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the N-O bond in NO2 - is shorter than the N-O bond NO3 -. State the reason.

in NO2- the lone pair is delocalised between the 2 O groups also. hence bond order equal to 1 + 1/2 = 3/2

 

in NO3- lone pair shared between three O atoms hence bond order od NO bond is 1 + 1/3 = 4/3

 

greater the bond order shorter the bond. hence bond length of NO2- less than that of NO3-

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in NO2-,bond order is 1.5,in NO3-,it is 1.33,

therefore,bond length is shorter in NO2-

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 if you look at the structure of NO3- you'll notice that N makes 1 double bond and 2 single bonds. Thus because of hybridization, you can say each oxygen atom has 1/3 of a double bond on average. 

Now look at NO2- (O=N-O-). There is one double bond and one single bond. Since each oxygen atom has about 1/2 of a double bond, the average bond length will be shorter than those in NO3-.

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in the resonance structure of NO2- two bonds are sharing a double bond but in NO3- three bonds are sharing the double bond 
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