#"m-nitrophenol"# #;pK_a=8.36#, see this site.
#"o-nitrophenol"# #;pK_a=7.23#, see this site.
#"p-nitrophenol"# #;pK_a=7.15#, see this site.
So why should #"p-nitrophenol"# be more acidic? Well, perhaps because the lone pair of the oxygen is capable of resonance with the quaternized nitrogen centre, a more stable mesomer than that available for #"m-nitrophenol"#; and thus the phenoxide anion, the conjugate base, is less charge-localized, and thus entropically favoured. Anyway you will have to draw out the resonance isomers for each phenoxide, and if it does not make sense, tackle your prof for his interpretation; that is why they pay him/her the big bux..........