Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) has three possible Lewis structures: Given the following bond lengths, $$ \begin{array}{llll} \mathrm{N}-\mathrm{N} & 167 \mathrm{pm} & \mathrm{N}=\mathrm{O} & 115 \mathrm{pm} \\ \mathrm{N}=\mathrm{N} & 120 \mathrm{pm} & \mathrm{N}-\mathrm{O} & 147 \mathrm{pm} \\ \mathrm{N} \equiv \mathrm{N} & 110 \mathrm{pm} & & \end{array} $$ rationalize the observations that the \(\mathrm{N}-\mathrm{N}\) bond length in \(\mathrm{N}_{2} \mathrm{O}\) is \(112 \mathrm{pm}\) and that the \(\mathrm{N}-\mathrm{O}\) bond length is \(119 \mathrm{pm}\). Assign formal charges to the resonance structures for \(\mathrm{N}_{2} \mathrm{O}\). Can you eliminate any of the resonance structures on the basis of formal charges? Is this consistent with observation?

Step by step solution

01

Analyze the given bond lengths

Here are the given bond lengths for N-N, N=O, N=N, and N-O bonds: - Single N-N bond: 167 pm - Double N=O bond: 115 pm - Double N=N bond: 120 pm - Single N-O bond: 147 pm Additionally, we are given the following bond lengths observed in N2O: - N-N bond length in N2O: 112 pm - N-O bond length in N2O: 119 pm Now, we'll assign formal charges to the resonance structures of N2O.

02

Assign formal charges to the resonance structures

In order to assign formal charges to the resonance structures, let's consider the three possible Lewis structures of N2O: 1) N-N=O 2) N=N-O 3) N≡N+ - O- Now, let's calculate formal charges: 1) N-N=O: Formal charge on left N: \(5 -3 - (0.5 \times 4) = 0\) Formal charge on right N: \(5 -2 - (0.5 \times 6) = +1\) Formal charge on O: \(6 -2 - (0.5 \times 6) = -1\) 2) N=N-O: Formal charge on left N: \(5 -2 - (0.5 \times 6) = +1\) Formal charge on central N: \(5 -2 - (0.5 \times 6) = +1\) Formal charge on O: \(6 -3 - (0.5 \times 4) = 0\) 3) N≡N+ - O-: Formal charge on left N: \(5 -1 - (0.5 \times 8) = +1\) Formal charge on central N: \(5 -1 -(0.5 \times 8) = +1\) Formal charge on O: \(6-1 - (0.5 \times 6) = -1\)

03

Eliminate resonance structures based on formal charges and observed bond lengths

From the formal charges calculated for all three possibilities, we can notice that the structures 2 and 3 have more formal charges distributed on the nitrogen atoms. Since the observed N-N bond length (112 pm) is shorter than the given single N-N bond length (167 pm), this indicates that there is a significant contribution from structures with double and triple N-N bonds, structures 2 and 3. Thus, we can eliminate structure 1. Similarly, the observed N-O bond length (119 pm) is shorter than the given single N-O bond length (147 pm), indicating a stronger bond (double bond) between N and O. Therefore, structure 2 (N=N-O) is consistent with the observation, while structure 3 (N≡N+ - O-) is not.

04

Conclusion

After analyzing the given bond lengths and assigning formal charges to the resonance structures of nitrous oxide (N2O), we can eliminate structures 1 and 3 based on the formal charges and observed bond lengths. The most consistent resonance structure for N2O with the observed bond lengths is N=N-O, as it provides a better explanation for the observed N-N (112 pm) and N-O (119 pm) bond lengths.

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