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To calculate the bond length, it is important to take into account the resonance structures. In the example NO3-, there are three resonance structures each with one double bond and two single bonds. This tells us that the bond length is shorter than a double bond but longer than a single bond.
I would think that you would have to be fairly exact because we would be given bond lengths for a single and a double bond and then you would have to calculate the average bond length from the three resonance structures of NO3-. For example, if a N-O single bond was 1.8 A and a N-O double bond was 1.4 A then you would first notice from the resonance structures that there is a double bond 1/3 of the time and a single bond 2/3 of the time. Therefore you would write: 1/3(1.4 A) + 2/3 (1.8 A) to find the average which would be approximately 1.7 A (1 2/3 exactly). This average would make sense because the number 1.7 is between a double and single bond yet closer to a single bond length of 1.8 A than a double bond length of 1.4 A because the resonance structure shows the single bond present between N-O more frequently. Hope this makes sense.
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