IMAT Chemistry · Formula sheet

Chemical Bonding formulas

4 formulas, 11 reference tables and 21 common traps for IMAT Chemistry Chemical Bonding, grouped by subtopic.

Ionic, Covalent and Metallic Bonds

Electronegativity difference and bond character

Electronegativity difference

\Delta\chi = \left|\chi_A - \chi_B\right|

$\chi_A, \chi_B$ Pauling electronegativities of the two bonded atoms
$\Delta\chi$ the difference, always taken as positive

Ionic bonds and the formula of an ionic compound

Charge balance in an ionic formula

\mathrm{M}_a\mathrm{X}_b: \quad a \times (\text{charge of M}) + b \times (\text{charge of X}) = 0

$a, b$ the smallest whole numbers that balance the charges

Metallic bonding and the properties it explains

Property	Explanation
Conducts electricity as a solid and as a liquid	Delocalised electrons move through the lattice when a voltage is applied
Good conductor of heat	Free electrons carry energy quickly through the metal
Malleable and ductile	Layers of ions slide over each other and the electron sea still holds them
Usually high melting point	Strong attraction between the ions and the electron sea
Melting point rises from Na to Mg to Al	More delocalised electrons per atom (1, 2, 3) and smaller, more charged ions

Common traps

Pure covalent means identical atoms, not just similar ones

A bond is purely covalent only when

\Delta\chi = 0

, which means two atoms of the same element. Atoms with similar electronegativities (C and H) make a bond that is nearly non-polar, but not pure. An option saying "atoms of quite similar electronegativity" describes a weakly polar bond.

A metal and a non-metal are not always ionic

Beryllium, and aluminium with chlorine, sit close to the boundary and form largely covalent compounds. When an option pairs beryllium with a halogen, expect covalent, not ionic.

An ionic formula is a ratio, not a molecule

\mathrm{NaCl}

does not exist as NaCl molecules. Each ion is surrounded by ions of the opposite charge throughout a lattice, and the formula only gives their ratio. An option calling solid sodium chloride molecular is wrong.

Solid ionic compounds do not conduct; solid metals do

Both contain charged particles, but in a solid ionic compound the ions are locked in place. It conducts only when molten or dissolved. A metal conducts as a solid because its electrons are free to move.

Covalent Bonds, Lewis Structures and the Octet Rule

Learn this subtopic in the notes

Drawing a Lewis structure by counting electrons

Electrons to place in a Lewis structure

N_e = \sum V - q

$V$ valence electrons of each atom (its group number for groups 13 to 17)
$q$ charge of the ion, with its sign (0 for a neutral molecule)
$N_e$ total electrons to place; $N_e/2$ pairs

Single, double and triple covalent bonds

Carbon to carbon bond	Shared electrons	Made of	Length (pm)	Bond energy (kJ/mol)
Single, as in ethane	2	1 σ	154	about 348
Double, as in ethene	4	1 σ + 1 π	134	about 614
Triple, as in ethyne	6	1 σ + 2 π	120	about 839

Twice the single bond would be 696 kJ/mol, so the double bond (614) is less than twice as strong.

Exceptions to the octet rule

Molecule	Kind of exception	Electrons around central atom	Note
$\mathrm{BeCl_2}$ (gas)	Incomplete octet	4	Two bonding pairs, linear
$\mathrm{BF_3}$	Incomplete octet	6	Accepts a lone pair to reach 8
$\mathrm{AlCl_3}$	Incomplete octet	6	Pairs up as $\mathrm{Al_2Cl_6}$ , where each Al has 8
$\mathrm{PCl_5}$	Expanded octet	10	Five bonding pairs
$\mathrm{SF_6}$	Expanded octet	12	Six bonding pairs
NO	Odd electron	11 valence electrons in total	One unpaired electron

Common traps

A triple bond shares six electrons, not three

Each bond is a pair. A double bond shares four electrons and a triple bond six. Options that count the bond lines (2 or 3) as the number of electrons are wrong.

