Question

Nitrogen is the central atom in molecules of nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right) .\) Draw Lewis structures for another possible arrangement: \(\mathrm{N}-\mathrm{O}-\mathrm{N} .\) Assign formal charges and suggest a reason why the structure is not likely to be stable.

Short answer

Answer: The N-O-N arrangement of the nitrous oxide molecule is likely to be unstable due to its less ideal distribution of charges, resulting in higher electrostatic repulsion and potential energy. In this arrangement, the right Nitrogen atom carries a formal charge of +1, while the other Nitrogen atom and Oxygen atom have formal charges of 0. Molecules with smaller formal charges are usually more stable, and the N-O-N structure has a greater formal charge than the actual N2O molecule (where nitrogen is the central atom).

Step-by-step solution

Determine the total number of valence electrons

First, we need to find the total number of valence electrons in the N2O molecule. Nitrogen has 5 valence electrons, and Oxygen has 6 valence electrons. Total valence electrons = 2 * (valence electrons of N) + (valence electrons of O) = 2 * 5 + 6 = 10 + 6 = 16

Draw the skeleton structure of the molecule and place electrons

Next, draw the skeleton of the molecule, N-O-N, and place a single bond between each pair of adjacent atoms. In a single bond, there are two shared electrons, so after creating the single bonds between Nitrogen and Oxygen, we have 16 - (2×2) = 12 electrons left. Now, distribute the remaining 12 electrons to the outer atoms (both Nitrogen atoms) in pairs. At this point, each Nitrogen atom has 6 electrons and the Oxygen atom has 8 electrons.

Assign formal charges to each atom

To calculate the formal charge of each atom, we use the formula: Formal charge = [Number of valence electrons] - [Number of nonbonding electrons] - 1/2 [Number of bonding electrons] For the left Nitrogen atom (N1): Formal charge = 5 - 4 - 1/2 (2) = 5 - 4 - 1 = 0 For the Oxygen atom (O): Formal charge = 6 - 4 - 1/2 (4) = 6 - 4 - 2 = 0 For the right Nitrogen atom (N2): Formal charge = 5 - 2 - 1/2 (4) = 5 - 2 - 2 = 1

Determine the stability of the structure

In the N-O-N molecule, both Nitrogen and Oxygen atoms have formal charges of 0, and the right Nitrogen atom has a formal charge of +1. This molecule has a greater formal charge than the actual N2O molecule (where nitrogen is the central atom). Because molecules with smaller formal charges are usually more stable, the N-O-N structure is less stable and not likely to be the actual structure of the nitrous oxide molecule. This is mainly due to the fact that the molecule has a less ideal distribution of charges, which leads to higher electrostatic repulsion and potential energy.

Key concepts

Formal Charge

Formal charge is an essential concept when drawing Lewis structures. It helps us understand how the electrons are distributed around the atoms in a molecule. This is crucial for understanding the molecule's stability and reactivity. The formal charge of an atom is calculated using the formula:\[\text{Formal charge} = \text{(Number of valence electrons)} - \text{(Number of nonbonding electrons)} - \frac{1}{2} \text{(Number of bonding electrons)}\]For example, in the N-O-N structure of nitrous oxide, we found that the oxygen atom has a formal charge of 0. The left nitrogen also has a formal charge of 0, whereas the right nitrogen has a formal charge of +1.

• Atoms prefer to have formal charges close to zero to be more stable.
• A structure with atoms having non-zero formal charges can lead to instability.
• The sum of formal charges for a molecule should equal the overall charge of the molecule.

Typically, Lewis structures with fewer and smaller formal charges are considered more stable, as these structures have reduced stress from electrostatic forces.

Valence Electrons

Valence electrons are the outermost electrons of an atom that participate in chemical bonding. They are fundamental in determining the way atoms interact and form bonds in molecules. In Lewis structures, valence electrons are depicted as dots around atomic symbols or lines representing bonds. To find the number of valence electrons in a molecule, consider the group number of the element in the periodic table. For example:

• Nitrogen, found in Group 15, has five valence electrons.
• Oxygen, found in Group 16, has six valence electrons.

In the nitrous oxide molecule, N-N-O, we calculated the total number of valence electrons to be 16. This includes two nitrogen atoms contributing 5 electrons each and one oxygen atom contributing 6 electrons. Correctly accounting for valence electrons ensures that our Lewis structure accurately reflects the molecule, aiding in bonding understanding.

Molecular Stability

Molecular stability refers to how likely a molecule is to exist in a particular structure with minimal energy. Stability is greatly influenced by the distribution of electrons and the resulting formal charges of the atoms in the molecule. The N-O-N configuration of nitrous oxide is less stable compared to its more common N2O structure. This is because:

• Molecules strive to minimize formal charges across their atoms.
• Zero or smaller formal charges usually imply a stable configuration.
• The N-O-N structure contains a +1 formal charge, indicating higher energy and less stability.

Furthermore, molecules tend to be more stable when the negative charge is on the more electronegative atom. Oxygen, being more electronegative than nitrogen, prefers to carry less positive or even negative formal charges when possible, enhancing molecular stability. In essence, a stable molecule is likely to have an even and minimal charge distribution, reducing internal repulsions and conserving energy.