Step 1: Understanding the Concept:
Total lone pairs in a molecule include those on the central atom and all the surrounding ligand atoms.
Step 2: Detailed Explanation:
1. Central Xenon (Xe): Xe has 8 valence electrons. In \(XeOF_4\), it uses 2 electrons for the \(Xe=O\) bond and 4 electrons for the four \(Xe-F\) bonds. Total used = 6. Remaining = 2 electrons = 1 lone pair.
2. Fluorine atoms (4F): Each F has 7 valence electrons. After forming 1 bond, each has 6 electrons left = 3 lone pairs per F. Total = \(4 \times 3 = 12\).
3. Oxygen atom (1O): Oxygen has 6 valence electrons. After forming a double bond, it has 4 electrons left = 2 lone pairs.
4. Grand Total: \(1 (\text{Xe}) + 12 (\text{F}) + 2 (\text{O}) = 15\).
Step 3: Final Answer:
The total number of lone pairs is 15.