A C=C bond is not twice as strong as a C-C bond

The π bond is weaker than the σ bond, so the carbon double bond (about 614 kJ/mol) is less than double the single bond (about 348 kJ/mol). It is still stronger and shorter than the single bond.

Count the charge of an ion

A negative ion has extra electrons and a positive ion has fewer. Leaving the charge out gives the wrong number of lone pairs, and IMAT offers that wrong count among the options.

A dative bond is not weaker or different once formed

The arrow only records where the electrons came from. In

\mathrm{NH_4^+}

all four N to H bonds have the same length and strength, and the ion is a regular tetrahedron.

Only period 3 and lower can expand the octet

Phosphorus and sulfur can hold 10 or 12 electrons; nitrogen and oxygen, just above them in the same groups, cannot. An option giving nitrogen five bonds or oxygen four bonds in a neutral molecule is wrong.

VSEPR Shapes, Bond Angles and Polar Molecules

Learn this subtopic in the notes

Counting electron domains on the central atom (VSEPR)

Domains on the central atom

D = \frac{V + m - q}{2}

$V$ valence electrons of the central atom
$m$ number of H or halogen atoms bonded to it (O and S atoms add nothing)
$q$ charge of the ion, with its sign (so a 2− ion adds 2)
$D$ number of electron domains; round a half up (odd-electron molecules)

The VSEPR shapes and their bond angles

Domains	Lone pairs	Shape	Bond angle	Examples
2	0	Linear	180°	$\mathrm{BeCl_2}$ , $\mathrm{CO_2}$ , $\mathrm{C_2H_2}$
3	0	Trigonal planar	120°	$\mathrm{BF_3}$ , $\mathrm{SO_3}$ , $\mathrm{CO_3^{2-}}$
3	1	Bent	just under 120°	$\mathrm{SO_2}$ , $\mathrm{O_3}$
4	0	Tetrahedral	109.5°	$\mathrm{CH_4}$ , $\mathrm{NH_4^+}$ , $\mathrm{SO_4^{2-}}$
4	1	Trigonal pyramidal	about 107°	$\mathrm{NH_3}$ , $\mathrm{PCl_3}$ , $\mathrm{H_3O^+}$
4	2	Bent	about 104.5°	$\mathrm{H_2O}$ , $\mathrm{H_2S}$
5	0	Trigonal bipyramidal	120° and 90°	$\mathrm{PCl_5}$
5	1	Seesaw	below 120° and 90°	$\mathrm{SF_4}$
5	2	T-shaped	about 90°	$\mathrm{ClF_3}$
6	0	Octahedral	90°	$\mathrm{SF_6}$
6	2	Square planar	90°	$\mathrm{XeF_4}$

Polar and non-polar molecules: when bond dipoles cancel

Molecule	Shape	Bond dipoles cancel?	Polar molecule?
$\mathrm{CO_2}$	Linear	Yes	No
$\mathrm{H_2O}$	Bent	No	Yes
$\mathrm{BF_3}$	Trigonal planar	Yes	No
$\mathrm{NH_3}$ , $\mathrm{PCl_3}$	Trigonal pyramidal	No	Yes
$\mathrm{CCl_4}$	Tetrahedral, four identical atoms	Yes	No
$\mathrm{CHCl_3}$ , $\mathrm{CH_3Cl}$	Tetrahedral, mixed atoms	No	Yes
$\mathrm{PCl_5}$ , $\mathrm{SF_6}$	Trigonal bipyramidal, octahedral	Yes	No
HCl, HBr	Linear, two different atoms	Only one bond	Yes

Common traps

Forgetting the charge changes the shape

\mathrm{SO_3}

is trigonal planar but

\mathrm{SO_3^{2-}}

is trigonal pyramidal: the two extra electrons make a lone pair. Always add the negative charge (or subtract the positive charge) before counting domains.

