Step 1: Understanding the Concept:
To accurately determine the number of lone pairs residing on the central atom of a molecule, we must apply the principles of VSEPR theory. This involves finding the total number of valence electrons on the central atom and subtracting the electrons that are shared in covalent bonds to find the remaining non-bonding electrons (lone pairs).
Step 2: Key Formula or Approach:
The number of lone pairs (LP) can be quickly calculated using the logic:
\[ \text{LP} = \frac{\text{Valence } e^- \text{ on central atom} - \text{Number of bonding } e^-}{2} \]
For molecules with single bonds, this simplifies to: $\text{LP} = \frac{\text{Group Number} - \text{Valency}}{2}$.
Step 3: Detailed Explanation:
Let's systematically analyze each molecule to count the lone pairs:
(A) $\text{NH_3$:} The central atom is Nitrogen (N), which is located in Group 15 and possesses 5 valence electrons. It forms 3 single bonds with 3 Hydrogen atoms, utilizing 3 electrons.
Remaining non-bonding electrons = $5 - 3 = 2$. This pair constitutes exactly 1 lone pair.
(B) $\text{SF_4$:} The central atom is Sulfur (S), located in Group 16, possessing 6 valence electrons. It forms 4 single bonds with 4 Fluorine atoms, utilizing 4 electrons.
Remaining non-bonding electrons = $6 - 4 = 2$. This pair constitutes exactly 1 lone pair.
(C) $\text{ICl_3$:} The central atom is Iodine (I), a halogen located in Group 17, possessing 7 valence electrons. It forms 3 single bonds with 3 Chlorine atoms, utilizing 3 electrons.
Remaining non-bonding electrons = $7 - 3 = 4$. These 4 electrons constitute exactly 2 lone pairs.
(D) $\text{PCl_3$:} The central atom is Phosphorus (P), located in Group 15, possessing 5 valence electrons. It forms 3 single bonds with 3 Chlorine atoms, utilizing 3 electrons.
Remaining non-bonding electrons = $5 - 3 = 2$. This pair constitutes exactly 1 lone pair.
Comparing the tabulated results, $\text{ICl}_3$ clearly has the highest number of lone pairs on its central atom among the given choices.
Step 4: Final Answer:
The molecule $\text{ICl}_3$ has the highest number of lone pairs (two) on its central atom.