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Baking soda is another name for Sodium Bicarbonate. This is a monosodic salt of Carbonic Acid. If you add vinegar (acetic acid), you will protonate the sodium bicarbonate, yielding carbonic acid. Carbonic acid, then, quickly decomposes into water and carbon dioxide (a gas), giving the characteristic "fizzing" of this reaction.

In simpler terms, just look at the chemical equation for this reaction

Na2CO3+2HC2H3O2-->2NaC2H3O2+H2O+CO2

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