What makes the Arrhenius acid and an Arrhenius base definition incomplete or lacking

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Explanation:

The Arrhenius acid-base theory defines an acid as a compound which when added into water increases the hydronium ion (H₃O⁺) concentration and the base as a compound which when added into water increases the hydroxide (OH⁻) ion concentration. As such, an acid-base reaction is limited to proton transfer to only OH⁻ ions forming water. Such would imply that all acid-base reactions produce water only in addition to a salt. This is not always the case as conjugate base anions for many substances can receive proton transfer.

Example: The reaction HOAc + NaCN => HCN + OAc-  will occur in aqueous media because the proton (H⁺) on acetic acid (HOAc) will transfer to the cyanate ion forming hydrocyanic acid (HCN). Such occurs because the CN⁻ ion is a stronger conjugate base than the acetate ion (OAc⁻) and forms the more stable weak acid.  Such is the basis of the Bronsted-Lowry Acid-Base system and states that an acid (proton donor) will transfer its ionizable hydrogen to a conjugate base (proton acceptor) if the transfer forms a weaker acid.