The enhanced acidity of pyrophosphoric acid (H₄P₂O7) compared to phosphoric acid (H₃PO₄) can be attributed to the presence of the additional phosphate group. The induction effect of the adjacent P=O group in pyrophosphoric acid makes the O-H bond more polarized, making it easier for the molecule to donate a proton, thereby increasing its acidity. This effect is a result of the electron-withdrawing nature of the phosphate group, which strengthens the acidity of the compound.

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There is an additional mesomeric effect, which is closely correlated witb the inductive one.

When phosphoric acid is singly deprotonated, the negative charge is delocalized, and thus stabilized, through pi backdonation from the unprotonated oxygen atoms (shown here with negative formal charges as in a model with no $d$-orbital contribution) to the sigma antibonding orbitals. This is shown in valence-bond form in the top pair of resonance structures below; since sigma antobinding orbitals are involved the hydroxyl group on the bottom is displaced from the covalent bonding. With pyrophosphoric acid, shown in the bottom, a hydroxyl group is replaced by a dihrogenphosphate group, which better accepts the negative charge. This enhances the charge delocalization and further stabilizes the pyrophosphate monoanion.

enter image description here

[Note: my device does not gave good enough drawing software to render these structures, so I had to resort to a screenshot.]

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