A free radical has one or more unpaired electrons. Most free radicals have an odd-number of electrons.
N2O = 2(5)+6 = 16 electrons (not a free radical)
OCl- = 6+7+1 = 14 electrons (not a free radical)
ClO2 = 7+2(6) = 19 electrons (this is a free radical)
O-Cl-O has one lone pairs on Cl, plus one additional electron on Cl. This is why ClO2 is stabilized by one more electron to make the chlorite ion, ClO2^-, which has 20 electrons and two lone pairs on Cl.
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Only the valence electrons are counted when writing the Lewis structure. Nitrogen has 5 (not 7) and oxygen has 6 (not 8), which chlorine has 7 valence electrons.
N2O: 2*7 + 8 = 22 electrons
OCl-: 8 + 17 + 1 = 26 electrons
ClO2: 17 + 2*8 = 33 electrons
33 is odd number, so ClO2 is a free radical because it has one unpaired electron.
Free Radical MoleculesSource(s): https://shorte.im/a843e