Mission 1: What's in the bubbles of boiling water?

Elements, compounds, mixtures

• An element cannot be broken down into simpler substances by chemical means.
• A compound contains atoms of different elements, bonded in a fixed ratio.
• A mixture has no fixed ratio, and its components are not bonded to each other.
• O₂ is an element: two atoms, but of the same element.
• A compound's properties differ from its elements' (sodium + chlorine → sodium chloride).
• A mixture keeps its components' properties, and melts or boils over a range of temperatures.

Separating mixtures

• Mixtures separate by physical methods; no new substance is made.
• Dissolving is solvation: solvent molecules surround each solute particle.
• Filtration: insoluble solid from a liquid. Dissolved particles pass through.
• Evaporation: recovers a dissolved solid; the solvent is lost.
• Distillation: the vapour is condensed, so the solvent is recovered too.
• Recrystallization: dissolve in the minimum of hot solvent, then cool; impurities stay in solution.
• Paper chromatography: components travel different distances because they are attracted differently to the paper and the solvent.
• Homogeneous mixtures are uniform (salt solution, air); heterogeneous ones show separate phases (sand in water).

Particles in the three states

• Kinetic molecular theory: matter is moving particles with attractions between them.
• Solid: particles vibrate about fixed positions. Fixed shape and volume.
• Liquid: particles close together but slide past each other. Fixed volume.
• Gas: particles far apart, moving fast and randomly. Easily compressed.

Changes of state and state symbols

• Melting, freezing, vaporization, condensation, sublimation (solid → gas), deposition (gas → solid).
• Evaporation happens at the surface at any temperature; boiling happens throughout the liquid, at the boiling point.
• State symbols: (s), (l), (g), and (aq) for dissolved in water.
• H₂O(l) → H₂O(g) is vaporization. Water itself is never H₂O(aq).

What temperature measures

• Temperature in kelvin is proportional to the average kinetic energy of the particles.
• Absolute zero: 0 K = −273.15 °C. Kelvin temperatures are never negative.
• T/K = T/°C + 273 (273 is fine for calculations). A change of 1 K equals a change of 1 °C.
• Particles in a sample have a range of kinetic energies.
• Heat is energy transferred because of a temperature difference; it is not the same as temperature.

Why the temperature stops rising

• For a pure substance, the temperature stays constant during a change of state.
• The energy supplied overcomes attractions between particles, so average kinetic energy does not rise.
• Melting and boiling a molecular substance do not break the covalent bonds inside its molecules.

Mission 2: Why is chlorine's relative atomic mass 35.45 when no chlorine atom weighs that?

The nuclear atom

• Nearly all of an atom's mass is in a tiny, dense nucleus.
• Nucleus about 10⁻¹⁵ m across; the atom about 10⁻¹⁰ m.

Reading the nuclear symbol

• In AZX, Z (atomic number) = number of protons. It fixes the element.
• A (mass number) = protons + neutrons, so neutrons = A − Z.
• A neutral atom has Z electrons. An ion has Z minus its charge: a 2− ion has Z + 2.
• 5626Fe³⁺: 26 protons, 30 neutrons, 23 electrons.
• 168O²⁻: 8 protons, 8 neutrons, 10 electrons.
• Ions form by losing or gaining electrons; the number of protons never changes.

Isotopes

• Isotopes: same number of protons, different numbers of neutrons.
• Same electron arrangement, so the same chemical properties.
• Different mass, so different physical properties: density, rate of diffusion, melting and boiling points.

Relative atomic mass, a weighted mean

• A_r = Σ(relative isotopic mass × % abundance) ÷ 100. A_r has no units.
• A_r lies between the lightest and heaviest isotope, closer to the more abundant one.
• Worked example, boron: ¹⁰B 19.9% (10.01), ¹¹B 80.1% (11.01).
• A_r = (10.01 × 19.9 + 11.01 × 80.1) ÷ 100 = (199.2 + 881.9) ÷ 100 = 10.81.
• Don't divide again by the number of isotopes: the weighted sum is already the mean.
• Working back from A_r: call one abundance x% and the other (100 − x)%, then solve for x.

Reading a mass spectrum

• Each peak from a 1+ ion is one isotope; m/z = its relative isotopic mass.
• Peak height = relative abundance. Number of peaks = number of isotopes.
• If the tallest peak is set to 100, the abundances add to more than 100.
• Then A_r = Σ(m/z × abundance) ÷ Σ(abundances), not ÷ 100.
• The tallest peak is only the most abundant isotope, not A_r.

Mission 3: Why do fireworks come in different colours?

Wavelength, frequency, energy

• Light travels as photons. For light, c = λf (in the data booklet).
• Shorter wavelength → higher frequency → more energy per photon.
• Visible light: red has the lowest energy, violet the highest.
• Beyond violet is ultraviolet; beyond red is infrared.

