Why all P - F bonds in `PF_(5)` are not equivalent?

Options

A. `PF_(5)" has "sp^(3)d` hybridisation, out of five P-F bonds three are equatorial which have different lengths.
B. `PF_(5)" has "sp^(3)` hybridisation, out of five P-F bonds two are equatorial which have different lengths.
C. Out of five P-F bonds two are axial and three equatorial. All five bonds have different bond lengths.
D. `PF_(5)` is made up of two types of bonds namely covalent and coordinate, hence are not equivalent.

Answer

To understand why all P-F bonds in PF₅ are not equivalent, we need to analyze the molecular structure and hybridization of phosphorus in PF₅. Here’s a step-by-step solution:

### Step 1: Determine the Hybridization of Phosphorus in PF₅
Phosphorus in PF₅ undergoes hybridization to form five equivalent orbitals. The hybridization involved is sp³d, which means one s orbital, three p orbitals, and one d orbital combine to form five sp³d hybrid orbitals.

**Hint:** Remember that hybridization involves mixing atomic orbitals to form new hybrid orbitals that can accommodate bonding.

### Step 2: Understand the Molecular Geometry
The molecular geometry of PF₅ is trigonal bipyramidal. In this structure, there are three equatorial positions and two axial positions. The three equatorial bonds are arranged in a plane, while the two axial bonds are oriented above and below this plane.

**Hint:** Visualize the geometry using a model or diagram to see how the atoms are arranged in space.

### Step 3: Analyze Bond Positions and Repulsions
In PF₅, the three equatorial P-F bonds experience less steric repulsion compared to the axial P-F bonds. This is because the equatorial bonds are 120 degrees apart, while the axial bonds are 180 degrees apart from each other and 90 degrees from the equatorial bonds. The difference in bond angles leads to different bond lengths and strengths.

**Hint:** Consider how the arrangement of bonds affects the overall stability and energy of the molecule.

### Step 4: Conclusion on Bond Equivalence
Due to the differences in bond angles and the spatial arrangement of the bonds, the P-F bonds in PF₅ are not equivalent. The equatorial bonds are longer and weaker than the axial bonds due to the differences in electron repulsion and bond angles.

**Hint:** Think about how molecular geometry influences the properties of bonds in a molecule.

### Final Answer
In summary, the P-F bonds in PF₅ are not equivalent because of the trigonal bipyramidal geometry, where the three equatorial bonds and two axial bonds have different bond lengths and angles due to varying repulsions.