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I was presented with the following reaction when we were just learning about acids and bases:

$$\ce{2NaOH + H2CO3 -> H2O + Na2CO3}$$ however I had thought it might've been something like

$$\ce{NaOH + H2CO3 -> H2O + NaHCO3}$$

They both seem to fit the notion of a neutralization reaction creating a salt so how do I know that the first one is correct? The second reaction looks fine to me (is it that bicarbonate is too reactive?) and more intuitive as the carbonic acid just gives a proton away ending up as an ion to bond with $Na$, so how do I distinguish between these kind of cases?

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You're right, both of these reactions take place.

From Wikipedia, the Free Encyclopedia

In aqueous solution, carbonate, bicarbonate, carbon dioxide, and carbonic acid exist together in a dynamic equilibrium.

Now, the answer to the question depends on context. If you're asked to do this reaction in a mildly acidic/weakly basic medium, then the answer would be the bicarbonate, while in a strongly basic medium, the answer would be the carbonate.

Interesting for further reading:

This $\ce{pH}$ dependent equilibrium between carbonate and bicarbonate is one of the ways in which the blood $\ce{pH}$, and the $\ce{pH}$ of the mouth is maintained. It also helps aquatic life to survive in ocean waters. (Also see urea cycle and carbon cycle)

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  • $\begingroup$ @ AbhigyanC What about $\pu{pH}$ at the second equivalence point, more or less than 7? $\endgroup$ – Adnan AL-Amleh Jan 31 at 15:35
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    $\begingroup$ @AdnanAL-Amleh $\ce{pK_{a1}}$ and $\ce{pK_{a2}}$ of carbonic acid are $4.5\times10^{-7}$ and $4.7\times10^{-11}$, respectively. So it happens at $\ce{pH}=8.34$, using the formula for pH of a amphiprotic anion is the average of the two pK values. See chembuddy.com/… $\endgroup$ – AbhigyanC Jan 31 at 15:44

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