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Generally we compare acidic strengths by comparing relative stability of negative charge formed by removal of acidic hydrogen. However I can't understand the following comparison
The solution given was
Now I can't understand why the 7-member ring is getting a positive character and the 5-member ring a negative character. I can't get any resources related to it.
Is this related to aromaticity in some way?
Yes, it is because of Huckel's rule of aromaticity. This states that for a ring to be aromatic, it must have 4n+2 pi electrons, where n is an integer. For the conjugate bases to be stabilized they would need to be aromatic. For the five-membered ring, the -1 charge is stable as it has 4(1)+2=6 pi electrons. For the seven-membered ring, the +1 charge is stable as it has 4(1)+2=6 pi electrons.
https://en.wikipedia.org/wiki/H%C3%BCckel's_rule
Note: the compound azulene is quite similar and also exhibits dipoles due to aromatic stabilization: https://en.wikipedia.org/wiki/Azulene
