Chemical Bonding and Molecular Structure

Lewis Structures, Formal Charge and the Octet Rule

Counting lone pairs and formal charge

Lone pairs and formal charge

\text{lone pairs} = \frac{N_{\text{valence}} - 2\,n_{\text{bonds}}}{2} \qquad \text{FC} = V - L - \tfrac{1}{2}S

The octet rule and its three exceptions

Type	Electrons on the central atom	Examples
Obeys the octet rule	8	$\mathrm{CH_4}$ , $\mathrm{CO_2}$ , $\mathrm{CCl_4}$ , $\mathrm{NH_3}$ , $\mathrm{SiF_4}$ , $\mathrm{H_2S}$
Incomplete octet	4 for Be, 6 for B and Al	$\mathrm{BeF_2}$ , $\mathrm{BeH_2}$ (4); $\mathrm{BF_3}$ , $\mathrm{BCl_3}$ , $\mathrm{AlCl_3}$ (6)
Electron deficient	Bridging B–H–B bonds hold 2 electrons over 3 atoms	$\mathrm{B_2H_6}$ ; $\mathrm{BCl_3}$ is also called electron deficient
Odd-electron species	An odd total: NO 11, NO₂ 17, ClO₂ 19	$\mathrm{NO}$ , $\mathrm{NO_2}$ , $\mathrm{ClO_2}$ These are also the paramagnetic oxides: an odd electron cannot pair.
Expanded octet	10 or 12 (14 in IF₇)	$\mathrm{PCl_5}$ , $\mathrm{SF_4}$ (10); $\mathrm{SF_6}$ , $\mathrm{H_2SO_4}$ , $\mathrm{SO_3}$ (12); $\mathrm{IF_7}$ (14)

Only period 3 and heavier atoms can expand the octet; N, O and F never do.

Lewis acids and Lewis bases

Species	Role	Reason
$\mathrm{BF_3}$ , $\mathrm{BCl_3}$	Lewis acid	B has 6 electrons and an empty p orbital; $sp^2$ , trigonal planar
$\mathrm{AlCl_3}$	Lewis acid	Al has 6 electrons; it dimerises to $\mathrm{Al_2Cl_6}$ to fill the gap
$\mathrm{BI_3}$	Strongest boron halide acid	Back-bonding from large I into B is weakest
$\mathrm{NH_3}$ , $\mathrm{NF_3}$	Lewis base	One lone pair on N; $sp^3$ , pyramidal
$\mathrm{SF_4}$ , $\mathrm{ClF_3}$	Lewis base	One lone pair on S; two on Cl
$\mathrm{PCl_5}$	Not a Lewis base	All five P electrons are in bonds; no lone pair PCl₅ can accept a pair (forming PCl₆⁻), but it cannot donate one.

An empty orbital makes an acid; a lone pair on the central atom makes a base.

Common traps

Count every atom, not just the centre

Most of a molecule's lone pairs sit on the outer atoms. In

\mathrm{NF_3}

nitrogen has one lone pair but each fluorine has three, so the molecule has 10. Check whether the question asks for the whole molecule or the central atom.

The charge changes the electron count

An anion has extra electrons and a cation has fewer. Forgetting the charge of

\mathrm{NO_2^-}

gives 17 electrons instead of 18, and a half lone pair, which is the sign that something is wrong.

Sulphur acids and oxides are expanded

Drawn with S=O double bonds, S in

\mathrm{H_2SO_4}

and

\mathrm{SO_3}

has 12 electrons and S in

\mathrm{SO_2}

has 10. JEE keys count all three as expanded octets, so do not call them octet-obeying.

Odd electrons mean an exception, even with a small atom

\mathrm{NO}

and

\mathrm{NO_2}

contain only period 2 atoms, yet they break the rule because 11 and 17 cannot be shared out as complete pairs. Check the total before looking at the central atom.

Electronegativity does not rank the boron halides

F is the most electronegative halogen, so

\mathrm{BF_3}

looks like it should be the strongest acid. It is the weakest, because back-bonding from F fills boron's empty orbital. The order is

\mathrm{BI_3 > BBr_3 > BCl_3 > BF_3}

.

Amphoteric water is a Brønsted idea

Water acts as an acid with

\mathrm{NH_3}

and as a base with

\mathrm{H_2S}

by passing protons. An assertion that this is explained by the Lewis concept is false.