Ammonia is pyramidal, not tetrahedral

Its four domains point to the corners of a tetrahedron, but one is a lone pair, and the shape is named from the atoms: trigonal pyramidal, about 107°. Four atoms around a centre with a lone pair is never trigonal planar either.

Polar bonds can still give a non-polar molecule

The C to O bonds in

\mathrm{CO_2}

and the B to F bonds in

\mathrm{BF_3}

are strongly polar, but the shapes are symmetric and the dipoles cancel. Ask about the shape before answering "polar".

A tetrahedral molecule can be polar

Tetrahedral cancels only when all four outer atoms are the same.

\mathrm{CHCl_3}

is tetrahedral and polar, because its C to Cl and C to H bonds pull with different strengths.

Intermolecular Forces, Boiling Points and Solubility

Learn this subtopic in the notes

The three intermolecular forces and where each acts

Force	Acts between	Cause	Relative strength
London (dispersion)	All molecules and noble gas atoms	Temporary dipole inducing a dipole in a neighbour	Weakest for small molecules; grows with size
Dipole-dipole	Polar molecules	Permanent $\delta^+$ and $\delta^-$ ends attracting	Stronger than London for molecules of similar size
Hydrogen bond	Molecules with H bonded to N, O or F	Very $\delta^+$ H attracted to a lone pair on N, O or F	Strongest intermolecular force
Ion-dipole	An ion and a polar molecule	Ion charge attracting the opposite end of the dipole	Strong; explains salts dissolving in water

Hydrogen bonding: which substances have it

Substance	H bonded to N, O or F?	Hydrogen bonds between its molecules?
Water, $\mathrm{H_2O}$	Yes, O to H	Yes
Ammonia, $\mathrm{NH_3}$	Yes, N to H	Yes
Hydrogen fluoride, HF	Yes, F to H	Yes
Ethanol, $\mathrm{C_2H_5OH}$	Yes, O to H	Yes
Methylamine, $\mathrm{CH_3NH_2}$	Yes, N to H	Yes
Methane, $\mathrm{CH_4}$	No	No
Hydrogen sulfide, $\mathrm{H_2S}$	No, H on S	No
Dimethyl ether, $\mathrm{CH_3OCH_3}$	No, every H is on C	No
Propanone, $\mathrm{CH_3COCH_3}$	No, every H is on C	No

Solubility: like dissolves like

Substance	Dissolves well in	Reason
Sodium chloride	Water, not hexane	Ion-dipole attraction to water molecules
Ethanol	Water, in any proportion	Hydrogen bonds with water
Glucose	Water	Several O to H groups hydrogen bond with water
Iodine, $\mathrm{I_2}$	Hexane, only slightly in water	Non-polar, London forces only
Cooking oil	Hexane, not water	Long non-polar chains
Hexan-1-ol	Hexane better than water	The long chain outweighs one O to H group

Common traps

London forces act in polar molecules too

London forces are present in every molecule. In large molecules they can outweigh dipole forces: HI boils higher than HCl even though HCl is more polar, because HI has far more electrons. When asked why a heavier hydrogen halide boils higher, the answer is London forces, not dipoles.

Having O or F in the molecule is not enough

A hydrogen bond needs H attached directly to N, O or F. Fluoromethane, ethers and aldehydes contain O or F but all their H atoms are on carbon, so their pure liquids have no hydrogen bonds.

Boiling breaks intermolecular forces, not covalent bonds

Steam is made of whole

\mathrm{H_2O}

molecules. A stronger O to H or C to H bond inside a molecule does not raise the boiling point. Options that explain a boiling point with the strength of the bonds inside the molecule (intramolecular forces) are wrong.

Isomers with the same mass can boil at different temperatures

Equal

M_r

does not mean equal boiling points. A branched isomer is more compact, touches its neighbours less, and has weaker London forces, so it boils lower than the straight-chain isomer.

