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My professor told us the following:

$\ce{NaHCO3}$ will react to evolve $\ce{CO2}$ whenever the acidic nature of the reactant exceeds the acidic nature of benzoic acid.

I want to know why this is. And is the given statement valid? He didn't give us the reason. And in that case should $\ce{NaHCO3}$ react with 1,2-dihydroxy cyclobutanedione to evolve carbon dioxide?

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$\ce{NaHCO3}$ is the basic sodium salt of carbonic acid, a diprotic acid which exists only in small amounts in aqueous solution, because the equilibrium

$$\ce{CO2 + H2O <=> H2CO3}$$

lies mainly on the educt side (this is also the reason why $\ce{CO2}$ evolution is observed). When this fact is taken into account, a $\ce{pK_{a}}$ value of 6.3 at 25 °C is obtained for the first protolysis step (source). Benzoic acid has a lower $\ce{pK_{a}}$ value of 4.19 and is therefore able to liberate carbonic acid from its salts, like any other acid that is significantly stronger than $\ce{H2CO3}$.

$$\ce{C6H5CO2H + NaHCO3 -> C6H5CO2Na + CO2 + H2O}$$

Just in case that you mean 3,4-Dihydroxycyclobut-3-ene-1,2-dione, which is also known as squaric acid, then a reaction with $\ce{CO2}$ evolution is likely. Squaric acid is a fairly strong diprotic acid, with $\ce{pK_{a}}$ values of 1.5 and 3.4, respectively. The acidity can be attributed to the stabilization of the dianion by resonance:

enter image description here

If carbon dioxide evolution with 1,2-dihydroxy cyclobutanedione is possible depends on the $\ce{pK_{a}}$ value of this compound. However, I would expect it to be less acidic than squaric acid.

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    $\begingroup$ One could call the squaric acid anion aromatic... $\endgroup$ – Martin - マーチン May 8 '16 at 16:20
  • $\begingroup$ @Martin-マーチン , How is squaric acid supposed to be aromatic without satisfying the Huckel (4n+2) pi electron rule? $\endgroup$ – Aaron John Sabu Mar 8 '17 at 11:22
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    $\begingroup$ @Aaron Hückel's rule is strictly applicable to monocyclic hydrocarbons only. Extending it to systems with heteroatoms is done frequently and yields remarkable results by coincidence. (There really is not much rigour to it.) However, since the squaric acid anion has a very high symmetry (D4h) it works with the same premise. Depending how you would like to count the electrons in the pi-system, you can come up with 2, 6, or 10; all of which fit Hückel's scheme. $\endgroup$ – Martin - マーチン Mar 8 '17 at 11:36
  • $\begingroup$ I'm sorry but thophene, furan, pyrrole etc all follow Huckel's rule, although they have got heteroatoms(not by coincidence). The lone pair on the heteroatom is considered to be two of those considered pi electrons, since they are delocalised. $\endgroup$ – Aaron John Sabu Mar 8 '17 at 11:42
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    $\begingroup$ @AaronJohnSabu no, these compounds do not follow Hückel's rule (by definition). They are indeed considered to have 4n+2 pi electrons, but there is more to these rules than this number. Just keep in mind that there is more to aromaticity than Hückel's rules. $\endgroup$ – Martin - マーチン Mar 9 '17 at 18:41

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