adder
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In 6-membered pyridine derivatives the pKa drops with more nitrogen atoms as they all act as if they were electron-withdrawing groups built into the ring, so the basicity drops similarly as it does when you put an EWG onto pyridine or anilines. In caffeine I suppose the 6-membered ring as a whole withdraws electron density from the imidazole ring (the amide moiety at C5 is electron-withdrawing, the imide at C4 is very mildly donating at best if at all).
Imidazole being more basic than pyridine is due to electron-rich -NH- moiety I suppose (pyrrole much more activated than benzene for instance), however, no wonder they both have lower pKa (their conjugate acids have, I mean) than amines as the basic nitrogen atoms are sp2-hybridized and part of the aromatic ring, in amines alkyl groups are donating to the nitrogen atom (although sterics also come into play).
Imidazole being more basic than pyridine is due to electron-rich -NH- moiety I suppose (pyrrole much more activated than benzene for instance), however, no wonder they both have lower pKa (their conjugate acids have, I mean) than amines as the basic nitrogen atoms are sp2-hybridized and part of the aromatic ring, in amines alkyl groups are donating to the nitrogen atom (although sterics also come into play).