Step 1: Understanding the Question:
We need to analyze the VSEPR (Valence Shell Electron Pair Repulsion) geometry of several pairs of molecules and identify the pair where both molecules share the exact same structural shape.
Step 2: Detailed Explanation:
Let's analyze the shapes of the molecules in each option:
(a) $\text{NH_3$ and $\text{SO}_2$:}
- $\text{NH}_3$: N has 5 valence electrons. It forms 3 single bonds with H and has 1 lone pair ($sp^3$). Geometry is Trigonal Pyramidal.
- $\text{SO}_2$: S has 6 valence electrons. It forms 2 double bonds with O and has 1 lone pair ($sp^2$). Geometry is Bent (V-shaped).
Mismatch.
(b) $\text{XeF_4$ and $\text{SF}_4$:}
- $\text{XeF}_4$: Xe has 8 valence electrons. It forms 4 single bonds with F and has 2 lone pairs ($sp^3d^2$). Geometry is Square Planar.
- $\text{SF}_4$: S has 6 valence electrons. It forms 4 single bonds with F and has 1 lone pair ($sp^3d$). Geometry is See-saw.
Mismatch.
(c) $\text{H_2\text{O}$ and $\text{SCl}_2$:}
- $\text{H}_2\text{O}$: O has 6 valence electrons. It forms 2 single bonds with H and has 2 lone pairs ($sp^3$). Geometry is Bent (V-shaped).
- $\text{SCl}_2$: S has 6 valence electrons. It forms 2 single bonds with Cl and has 2 lone pairs ($sp^3$). Geometry is also Bent (V-shaped).
Match! Both have the exact same shape.
(d) $\text{PCl_5$ and $\text{BrF}_5$:}
- $\text{PCl}_5$: P has 5 valence electrons. It forms 5 single bonds with no lone pairs ($sp^3d$). Geometry is Trigonal Bipyramidal.
- $\text{BrF}_5$: Br has 7 valence electrons. It forms 5 single bonds with F and has 1 lone pair ($sp^3d^2$). Geometry is Square Pyramidal.
Mismatch.
Step 3: Final Answer:
The matching pair is $\text{H}_{2}\text{O},\text{SCl}_{2}$, corresponding to option (c).