Ionic Bonding, Lattice Enthalpy and Fajans' Rules

Learn this subtopic in the notes

The Born-Haber cycle and lattice enthalpy

Born-Haber cycle

\Delta_f H = \Delta_{sub}H + \Delta_i H + \tfrac{1}{2}\Delta_{diss}H + \Delta_{eg}H + \Delta_{lattice}H

Fajans' rules and covalent character

Rule	Order of covalent character	Why
Smaller cation	$\mathrm{LiCl > NaCl > KCl > CsCl}$	$\mathrm{Li^+}$ is the smallest and most polarising
Higher cation charge	$\mathrm{AlCl_3 > MgCl_2 > NaCl}$ ; $\mathrm{SnCl_4 > SnCl_2}$	More charge on a smaller ion
Larger anion	$\mathrm{CaI_2 > CaBr_2 > CaCl_2 > CaF_2}$ ; $\mathrm{KI > KF}$	$\mathrm{I^-}$ has the largest, softest cloud
18-electron cation	$\mathrm{CuCl > NaCl}$ ; $\mathrm{AgCl > KCl}$	d electrons shield the nuclear charge poorly
Electronegativity difference	Ionic character: $\mathrm{N_2 < ClF_3 < SO_2 < K_2O < LiF}$	$\Delta\chi$ is 0 for $\mathrm{N_2}$ , about 0.8 for Cl–F, 0.9 for S–O

The same polarisation that adds covalent character lowers the melting point and the solubility in water.

Common traps

Half the bond enthalpy, not all of it

One formula unit of MX needs one X atom, which is half an

\mathrm{X_2}

molecule. Adding the whole bond enthalpy shifts the answer by half of it.

Check which way the lattice step runs

Lattice enthalpy is quoted both for the solid breaking into ions (positive) and for ions forming the solid (negative). Write the step in the direction of the cycle and give it the matching sign, then answer with the magnitude if that is what is asked.

A bigger cation means LESS covalent

Size works in opposite directions for the two ions. A large anion raises covalent character; a large cation lowers it. So KF is less covalent than LiF, and KI is more covalent than KF.

Rank electron gain by magnitude

For one metal bonded to several non-metals, the most ionic product comes from the partner that releases the most energy on gaining an electron, the most negative value. Ranking the values as signed numbers puts the order backwards.

Bond Length, Bond Angle and Resonance

Learn this subtopic in the notes

Resonance and fractional bond order

Bond order in a resonance hybrid

\text{bond order} = \frac{\text{total bonds to the equivalent atoms}}{\text{number of equivalent atoms}}

Bond length and what sets it

Bond	Typical length (pm)	Note
C–H	109	Shortest here: hydrogen is tiny
C≡C	120	Triple bond
C=C	134	Double bond
C–C	154	Single bond
C≡N	116	Shorter than C=O despite N being larger than C
C=O	122	Carbonyl
C–O	143	Alcohols and ethers
O=O	121	In O₂
O–O	148	In H₂O₂
P–Cl in PCl₅	219 axial, 204 equatorial	Axial bonds are the longer, weaker pair Calling the axial bonds of PCl₅ stronger is a standard wrong statement.

For the same pair of atoms: triple shorter than double, double shorter than single.

Bond angles and lone-pair repulsion

Species	Pairs on the centre	Bond angle
$\mathrm{BF_3}$	3 bond, 0 lone	120°
$\mathrm{SO_2}$	2 bond (plus π), 1 lone	about 119°
$\mathrm{CH_4}$	4 bond, 0 lone	109.5°
$\mathrm{NH_3}$	3 bond, 1 lone	107°
$\mathrm{H_2O}$	2 bond, 2 lone	104.5°
$\mathrm{NF_3}$	3 bond, 1 lone	102°
$\mathrm{PF_3}$	3 bond, 1 lone	about 98°
$\mathrm{ClF_3}$	3 bond, 2 lone	about 87.5° (axial F–Cl–equatorial F) The two lone pairs bend the axial F atoms back below 90°.

More lone pairs on the centre, or more electronegative outer atoms, means a smaller angle.

Common traps

The hybrid does not flip between forms

Options such as 'the structures are in dynamic equilibrium' or 'each structure exists for an equal time' are always wrong. Resonance forms are not real species; there is one structure, the hybrid.

