Order of Acidic strength: Phosphorus oxoacids I was asked to compare the acidic strength of the following phosphorus oxoacids,


  


I thought the order (of strength) would be $\ce{H3PO4 &gt; H3PO3 &gt; H3PO2}$, 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:
$\ce{H3PO2 &gt; H3PO3 &gt; H3PO4}$. 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  $\ce{H3PO2 &gt; H3PO3 &gt; H3PO4}$, 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:
$$\ce{H3PO2 &gt; H3PO3 &gt; H3PO4}$$
(I hope it's clear.)