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Question 8.3.2: a. What is the bond order of the nitrogen–oxygen bonds in th......

a. What is the bond order of the nitrogen–oxygen bonds in the nitrate (NO_{3}^{−}) ion?
b. In which ion (NO_{2}^{−} or NO_{3}^{−}) are the nitrogen–oxygen bonds longer?
c. In which ion (NO_{2}^{−} or NO_{3}^{−}) are the nitrogen–oxygen bonds stronger?

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You are asked to identify the bond order in a molecule or ion that has resonance structures and to use bond order to make predictions about relative bond length or bond order in a series of molecules or ions that have resonance structures.
You are given the chemical formula of a molecule or ion, or a series of molecules or ions.
a. The nitrate ion has three equivalent resonance structures.

\left[\begin{matrix}:\overset{..}{\underset{|}{O}} :\\\overset{..}{\underset{..}{O}}=N- \overset{..}{\underset{..}{O}}: \end{matrix} \right] ^{-}\longleftrightarrow \left[\begin{matrix} :\underset{||}{O}: \\:\overset{..}{\underset{..}{O}}- N- \overset{..}{\underset{..}{O}}: \end{matrix} \right]^{-}\longleftrightarrow \left[\begin{matrix} :\overset{..}{\underset{|}{O}} \\ :\overset{..}{\underset{..}{O}}- N=\overset{..}{\underset{..}{O}} \end{matrix} \right]^{-}

There are four NO bonding pairs distributed over three NO bonding locations.
each NO bond order in NO_{3}^{-}=\frac{\text{total number of NO bonding pairs}}{\text{number of NO bond locations}} =\frac{4}{3}=1.3

b. Bond length increases with decreasing bond order. The nitrogen–oxygen bond order in NO_{3}^{-}  is less than the nitrogen–oxygen bond order in NO_{2}^{-} (1.3 versus 1.5, respectively). Therefore, NO_{3}^{-} has longer nitrogen–oxygen bonds than does NO_{2}^{-}.
c. Bond energy increases with increasing bond order. The nitrogen–oxygen bond order in NO_{2}^{-} is greater than the nitrogen–oxygen bond order in NO_{3}^{-} (1.5 versus 1.3, respectively). Therefore, NO_{2}^{-} has stronger nitrogen–oxygen bonds than does NO_{3}^{-}.

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