How atoms give out light

• An electron absorbs energy and moves up to a higher level: an excited state.
• When it falls back, it emits a photon. Photon energy = the energy gap.
• A continuous spectrum contains all wavelengths. An emission line spectrum is bright lines on a dark background.
• Light is emitted only on the way down, never as the electron moves up.

What hydrogen's spectrum proves

• Hydrogen gives lines, not a continuous band, so its electron has discrete energy levels.
• Levels get closer together as n rises, so each set of lines converges at high frequency.
• Falls to n = 1 emit ultraviolet; to n = 2, mainly visible; to n = 3, infrared.
• One electron, many lines: each line is a different transition, in different atoms of the sample.

How many electrons a level holds

• Main levels are numbered n = 1, 2, 3 … outwards from the nucleus.
• Level n holds at most 2n² electrons: 2, 8, 18, 32.
• That's n² orbitals, each holding two electrons.
• The third level holds 18, not 8. "2, 8, 8" is the filling pattern of the first 20 elements, not a capacity.

Mission 4: If an electron isn't in an orbit, where is it?

Sublevels

• Each main level splits into sublevels: s, p, d, f, rising in energy in that order.
• n = 1: 1s. n = 2: 2s, 2p. n = 3: 3s, 3p, 3d. n = 4 adds 4f.
• s, p, d, f have 1, 3, 5 and 7 orbitals, so they hold 2, 6, 10 and 14 electrons.

Orbitals

• An orbital is a region where an electron is likely to be found, not a path.
• An s orbital is spherical, centred on the nucleus.
• The three p orbitals are dumbbells along the x, y and z axes, at 90° to each other.

Three filling rules

• Aufbau: fill the lowest energy first: 1s 2s 2p 3s 3p 4s 3d 4p.
• Pauli: at most two electrons per orbital, with opposite spins.
• Hund: in orbitals of equal energy, electrons go in singly, spins parallel, before pairing.
• Hund decides how one sublevel fills; Aufbau decides which sublevel fills next.

Writing configurations

• Iron, Z = 26: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s², condensed to [Ar] 3d⁶ 4s².
• 4s fills before 3d, but either written order is accepted: [Ar] 4s² 3d⁶ is also correct.
• Two exceptions up to krypton: Cr [Ar] 3d⁵ 4s¹ and Cu [Ar] 3d¹⁰ 4s¹.
• Transition metal ions lose 4s electrons first: Fe³⁺ is [Ar] 3d⁵.
• Main-group ions change the outer sublevel: S²⁻ is 1s² 2s² 2p⁶ 3s² 3p⁶.

Mission 5: How much energy does it take to pull an electron out of an atom?

The convergence limit is ionization

• In the set of lines ending at n = 1, the lines crowd together to a convergence limit.
• The limit line is a fall from n = ∞ to n = 1.
• Its energy equals the energy to remove the electron from the ground state.
• First ionization energy: the minimum energy to remove one mole of electrons from one mole of gaseous atoms in their ground state: X(g) → X⁺(g) + e⁻.
• The lowest-energy line in the set (n = 2 → 1) is not the ionization energy.

From the limit to kJ mol⁻¹

• Energy of one photon: E = hf; if you are given a wavelength, find f from c = λf.
• That is the energy per atom. Multiply by N_A, then divide by 1000 for kJ mol⁻¹.
• Worked example: hydrogen's limit is at f = 3.29 × 10¹⁵ s⁻¹.
• E = 6.63 × 10⁻³⁴ × 3.29 × 10¹⁵ = 2.181 × 10⁻¹⁸ J per atom: keep the extra figure.
• × 6.02 × 10²³ = 1.313 × 10⁶ J mol⁻¹ = 1313 kJ mol⁻¹ (data booklet value 1312).

Trends in first ionization energy

• Across a period IE rises: more nuclear charge, same main level, similar shielding.
• Down a group IE falls: the outer electron is further out and more shielded.
• Two dips across a period. Group 2 → 13: the electron now comes from a higher-energy p sublevel.
• Group 15 → 16: it comes from a doubly occupied p orbital, where repulsion makes it easier to remove.
• Explain with these energies, not "half-full sublevels are stable".

Successive ionization energies give the group

• Successive ionization energies always rise: each electron leaves a more positive ion.
• A big jump marks the first electron taken from an inner, less shielded level.
• Count the electrons removed before the jump: these are the outer electrons.
• One → group 1. Two → group 2. Three → group 13; four → group 14, and so on.
• In groups 13–18, group number = outer electrons + 10.

The big ideas

• Mixtures separate physically; compounds have bonded atoms in a fixed ratio.
• Temperature in kelvin tracks average kinetic energy; for a pure substance it stays constant during a change of state.
• Z fixes the element; isotopes differ in neutrons; A_r is an abundance-weighted mean.
• Line spectra prove discrete energy levels, which converge at higher energy.
• Configurations: Aufbau, Pauli, Hund; Cr and Cu are exceptions; 4s is lost first.
• AHLIonization energy comes from the convergence limit; electrons before the big jump give the group.