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I want to know the difference b/w phosphonic acid and phosphorous acid.

The formula for both is H3PO3.

Websites give me conflicting answers. Which one of them is dibasic and which one is tribasic?

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The difference is that phosphonic acid ($\ce{HPO(OH)2}$) is an existing, shelf-stable compound while phosphorous acid ($\ce{P(OH)3}$) is extremely short-lived if at all and immediately tautomerises to phosphonic acid.

All the -ous acids are theoretically produced in the same manner: take the -ic acid and remove one unprotonated oxygen, leaving an additional electron pair with the central atom which reduces its oxidation state by two. So while sulphuric acid is $\ce{SO2(OH)2}$, sulphurous acid is $\ce{SO(OH)2}$.

Likewise, you can always theoretically generate the -onic acids by tautomerisation from the ‘parent’ -ous acid; one proton that previously was attached to an oxygen bonds to the central atom‘s newly-formed (when coming from the -ic acid) lone pair. Thus, sulphonic acid is $\ce{HSO2(OH)}$.

In case of sulphur, while both acids have been observed and crystal structures of both have been determined to the best of my knowledge,[citation needed] the two can still tautomerise. In the case of phosphorus, only the phosphonic acid is shelf-stable and all isolated salts have been determined to be phosphonate salts.[citation needed]

In both cases, however, organic esters have been generated in both ways. Thus, you can have e.g. triethyl phosphite $\ce{P(OEt)3}$ or diethyl ethylphosphonate $\ce{EtPO(OEt)2}$.

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As already mentioned by Jan, phosphonic acid actually the stable, existing compound while phosphorous acid is unstable, short-lived and quickly tautomerizes to phosphonic acid. Wikipedia supports this fact:

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$\ce{H3PO3}$ is more clearly described with the structural formula $\ce{HPO(OH)2}$. In the solid state, $\ce{HPO(OH)2}$ is tetrahedral with one shorter $\ce{P=O}$ bond of 148 pm and two longer $\ce{P–O(H)}$ bonds of 154 pm. This species exists in equilibrium with an extremely minor tautomer $\ce{P(OH)3}$. IUPAC recommends that the latter be called phosphorous acid, whereas the dihydroxy form is called phosphonic acid. Only the reduced phosphorus compounds are spelled with an "ous" ending.

$\ce{H3PO3}$ is described by the name of phosphorous acid but the name is actually quite misleading. As mentioned in Wikipedia, $\ce{H3PO3}$ actually has the structural formula $\ce{HPO(OH)2}$(dihydroxy form) which is actually called phosphonic acid and for which the acid is diprotic and not triprotic as might suggested by the formula. The tautomer of this acid is $\ce{P(OH)3}$ which is called phosphorous acid. This is unstable and quickly converts to its dihydroxy form.

Sometimes things may look very obvious but if you look for the story behind it, you may find that 'it was not that I thought of'.

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