Resonance, not repulsion, sets ozone's bond length

Ozone's two O–O bonds are equal at 128 pm because the double bond is spread over both positions. A statement that lone-pair repulsion alone causes the intermediate length is false.

Bond length is not set by bond order alone

C≡N (116 pm) is shorter than C=O (122 pm), and C–H (109 pm) is shorter than both, though it is a single bond. Compare orders only between the same two atoms; otherwise size matters too.

See-saw and trigonal bipyramid give unequal bonds

Four bonds do not mean four equal bonds. Tetrahedral

\mathrm{SiF_4}

and square planar

\mathrm{XeF_4}

have equal bonds, but see-saw

\mathrm{SF_4}

has two long axial and two short equatorial bonds.

Both SO₂ and H₂O are bent, at very different angles

S in

\mathrm{SO_2}

has three electron domains (

sp^2

) and one lone pair, so its angle is near 119°. O in water has four domains (

sp^3

) and two lone pairs, so 104.5°. Same shape, larger angle for

\mathrm{SO_2}

.

Fluorine closes the angle; chlorine opens it

\mathrm{OF_2}

(103°) is smaller than

\mathrm{H_2O}

, but

\mathrm{Cl_2O}

(about 111°) is larger. Electronegative F draws the bond pairs outward; the big Cl atoms push each other apart.

VSEPR Theory and Lone Pairs

Learn this subtopic in the notes

Counting lone pairs on the central atom

Steric number and lone pairs

SN = \tfrac{1}{2}(V + M - c + a) \qquad \text{lone pairs} = SN - (\text{atoms bonded to the centre})

Where lone pairs sit: equatorial and trans

Species	Bond pairs, lone pairs	Lone pairs sit	Shape
$\mathrm{SF_4}$ , $\mathrm{SeF_4}$	4, 1	Equatorial	See-saw
$\mathrm{ClF_3}$ , $\mathrm{BrF_3}$	3, 2	Both equatorial	T-shaped (bent T), about 87.5°
$\mathrm{XeF_2}$ , $\mathrm{I_3^-}$ , $\mathrm{ICl_2^-}$	2, 3	All three equatorial	Linear, 180°
$\mathrm{XeO_2F_2}$	4, 1	Equatorial, with the two O	See-saw, F atoms axial
$\mathrm{BrF_5}$ , $\mathrm{IF_5}$	5, 1	Any one octahedral site	Square pyramidal
$\mathrm{XeF_4}$ , $\mathrm{BrF_4^-}$	4, 2	Trans, opposite each other	Square planar, 90°
$\mathrm{BrF_2^+}$	2, 2	Two corners of a tetrahedron	Bent

Five pairs: lone pairs equatorial. Six pairs: two lone pairs trans.

Common traps

A double bond to oxygen uses two electrons

Xe in

\mathrm{XeO_3}

uses 6 of its 8 electrons on three Xe=O bonds and keeps one lone pair. Counting each Xe=O as one electron leaves 5 electrons, which cannot pair: a sure sign of a slip.

Know what the question calls a bond pair

Some questions count π pairs as bond pairs. On that count

\mathrm{SO_2}

has 4 bond pairs and 1 lone pair, not 2 and 1. Read the options: if no option fits the σ-only count, the π pairs are included.

Lone pairs are never axial in a trigonal bipyramid

An axial lone pair would meet three bond pairs at 90°. The stable structure puts every lone pair equatorial, so a statement that axial lone pairs minimise repulsion in

\mathrm{ClF_3}

is false.

Three lone pairs make a straight molecule

\mathrm{XeF_2}

and

\mathrm{I_3^-}

have five electron pairs, yet they are linear. The three lone pairs fill the equator and the two atoms sit on the axis, 180° apart.

