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Why do the basicities of ${H_3}P{O_3}\,and\,{H_3}P{O_2}$ are 2 and 1 respectively?

Answer
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Hint: In order to answer this question, we will explain the reason why the basicity of the given compounds are 2 and 1 respectively. And then we will elaborate the explanation of the basicity. We will discuss more about it.

Complete answer:
For an acid, basicity is the number of $OH$ bonds. ${H_3}P{O_2}$ has one free OH bond the basicity is 1.
This is because it has only one ionisable $OH$ group.
For ${H_3}P{O_3}$ basicity is 2 it has two $OH$ bonds.
Phosphorous acid (${H_3}P{O_3}$ ) forms salts known as phosphites which are sometimes used as reduction agents. \[{H_3}P{O_4} \to 2{H^ + } + P{O_4}\] – For hydrogen to be acidic it must be attached to a strongly electronegative atom. It has two \[P - OH\] bonds and one \[P - H\] bond. Hence, its basicity is 2.Here it is attached to 2 oxygen. Hence basicity of ${H_3}P{O_3}$ is 2.
Basicity of ${H_3}P{O_2}$ depends upon the number of ionizable \[ - OH\] groups present in the molecule. That is the number of hydrogen attached to the electronegative atom oxygen. ${H_3}P{O_2}$ has one ionizable \[ - OH\] group, thus its basicity is 1.

Note:
Among organic compounds, such compounds as carboxylic acids and phenols exhibit acidity and such compounds as amines show basicity. Their acidity/basicity is changed in accordance with the change in structure. This all depends on the substituents that the molecules have.