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While comparing the strengths of o-nitrophenol and p-nitrophenol, p-nitrophenol is found to be more acidic. The reason I studied for this is $\ce{H}$-bonding in o-nitrophenol which makes the acid more stable, making it a weak acid.

But between o-methoxyphenol and p-methoxyphenol, o-methoxyphenol is more acidic because of more -I effect at o-position. Doesn't $\ce{H}$-bonding happen here?

Can someone please clarify the exact reason for opposite orders?

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That's a really good question. The difference arises because -NO2 is -M group but -OCH3 is +M So even if we think that the hydrogen of -OH group is doing Hydrogen bonding with OCH3 in the end the acidic strength will be decided by inductive effect of -OCH3 group at ortho and para position. Since ortho is close its -I is dominating. In NO2 it is a +I group so we didn't look at inductive

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