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Chemical Bonding And Molecular Structure

Question
CBSEENCH11005788

Discuss the relatives stabilities, bond dissociation energies and bond lengths of O2
space space straight O subscript 2 superscript plus comma space straight O subscript 2 superscript minus space an space straight O subscript 2 superscript 2 minus end superscript species. 
      

Solution

For O2 molecule:
              Nb = 8,   Na = 4
space space Bond space order space equals space 1 half open square brackets straight N subscript straight b space minus space straight N subscript straight a close square brackets space equals space 1 half left square bracket 8 minus 4 right square bracket space equals space 2
space space space space For space straight O subscript 2 superscript plus space ion colon
space space space space space space space space space space space space space space space space space straight N subscript straight b space equals space 8 comma space space space straight N subscript straight a space equals space 3
space space Bond space order space equals space 1 half open square brackets straight N subscript straight b space minus space straight N subscript straight a close square brackets
space space space space space space space space space space space space space space space space equals 1 half open square brackets 8 minus 3 close square brackets space equals space 5 over 2 space equals 2 1 half
space space For space straight O subscript 2 superscript minus space left parenthesis superoxide space ion right parenthesis colon
space space space space space space space space space space space space space space space space space space space space space straight N subscript straight b space equals space 8 space comma space space straight N subscript straight a space equals space 5
space space Bond space order space equals space 1 half left square bracket 8 minus 5 right square bracket space equals space 3 over 2 space equals space 1 1 half
space space For space straight O subscript 2 superscript 2 minus end superscript space left parenthesis peroxide space ion right parenthesis colon
                     space space straight N subscript straight b space equals space 8 comma space space straight N subscript straight a space equals 6
space space Bond space order space equals space 1 half open square brackets straight N subscript straight b space minus space straight N subscript straight a close square brackets space equals space 1 half open square brackets 8 minus 6 close square brackets space equals space 1
As bond dissociation energies are directly proportional to the bond order, therefore, the dissociation energies of these molecular species are in order:
space space straight O subscript 2 superscript plus greater than space straight O subscript 2 greater than space straight O subscript 2 superscript minus greater than space straight O subscript 2 superscript 2 minus end superscript
As greater the bond dissociation energy, greater is the stability; the stability of these species is also as in the above order.
As bond length is inversely proportional to bond order, therefore their bond lengths will be in order:
space space straight O subscript 2 superscript 2 minus end superscript space greater than space straight O subscript 2 superscript minus space greater than space straight O subscript 2 space greater than space straight O subscript 2 superscript plus