Complete the three Lewis structures for N(NO₂)₂^– by adding missing lone pair electrons and assigning formal charges. Do not add resonance arrows.

### Completing the Lewis Structures for \( N(NO_2)_2^- \)

To complete the three Lewis structures for \( N(NO_2)_2^- \), we will add the missing lone pair electrons and assign formal charges systematically, ensuring each structure follows the rules of electron distribution and charge calculation.

### **Step 1: Molecular Information**

The molecular formula \( N(NO_2)_2^- \) indicates:

- A central nitrogen atom (\( N_c \)) bonded to two nitro groups (\( NO_2 \)).

- Each nitro group (\( NO_2 \)) contains:

- One nitrogen atom.

- Two oxygen atoms.

- The molecule carries a net charge of \( -1 \).

### **Step 2: Valence Electrons**

To calculate the total number of valence electrons:

- Nitrogen (\( N \)): \( 5 \, \text{electrons} \times 3 \, \text{atoms} = 15 \, \text{electrons} \).

- Oxygen (\( O \)): \( 6 \, \text{electrons} \times 4 \, \text{atoms} = 24 \, \text{electrons} \).

- \( -1 \) charge: Adds 1 extra electron.

\[\text{Total valence electrons: } 15 + 24 + 1 = 40\]

### **Step 3: Bond Distribution**

Each structure contains 4 single bonds and 2 double bonds.

Thus, \( 4 \, \text{single bonds} + 2 \, \text{double bonds} = 16 \, \text{bonding electrons} \).

The remaining \( 40 - 16 = 24 \, \text{electrons} \) are assigned as lone pairs on oxygen atoms to satisfy the octet rule.

### **Step 4: Assigning Lone Pairs and Formal Charges**

#### Formal Charge Formula:

\[FC = \text{Valence electrons} - \text{Non-bonding electrons} - \frac{\text{Bonding electrons}}{2}\]

We calculate the formal charges for each atom in the molecule.

### **Structure I**

1. **Central Nitrogen (\( N_c \))**:

- Forms a single and a double bond to the nitro groups.

- Valence: \( 5 \), Bonding: \( 6 \), Nonbonding: \( 2 \).

\[FC = 5 - 2 - \frac{6}{2} = 5 – 2 – 3 = 0\]

2. **Left Nitro Group Nitrogen**:

- Forms one single bond to \( N_c \), one double bond to oxygen, and one single bond to oxygen.

- Valence: \( 5 \), Bonding: \( 8 \), Nonbonding: \( 0 \).

\[FC = 5 - 0 - \frac{8}{2} = 5 - 4 = +1\]

3. **Right Nitro Group Nitrogen**:

- Forms one double bond to \( N_c \), and two single bonds to oxygen.

- Valence: \( 5 \), Bonding: \( 8 \), Nonbonding: \( 0 \).

\[FC = 5 - 0 - \frac{8}{2} = 5 - 4 = +1\]

4. **Double-Bonded Oxygen**:

- Valence: \( 6 \), Bonding: \( 4 \), Nonbonding: \( 4 \).

\[ FC = 6 - 4 - \frac{4}{2} = 6 - 4 = 0\]

5. **Single-Bonded Oxygen**:

- Valence: \( 6 \), Bonding: \( 2 \), Nonbonding: \( 6 \).

\[FC = 6 - 6 - \frac{2}{2} = 6 - 7 = -1\]

**Net Charge:** \[+1 + (-1) + (-1) = -1\]

Repeat the same calculations for Structure I and II.

### **Structure II**

### **Structure III**

The total net charge in all cases is \( -1 \), consistent with the molecular formula \( N(NO_2)_2^- \).

These are the three valid Lewis structures for \( N(NO_2)_2^- \), with lone pairs and formal charges distributed correctly.

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