A molecule with polar bonds may still be non-polar and insoluble in water

\mathrm{CCl_4}

has four polar C to Cl bonds, but its symmetric tetrahedral shape cancels the dipoles, so it hardly dissolves in water. Solubility follows the polarity of the whole molecule, not of its bonds.

Giant Structures, Simple Molecules and Types of Solid

Learn this subtopic in the notes

The four types of crystalline solid and their properties

Type	Particles and what holds them	Typical properties	Examples
Giant ionic	Ions; ionic bonds in all directions	High melting point; brittle; conducts molten or in solution	NaCl, MgO, $\mathrm{CaF_2}$
Giant covalent	Atoms; covalent bonds throughout	Very high melting point; hard; insoluble; insulator (graphite apart)	Diamond, graphite, $\mathrm{SiO_2}$ , silicon
Metallic	Cations in delocalised electrons	Conducts as a solid; malleable; shiny	Cu, Fe, Na
Simple molecular	Molecules; intermolecular forces	Low melting point; soft; insulator	Ice, $\mathrm{I_2}$ , dry ice ( $\mathrm{CO_2}$ ), sugar

Diamond, graphite, silicon dioxide and the sodium chloride lattice

Structure	Arrangement	Bonding	Key properties
Diamond	Each C joined to 4 C, tetrahedral	Covalent, 3D network	Very hard; very high melting point; does not conduct
Graphite	Each C joined to 3 C in hexagonal layers	Covalent in layers; weak forces between layers	Soft, slippery; conducts along layers; high melting point
Silicon dioxide	Each Si joined to 4 O, each O to 2 Si	Covalent, 3D network	Hard; high melting point; does not conduct
Sodium chloride	Each ion surrounded by 6 of the opposite charge	Ionic	High melting point; brittle; conducts molten or dissolved

Elements, compounds, atoms and molecules: classifying substances

Substance	Element or compound	Smallest units
Helium, He	Element	Single atoms
Oxygen, $\mathrm{O_2}$ ; ozone, $\mathrm{O_3}$	Element	Molecules
Sulfur, $\mathrm{S_8}$	Element	Molecules
Diamond, C	Element	Giant covalent network (no molecules)
Iron, Fe	Element	Metallic lattice (no molecules)
Ammonia, $\mathrm{NH_3}$	Compound	Molecules
Potassium bromide, KBr	Compound	Ions (no molecules)

Common traps

Simple molecular does not mean weak covalent bonds

Iodine melts easily, but the I to I bond inside each molecule is a strong covalent bond. What is weak is the attraction between molecules. Melting or boiling a molecular solid leaves its molecules intact.

Graphite is soft but melts very high

Softness comes from the weak forces between layers. Melting must break the strong covalent bonds within the layers, so graphite's melting point is even higher than most metals'. Do not link softness with a low melting point here.

"Molecule" and "compound" are different ideas

\mathrm{N_2}

is a molecule but not a compound; NaCl is a compound but not made of molecules. Check one kind of atom versus several, and separate units versus a lattice, as two separate questions.

Chemical Bonding formulas

Ionic, Covalent and Metallic Bonds

Electronegativity difference and bond character

Ionic bonds and the formula of an ionic compound

Metallic bonding and the properties it explains

Common traps

Covalent Bonds, Lewis Structures and the Octet Rule

Drawing a Lewis structure by counting electrons

Single, double and triple covalent bonds

Exceptions to the octet rule

Common traps

VSEPR Shapes, Bond Angles and Polar Molecules

Counting electron domains on the central atom (VSEPR)

The VSEPR shapes and their bond angles

Polar and non-polar molecules: when bond dipoles cancel

Common traps

Intermolecular Forces, Boiling Points and Solubility

The three intermolecular forces and where each acts

Hydrogen bonding: which substances have it

Solubility: like dissolves like

Common traps

Giant Structures, Simple Molecules and Types of Solid

The four types of crystalline solid and their properties

Diamond, graphite, silicon dioxide and the sodium chloride lattice

Elements, compounds, atoms and molecules: classifying substances

Common traps

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