Question

Nitrous oxide $\left({\mathrm{N}}_2\mathrm{O}\right)$ has three possible Lewis structures: $$:\mathrm{N}=\mathrm{N}=\dot{\mathrm{O}}⟷:\mathrm{N}\equiv \mathrm{N}-\ddot{\mathrm{Q}}:⟷:\dot{\mathrm{N}}-\mathrm{N}\equiv \mathrm{O}$$ Given the following bond lengths, $\mathrm{N}-\mathrm{N}167\mathrm{pm}\mathrm{N}=\mathrm{O}115\mathrm{pm}$ $\mathrm{N}=\mathrm{N}120\mathrm{pm}\mathrm{N}-\mathrm{O}147\mathrm{pm}$ $\mathrm{N}\equiv \mathrm{N}110\mathrm{pm}$ rationalize the observations that the N-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?

Short answer

In summary, resonance structure 2 ($:N\equiv N-\ddot{O}:$) is the most consistent with the observed bond lengths of N2O (112 pm for N-N bond and 119 pm for N-O bond) and formal charges. It has two neutral atoms (N and O) with a -1 charge on the central N atom, while structures 1 and 3 exhibit higher formal charges and inconsistent bond lengths with the observations. Hence, resonance structures 1 and 3 can be eliminated based on formal charges and the provided experimental observations.

Step-by-step solution

Calculate the expected bond lengths based on given Lewis structures

Using the given bond lengths for N-N, N=O, N=N, N-O, and N≡N bonds, we can calculate the expected bond lengths for each resonance structure of N2O. For resonance structure 1 ($:N=N=\dot{O}$): N-N bond length: 120 pm (double bond N=N) N-O bond length: 115 pm (double bond N=O) For resonance structure 2 ($:N\equiv N-\ddot{O}:$): N-N bond length: 110 pm (triple bond N≡N) N-O bond length: 147 pm (single bond N-O) For resonance structure 3 ($\dot{N}-N\equiv O$ ): N-N bond length: 167 pm (single bond N-N) N-O bond length: 115 pm (double bond N=O)

Compare observed bond lengths with expected bond lengths

The observed bond lengths are 112 pm for the N-N bond and 119 pm for the N-O bond. Comparing these values with the expected bond lengths for each resonance structure, we can see that none of them perfectly match the observed bond lengths. However, resonance structure 2 seems to have a closer average bond length when comparing the differences between the expected and observed bond lengths.

Assign formal charges to each resonance structure

Using the Lewis structures, calculate the formal charges for each atom in the resonance structures: For resonance structure 1 ($:N=N=\dot{O}$): N: Formal charge = valence electrons - (non-bonding electrons + 0.5 * bonding electrons) = 5 - (2 + 0.5 * 6) = 0 N: Formal charge = 5 - (0 + 0.5 * 6) = +1 O: Formal charge = 6 - (5 + 0.5 * 2) = -1 For resonance structure 2 ($:N\equiv N-\ddot{O}:$): N: Formal charge = 5 - (2 + 0.5 * 6) = 0 N: Formal charge = 5 - (1 + 0.5 * 8) = -1 O: Formal charge = 6 - (6 + 0.5 * 2) = 0 For resonance structure 3 ($\dot{N}-N\equiv O$ ): N: Formal charge = 5 - (3 + 0.5 * 4) = 0 N: Formal charge = 5 - (0 + 0.5 * 8) = +1 O: Formal charge = 6 - (4 + 0.5 * 4) = 0

Analyze formal charges and compare with observations

Now, we will analyze the formal charges of each resonance structure. Resonance structure 2 is the only one with two neutral atoms (N and O) with a -1 charge on the central N atom. All other resonance structures have at least one atom with a formal charge of +1 or -1, which tends to make the structure less stable. Based on the formal charges, we can eliminate resonance structures 1 and 3, as they have higher formal charges. This conclusion is consistent with our observation from step 2, where resonance structure 2 had the closest average bond lengths to the observed bond lengths in N2O. In conclusion, the resonance structure 2 ($:N\equiv N-\ddot{O}:$) is the one most consistent with the observed bond lengths of N2O and formal charges.

Key concepts

Lewis Structures

Lewis structures are diagrams that show the arrangement of atoms and electrons in a molecule. They are essential for understanding the bonding and geometry of molecules. In nitrous oxide (${\mathrm{N}}_2\mathrm{O}$), we can draw several Lewis structures, reflecting its resonance forms. Resonance occurs when more than one valid Lewis structure exists for a molecule.

- The structure $:\mathrm{N}=\mathrm{N}=\dot{\mathrm{O}}$ indicates nitrogen with a double bond to another nitrogen and an oxygen.- Structure $:\mathrm{N}\equiv \mathrm{N}-\ddot{\mathrm{O}}:$ shows a nitrogen triple bond, highlighting a strong bond.- In $\dot{\mathrm{N}}-\mathrm{N}\equiv \mathrm{O}$, the single N-N bond is emphasized.

Lewis structures are used to visualize how electrons are distributed and help predict the molecular shape. By drawing all possible structures, we better appreciate the resonance and the electron arrangement in molecules like ${\mathrm{N}}_2\mathrm{O}$.

Formal Charges

Formal charges help determine the most stable resonance structure for a molecule. They are calculated using the formula: $\text{Formal charge}=\text{valence electrons}-(\text{non-bonding electrons}+0.5\times \text{bonding electrons})$.

For nitrous oxide (${\mathrm{N}}_2\mathrm{O}$):

• In the structure $:\mathrm{N}=\mathrm{N}=\dot{\mathrm{O}}$, the end nitrogen carries a +1 charge, and the oxygen a -1 charge.
• In $:\mathrm{N}\equiv \mathrm{N}-\ddot{\mathrm{O}}:$, central nitrogen has a -1 charge, making it more stable due to balanced charges.
• In $\dot{\mathrm{N}}-\mathrm{N}\equiv \mathrm{O}$, one nitrogen and oxygen are neutral, but one nitrogen carries a +1 charge.

Structures with minimized formal charges are typically more stable. In this case, resonance structure 2 has the lowest and balanced formal charges, making it the favored form, aligning with the observed and calculated bond lengths.

Bond Lengths

Bond lengths are the distances between the nuclei of bonded atoms. They can vary depending on the types of bonds (single, double, triple) and resonance effects.

For ${\mathrm{N}}_2\mathrm{O}$, the observed bond lengths are:
- N-N bond: 112 pm- N-O bond: 119 pm

Comparing these to typical bond lengths:

• N-N single: 167 pm
• N=N double: 120 pm
• N≡N triple: 110 pm
• N-O single: 147 pm
• N=O double: 115 pm

The observed N-N bond length of 112 pm suggests a bond strength closer to a triple bond. The N-O bond length of 119 pm is between a single and double bond, indicating resonance stabilization.

Resonance structures share characteristics in the molecule, leading to bond lengths that are averages of possible structures. This principle helps explain why the bond lengths in ${\mathrm{N}}_2\mathrm{O}$ don't match perfectly to any single resonance structure but instead fall between them, showing the powerful influence of resonance in molecular structure.