Question
o-nitrophenol is more acidic than o-methoxyphenol.

Answer

$-R$ and $-I$ effect of $-NO_2$ group decreases the electron density in $O-H$ bond and make loss of proton easy in $O-$nitrophenol whereas $+R$ effect of $-OCH_3$ group increases the electron density in $O-H$ bond and makes release of proton difficult in $o-$methoxyphenol. That is, why o-nitrophenol is stronger acid than o-methoxyphenol.

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