Which of the following pair of species have identical shape?

Options

A. `CO_(2), SO_(2)`
B. `CIF_(3), BF_(3)`
C. `XeF_(2), I_(3)^(-)`
D. `SO_(4)^(2-), XeF_(4)`

Answer

To determine which pair of species has identical shapes, we will analyze the hybridization and molecular geometry of each pair.

### Step-by-Step Solution:

1. **Identify the first pair: CO2 and SO2**
- **CO2**:
- Carbon (C) has 4 valence electrons, and each Oxygen (O) has 6 valence electrons.
- Using the formula for hybridization:
\[ \text{Hybridization} = \frac{1}{2} \left( \text{Valence electrons of C} + \text{Valence electrons of O} + \text{Monovalent atoms} + \text{Charge} \right) \]
\[ = \frac{1}{2} \left( 4 + 2 \times 6 + 0 \right) = \frac{1}{2} \left( 16 \right) = 8 \rightarrow \text{SP hybridization} \]
- CO2 has a linear shape.
- **SO2**:
- Sulfur (S) has 6 valence electrons, and each Oxygen has 6 valence electrons.
\[ = \frac{1}{2} \left( 6 + 2 \times 6 + 0 \right) = \frac{1}{2} \left( 18 \right) = 9 \rightarrow \text{SP2 hybridization} \]
- SO2 has a bent shape.
- **Conclusion**: CO2 and SO2 do not have identical shapes.

2. **Identify the second pair: CLF3 and BF3**
- **CLF3**:
- Chlorine (Cl) has 7 valence electrons, and each Fluorine (F) has 7 valence electrons.
\[ = \frac{1}{2} \left( 7 + 3 \times 7 + 0 \right) = \frac{1}{2} \left( 28 \right) = 14 \rightarrow \text{SP3D hybridization} \]
- CLF3 has a T-shaped geometry.
- **BF3**:
- Boron (B) has 3 valence electrons, and each Fluorine has 7 valence electrons.
\[ = \frac{1}{2} \left( 3 + 3 \times 7 + 0 \right) = \frac{1}{2} \left( 24 \right) = 12 \rightarrow \text{SP2 hybridization} \]
- BF3 has a trigonal planar shape.
- **Conclusion**: CLF3 and BF3 do not have identical shapes.

3. **Identify the third pair: XeF2 and I3-**
- **XeF2**:
- Xenon (Xe) has 8 valence electrons, and each Fluorine has 7 valence electrons.
\[ = \frac{1}{2} \left( 8 + 2 \times 7 + 0 \right) = \frac{1}{2} \left( 22 \right) = 11 \rightarrow \text{SP3D hybridization} \]
- XeF2 has a linear shape due to 3 lone pairs.
- **I3-**:
- Iodine (I) has 7 valence electrons, and with 2 Iodine atoms and a -1 charge:
\[ = \frac{1}{2} \left( 7 + 2 \times 7 + 1 \right) = \frac{1}{2} \left( 22 \right) = 11 \rightarrow \text{SP3D hybridization} \]
- I3- also has a linear shape due to 3 lone pairs.
- **Conclusion**: XeF2 and I3- have identical shapes.

4. **Identify the fourth pair: SO4^2- and XeF4**
- **SO4^2-**:
- Sulfur (S) has 6 valence electrons, and each Oxygen has 6 valence electrons with a -2 charge:
\[ = \frac{1}{2} \left( 6 + 4 \times 6 + 2 \right) = \frac{1}{2} \left( 26 \right) = 13 \rightarrow \text{SP3 hybridization} \]
- SO4^2- has a tetrahedral shape.
- **XeF4**:
- Xenon (Xe) has 8 valence electrons, and each Fluorine has 7 valence electrons:
\[ = \frac{1}{2} \left( 8 + 4 \times 7 + 0 \right) = \frac{1}{2} \left( 36 \right) = 18 \rightarrow \text{SP3D2 hybridization} \]
- XeF4 has a square planar shape.
- **Conclusion**: SO4^2- and XeF4 do not have identical shapes.

### Final Answer:
The pair of species that have identical shapes is **XeF2 and I3-**.