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Why does \[{\text{C}}{{\text{H}}_3}{\text{COOH}}\] has a basicity of 1?

Answer
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Hint:Basicity of an acid is defined as the number of possible \[{{\text{H}}^ + }\] ions the acid can ionize. Acidity of a base is defined as the possible number of \[{\text{O}}{{\text{H}}^ - }\] ions it can liberate.

Complete step by step solution:
According to Arrhenius concept, acid are those which can give \[{{\text{H}}^ + }\] ion in aqueous solution and base are those which can give \[{\text{O}}{{\text{H}}^ - }\] ion its aqueous solution. However this concept doesn't define acidic behaviour of compounds like \[{\text{B}}{{\text{H}}_3}\] which shows acidic behaviour but do not liberate \[{{\text{H}}^ + }\] ion in its aqueous solution.
Basicity of an acid is define as the possible number of \[{{\text{H}}^ + }\] ion it can liberate and acidity is define for base which is define as possible number of \[{\text{O}}{{\text{H}}^ - }\] ion it can liberate.
For example; Basicity of \[{\text{HCl}}\] is 1 as it can only liberate 1 \[{{\text{H}}^ + }\] ion, basicity of \[{\text{C}}{{\text{H}}_3}{\text{COOH}}\] is 1 as it can only liberate 1 \[{{\text{H}}^ + }\] ion.

Thus, correct answer is basicity of \[{\text{C}}{{\text{H}}_3}{\text{COOH}}\] is 1 as it can liberate only 1 \[{{\text{H}}^ + }\] ion.

Additional Information:
Bronsted lowry concept defines acids as proton donors and bases as proton acceptors. However this theory also can't explain acidic behaviour of compounds like boron trihydride.
According to Lewis concept, acids are those which can accept electron(s) and bases are those which can donate electrons. For example, in \[{\text{B}}{{\text{H}}_3}\] boron has an electron deficit and has 6 electrons in the valence shell. So \[{\text{B}}{{\text{H}}_3}\] is an acid while compounds like \[{\text{N}}{{\text{H}}_3}\] which can donate electron are base.

Note:
Amphoteric compounds are those compounds which can act as both acid as well as base. As they can do both that is can accept \[{{\text{H}}^ + }\] ion and behave as acid and also can donate \[{{\text{H}}^ + }\] ion as behave as base. For example: bicarbonate and carbonate ion.