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In auto-protolysis a proton is transferred between two identical molecules, one of which acts as a Bronsted acid, releasing a proton which is accepted by the other molecule acting as a Bronsted base.
Auto-protolysis is also called the self-ionization. Auto-protolysis of water is a reaction in which self-ionization of water molecules takes place to produce hydronium ion (H3O+) and hydroxide ion (OH-).