Formulae, equations and state symbols

A balanced equation must conserve atoms and charge. State symbols — (s), (l), (g), (aq) — are part of the answer at A level.

An ionic equation strips out the spectator ions. Neutralisation of any strong acid by any strong alkali is really just:

Exam habit: after balancing, check charge as well as atoms. In half-equations such as MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O the left-hand charge is (−1) + (+8) + (−5) = +2, which matches Mn²⁺.

Balance it

The mole, molar mass and concentration

The mole is the amount of substance containing 6.02 × 10²³ particles (the Avogadro constant, L).

Watch the units: 25.0 cm³ is 0.0250 dm³. Forgetting the ÷ 1000 is the single most common titration error.

Your turn — moles from mass

Titration calculations

A titration finds an unknown concentration by reacting it with a solution of known concentration. The route is always the same:

• 1 — moles of the known solution: n = c × V
• 2 — use the balanced equation to get the mole ratio
• 3 — moles of the unknown → c = n ÷ V

Accuracy: use concordant titres (within 0.10 cm³ of each other) and take their mean — never average in a rough titre.

Your turn — titration

The ideal gas equation

The units are unforgiving. Convert before you substitute:

• kPa → Pa: × 1000. 100 kPa = 1.00 × 10⁵ Pa.
• cm³ → m³: ÷ 10⁶. dm³ → m³: ÷ 1000.
• °C → K: + 273.

Ideal gas assumptions: the molecules have negligible volume and there are no intermolecular forces. Real gases deviate most at high pressure and low temperature, where both assumptions collapse.

Your turn — pV = nRT

Percentage yield and atom economy

They measure different things. Yield is about how well the reaction actually went (losses, side reactions, reversibility). Atom economy is fixed by the equation itself — an addition reaction has 100% atom economy because there is only one product.

Green chemistry: a high atom economy means less waste, cheaper separation and fewer disposal problems — a reaction can have a 95% yield yet a terrible atom economy.

Your turn — atom economy

Your turn — percentage yield

Atoms, isotopes and the mass spectrometer

Isotopes are atoms of the same element (same atomic number) with different numbers of neutrons. They are chemically identical because chemistry is governed by the electrons.

A time-of-flight mass spectrometer ionises the sample, accelerates the ions, and separates them by mass/charge (m/z). The relative abundances give the relative atomic mass:

Your turn — relative atomic mass

Orbitals and electron configuration

Electrons occupy orbitals — regions holding a maximum of 2 electrons of opposite spin. An s orbital is spherical; the three p orbitals are dumb-bell shaped and mutually perpendicular; there are five d orbitals.

• Capacity: s = 2, p = 6, d = 10, f = 14.
• Aufbau: fill lowest energy first. 4s fills before 3d — but 4s is also lost first on ionisation.
• Hund's rule: singly occupy degenerate orbitals before pairing up.

The two anomalies: Cr is [Ar] 3d⁵ 4s¹ and Cu is [Ar] 3d¹⁰ 4s¹ — a half-filled or full d subshell is the more stable arrangement.

Configuration of an ion

Ionisation energies

The first ionisation energy is the energy to remove one electron from each atom in one mole of gaseous atoms:

Three factors control its size: nuclear charge, atomic radius (distance) and shielding by inner shells.

• Across a period the first IE generally rises — more protons, similar shielding, smaller radius.
• Down a group it falls — more shells, so more distance and more shielding outweigh the extra protons.
• Two dips in Period 3: Al < Mg (the outer electron is in a higher-energy 3p orbital) and S < P (in sulfur two electrons are paired in one 3p orbital and repel).

Successive ionisation energies always increase, and a big jump marks the start of a new, closer shell — the number of electrons removed before the jump gives the group number.

Explain the dip

Your turn — successive ionisation energies

Bonding, electronegativity and polarity

• Ionic — electrostatic attraction between oppositely charged ions (metal + non-metal).
• Covalent — a shared pair of electrons. In a dative (coordinate) bond both electrons come from the same atom, e.g. the fourth N–H bond in NH₄⁺.
• Metallic — positive ions in a sea of delocalised electrons.

Electronegativity is the power of an atom to attract the electrons in a covalent bond. It increases across a period and decreases down a group; F is the most electronegative element.

A difference in electronegativity makes a bond polar (δ+ / δ−). But a molecule with polar bonds is only polar overall if the dipoles do not cancel: CO₂ is linear and non-polar; H₂O is bent and polar.

Shapes of molecules — VSEPR

Valence Shell Electron Pair Repulsion: electron pairs around the central atom repel to get as far apart as possible. Lone pairs repel more strongly than bonding pairs, so each lone pair squeezes the bond angle by roughly 2.5°.

• 2 pairs, 0 lone → linear, 180° (CO₂, BeCl₂)
• 3 pairs, 0 lone → trigonal planar, 120° (BF₃, SO₃)
• 4 pairs, 0 lone → tetrahedral, 109.5° (CH₄, NH₄⁺)
• 4 pairs, 1 lone → trigonal pyramidal, 107° (NH₃)
• 4 pairs, 2 lone → bent / non-linear, 104.5° (H₂O)
• 5 pairs → trigonal bipyramidal, 120° and 90° (PCl₅); 6 pairs → octahedral, 90° (SF₆)

Method: count the electron pairs around the central atom, then subtract for lone pairs. Repulsion order: lone–lone > lone–bond > bond–bond.

Sort by shape

Tap a molecule, then tap the shape it adopts. Think: how many electron pairs, and how many are lone pairs?

The ammonia angle

Intermolecular forces and hydrogen bonding

Three forces act between molecules, all far weaker than a covalent bond:

• van der Waals (London / temporary dipole–induced dipole) — present in everything. Stronger with more electrons and a larger contact surface, which is why boiling points rise down the alkanes and why branching lowers them.
• Permanent dipole–dipole — between polar molecules.
• Hydrogen bonding — the strongest. Requires H bonded directly to N, O or F, plus a lone pair on the N, O or F of the neighbour.

Ice is less dense than water because hydrogen bonds hold the molecules in an open tetrahedral lattice. Hydrogen bonding also explains why HF, H₂O and NH₃ have anomalously high boiling points against the trend of their groups.

Four kinds of solid structure

Physical properties follow directly from structure and bonding:

• Giant ionic (NaCl) — high m.p.; conducts only when molten or aqueous, because the ions must be free to move.
• Giant covalent (diamond, SiO₂) — very high m.p., hard, non-conducting. Graphite is the exception: it conducts because one electron per carbon is delocalised, and its layers slide.
• Simple molecular (I₂, CO₂) — low m.p. because only weak intermolecular forces are broken on melting; never conducts.
• Metallic (Mg) — malleable and conducting because of delocalised electrons.

The classic misconception: melting iodine does not break the I–I covalent bond. It only overcomes the van der Waals forces between I₂ molecules — that is why the melting point is so low.

Match structure to substance

Tap a description on the left, then the substance on the right.

The big ideas to know

That is the whole of C1. Press Finish to see your score.