Shapes of Molecules and Ions

Learn this subtopic in the notes

Shapes from the AXE formula

Type	Pairs (X + E)	Shape	Examples
AX₂	2	Linear	$\mathrm{BeCl_2}$ , $\mathrm{CO_2}$ , $\mathrm{NO_2^+}$ , $\mathrm{N_3^-}$ , $\mathrm{HC{\equiv}C^-}$
AX₃	3	Trigonal planar	$\mathrm{BF_3}$ , $\mathrm{SO_3}$ , $\mathrm{NO_3^-}$ , $\mathrm{CO_3^{2-}}$
AX₂E	3	Bent	$\mathrm{SO_2}$ , $\mathrm{O_3}$ , $\mathrm{NO_2^-}$
AX₄	4	Tetrahedral	$\mathrm{CH_4}$ , $\mathrm{NH_4^+}$ , $\mathrm{SO_4^{2-}}$ , $\mathrm{SO_2Cl_2}$
AX₃E	4	Trigonal pyramidal	$\mathrm{NH_3}$ , $\mathrm{H_3O^+}$ , $\mathrm{SO_3^{2-}}$ , $\mathrm{ClO_3^-}$ , $\mathrm{BrO_3^-}$ , $\mathrm{XeO_3}$
AX₂E₂	4	Bent	$\mathrm{H_2O}$ , $\mathrm{OF_2}$ , $\mathrm{ClO_2^-}$ , $\mathrm{BrF_2^+}$
AX₅	5	Trigonal bipyramidal	$\mathrm{PCl_5}$ , $\mathrm{PF_5}$ , $\mathrm{Fe(CO)_5}$
AX₄E	5	See-saw	$\mathrm{SF_4}$ , $\mathrm{SeF_4}$ , $\mathrm{IF_4^+}$ , $\mathrm{XeO_2F_2}$
AX₃E₂	5	T-shaped	$\mathrm{ClF_3}$ , $\mathrm{BrF_3}$ , $\mathrm{IF_3}$
AX₂E₃	5	Linear	$\mathrm{XeF_2}$ , $\mathrm{I_3^-}$ , $\mathrm{IBr_2^-}$
AX₆	6	Octahedral	$\mathrm{SF_6}$ , $\mathrm{[CrF_6]^{3-}}$
AX₅E	6	Square pyramidal	$\mathrm{BrF_5}$ , $\mathrm{IF_5}$ , $\mathrm{XeOF_4}$
AX₄E₂	6	Square planar	$\mathrm{XeF_4}$ , $\mathrm{ICl_4^-}$ , $\mathrm{BrF_4^-}$
AX₇	7	Pentagonal bipyramidal	$\mathrm{IF_7}$
AX₆E	7	Distorted octahedral	$\mathrm{XeF_6}$

Same total of pairs, same arrangement; the lone pairs decide the name of the shape.

Common traps

Name the shape from the atoms, not the pairs

\mathrm{NH_3}

has a tetrahedral arrangement of pairs, but its shape is trigonal pyramidal.

\mathrm{XeF_4}

has an octahedral arrangement, but it is square planar. Options often offer the arrangement as a decoy.

Same formula type, different shape

\mathrm{SF_4}

(see-saw) and

\mathrm{XeF_4}

(square planar) are both AF₄, and

\mathrm{PCl_5}

(trigonal bipyramidal) and

\mathrm{BrF_5}

(square pyramidal) are both AX₅ formulas. Count the lone pairs before naming the shape.

Charge changes the shape

\mathrm{I_3^-}

is linear (three lone pairs) but

\mathrm{I_3^+}

is bent (two lone pairs).

\mathrm{NO_2^+}

is linear but

\mathrm{NO_2^-}

is bent. Always put the charge into the steric number.

Two nickel complexes, two shapes

Strong-field

\mathrm{CN^-}

pairs up nickel's d electrons, so

\mathrm{[Ni(CN)_4]^{2-}}

is

dsp^2

and square planar. Weak-field

\mathrm{Cl^-}

does not, so

\mathrm{[NiCl_4]^{2-}}

is

sp^3

and tetrahedral.

Hybridisation and Sigma and Pi Bonds

Learn this subtopic in the notes

Counting σ and π bonds

Counting bonds in an open chain

n_\sigma = N_{\text{atoms}} - 1 \ (+1 \text{ per ring}) \qquad n_\pi = n_{\text{double}} + 2\,n_{\text{triple}}

Hybridisation from the steric number

Steric number to hybridisation

SN = n_\sigma + n_{\text{lp}}: \ 2 \to sp,\ 3 \to sp^2,\ 4 \to sp^3,\ 5 \to sp^3d,\ 6 \to sp^3d^2,\ 7 \to sp^3d^3

