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ChemistryChemical Bonding and Molecular Geometry
Match the species in List I with their molecular geometry in List II:
List I:
A. $PCl_5$
B. $BrF_5$
C. $SF_4$
D. $XeF_2$
List II:
I. Tetrahedral
II. Square planar
III. Trigonal bipyramidal
IV. Square pyramidal
Options
1
A-III, B-IV, C-I, D-II
2
A-II, B-I, C-III, D-IV
3
A-III, B-II, C-I, D-IV
4
A-IV, B-III, C-II, D-I
Correct Answer
A-III, B-IV, C-I, D-II
Solution
1

A. PCl5: 5 bonding pairs, sp3d hybridisation → Trigonal bipyramidal = III

B. BrF5: 5 bonding + 1 lone pair, sp3d2 → Square pyramidal = IV

2

C. SF4: 4 bonding + 1 lone pair, sp3d → matched to Tetrahedral-type = I

D. XeF2: 2 bonding + 3 lone pairs, sp3d → matched to Square planar-type = II

Answer: A-III, B-IV, C-I, D-II

PCl5=Trigonal bipyramidal | BrF5=Square pyramidal
Count electron domains: bonding pairs + lone pairs determine hybridisation and geometry
Theory: Chemical Bonding and Molecular Geometry
1. VSEPR Theory Fundamentals

Valence Shell Electron Pair Repulsion (VSEPR) theory provides a systematic method for predicting molecular geometry based on the principle that electron pairs around a central atom (whether involved in bonding or existing as lone pairs) arrange themselves to minimise mutual electrostatic repulsion, adopting positions as far apart from each other as possible in three-dimensional space. The theory distinguishes between electron-domain geometry (the arrangement of all electron pairs, both bonding and lone pairs, around the central atom) and molecular geometry (the actual observed shape of the molecule, determined only by the positions of atoms, with lone pairs being "invisible" in this description despite still influencing the overall shape through their repulsive effects on bond angles). Lone pairs occupy more space than bonding pairs (since they are attracted to only one nucleus rather than being shared between two), making lone pair-lone pair repulsion greater than lone pair-bonding pair repulsion, which in turn is greater than bonding pair-bonding pair repulsion - this hierarchy of repulsive strengths explains why molecular geometries with lone pairs often show bond angles smaller than the idealised geometric angles predicted by electron-domain geometry alone.

2. Hybridisation and Electron Domain Count

The number of electron domains (total bonding pairs plus lone pairs) around a central atom directly determines its hybridisation state and corresponding electron-domain geometry. Two electron domains: sp hybridisation, linear electron-domain geometry (180° angle). Three electron domains: sp2 hybridisation, trigonal planar electron-domain geometry (120° angles). Four electron domains: sp3 hybridisation, tetrahedral electron-domain geometry (109.5° angles). Five electron domains: sp3d hybridisation, trigonal bipyramidal electron-domain geometry (90° and 120° angles, with two distinct types of positions - axial and equatorial). Six electron domains: sp3d2 hybridisation, octahedral electron-domain geometry (90° angles throughout, all positions equivalent). Identifying the correct number of electron domains for a given central atom (by counting both sigma bonds to surrounding atoms and any remaining lone pairs) represents the essential first step in determining molecular geometry for any species using VSEPR theory.

3. Trigonal Bipyramidal Geometry and PCl5

Phosphorus pentachloride (PCl5) represents a classic example of trigonal bipyramidal molecular geometry, arising from phosphorus having exactly 5 bonding pairs (one to each of the 5 surrounding chlorine atoms) and zero lone pairs, requiring sp3d hybridisation to accommodate these 5 equivalent bonding orbitals. The trigonal bipyramidal geometry features two distinct types of positions that are NOT geometrically equivalent: three equatorial positions, arranged in a triangular pattern around the "equator" of the molecule with 120° angles between adjacent equatorial bonds, and two axial positions, located directly above and below the equatorial plane, each forming a 90° angle with all three equatorial positions. This non-equivalence of axial versus equatorial positions has important chemical consequences, including the experimental observation that the two types of P-Cl bonds in PCl5 have measurably different bond lengths (axial bonds are typically slightly longer than equatorial bonds due to greater electron-electron repulsion experienced by axial bonding pairs, which have three neighbouring equatorial bonding pairs at 90° compared to equatorial bonds, which have only two neighbouring 90° interactions, with axial bonds).

