Total no of lone pairs in `XeO_(3)F_(2)` is `2x`. Find the value of `x`

Explanation

To solve the problem of finding the value of \( x \) in the equation \( 2x \) representing the total number of lone pairs in \( XeO_3F_2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Valence Electrons**:
- **Xenon (Xe)**: As a noble gas in Group 18, xenon has 8 valence electrons.
- **Oxygen (O)**: Each oxygen atom in Group 16 has 6 valence electrons. Since there are 3 oxygen atoms, the total is \( 3 \times 6 = 18 \) valence electrons.
- **Fluorine (F)**: Each fluorine atom in Group 17 has 7 valence electrons. Since there are 2 fluorine atoms, the total is \( 2 \times 7 = 14 \) valence electrons.

2. **Calculate Total Valence Electrons**:
\[ \text{Total valence electrons} = \text{Valence of Xe} + \text{Valence of O} + \text{Valence of F} = 8 + 18 + 14 = 40 \]

3. **Draw the Lewis Structure**:
- In \( XeO_3F_2 \), xenon is the central atom.
- It forms double bonds with each of the three oxygen atoms and single bonds with the two fluorine atoms.
- Each double bond uses 4 electrons (2 from Xe and 2 from O), and each single bond uses 2 electrons (1 from Xe and 1 from F).

4. **Count the Electrons Used in Bonds**:
- **For 3 double bonds with O**: \( 3 \times 4 = 12 \) electrons.
- **For 2 single bonds with F**: \( 2 \times 2 = 4 \) electrons.
- **Total electrons used in bonding**: \( 12 + 4 = 16 \) electrons.

5. **Calculate Remaining Electrons**:
\[ \text{Remaining electrons} = \text{Total valence electrons} - \text{Electrons used in bonds} = 40 - 16 = 24 \]

6. **Determine Lone Pairs**:
- Each oxygen atom, after forming a double bond, will have 2 lone pairs (4 electrons).
- Each fluorine atom, after forming a single bond, will have 3 lone pairs (6 electrons).
- Total lone pairs from oxygen: \( 3 \times 2 = 6 \).
- Total lone pairs from fluorine: \( 2 \times 3 = 6 \).
- Therefore, total lone pairs = \( 6 + 6 = 12 \).

7. **Set Up the Equation**:
\[ 2x = 12 \]

8. **Solve for \( x \)**:
\[ x = \frac{12}{2} = 6 \]

### Final Answer:
The value of \( x \) is \( 6 \).