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Why is it referred to as "carbonation" and we drink "carbonated" beverages when carbonate is $\ce{CO3}$ while $\ce{CO2}$ (carbonite?) is present in carbonation?

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Nope. Carbonate is $\ce{CO}_3^\color{red}{2-}$ (an ion), not $\ce{CO3}$. Carbonite is $\ce{CO}_2^\color{red}{2-}$.

Carbonation involves dissolving $\ce{CO2}$ gas in water. It turns out that $\ce{CO2}$ reacts (maybe not the best term to use here*) with water via the following reaction $$\ce{CO2 + H2O -> CO3^{2-} + 2H+}$$

So you have effectively carbonated the soft drink.

When you depressurize the bottle by opening it, the reverse reaction occurs and you get carbon dioxide.

*Such dissociation is normal and integral to dissolution of polar solutes in water, so generally it is considered as part of the dissolution

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    $\begingroup$ I've always wondered about carbonite. Has anyone ever produced salts of it? Can you be frozen in it? $\endgroup$ – Ben Norris Sep 10 '12 at 10:56
  • $\begingroup$ @BenNorris: Apparently it's a hypothetical radical, used to explain certain phenomena. Its conjugate acid exists in the gas phase, but not yet known to exist as a solution. Go figure :S $\endgroup$ – ManishEarth Sep 10 '12 at 11:48

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