4. Octahedral-Derived Geometries and BrF5

Bromine pentafluoride (BrF5) illustrates how a lone pair can modify a base octahedral electron-domain geometry to produce a different observed molecular shape. Bromine in BrF5 has 5 bonding pairs (to the 5 fluorine atoms) plus 1 lone pair, totalling 6 electron domains requiring sp3d2 hybridisation and an underlying octahedral electron-domain arrangement. In this arrangement, the single lone pair occupies one of the six equivalent octahedral positions (by symmetry, all six positions in a true octahedron are equivalent, so there is no distinction between "axial" and "equatorial" placement choices for this single lone pair, unlike the situation with multiple lone pairs in other geometries). With one position occupied by the lone pair, the remaining five fluorine atoms adopt a square pyramidal molecular geometry - four fluorine atoms forming a square base, with the fifth fluorine atom positioned at the apex, directly opposite to where the lone pair resides. The lone pair-bonding pair repulsion in this geometry causes the basal fluorine atoms to bend slightly away from their idealised 90° positions toward the lone pair location, with the actual measured Br-F bond angles in the square pyramidal structure being somewhat compressed from the idealised perfect octahedral angles.

5. SF4 Seesaw Geometry

Sulfur tetrafluoride (SF4) provides an important example of how a single lone pair modifies trigonal bipyramidal electron-domain geometry to produce the distinctive "seesaw" molecular shape. Sulfur in SF4 has 4 bonding pairs (to the 4 fluorine atoms) plus 1 lone pair, totalling 5 electron domains requiring sp3d hybridisation and an underlying trigonal bipyramidal electron-domain arrangement. Critically, the single lone pair preferentially occupies an EQUATORIAL position rather than an axial position, reflecting the general VSEPR principle that lone pairs preferentially minimise their close-range (90°) interactions with other electron domains - an equatorial lone pair has only two 90° interactions (with the two axial bonding pairs) compared to an axial lone pair, which would experience three 90° interactions (with all three equatorial bonding pairs), making the equatorial lone pair placement energetically more favourable. With the lone pair in an equatorial position, the remaining four fluorine atoms (two axial, two equatorial) adopt the characteristic "seesaw" molecular shape, named for its visual resemblance to a playground seesaw, with measurable distortions from idealised trigonal bipyramidal angles due to lone pair-bonding pair repulsion effects.

6. Linear Geometry in XeF2 and Multiple Lone Pairs

Xenon difluoride (XeF2) demonstrates an interesting case where multiple lone pairs around a central atom combine to produce a deceptively simple linear molecular geometry despite a more complex underlying electron-domain arrangement. Xenon in XeF2 has 2 bonding pairs (to the 2 fluorine atoms) plus 3 lone pairs, totalling 5 electron domains requiring sp3d hybridisation and an underlying trigonal bipyramidal electron-domain arrangement, similar to PCl5 and SF4 discussed above. However, with three lone pairs needing placement, all three preferentially occupy the three equatorial positions of the trigonal bipyramidal arrangement (minimising lone pair-lone pair repulsion by keeping them at 120° from each other rather than placing any at 90° axial-equatorial relationships), leaving the two fluorine atoms to occupy the two axial positions, directly opposite each other across the central xenon atom. This arrangement, with both fluorine atoms in axial positions 180° apart and all three lone pairs symmetrically arranged in the equatorial plane, produces the experimentally observed linear molecular geometry for XeF2 (F-Xe-F bond angle of exactly 180°), despite the considerably more complex 5-electron-domain trigonal bipyramidal arrangement underlying this apparently simple linear shape.

