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Chemical Bonding And Molecular Structure

Question
CBSEENCH11005789

Is the bond order in superoxide ion more or less than in peroxide ion? Explain on the basis of MO theory.

Solution

The MO electronic configuration of superoxide ion left parenthesis straight O subscript 2 superscript minus right parenthesis is
                space open square brackets KK left parenthesis straight sigma 2 straight s right parenthesis squared space left parenthesis straight sigma asterisk times 2 straight s right parenthesis squared space left parenthesis straight sigma 2 straight p subscript straight z right parenthesis squared space left parenthesis straight pi 2 straight p subscript straight x right parenthesis squared left parenthesis straight pi 2 straight p subscript straight y right parenthesis squared space left parenthesis straight pi asterisk times 2 straight p subscript straight x right parenthesis squared thin space left parenthesis straight pi asterisk times 2 straight p subscript straight y right parenthesis to the power of 1 close square brackets
Here straight N subscript straight b space equals space 8 space space and space straight N subscript straight a space equals space 5
therefore space 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 5 close square brackets space equals space 3 over 2 space equals space 1 1 half
The M.O. electronic configuration of peroxide ion open parentheses straight O subscript 2 superscript 2 minus end superscript close parentheses is                                         open square brackets KK left parenthesis straight sigma 2 straight s right parenthesis squared space space left parenthesis straight sigma asterisk times 2 straight s right parenthesis squared space left parenthesis straight pi 2 straight p subscript straight z right parenthesis squared space left parenthesis straight pi 2 straight p subscript straight x right parenthesis squared space left parenthesis straight pi 2 straight p subscript straight y right parenthesis squared space left parenthesis straight pi asterisk times 2 straight p subscript straight x right parenthesis squared space left parenthesis straight pi asterisk times 2 straight p subscript straight y right parenthesis squared close square brackets
 Here space space space straight N subscript straight b space equals space 8 space space and space straight N subscript straight a space equals space 6
therefore space 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
So, the bond order in superoxide ion is more than in peroxide ion.