Hybridisation, orientation and complexes

Hybridisation	Orientation	Main-group examples	Complex examples
$sp$	Linear, 180°	$\mathrm{BeCl_2}$ , $\mathrm{CO_2}$ , $\mathrm{NO_2^+}$	$\mathrm{[Ag(NH_3)_2]^+}$
$sp^2$	Trigonal planar, 120°	$\mathrm{BF_3}$ , $\mathrm{SO_2}$ , $\mathrm{NO_2^-}$	Rare in complexes
$sp^3$	Tetrahedral, 109.5°	$\mathrm{CH_4}$ , $\mathrm{NH_4^+}$ , $\mathrm{XeO_3}$	$\mathrm{Ni(CO)_4}$ , $\mathrm{[NiCl_4]^{2-}}$
$dsp^2$	Square planar, 90°	None	$\mathrm{[PtCl_4]^{2-}}$ , $\mathrm{[Ni(CN)_4]^{2-}}$
$sp^3d$	Trigonal bipyramidal	$\mathrm{PCl_5}$ , $\mathrm{SF_4}$ , $\mathrm{ClF_3}$ , $\mathrm{XeF_2}$	$\mathrm{Fe(CO)_5}$ is often written $dsp^3$
$sp^3d^2$	Octahedral, 90°	$\mathrm{SF_6}$ , $\mathrm{BrF_5}$ , $\mathrm{XeF_4}$	$\mathrm{[CoF_6]^{3-}}$ (outer orbital)
$d^2sp^3$	Octahedral, 90°	None	$\mathrm{[Co(NH_3)_6]^{3+}}$ , $\mathrm{[Fe(CN)_6]^{3-}}$ (inner orbital) [Co(NH₃)₆]³⁺ is d²sp³, not sp³d²: a stated match of it with SF₆ is false.
$sp^3d^3$	Pentagonal bipyramidal	$\mathrm{IF_7}$ , $\mathrm{XeF_6}$ (distorted)	None

The hybridisation fixes the arrangement of pairs; the shape then depends on how many are lone pairs.

Common traps

Every C–H bond is a σ bond

The hydrogens are easy to forget because the name does not list them. Draw the full structure: in a six-carbon chain the C–H bonds are often more than half of the σ total.

Give σ and π in the order asked

Options often list the same pair twice, as '13 and 3' and '3 and 13'. The question says which comes first; match that order.

π bonds do not add hybrid orbitals

\mathrm{SO_3}

has three S=O double bonds but only three σ bonds, so it is

sp^2

, not

sp^3d^2

. Count σ bonds and lone pairs only.

Five atoms around the centre can still be sp³d²

\mathrm{BrF_5}

has five bonds and one lone pair, a steric number of 6:

sp^3d^2

, not

sp^3d

. Only lone-pair-free

\mathrm{PF_5}

and

\mathrm{PCl_5}

are

sp^3d

with five bonds.

sp³d with a lone pair gives unequal bonds

Of

\mathrm{PF_5}

,

\mathrm{XeF_4}

,

\mathrm{SF_4}

and

\mathrm{XeF_2}

, only

\mathrm{SF_4}

is

sp^3d

, carries a lone pair and has two bond lengths.

\mathrm{XeF_2}

is

sp^3d

with lone pairs, but its two bonds are equal.

Square planar means dsp², not sp³

Four ligands do not always mean tetrahedral.

\mathrm{[PtCl_4]^{2-}}

uses one inner d orbital and is square planar;

\mathrm{[NiCl_4]^{2-}}

is

sp^3

and tetrahedral.

Molecular Orbital Theory

Learn this subtopic in the notes

Bond order from the MO diagram

Bond order

\text{bond order} = \tfrac{1}{2}(N_b - N_a)

Combining atomic orbitals (LCAO)

Pair of orbitals (axis z)	Symmetry of each	Do they combine?
1s and 1s	σ and σ	Yes: σ1s and σ*1s
$2p_z$ and $2p_z$	σ and σ	Yes: σ2p and σ*2p (head-on)
$2p_x$ and $2p_x$	π and π	Yes: π2p and π*2p (sideways)
2s and $2p_z$	σ and σ	Yes, if their energies are close
2s and $2p_y$	σ and π	No: zero net overlap
$2p_x$ and $2p_y$	π, but at right angles	No: they are orthogonal
$3d_{xz}$ and $2p_x$	π and π	Yes: a π overlap
$3d_{xy}$ and $3d_{x^2-y^2}$	δ and δ, but rotated 45°	No: orthogonal to each other Both are δ type, yet they cancel; same symmetry label is not enough when the lobes are turned 45°.