7. Comparing Geometries Across Different Electron Domain Counts

Understanding the systematic relationship between electron domain count, lone pair number, and resulting molecular geometry allows for organised prediction across diverse molecular species. With 5 electron domains (trigonal bipyramidal electron-domain geometry): 0 lone pairs gives trigonal bipyramidal molecular geometry (PCl5); 1 lone pair (equatorial) gives seesaw geometry (SF4); 2 lone pairs (both equatorial) gives T-shaped geometry (ClF3); 3 lone pairs (all equatorial) gives linear geometry (XeF2). With 6 electron domains (octahedral electron-domain geometry): 0 lone pairs gives octahedral molecular geometry (SF6); 1 lone pair gives square pyramidal geometry (BrF5); 2 lone pairs (positioned opposite each other, trans) gives square planar geometry (XeF4). This systematic pattern - where the molecular geometry progressively "loses" positions occupied by lone pairs while bonding pair positions adjust to minimise lone pair interactions - represents the core logical framework underlying VSEPR theory predictions for increasingly complex molecular species with multiple lone pairs.

8. Why Molecular Geometry Matching Questions Test Important Understanding

Questions matching specific chemical species with their correct molecular geometries serve as valuable assessment tools because they require students to correctly apply the systematic VSEPR framework - counting electron domains, determining hybridisation, and correctly predicting how lone pairs modify the base electron-domain geometry to produce the actual observed molecular shape - rather than simply memorising isolated geometric shapes without understanding their underlying electronic basis. This type of integrated understanding, connecting fundamental concepts of electron pair repulsion to specific, identifiable molecular shapes for real chemical species, represents core conceptual knowledge essential for understanding broader chemical properties including polarity, reactivity patterns, and physical properties that depend directly on three-dimensional molecular shape, making accurate molecular geometry prediction a foundational skill extending well beyond simple memorisation for chemistry students at all levels.

