Problem 104 - Chemistry An Atoms First Approach

Question

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) has three possible Lewis structures: $$\therefore N=N=O^{\cdot} \leftrightarrow: N \equiv N-\vec{O}: \longleftrightarrow: N-N \equiv 0$$ Given the following bond lengths, $$\begin{aligned} &\mathrm{N}-\mathrm{N} \quad 167 \mathrm{pm} \quad \mathrm{N}=\mathrm{O} \quad 115 \mathrm{pm}\\\ &\mathrm{N}=\mathrm{N} \quad 120 \mathrm{pm} \quad \mathrm{N}-\mathrm{O} \quad 147 \mathrm{pm}\\\ &\mathrm{N} \equiv \mathrm{N} \quad 110 \mathrm{pm} \end{aligned}$$ 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

Answer

The second resonance structure (N≡N-O) is the most plausible among all the resonance structures provided for Nitrous oxide (N2O) as it has the closest bond lengths to the observed values and consistent formal charges. The other resonance structures can be eliminated on the basis of formal charges and bond length consistency.

Step 1: Calculate Average Bond Lengths for N2O

To begin with, we will calculate the expected N-N and N-O bond lengths in N2O using the bond length data provided in the Lewis structures. Let's just focus on the bond lengths for now: - N-N Single bond: 167 pm - N-N Double bond: 120 pm - N-N Triple bond: 110 pm - N-O Single bond: 147 pm - N-O Double bond: 115 pm In the first Lewis structure, we have a double bond between the two Nitrogen atoms and a single bond with an unshared electron on the Oxygen atom. While in the second Lewis structure, we have a triple bond between the two Nitrogen atoms and a single bond between N and O. Lastly, in the third Lewis structure, we have a single bond between the Nitrogen atoms and a double bond between N and O.

Step 2: Calculate Bond Lengths in Resonance Structures

Now that we have defined the average bond lengths for N-N and N-O bonds, we will try to find the expected N-N and N-O bond lengths for each resonance structure using the following method: \[\text{Expected Bond Length} = \frac{\text{(Single Bond Length + Double Bond Length)}{2}\] For the first resonance structure (N=N=O.), N-N and N-O bond lengths can be calculated as: N-N bond length: \[\frac{(167 + 120)}{2} = 143.5 \mathrm{pm}\] N-O bond length: \[147 \mathrm{pm}\] (single bond) For the second resonance structure (N≡N-O), N-N and N-O bond lengths can be calculated as: N-N bond length: \[110 \mathrm{pm}\] (triple bond) N-O bond length: \[147 \mathrm{pm}\] (single bond) For the third resonance structure (N-N≡O), N-N and N-O bond lengths can be calculated as: N-N bond length: \[167 \mathrm{pm}\] (single bond) N-O bond length: \[\frac{(147 + 115)}{2} = 131 \mathrm{pm}\]

Step 3: Compare the Calculated Bond Lengths and Assign Formal Charges

Next, we will compare the calculated bond lengths from each resonance structure to see which is consistent with the observed bond lengths given (N-N: 112 pm, N-O: 119 pm). For the first resonance structure (N=N=O.): N-N bond length: \(143.5 \mathrm{pm}\) vs Observed: \(112 \mathrm{pm}\) N-O bond length: \(147 \mathrm{pm}\) vs Observed: \(119 \mathrm{pm}\) For the second resonance structure (N≡N-O): N-N bond length: \(110 \mathrm{pm}\) vs Observed: \(112 \mathrm{pm}\) N-O bond length: \(147 \mathrm{pm}\) vs Observed: \(119 \mathrm{pm}\) For the third resonance structure (N-N≡O): N-N bond length: \(167 \mathrm{pm}\) vs Observed: \(112 \mathrm{pm}\) N-O bond length: \(131 \mathrm{pm}\) vs Observed: \(119 \mathrm{pm}\) Now we'll assign formal charges to each resonance structure: First resonance structure (N=N=O.): Formal charges: N: +1, N: 0, O: -1 Second resonance structure (N≡N-O): Formal charges: N: 0, N: +1, O: -1 Third resonance structure (N-N≡O): Formal charges: N: -1, N: 0, O: +1

Step 4: Analyze and Conclude

Between the calculated bond lengths and the formal charges of each resonance structure, we can see that the second resonance structure (N≡N-O) has the closest bond lengths to the observed values. Further, the formal charges of each atom in this Lewis structure are consistent with their overall bonding patterns. The other resonance structures are less consistent with the observed bond lengths and have more polar atoms leading to instability. Thus, we can eliminate the first and third resonance structures on the basis of formal charges and bond length consistency. Therefore, the second resonance structure (N≡N-O) is the most plausible among all the resonance structures provided for Nitrous oxide (N2O).

Key Concepts

Resonance Structures

Resonance structures are different ways to draw Lewis structures for a single molecule that cannot be accurately depicted with just one structure. Instead of being separate entities, these structures represent various possibilities in the distribution of electrons across the molecule. In the case of nitrous oxide (N₂O), three potential resonance structures exist:

• N=N=O
• N≡N-O
• N-N≡O

Each resonance structure differs in the placement of electrons and the types of bonds (single, double, or triple) between nitrogen and oxygen atoms.
Resonance helps explain why molecular properties, like bond lengths, are sometimes averages of single, double, or even triple bonds. None of the resonance structures alone fully describe the actual electron distribution of the molecule, but together, they provide a complete picture.

Bond Length Calculation

Understanding bond length calculations facilitates comprehension of molecular geometry. Bond length refers to the distance between the nuclei of two bonded atoms. Different types of bonds have distinct lengths. For instance, in the case of N₂O, we encounter:

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

To predict the actual bond length in a molecule with resonance structures, you calculate the average of the possible bond lengths. For example, if a resonance structure shows a N=N bond but exists in partial states like single and double bonds, the calculated bond length is \[\text{Average Bond Length} = \frac{\text{(Single Bond Length) + (Double Bond Length)}}{2}.\]This accounts for the mixture of bond types and their respective lengths, providing an understanding of observed bond lengths like the 112 pm N-N and 119 pm N-O in nitrous oxide.

Formal Charges

Formal charges are essential in evaluating the stability of resonance structures. They help us understand the hypothetical charge an atom would have if all atoms had the same electronegativity. The formal charge \(FC\) of each atom in a molecule can be calculated using the formula:\[FC = \text{(Valence Electrons) - (Non-bonding Electrons) - \frac{1}{2} (Bonding Electrons)}\].In N₂O, the resonance structures yield the following formal charges:

• First structure (N=N=O): N(+1), N(0), O(-1)
• Second structure (N≡N-O): N(0), N(+1), O(-1)
• Third structure (N-N≡O): N(-1), N(0), O(+1)

By analyzing these charges, we discard structures with more electronegative atoms bearing a positive charge when it's less typical, as seen in the first and third resonance structures. This leaves us with the second structure (N≡N-O) as the most stable and plausible representation of N₂O, consistent with the observed bond lengths.