To determine which compound has a molecular shape of trigonal bipyramidal, we need to follow a systematic approach involving the concept of steric number, bond pairs, and lone pairs.
### Step-by-Step Solution:
1. **Understand the Trigonal Bipyramidal Shape**:
- The trigonal bipyramidal shape occurs when the steric number (the number of bond pairs plus lone pairs around the central atom) is 5.
- For a trigonal bipyramidal shape, there should be 5 bond pairs and 0 lone pairs.
2. **Identify the Compounds**:
- We need to analyze the given compounds to determine their steric numbers and the arrangement of their electrons.
3. **Analyze PF3Cl2**:
- Phosphorus (P) has 5 valence electrons.
- Each fluorine (F) has 1 valence electron, and there are 3 fluorine atoms contributing 3 electrons.
- Chlorine (Cl) also has 1 valence electron, and there are 2 chlorine atoms contributing 2 electrons.
- Total valence electrons = 5 (P) + 3 (F) + 2 (Cl) = 10 electrons, which corresponds to 5 bond pairs.
- Since there are no lone pairs, the steric number is 5.
- Therefore, PF3Cl2 has a trigonal bipyramidal shape.
4. **Analyze IF5**:
- Iodine (I) has 7 valence electrons.
- Each fluorine (F) has 1 valence electron, and there are 5 fluorine atoms contributing 5 electrons.
- Total valence electrons = 7 (I) + 5 (F) = 12 electrons, which corresponds to 6 bond pairs.
- Since there is 1 lone pair, the steric number is 6, leading to an octahedral geometry, not trigonal bipyramidal.
5. **Analyze BrF5**:
- Bromine (Br) has 7 valence electrons.
- Each fluorine (F) has 1 valence electron, and there are 5 fluorine atoms contributing 5 electrons.
- Total valence electrons = 7 (Br) + 5 (F) = 12 electrons, which corresponds to 6 bond pairs.
- Since there is 1 lone pair, the steric number is 6, leading to an octahedral geometry, not trigonal bipyramidal.
6. **Conclusion**:
- The only compound that has a trigonal bipyramidal shape is PF3Cl2.
### Final Answer:
The compound with a molecular shape of trigonal bipyramidal is **PF3Cl2**.
