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Is an intramolecular hydrogen bond possible in such compounds?
What are the requisites to have intramolecular hydrogen bonding?

proposed intramolecular hydrogen bond in H2CO3 and gem-diol

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  • $\begingroup$ In second one the two R groups are +I group as well as steric hindering hence drastically reduces stability, also there is repulsions due to lone pairs on oxygen. $\endgroup$ – Sujith Sizon Jan 4 '16 at 5:07
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As the intramolecular H-bonding is absent in both cases.

Carbonic acid

In aqueous solution of carbonic acid is a weak acid. It dissociates into its constituent ions as carbonate ions and hydrogen ions. Now, the CO3-2 ion, is stabilized by resonance and produce three equivalent resonating structures.

enter image description here

This makes carbonate ion more stable rather than through intra molecular H-bonding. Now, I already said that carbonic acid is weak acid means all the molecules of carbonic acid are not dissociated. The molecules of carbonic acid which remain undissociated form inter-molecualr H-bonding with each other.

enter image description here

One thing that carbonic acid does not exist via intra-molecular H-bonding because, there is too much ring strain.

Gem-diols

In gem-diols there are two -OH groups present on a single carbon. You can get detail reason that why intra-molecular H-bonding is absent in gem-diols.

There is a common example of gem-diol where intra molecular H-bonding is present is chloral hydrate.

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  • $\begingroup$ Welcome to Chemistry.SE! The dissociation $$\ce{H2CO3 (aq) <=> CO2 (aq) + H2O}$$ is indeed the predominant reaction, favouring carbon dioxide. That is one of the main reasons, why many carbonates readily decompose at low pHs. || Mathematical expressions and equations can be formatted using $\LaTeX$ syntax. If you want to know more, please also have a look here. $\endgroup$ – Martin - マーチン Jan 4 '16 at 10:41
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Is this possible?

Probably not possible. An elementary explanation would be "too much ring strain."

https://en.wikipedia.org/wiki/Ring_strain

I'm a bit confused: What are the requisites to occur a intramolecular hydrogen bonding?

5 and 6-membered rings are more favorable. As a matter of fact, beta-ketoacids, when warmed, readily decarboxylate. Why? The intermediate to decarboxylation is stabilized through hydrogen bonding.

Note the 6-membered ring in the picture below.

enter image description here

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