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The negative oxygen is the site of protonation. Size and EN are the same for both oxygens. We are mainly looking at resonance (and possibly inductive) effects here. We want the least resonance withdrawal of electron density from the oxygen. And if possible, the least inductive withdrawal of electron density from the oxygen (although this is not a major issue; resonance trumps induction). Recall that the nitro group cannot withdraw electron density via resonance effects at the meta position. Therefore meta-nitrophenoxide should be more basic than para¬-nitrophenoxide.

Is my reasoning correct?

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Yes, it is. These resonance structures describe basicity in para-nitrophenoxide.

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