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To identify the most significant Lewis structure for dinitrogen monoxide ([tex]\(N_2O\)[/tex]), we can start by assigning formal charges to each atom in the three possible structures. Formal charge ([tex]\(FC\)[/tex]) for an atom in a molecule is calculated using the formula:
[tex]\[ FC = \text{(valence electrons on the free atom)} - \text{(non-bonding electrons)} - \frac{1}{2} \times \text{(bonding electrons)} \][/tex]
Let's first draw the three possible Lewis structures for [tex]\(N_2O\)[/tex]:
Structure 1:
[tex]\[ \text{N} \equiv \text{N} - \text{O} \][/tex]
[tex]\[ :N \equiv N - O: \][/tex]
Structure 2:
[tex]\[ \text{N} = \text{N} = \text{O} \][/tex]
[tex]\[ :N = N = O: \][/tex]
Structure 3:
[tex]\[ \text{N} - \text{N} \equiv \text{O} \][/tex]
[tex]\[ :N - N \equiv O: \][/tex]
Now, let's assign the formal charges for each atom in each structure.
### Structure 1: [tex]\(:N \equiv N - O:\)[/tex]
[tex]\[ \begin{array}{ccc} N & \equiv & N - O \\ \end{array} \][/tex]
1. N (left):
- Valence electrons: 5
- Non-bonding electrons: 2
- Bonding electrons: [tex]\(\frac{1}{2} \times 6\)[/tex]
[tex]\[ FC = 5 - 2 - \frac{1}{2} \times 6 = 0 \][/tex]
2. N (middle):
- Valence electrons: 5
- Non-bonding electrons: 0
- Bonding electrons: [tex]\(\frac{1}{2} \times 8\)[/tex]
[tex]\[ FC = 5 - 0 - \frac{1}{2} \times 8 = +1 \][/tex]
3. O (right):
- Valence electrons: 6
- Non-bonding electrons: 6
- Bonding electrons: [tex]\(\frac{1}{2} \times 2\)[/tex]
[tex]\[ FC = 6 - 6 - \frac{1}{2} \times 2 = -1 \][/tex]
So, the formal charges for Structure 1 are:
[tex]\[ (0, +1, -1) \][/tex]
### Structure 2: [tex]\(:N = N = O:\)[/tex]
[tex]\[ \begin{array}{ccc} N & = & N = O \\ \end{array} \][/tex]
1. N (left):
- Valence electrons: 5
- Non-bonding electrons: 2
- Bonding electrons: [tex]\(\frac{1}{2} \times 4\)[/tex]
[tex]\[ FC = 5 - 2 - \frac{1}{2} \times 4 = -1 \][/tex]
2. N (middle):
- Valence electrons: 5
- Non-bonding electrons: 0
- Bonding electrons: [tex]\(\frac{1}{2} \times 4\)[/tex]
[tex]\[ FC = 5 - 0 - \frac{1}{2} \times 4 = +1 \][/tex]
3. O (right):
- Valence electrons: 6
- Non-bonding electrons: 4
- Bonding electrons: [tex]\(\frac{1}{2} \times 4\)[/tex]
[tex]\[ FC = 6 - 4 - \frac{1}{2} \times 4 = 0 \][/tex]
So, the formal charges for Structure 2 are:
[tex]\[ (-1, +1, 0) \][/tex]
### Structure 3: [tex]\(:N - N \equiv O:\)[/tex]
[tex]\[ \begin{array}{ccc} N & - & N \equiv O \\ \end{array} \][/tex]
1. N (left):
- Valence electrons: 5
- Non-bonding electrons: 2
- Bonding electrons: [tex]\(\frac{1}{2} \times 2\)[/tex]
[tex]\[ FC = 5 - 2 - \frac{1}{2} \times 2 = 0 \][/tex]
2. N (middle):
- Valence electrons: 5
- Non-bonding electrons: 2
- Bonding electrons: [tex]\(\frac{1}{2} \times 6\)[/tex]
[tex]\[ FC = 5 - 2 - \frac{1}{2} \times 6 = +2 \][/tex]
3. O (right):
- Valence electrons: 6
- Non-bonding electrons: 4
- Bonding electrons: [tex]\(\frac{1}{2} \times 4\)[/tex]
[tex]\[ FC = 6 - 4 - \frac{1}{2} \times 4 = 0 \][/tex]
So, the formal charges for Structure 3 are:
[tex]\[ (0, +2, 0) \][/tex]
Comparing the formal charges, Structure 1 (0, +1, -1) is the most significant because it has the smallest separation of formal charges and the fewest atoms with nonzero formal charges. Additionally, the negative formal charge is on the more electronegative atom (Oxygen).