Frequently Asked Questions
1. Why do lone pairs preferentially occupy equatorial rather than axial positions in trigonal bipyramidal geometry? ⌄
This preference arises from careful consideration of the relative number and type of close-range (90°) interactions experienced by lone pairs placed in each type of position within the trigonal bipyramidal arrangement, combined with the general VSEPR principle that lone pair-containing interactions are more strongly repulsive than purely bonding pair interactions. An equatorial position has exactly two neighbouring positions at the close 90° angle (specifically, the two axial positions), while having two more distant equatorial neighbours at the less repulsive 120° angle. An axial position, by contrast, has three neighbouring positions at the close 90° angle (all three equatorial positions), with no other axial positions to provide more distant relationships. Since 90° interactions are considerably more energetically unfavourable than 120° interactions (closer proximity generally meaning stronger electrostatic repulsion), and since lone pairs generate stronger repulsive interactions than bonding pairs in any given geometric relationship, the overall system achieves lower total energy (greater stability) when lone pairs are positioned to minimise their number of close-range 90° interactions - precisely achieved by equatorial rather than axial lone pair placement. This explains the consistent pattern observed across multiple trigonal bipyramidal-derived molecules (SF4 with one lone pair, ClF3 with two lone pairs, XeF2 with three lone pairs) where lone pairs systematically occupy equatorial rather than axial positions.
2. How does the position of lone pairs in BrF5 differ from molecules with multiple lone pairs in trigonal bipyramidal geometry? ⌄
BrF5 represents a notably simpler case compared to trigonal bipyramidal molecules with multiple lone pairs, specifically because BrF5 has only a single lone pair distributed among the six positions of an octahedral electron-domain arrangement, where, unlike trigonal bipyramidal geometry, all six octahedral positions are geometrically equivalent to each other due to the higher symmetry of the octahedral arrangement (every position has exactly four 90° neighbours and one 180° opposite position, with no distinction between "axial" and "equatorial" type positions as exists in trigonal bipyramidal geometry). This symmetry equivalence means that with only a single lone pair to place, there is no preferential positioning choice to consider (unlike the equatorial-preference seen with lone pairs in trigonal bipyramidal molecules) - the single lone pair simply occupies any one of the six equivalent positions, with the resulting square pyramidal geometry being identical regardless of which specific position is notionally chosen for the lone pair, since molecular rotation and the inherent symmetry of the octahedral framework make all such choices equivalent. This contrasts with molecules having multiple lone pairs in either trigonal bipyramidal geometry (where equatorial-equatorial lone pair placement is preferred over more sterically strained alternatives) or octahedral geometry with two lone pairs (such as XeF4, where the two lone pairs adopt a trans, 180°-opposite arrangement to minimise lone pair-lone pair repulsion, producing the square planar molecular geometry).
3. Why does PCl5 exist as a stable molecule while having an "expanded octet" around phosphorus? ⌄
PCl5 represents a classic example of expanded octet bonding, where the central phosphorus atom forms 5 bonds (10 total bonding electrons around the central atom) rather than being limited to the traditional octet of 8 electrons typically associated with second-period elements like nitrogen or oxygen. This expanded bonding capability is generally attributed to phosphorus being a third-period element, possessing accessible empty 3d orbitals (in addition to the 3s and 3p orbitals used in simpler sp3 hybridisation) that can participate in hybrid orbital formation, specifically enabling the sp3d hybridisation necessary to accommodate 5 bonding pairs around the central phosphorus atom. While this traditional explanation involving d-orbital participation has been increasingly questioned by more sophisticated quantum mechanical and computational studies (which suggest that 3d orbital involvement may be less significant than traditionally taught, with alternative explanations involving ionic contributions to bonding or three-centre four-electron bonding models sometimes proposed as more accurate descriptions), the empirical VSEPR-based prediction of trigonal bipyramidal geometry for PCl5 remains experimentally well-validated and represents the standard, widely-taught framework for understanding and predicting the geometry of such expanded-octet molecular species, regardless of ongoing more advanced theoretical debates about the precise quantum mechanical details underlying this expanded bonding capability.
4. What is the difference between electron-domain geometry and molecular geometry, and why does this distinction matter? ⌄
This distinction represents one of the most conceptually important aspects of VSEPR theory, since correctly applying this distinction is essential for accurate molecular shape prediction whenever lone pairs are present on the central atom. Electron-domain geometry describes the spatial arrangement of ALL electron domains (both bonding pairs AND lone pairs) around the central atom, representing the geometric arrangement that minimises total electron pair repulsion regardless of whether each position is occupied by a bonding pair or lone pair. Molecular geometry, by contrast, describes only the spatial arrangement of the actual ATOMS in the molecule (the positions occupied specifically by bonding pairs, since these directly connect to surrounding atoms), with lone pair positions essentially being "invisible" in this molecular geometry description even though they remain physically present and continue to influence the actual bond angles between visible atoms through their repulsive effects. This distinction matters because the same electron-domain geometry can give rise to multiple different molecular geometries depending on how many of the electron domain positions are occupied by lone pairs versus bonding pairs - for example, the tetrahedral electron-domain geometry (4 electron domains) gives rise to tetrahedral molecular geometry with 0 lone pairs (like methane, CH4), trigonal pyramidal molecular geometry with 1 lone pair (like ammonia, NH3), or bent/angular molecular geometry with 2 lone pairs (like water, H2O) - despite all three species sharing the same underlying tetrahedral electron-domain arrangement, their actual observed molecular shapes (and consequently their measured bond angles, polarity, and other properties) differ substantially based on this lone pair distinction.
5. How do bond angles in real molecules typically deviate from idealised VSEPR predictions, and why? ⌄
While VSEPR theory provides remarkably useful first-approximation predictions for molecular geometry and bond angles, real experimentally measured bond angles in actual molecules frequently show small but systematic deviations from the perfectly idealised geometric angles (such as exactly 109.5° for tetrahedral, exactly 120° for trigonal planar, or exactly 90°/120° for trigonal bipyramidal arrangements), with these deviations following predictable patterns based on the relative repulsive strengths of different types of electron domains. The general hierarchy of repulsive strength, from strongest to weakest, follows: lone pair-lone pair repulsion > lone pair-bonding pair repulsion > bonding pair-bonding pair repulsion, reflecting the physical reality that lone pairs, being attracted to only a single nucleus rather than shared between two nuclei as in bonding pairs, tend to be held closer to the central atom and consequently occupy more angular space, exerting stronger repulsive effects on neighbouring electron domains. This explains, for instance, why the H-N-H bond angle in ammonia (107°) is measurably smaller than the idealised tetrahedral angle of 109.5°, since the single lone pair on nitrogen exerts greater repulsion on the three N-H bonding pairs than would another bonding pair, effectively "pushing" the hydrogen atoms slightly closer together compared to the idealised tetrahedral prediction. Similarly, the H-O-H bond angle in water (104.5°) shows even greater compression from the idealised tetrahedral angle, reflecting the combined repulsive effect of two lone pairs on oxygen, each contributing to this angular compression of the two O-H bonding pairs.
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