The total number of lone pairs of electrons in `N_(2)O_(3)` is

Explanation

To determine the total number of lone pairs of electrons in \( N_2O_3 \) (dinitrogen trioxide), we can follow these steps:

### Step 1: Determine the Lewis Structure of \( N_2O_3 \)

1. **Count the total number of valence electrons**:
- Nitrogen (N) has 5 valence electrons, and there are 2 nitrogen atoms: \( 2 \times 5 = 10 \) electrons.
- Oxygen (O) has 6 valence electrons, and there are 3 oxygen atoms: \( 3 \times 6 = 18 \) electrons.
- Total valence electrons = \( 10 + 18 = 28 \) electrons.

### Step 2: Draw the skeletal structure

2. **Arrange the atoms**:
- A common skeletal structure for \( N_2O_3 \) is \( N-N-O-O \) with one nitrogen bonded to the other nitrogen and each nitrogen bonded to an oxygen atom.

### Step 3: Distribute the electrons

3. **Form bonds and distribute remaining electrons**:
- Connect the nitrogen atoms with a single bond and each nitrogen to an oxygen with a double bond. This uses up 12 electrons (6 for 3 double bonds).
- Remaining electrons = \( 28 - 12 = 16 \) electrons.
- Place the remaining electrons to satisfy the octet rule for oxygen atoms first, which will take 12 electrons (6 for each oxygen).
- This leaves us with \( 16 - 12 = 4 \) electrons.

### Step 4: Assign lone pairs

4. **Complete the octets**:
- Each nitrogen atom will have one lone pair of electrons (2 electrons) remaining.
- The total lone pairs from nitrogen = 2 (1 from each nitrogen).
- The oxygen atoms will have 2 lone pairs each (4 electrons) because they are already bonded to nitrogen with double bonds.

### Step 5: Count the total lone pairs

5. **Calculate total lone pairs**:
- From nitrogen: 2 lone pairs (1 from each nitrogen).
- From oxygen: 6 lone pairs (3 oxygen atoms each having 2 lone pairs).
- Total lone pairs = \( 2 + 6 = 8 \) lone pairs.

### Final Answer

The total number of lone pairs of electrons in \( N_2O_3 \) is **8 lone pairs**.

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