Same symmetry about the axis and a matching orientation are both needed for a net overlap.

Unpaired electrons and magnetism

Species	Electrons	Bond order	Unpaired electrons	Magnetism
$\mathrm{H_2^+}$ , $\mathrm{He_2^+}$	1, 3	0.5	1	Paramagnetic
$\mathrm{Li_2}$	6	1	0	Diamagnetic
$\mathrm{B_2}$	10	1	2	Paramagnetic
$\mathrm{C_2}$	12	2	0	Diamagnetic
$\mathrm{C_2^-}$ , $\mathrm{N_2^+}$	13	2.5	1	Paramagnetic
$\mathrm{N_2}$ , CO, $\mathrm{CN^-}$ , $\mathrm{NO^+}$	14	3	0	Diamagnetic
$\mathrm{N_2^-}$ , $\mathrm{O_2^+}$ , NO	15	2.5	1	Paramagnetic
$\mathrm{O_2}$ , $\mathrm{N_2^{2-}}$	16	2	2	Paramagnetic
$\mathrm{O_2^-}$	17	1.5	1	Paramagnetic
$\mathrm{O_2^{2-}}$ , $\mathrm{F_2}$	18	1	0	Diamagnetic O₂²⁻ has 10 electrons in bonding orbitals and 8 in antibonding ones.

Species with the same electron count have the same bond order and the same number of unpaired electrons.

Common traps

Bonding π density is not low above the axis

A π bonding orbital puts its density above and below the internuclear axis, with none on the axis itself. A statement that it has lower density above and below the axis is false.

Maximum overlap, not minimum

The three LCAO conditions are comparable energy, same symmetry and maximum overlap. 'Minimum overlap' or 'different symmetry' in a list of conditions is always a wrong option.

Count every electron, core included, or none

Either count all electrons (σ1s and σ*1s cancel) or only the valence ones; the bond order is the same. Mixing the two, for example counting σ1s as bonding but skipping σ*1s, adds one to the answer.

A bond order of zero means no molecule

\mathrm{Be_2}

and

\mathrm{He_2}

have as many antibonding as bonding electrons, so they do not exist.

\mathrm{He_2^+}

,

\mathrm{He_2^-}

and

\mathrm{O_2^{2-}}

have positive bond orders and do.

O₂⁺ and O₂⁻ have the same number of unpaired electrons

\mathrm{O_2^+}

has one π* electron and

\mathrm{O_2^-}

has three, one of them unpaired. Both have exactly one unpaired electron, so any order that puts one above the other is false.

N₂²⁻ looks like N₂ but behaves like O₂

Adding two electrons to

\mathrm{N_2}

gives 16, the count of

\mathrm{O_2}

. So

\mathrm{N_2^{2-}}

has bond order 2 and two unpaired electrons: it is paramagnetic.

Dipole Moment, Hydrogen Bonding and Intermolecular Forces

Learn this subtopic in the notes

Dipole moment: size and direction

Dipole moment

\mu = q \times d \qquad 1\ \text{D} = 10^{-18}\ \text{esu cm}

Polar or non-polar: when symmetry cancels

Shape	Net dipole	Examples
Linear AX₂ or AX₂E₃	Zero	$\mathrm{CO_2}$ , $\mathrm{BeF_2}$ , $\mathrm{BeCl_2}$ , $\mathrm{XeF_2}$
Trigonal planar AX₃	Zero	$\mathrm{BF_3}$ , $\mathrm{BCl_3}$ , $\mathrm{SO_3}$
Tetrahedral AX₄	Zero	$\mathrm{CH_4}$ , $\mathrm{CCl_4}$ , $\mathrm{SiF_4}$
Square planar, TBP, octahedral	Zero	$\mathrm{XeF_4}$ , $\mathrm{PCl_5}$ , $\mathrm{SF_6}$
Bent	Non-zero	$\mathrm{H_2O}$ , $\mathrm{H_2S}$ , $\mathrm{SO_2}$
Pyramidal	Non-zero	$\mathrm{NH_3}$ , $\mathrm{NF_3}$ , $\mathrm{PCl_3}$
See-saw, T-shaped, square pyramidal	Non-zero	$\mathrm{SF_4}$ , $\mathrm{ClF_3}$ , $\mathrm{BrF_5}$
Tetrahedral with mixed atoms	Non-zero	$\mathrm{CHCl_3}$ , $\mathrm{CH_2Cl_2}$
Heteronuclear diatomic	Non-zero	HF, HCl, HBr H₂ has zero dipole; HF, with the biggest electronegativity gap, has the largest of the hydrogen halides.

