# Structure of phosphorus pentachloride

Why is the shape of $\ce{PCl5}$ trigonal bipyramidal? All the $\ce{Cl}$ atoms must be at equal distances forming a star like shape. However, in the actual shape, the distance between the $\ce{Cl}$ atoms in the equatorial position is less than the ones in the axial position.

• Welcome to Chemistry.SE! Take the tour to get familiar with this site. Mathematical expressions and equations can be formatted using $\LaTeX$ syntax. Have a look at this question, it might already contain an answer. – Martin - マーチン Jun 21 '16 at 14:26
• see the last para of the answer to this question. It basically covers up your question. – Nilay Ghosh Jun 21 '16 at 18:25
• I can’t believe that this is not a dupe! =O – Jan Jun 21 '16 at 20:19

This website from the School of Mathematics and Statistics at UNSW explains why distributing points on a sphere is tough and that perfect distribution is possible only in certain cases $(n=1,2,4,6,8,12,\&\ 20)$. These cases have been known for a long time — they correspond to the platonic solids (plus a point and a line segment). Even trigonal planar does not represent an even distribution on the sphere.
## The geometry of $sp^3d" hybridisation, i.e: trigonal bipyramidal happens because of unequal hybridization of atomic orbitals. The hybrid orbitals of a trigonal bipyramidal structure consist of two sets namely axial and equatorial orbitals. The two axial orbitals are made by inter-mixing of$p$and$d$atomic orbitals whereas the three equatorial orbitals are formed by intermixing of one$s$and two$p$orbitals. Since the equatorial orbitals have a higher percentage of$s$character compared to the axial orbitals, they are shorter than axial orbitals. This is why you have two set of distances in$PCl_5$. This is NOT true when there are more than 1 atom except for one specific case which I will add to the answer if requested (did not add it here to avoid complication since the OP appears to be new to the topic) • This is a little bit backwards as orbital hybridization is a mathematical construct developed to rationalize observed geometry with the shapes and orientations of the canonical hydrogenic atomic orbitals. It is more appropriate to say that$\ce{PCl5}$is$sp^3 d$hybridized because it has trigonal planar geometry. – Ben Norris Jun 21 '16 at 15:27 •$PCl_5$is trigonal bipyramidal. Of course, hybridization is a mathematical construct developed to explain observed geometry but I believe that the OP isn't through with the basics yet. So I thought an answer based on VSEPR theory would be sufficient. – Yashas Jun 21 '16 at 15:30 • Most, if not all, trigonal bipyramidal structures I know, including$\ce{PCl5}$, have no contribution of d-orbitals.$-1$. – Jan Jun 21 '16 at 20:11 • huh? You can't form 5 bonds with just s and p orbitals.$PCl_5\$ is a hypervalent molecule. – Yashas Jun 22 '16 at 6:18