Question

The following three Lewis structures can be drawn for \(\mathrm{N}_{2} \mathrm{O}:\) \(: \mathrm{N} \equiv \mathrm{N}-\ddot{O}: \longleftrightarrow: \ddot{\mathrm{N}}-\mathrm{N} \equiv \mathrm{O}: \longleftrightarrow: \ddot{\mathrm{N}}=\mathrm{N}=\ddot{\mathrm{O}}:\) (a) Using formal charges, which of these three resonance forms is likely to be the most important? (b) The \(\mathrm{N}-\mathrm{N}\) bond length in \(\mathrm{N}_{2} \mathrm{O}\) is \(1.12 \AA\), slightly longer than a typical \(\mathrm{N} \equiv \mathrm{N}\) bond; and the \(\mathrm{N}-\mathrm{O}\) bond length is \(1.19 \AA\), slightly shorter than a typical \(\mathrm{N}=\mathrm{O}\) bond. (See Table 8.5.) Rationalize these observations in terms of the resonance structures shown previously and your conclusion for (a).

Short answer

The most important resonance structures for N2O are the ones with formal charges closest to zero. Structures 1 and 2 (N≡N-O and N-N≡O) have all formal charges equal to zero, while structure 3 (N=N=O) has formal charges of -1, -1, and +2, making it less important. The overall electronic structure of N2O can be considered as a mixture of structures 1 and 2, which contribute to the bond orders between the atoms. This explains the deviation of the N-N and N-O bond lengths from typical double and triple bonds. The N-N bond length of 1.12 Å suggests a bond order between 1 and 3, and the N-O bond length of 1.19 Å indicates a bond order between 2 and 3.

Step-by-step solution

Recall the concept of formal charge

Formal charge is a way of determining the charge distribution within a molecule. The formal charge of an atom in a molecule is calculated as follows: Formal charge = (Valence electrons of the atom) - (Non-bonding electrons) - (1/2 × Bonding electrons) We will use the formal charge formula to assess the importance of each resonance form.

Calculate Formal Charges for the Three Resonance Forms

Let's calculate the formal charges for each atom in the three Lewis structures: 1. N≡N-O Formal charge of left N: \(5 - 0 - (1/2 × 8) = 0\) Formal charge of right N: \(5 - 2 - (1/2 × 6) = 0\) Formal charge of O: \(6 - 4 - (1/2 × 4) = 0\) 2. N-N≡O Formal charge of left N: \(5 - 2 - (1/2 × 6) = 0\) Formal charge of right N: \(5 - 0 - (1/2 × 8) = 0\) Formal charge of O: \(6 - 4 - (1/2 × 4) = 0\) 3. N=N=O Formal charge of left N: \(5 - 1 - (1/2 × 7) = -1\) Formal charge of right N: \(5 - 1 - (1/2 × 7) = -1\) Formal charge of O: \(6 - 2 - (1/2 × 6) = +2\)

Determine the Most Important Resonance Structure

Now that we've calculated the formal charges for each resonance structure, we choose the one that has formal charges closest to zero and the smallest absolute value formal charges. Structures 1 and 2 have all formal charges equal to zero, while structure 3 has a formal charge of -1, -1, and +2. Therefore, structure 3 is less important. Between structures 1 and 2, there is no significant difference in formal charges, so both of them are considered important.

Rationalize the bond lengths

In N2O, the N-N bond (1.12 Å) is longer than a typical N≡N bond, and the N-O bond (1.19 Å) is shorter than a typical N=O bond. As our answer in part (a), we concluded that structures 1 and 2 are the most important resonance structures. These structures contribute to the overall electronic structure of N2O. The important resonance structures 1 and 2 are a mixture of a triple bond and a single bond between the nitrogen atoms and a double bond and a triple bond between the nitrogen and oxygen atoms. This results in a bond order between the nitrogens that is between 1 and 3 (closer to a double bond), and a bond order between nitrogen and oxygen that is between 2 and 3 (closer to a double bond). This bond order distribution can help explain the given bond lengths' deviation from the typical triple and double bonds.

Key concepts

Lewis structures

Understanding Lewis structures is essential for visualizing the arrangement of valence electrons in molecules and polyatomic ions. Lewis structures, also known as electron dot structures, are diagrams that represent the bonding between atoms of a molecule and the lone pairs of electrons that may exist.

When drawing Lewis structures, atoms are represented by their chemical symbols while dots or lines are used to indicate valence electrons. These diagrams help discern the molecular geometry, potential resonance structures, and molecule polarity. The focus is on arranging the electrons to achieve the octet rule, where each atom strives to have eight electrons in its valence shell, hence reaching a stable noble gas configuration.

For molecules like N₂O, different Lewis structures can be drawn by shifting the position of electrons between atoms without changing the overall charge or composition of the molecule. These alternatives are called resonance structures and highlight the delocalized nature of electrons in the molecule.

Formal charge calculation

Formal charge calculation plays a crucial role in determining the most likely resonance structure among several possibilities. The formal charge is a hypothetical charge you would obtain if all the atoms in the molecule had an equal share of the bonding electrons. It is given by the equation:

Formal charge = (Valence electrons of the atom) - (Non-bonding electrons) - (1/2 × Bonding electrons)

In simple terms, to calculate the formal charge, you begin with the number of valence electrons in the free, unbonded atom. Then, you subtract the number of non-bonding (lone pairs) electrons and half the number of bonding (shared) electrons. This calculation helps to indicate how the electrons are dispersed within the molecule, which is vital in predicting the molecule's properties and reactivity. Achieving a formal charge that is close to zero for each atom within a resonance structure often indicates that the structure is stable and significant.

N2O molecular structure

The N₂O molecular structure is intriguing because its actual arrangement of atoms and electrons is not fully represented by a single Lewis structure. Instead, its true structure is a blend of multiple resonance structures. Resonance structures exemplify a molecule's delocalized electrons that cannot be fully represented by a single, static picture.

When evaluating the importance of the N₂O resonance forms, we can correlate the calculated formal charges and observed bond lengths. For instance, a N-N bond length of 1.12 Å, which is longer than a typical N≡N triple bond, and an N-O bond length of 1.19 Å, which is shorter than a typical N=O double bond, suggest that the bonding is somewhere between a double and triple bond. This is consistent with resonance structures where electron density is shared between multiple bonding configurations, indicating that no one structure fully captures the electronic environment in N₂O.

Thus, a thorough understanding of resonance structures, coupled with formal charge calculations and observed bond lengths, provides a broader understanding of the N₂O molecule beyond what a single Lewis structure could convey.