Explain why PCl5 is trigonal bipyramidal whereas IF5 is square pyramidal.

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Q. Explain why PCl5 is trigonal bipyramidal whereas IF5 is square pyramidal.

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Concept understanding — Orbital Hybridization Theory

Orbital Hybridization Theory – From Intuition to Precision

The Problem That Started It All

Imagine you are looking at a methane molecule, $\text{CH}_4$ . Carbon has four valence electrons: two in the $2s$ orbital and two in the $2p$ orbitals. If carbon used its pure atomic orbitals to bond, you would expect two bonds from the $2s$ (identical, but one direction) and two from the $2p$ (at $90^\circ$ to each other). That would give you three different bond types and bond angles of $90^\circ$ and something else.

But experiment says methane is perfectly tetrahedral: all four bonds are identical in length, strength, and energy, and the bond angle is $109.5^\circ$ , not $90^\circ$ . Something is fundamentally wrong with the "pure orbital" picture.

This is the puzzle that hybridization theory solves.

The Core Intuition

Think of atomic orbitals as shapes that an electron can occupy. The $s$ orbital is a sphere. The $p$ orbitals are dumbbells along the $x$ , $y$ , and $z$ axes. When an atom forms bonds, it wants to mix these shapes together to create new, hybrid shapes that point in directions that maximise bond strength and minimise repulsion.

It is like mixing primary colours to get new colours. You don't have to use red, blue, and yellow separately — you can blend them to get green, orange, or purple. Similarly, an atom can blend its $s$ and $p$ orbitals to get new hybrid orbitals that are better suited for bonding.

The key insight: hybridization is a mathematical mixing of atomic orbitals on the same atom to produce an equal number of new, equivalent hybrid orbitals. The number of hybrid orbitals formed always equals the number of atomic orbitals mixed.

The Precise Statement

s

The theory rests on three pillars:

Conservation of orbitals: Mixing $n$ atomic orbitals gives exactly $n$ hybrid orbitals. No orbitals are created or destroyed.
Energy averaging: The hybrid orbitals have energies that are intermediate between the original $s$ and $p$ energies.
Directionality: Hybrid orbitals point in specific directions to minimise electron pair repulsion, which directly determines molecular shape.

The Three Common Hybridizations

Hybridization	Orbitals Mixed	Number of Hybrids	Geometry	Bond Angle	Example
$sp$	one $s$ + one $p$	2	Linear	$180^\circ$	$\text{BeCl}_2$
$sp^2$	one $s$ + two $p$	3	Trigonal planar	$120^\circ$	$\text{BF}_3$
$sp^3$	one $s$ + three $p$	4	Tetrahedral	$109.5^\circ$	$\text{CH}_4$

Note

The superscript in $sp^2$ or $sp^3$ tells you how many $p$ orbitals were mixed. $sp^3$ means one $s$ and three $p$ orbitals were blended. It does not mean there are three $s$ orbitals — there is only one $s$ orbital per shell.

How It Works: The Methane Example

Carbon in its ground state has the configuration $1s^2 2s^2 2p_x^1 2p_y^1$ . Only two unpaired electrons — it should form only two bonds. But we know carbon forms four bonds.

Step 1: Promotion. One electron from the $2s$ orbital is promoted (excited) to the empty $2p_z$ orbital. This costs a small amount of energy, but it is more than compensated by the energy released when four strong bonds form instead of two.

Step 2: Hybridization. The one $2s$ orbital and three $2p$ orbitals mix to form four equivalent $sp^3$ hybrid orbitals. Each hybrid has 25% $s$ character and 75% $p$ character.

Step 3: Bonding. Each $sp^3$ hybrid overlaps with the $1s$ orbital of a hydrogen atom, forming four identical $\sigma$ bonds. The hybrids point to the corners of a tetrahedron, giving the $109.5^\circ$ angle. …

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PCl₅ has five bonding pairs and no lone pairs, adopting a trigonal bipyramidal geometry to minimize repulsion. IF₅ has five bonding pairs and one lone pair, which occupies an equatorial position in the octahedral electron geometry, leaving the five fluorines in a square pyramidal arrangement.

The shapes of molecules are dictated not just by the number of atoms bonded to the central atom, but by the total number of electron pairs—both bonding and lone pairs—around it. VSEPR (Valence Shell Electron Pair Repulsion) theory tells us that electron pairs arrange themselves to minimize repulsion, and lone pairs exert stronger repulsive forces than bonding pairs because they are held closer to the nucleus and occupy more angular space.

Hybridization provides the orbital framework for these geometries. The central atom mixes its atomic orbitals to form hybrid orbitals that point toward the positions of minimum repulsion. The key is to count all electron domains (bonds + lone pairs) to determine the electron geometry, then look at the positions of atoms alone to name the molecular shape.

Why PCl₅ is trigonal bipyramidal

Valence electrons and bonding in PCl₅

Phosphorus (group 15) has five valence electrons. Each of the five chlorine atoms contributes one electron for bonding, giving five $\ce{P–Cl}$ single bonds. Phosphorus uses all five valence electrons in bonding, leaving no lone pairs on the central atom.
Electron geometry

With five electron domains (all bonding pairs), the electron geometry that minimizes repulsion is trigonal bipyramidal. This corresponds to $sp^3d$ hybridization: one $s$ , three $p$ , and one $d$ orbital from phosphorus mix to form five equivalent hybrid orbitals.
Molecular geometry

Because there are no lone pairs, the molecular geometry is identical to the electron geometry: trigonal bipyramidal. Three chlorines occupy equatorial positions (in a plane, $120°$ apart), and two occupy axial positions (above and below the plane, $90°$ from the equatorial atoms).

\text{Steric number} = 5, \quad \text{Lone pairs} = 0 \quad \Rightarrow \quad \text{Trigonal bipyramidal}

Why IF₅ is square pyramidal

Valence electrons and bonding in IF₅

Iodine (group 17) has seven valence electrons. Five are used to form $\ce{I–F}$ single bonds with five fluorine atoms, leaving $7 - 5 = 2$ electrons, which form one lone pair on iodine.
Electron geometry

With six electron domains (five bonding pairs + one lone pair), the electron geometry is octahedral, corresponding to $sp^3d^2$ hybridization. Six hybrid orbitals point toward the corners of an octahedron.
Placement of the lone pair

In an octahedral arrangement, all six positions are equivalent—there is no distinction between "axial" and "equatorial" as there was in the trigonal bipyramid. The lone pair occupies one of these six positions.
Molecular geometry

The five fluorine atoms occupy the remaining five positions. With one position taken by a lone pair, the five atoms form a square pyramidal shape: four fluorines in a square base and one fluorine at the apex. …

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Q.Explain why PCl5 is trigonal bipyramidal whereas IF5 is square pyramidal.

Why PCl₅ is trigonal bipyramidal

Why IF₅ is square pyramidal

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