Describe the hydribisation in case of `PCl_(5)`. Why are the axial bonds longer as compared to equatorial bonds?

Explanation

The ground state and excited state outer electronic configuration of phosphorus (Z=15) are :
Ground state :

Excited state:

Phosphorus atom is `sp^(3)d` hybridized in the excited state. These orbitals are filled by the electron pairs donated by five Cl atoms as :
`PCl_(5)`

The five `sp^(3)d` hybrid orbitals are directed towards the five corners of the trigonal bypyramidals. Hence, the geometry of `PCl_(5)` can be represented as:

There are five P-Cl sigma bonds is `PCl_(5)`. Three P-Cl bonds lie in one plane and make an angle of `120^(@)` with each other. These bonds are called equatorial bonds.
The remaining two P-Cl bond lie above and below the equatorial plane and make an angle of `90^(@)` with the plane. These bonds are called axial bonds.
As the axial bond pairs suffer more repulsion from the equatorial bond pairs, axial bonds are slightly longer than equatorial bonds.