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What's a hydronium atom and what role does it play in Acids and Bases?

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It's not an atom, it's an ion. Basically protons cannot exist in solution so when a Bronsted-Lowry acid dissolves in water, the proton is transferred to a water molecule (i.e. the water acts as a base). With a strong acid, almost all protons will dissolve so you'll have as many moles of hydronium ions as you do of acid. Hope that helps!