Final answer:
The assertion that P-Cl bond lengths are equal in PCl₃ but different in PCl₅ is true due to their respective molecular geometries and hybridizations. PCl₃ has a trigonal pyramidal shape with sp³ hybridization, while PCl₅ has a trigonal bipyramidal shape with sp³d hybridization.
Step-by-step explanation:
The question addresses the bond lengths in two different phosphorus compounds: phosphorus trichloride (PCl₃) and phosphorus pentachloride (PCl₅). In PCl₃, all P-Cl bonds are equal in length, which can be attributed to the trigonal pyramidal molecular geometry and sp³ hybridization. This equality in bond length is due to the symmetric arrangement of the chlorine atoms around the central phosphorus atom. On the other hand, PCl₅ has different P-Cl bond lengths; this is due to the compound's trigonal bipyramidal geometry. There are axial and equatorial positions in this geometry with sp³d hybridization of the central P atom, leading to different bond lengths.
Moreover, the assertion and reason being analyzed are incomplete without context. However, the assertion that P-Cl bond lengths are equal in PCl₃ but different in PCl₅ is true. Yet, regarding PCl₃ and PCl₅ reacting with water to yield hydrogen chloride and an oxyacid, this is unrelated to the bond length issue.