If a base is added to a buffered solution containing H2O, K+, HC2H3O2, and C2H3O2, what reacts most readily with the base?

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I think that you have mistyped your question.  C2H3O2 is not a chemical species but I am sure that you are talking about acetic acid and potassium acetate.  A buffer is a solution that is designed to resist any change to pH with added acid or base.  One classic buffer solution is an aqueous (H2O) solution of acetic acid (CH3CO2H) and potassium acetate (CH3CO2K).  The acetic acid will react with any base added and the potassium acetate will react with any acid added.  So the answer is that acetic acid (CH3CO2H) will react with any added base.

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