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

Identifying the three possible Lewis structures for N2O

The first thing we need to do is identify the three possible Lewis structures for Nitrous oxide. Structure 1: N-N=O Structure 2: N=N-O Structure 3: N≡N-O

02

Using bond length data

Next, we will use the given bond length data to see which structure is more likely according to the observed bond lengths in N2O. The observed bond lengths are: N-N = 112 pm N-O = 119 pm The given bond lengths are: N-N Single bond (N-N) = 167 pm N-N Double bond (N=N) = 120 pm N-N Triple bond (N≡N) = 110 pm N-O Single bond (N-O) = 147 pm N-O Double bond (N=O) = 115 pm

03

Comparing observed and given bond lengths

Now let's compare the observed and given bond lengths to determine which structure is more likely. Structure 1: N-N=O N-N (single) bond length: 167 pm compared to observed 112 pm N=O (double) bond length: 115 pm compared to the observed 119 pm Structure 2: N=N-O N=N (double) bond length: 120 pm compared to observed 112 pm N-O (single) bond length: 147 pm compared to the observed 119 pm Structure 3: N≡N-O N≡N (triple) bond length: 110 pm compared to observed 112 pm N-O (single) bond length: 147 pm compared to the observed 119 pm

04

Assigning formal charges to the resonance structures

Next, we assign formal charges to each of the resonance structures. Structure 1: N-N=O Formal charge on left N: 5 - 4(shared electrons) - 1(non-shared electron) = 0 Formal charge on right N: 5 - 4(shared electrons) - 0(non-shared electron) = +1 Formal charge on O: 6 - 4(shared electrons) - 2(non-shared electrons) = 0 Structure 2: N=N-O Formal charge on left N: 5 - 4(shared electrons) - 0(non-shared electron)= +1 Formal charge on right N: 5 - 5(shared electrons) - 0(non-shared electron) = 0 Formal charge on O: 6 - 3(shared electrons) - 4(non-shared electrons) = -1 Structure 3: N≡N-O Formal charge on left N: 5 - 6(shared electrons) - 0(non-shared electron)= -1 Formal charge on right N: 5 - 5(shared electrons) - 0(non-shared electron) = 0 Formal charge on O: 6 - 3(shared electrons) - 4(non-shared electrons) = -1

05

Comparing the formal charges and bond length

Now, we compare the formal charges and bond lengths to determine which structure best represents N2O. Structure 1 has the lowest formal charges and bond lengths that are closest to the observed values. In conclusion, Structure 1 (N-N=O) with the formal charges of +1(right N) and 0(left N and O) is the most plausible resonance structure of Nitrous oxide based on bond length and formal charge comparisons. No structures can be definitively eliminated based on formal charges alone, but consistency with the observed bond lengths supports Structure 1 as the best representation.

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