Step 1: Understanding the Molecular Geometry
PCl$_5$ has a trigonal bipyramidal structure with two types of bond positions: axial and equatorial.
The three chlorine atoms in the equatorial plane are bonded at \( 120^\circ \), while the two axial chlorine atoms are at \( 90^\circ \) with respect to the equatorial bonds. Step 2: Bond Length Difference
Due to repulsion effects, axial bonds are longer than equatorial bonds.
The axial bonds experience greater repulsion from equatorial bonds, causing them to be longer. Final Answer: PCl$_5$ has unequal bond lengths due to its trigonal bipyramidal shape.