A lone pair on the centre breaks the symmetry unless the lone pairs themselves are placed symmetrically, as in XeF₂ and XeF₄.

Hydrogen bonding and intermolecular forces

Case	Kind of attraction	Effect
HF	Intermolecular H-bonds, zig-zag chains	The strongest single H-bond; the H sits nearer one F, so the bonds are not symmetrical
Ice, water, water with solute	Intermolecular H-bonds	Most in ice (each molecule bonded four ways), fewer in liquid water, fewer again with impurities
$o$ -Nitrophenol, salicylaldehyde	Intramolecular H-bond	Lower boiling point; steam volatile
$p$ -Nitrophenol, $p$ -hydroxybenzaldehyde	Intermolecular H-bonds	Higher boiling point; not steam volatile
$\mathrm{CH_4 < HCN < NH_3}$	None, weak C–H···N, N–H···N	Order of intermolecular H-bond strength
Noble gases, $\mathrm{CH_4}$	London forces only	Energy $\propto 1/r^6$ ; grows with molecular size
Ar, $\mathrm{CH_4}$ , $\mathrm{H_2O}$ , $\mathrm{C_6H_6}$	Van der Waals constant a (about 1.4, 2.3, 5.5, 18 L² bar mol⁻²)	Larger a means stronger attraction between molecules

H bonded to F, O or N gives a hydrogen bond; where it forms, inside or between molecules, decides the boiling point.

Common traps

More electronegative F does not mean a bigger dipole

Each N–F bond is more polar than an N–H bond, yet

\mathrm{NF_3}

(0.23 D) is far less polar than

\mathrm{NH_3}

(1.47 D). The lone-pair moment adds to the bond moments in

\mathrm{NH_3}

and opposes them in

\mathrm{NF_3}

.

The two arrow conventions point opposite ways

The chemist's arrow runs from positive to negative, following the electron density. The physicist's dipole vector runs from negative to positive. A statement that puts the tail on the negative centre describes the physics convention.

Polar bonds can give a non-polar molecule

C–Cl and B–F bonds are strongly polar, but

\mathrm{CCl_4}

and

\mathrm{BF_3}

have zero dipole moment. Ask whether the shape is symmetric, not whether the bonds are polar.

Lone pairs do not always make a molecule polar

\mathrm{XeF_4}

has two lone pairs and

\mathrm{XeF_2}

has three, yet both are non-polar: the lone pairs sit opposite each other or round the equator, and their moments cancel.

Ortho means intramolecular

The ortho isomer of a nitrophenol or hydroxybenzaldehyde bonds within itself; the para isomer bonds to its neighbours. Swapping them reverses every boiling-point and volatility answer.

HF has no intramolecular hydrogen bond

One HF molecule has a single H–F bond, so it cannot bond to itself. Its hydrogen bonds link separate molecules into chains, and they are not symmetrical.

Chemical Bonding and Molecular Structure formulas

Lewis Structures, Formal Charge and the Octet Rule

Counting lone pairs and formal charge

The octet rule and its three exceptions

Lewis acids and Lewis bases

Common traps

Ionic Bonding, Lattice Enthalpy and Fajans' Rules

The Born-Haber cycle and lattice enthalpy

Fajans' rules and covalent character

Common traps

Bond Length, Bond Angle and Resonance

Resonance and fractional bond order

Bond length and what sets it

Bond angles and lone-pair repulsion

Common traps

VSEPR Theory and Lone Pairs

Counting lone pairs on the central atom

Where lone pairs sit: equatorial and trans

Common traps

Shapes of Molecules and Ions

Shapes from the AXE formula

Common traps

Hybridisation and Sigma and Pi Bonds

Counting σ and π bonds

Hybridisation from the steric number

Hybridisation, orientation and complexes

Common traps

Molecular Orbital Theory

Bond order from the MO diagram

Combining atomic orbitals (LCAO)

Unpaired electrons and magnetism

Common traps

Dipole Moment, Hydrogen Bonding and Intermolecular Forces

Dipole moment: size and direction

Polar or non-polar: when symmetry cancels

Hydrogen bonding and intermolecular forces

Common traps

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