Order of Acidic strength: Phosphorus oxoacids [duplicate]








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[How is the trend of acidity in the sequence: phosphinic, phosphonic, phosphoric acid explained?](/questions/47799/how-is-the-trend-of-acidity-in-the-sequence-phosphinic-phosphonic-phosphoric)

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I was asked to compare the acidic strength of the following phosphorus oxoacids,



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I thought the order (of strength) would be $\ce{H3PO4 > H3PO3 > H3PO2}$, because they have three, two and one ionizable $\ce{O-H}$ bonds (that furnish protons / $\ce{H^+}$ ions).


However, looking up the $\pu{pK\_a}$ values on the respective Wikipedia pages of each of those acids, suggests the exact *opposite* order of acidic strength:
$\ce{H3PO2 > H3PO3 > H3PO4}$. Apparently the acid with *one* $\ce{O-H}$ bond is a far stronger than the acid with *three* $\ce{O-H}$ bonds!


This is horribly counter-intuitive :-(


So, **why** is the correct order of acidic strength $\ce{H3PO2 > H3PO3 > H3PO4}$, and not the other way around as I believed? What was wrong with my analysisi ( acidity in oxoacids $\propto$ number of $\ce{O-H}$ bonds)?




Acidic strength of the acids is determined on the relative tendency to donate one proton. 


The source where you have seen then $\mathrm{p}K\_\mathrm{a}$ value has considered the tendency of *first* deprotonation of the acids ($\ce{H3PO2}$ deprotonates once, $\ce{H3PO3}$ can deprotonate twice and $\ce{H3PO4}$ can deprotonate thrice).


The double bonded oxygen has negative inductive effect (*-I*). And this electron withdrawing effect is experienced by one $\ce{H}$ of the one $\ce{-OH}$ group in $\ce{H3PO2}$. Hence it has greatest acidic strength.


Similarly, the *-I* effect of $\ce{O}$ is experienced by two $\ce{H}$ of the two $\ce{-OH}$ groups in $\ce{H3PO3}$, hence electron withdrawing effect is reduced because it is getting distributed between two groups. Hence, it has lesser acidic strength. Similarly, in $\ce{H3PO4}$, it is distributed between 3 groups and so the acidic strength is least. 


Thus the acidic strength, is:
$$\ce{H3PO2 > H3PO3 > H3PO4}$$
(I hope it's clear.) 


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