Write the known structure of $PCl_5$

In valence bond description, phosphorus in $PCl_5$ is commonly taken to form five hybrid orbitals: $sp^3d$ This gives a trigonal bipyramidal arrangement.

Check option A

A: “In this molecule, orbitals of phosphorous are assumed to undergo $sp^3d$ hybridization.”

This is the standard textbook description for $PCl_5$.

So, A is correct.

Check option B

B: “The geometry of $PCl_5$ is trigonal bipyramidal.”

In $PCl_5$, there are:

• 3 equatorial positions
• 2 axial positions

Hence the molecular geometry is indeed trigonal bipyramidal.

So, B is correct.

Check option D

D: “The three equatorial bonds of $PCl_5$ lie in a plane.”

In trigonal bipyramidal geometry, the three equatorial bonds are arranged at $120^\circ$ in the same plane.

So, D is correct.

Check option C

C: “$PCl_5$ has two axial bonds stronger than three equatorial bonds.”

This is incorrect.

In $PCl_5$:

• Axial bonds experience more repulsion because each axial bond pair is at $90^\circ$ to the three equatorial bond pairs.
• Equatorial bonds experience less repulsion comparatively.

Therefore:

• axial $P-Cl$ bonds are longer and weaker
• equatorial $P-Cl$ bonds are shorter and stronger

Hence the statement saying axial bonds are stronger is false.

Conclusion

The incorrect statement is: $\boxed{\text{C}}$