Final answer:
The N-O bond lengths from shortest to longest are as follows: NO < NO3^- < NO2^-, with NO having a bond order of 2.5, NO3^- having resonating structures causing short bond lengths,
Step-by-step explanation:
The ordering of N-O bond lengths in NO (nitric oxide), NO&sub2;¹- (nitrite ion), and NO&sub3;¹- (nitrate ion) can be predicted based on the concept of bond order and resonance structures.
In NO, we have a bond order of 2.5, which suggests a very strong and therefore short bond. The NO&sub2;¹- ion shows resonance, meaning that the actual structure is a hybrid with equally shared electrons, resulting in two N-O bonds with equal and intermediate length between a single and double bond.
Lastly, NO&sub3;¹- also displays resonance with three equivalent N-O bonds, but each bond is somewhat shorter than a straight single bond due to partial double-bond character.
Therefore, the order from shortest to longest N-O bond length is NO < NO&sub3;¹- < NO&sub2;¹-.