[tex]\[ FC = \text{(valence electrons on the free atom)} - \text{(non-bonding electrons)} - \frac{1}{2} \times \text{(bonding electrons)} \][/tex]
Let's first draw the three possible Lewis structures for [tex]\(N_2O\)[/tex]:
Structure 1:
[tex]\[ \text{N} \equiv \text{N} - \text{O} \][/tex]
[tex]\[ :N \equiv N - O: \][/tex]
Structure 2:
[tex]\[ \text{N} = \text{N} = \text{O} \][/tex]
[tex]\[ :N = N = O: \][/tex]
Structure 3:
[tex]\[ \text{N} - \text{N} \equiv \text{O} \][/tex]
[tex]\[ :N - N \equiv O: \][/tex]
Now, let's assign the formal charges for each atom in each structure.
### Structure 1: [tex]\(:N \equiv N - O:\)[/tex]
[tex]\[ \begin{array}{ccc} N & \equiv & N - O \\ \end{array} \][/tex]
1. N (left):
- Valence electrons: 5
- Non-bonding electrons: 2
- Bonding electrons: [tex]\(\frac{1}{2} \times 6\)[/tex]
[tex]\[ FC = 5 - 2 - \frac{1}{2} \times 6 = 0 \][/tex]
2. N (middle):
- Valence electrons: 5
- Non-bonding electrons: 0
- Bonding electrons: [tex]\(\frac{1}{2} \times 8\)[/tex]
[tex]\[ FC = 5 - 0 - \frac{1}{2} \times 8 = +1 \][/tex]
3. O (right):
- Valence electrons: 6
- Non-bonding electrons: 6
- Bonding electrons: [tex]\(\frac{1}{2} \times 2\)[/tex]
[tex]\[ FC = 6 - 6 - \frac{1}{2} \times 2 = -1 \][/tex]
So, the formal charges for Structure 1 are:
[tex]\[ (0, +1, -1) \][/tex]
### Structure 2: [tex]\(:N = N = O:\)[/tex]
[tex]\[ \begin{array}{ccc} N & = & N = O \\ \end{array} \][/tex]
1. N (left):
- Valence electrons: 5
- Non-bonding electrons: 2
- Bonding electrons: [tex]\(\frac{1}{2} \times 4\)[/tex]
[tex]\[ FC = 5 - 2 - \frac{1}{2} \times 4 = -1 \][/tex]
2. N (middle):
- Valence electrons: 5
- Non-bonding electrons: 0
- Bonding electrons: [tex]\(\frac{1}{2} \times 4\)[/tex]
[tex]\[ FC = 5 - 0 - \frac{1}{2} \times 4 = +1 \][/tex]
3. O (right):
- Valence electrons: 6
- Non-bonding electrons: 4
- Bonding electrons: [tex]\(\frac{1}{2} \times 4\)[/tex]
[tex]\[ FC = 6 - 4 - \frac{1}{2} \times 4 = 0 \][/tex]
So, the formal charges for Structure 2 are:
[tex]\[ (-1, +1, 0) \][/tex]
### Structure 3: [tex]\(:N - N \equiv O:\)[/tex]
[tex]\[ \begin{array}{ccc} N & - & N \equiv O \\ \end{array} \][/tex]
1. N (left):
- Valence electrons: 5
- Non-bonding electrons: 2
- Bonding electrons: [tex]\(\frac{1}{2} \times 2\)[/tex]
[tex]\[ FC = 5 - 2 - \frac{1}{2} \times 2 = 0 \][/tex]
2. N (middle):
- Valence electrons: 5
- Non-bonding electrons: 2
- Bonding electrons: [tex]\(\frac{1}{2} \times 6\)[/tex]
[tex]\[ FC = 5 - 2 - \frac{1}{2} \times 6 = +2 \][/tex]
3. O (right):
- Valence electrons: 6
- Non-bonding electrons: 4
- Bonding electrons: [tex]\(\frac{1}{2} \times 4\)[/tex]
[tex]\[ FC = 6 - 4 - \frac{1}{2} \times 4 = 0 \][/tex]
So, the formal charges for Structure 3 are:
[tex]\[ (0, +2, 0) \][/tex]
Comparing the formal charges, Structure 1 (0, +1, -1) is the most significant because it has the smallest separation of formal charges and the fewest atoms with nonzero formal charges. Additionally, the negative formal charge is on the more electronegative atom (Oxygen).
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