Why are anions of weak acids able to act as bases?

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Under the Brønsted–Lowry definition, a base is defined as any species that has a tendency to accept a proton (H+).1

Anions of weak acids are able to act as bases because they possess a chemical tendency to accept a proton to reform the original acid. For example, the acetate ion (CH3CO2−), which is the anion of the weak acid acetic acid, acts as a base in water by accepting a proton to produce hydroxide ions (OH−), thereby creating a basic solution.12

While it is formally true that the anion of any acid can be considered a base, this property is only significant for anions derived from weak acids. For the anions of very strong acids—such as the chloride ion—the tendency to accept a proton is so weak that their basic properties are considered insignificant.1