The acidity of phenol arises from the loss of H of O – H group as H+ . This loss is facilitated if the polarity of the O – H bond increases and H carries substantial δ+ charge.
In (I), the presence of the highly electron withdrawing NO2group at the ortho position increases the polarity of the O – H bond.This helps in release of H‌+ and increases acidity. (II) is less acidic because –OCH3 is an electron releasing group and increases the e‌– density on O of OH and H‌+ release is suppressed.
This can be understood from the resonance structures of II which are