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Does dissolving sodium carbonate in water produce carbon dioxide?

I have been thinking about this for a long time but I'm getting inconsistent answers online.

My thinking is that $\ce{CO3^2-}$ accepts 2 protons from water to form $\ce{H2CO3}$. Then $\ce{H2CO3}$ decomposes in a side reaction to form $\ce{H2O}$ and $\ce{CO2}$. Is this right?

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    $\begingroup$ The OP has demonstrated clear thinking and logic in trying to solve this question. I don't think the homework closure is proper here. $\endgroup$ – Gaurang Tandon Jul 6 '18 at 16:06
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    $\begingroup$ Your correct since all species must be in equilbrium. However $\ce{[CO3^{2-}]} >> \ce{[HCO3^{-}]} >> \ce{[H2CO3]} >> \ce{[CO2(g)]}$. So there will be a extremely small concentration of $\ce{CO2(g)}$ $\endgroup$ – MaxW Jul 6 '18 at 16:32

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