Identify the species in different states

$PCl_5$ is known to have different structures in gaseous and solid states:

• In the gaseous state, it exists as a covalent molecule with trigonal bipyramidal geometry.
• In the solid state, it exists as an ionic lattice.

Ionic form of solid $PCl_5$

In the solid state, $PCl_5$ undergoes auto-ionisation: $2PCl_5 \rightarrow [PCl_4]^+ + [PCl_6]^-$

So the solid contains:

• $[PCl_4]^+$ cation
• $[PCl_6]^-$ anion

Geometry of $[PCl_4]^+$

For $[PCl_4]^+$:

• Central atom: $P$
• Number of bond pairs = 4
• No lone pair on phosphorus

Hence, by VSEPR, its geometry is tetrahedral.

Geometry of $[PCl_6]^-$

For $[PCl_6]^-$:

• Central atom: $P$
• Number of bond pairs = 6
• No lone pair on phosphorus

Hence, its geometry is octahedral.

Match with the options

• A: square pyramidal $\rightarrow$ incorrect
• B: tetrahedral $[PCl_4]^+$ and octahedral $[PCl_6]^-$ $\rightarrow$ correct
• C: square planar $[PCl_4]^+$ and octahedral $[PCl_6]^-$ $\rightarrow$ incorrect because $[PCl_4]^+$ is tetrahedral, not square planar
• D: trigonal bipyramidal $\rightarrow$ this is for gaseous $PCl_5$, not solid

Final Answer

The structure of $PCl_5$ in the solid state is: $\boxed{\text{tetrahedral } [PCl_4]^+ \text{ and octahedral } [PCl_6]^-}$

Hence, Option B is correct.