A Level Physical Chemistry
Complete Study Guide

🔢 Key Formulae

n = moles; m = mass (g); M = molar mass (g mol⁻¹)

c = concentration (mol dm⁻³)

📐 Molar Mass Examples

• H₂O: M = 2(1) + 16 = 18 g mol⁻¹
• NaCl: M = 23 + 35.5 = 58.5 g mol⁻¹
• H₂SO₄: M = 2 + 32 + 4(16) = 98 g mol⁻¹
• CaCO₃: M = 40 + 12 + 3(16) = 100 g mol⁻¹
• Na₂CO₃: M = 2(23)+12+3(16) = 106 g mol⁻¹

📊 Percentage Yield

Theoretical yield is calculated from stoichiometry assuming complete reaction.

♻️ Atom Economy

Higher atom economy = greener, less waste. Addition reactions have 100% atom economy.

📏 Units

• p = pressure in Pa (pascals)
• V = volume in m³
• n = moles
• R = 8.314 J K⁻¹ mol⁻¹
• T = temperature in K (= °C + 273)

🔢 Conversions

• 1 dm³ = 10⁻³ m³
• 1 cm³ = 10⁻⁶ m³
• 1 atm = 101 325 Pa
• STP: 273 K, 100 kPa
• RTP: 298 K, 100 kPa

🔵 Ionic Bonding

Electrostatic attraction between oppositely charged ions formed by transfer of electrons from metal to non-metal.

• Strong forces → high melting points
• Conduct electricity when molten or in solution
• Example: Na⁺Cl⁻, Mg²⁺O²⁻

🟢 Covalent Bonding

Sharing of a pair of electrons between two atoms, each contributing one electron (or both from one atom — dative bond).

• Single: 1 shared pair — H–H, H–Cl
• Double: 2 shared pairs — O=O, C=O
• Triple: 3 shared pairs — N≡N

⚪ Metallic Bonding

Lattice of positive metal ions surrounded by a 'sea' of delocalised electrons. Electrostatic attraction between ions and electrons.

• Good conductors (delocalised electrons)
• Malleable and ductile
• Generally high melting points

➕➖ Polar vs Non-Polar Molecules

• CCl₄: polar bonds but symmetric tetrahedral → dipoles cancel → non-polar
• CHCl₃: asymmetric → net dipole → polar
• CO₂: linear, dipoles cancel → non-polar
• H₂O: bent, dipoles don't cancel → polar

🔗 Dative Covalent (Co-ordinate) Bond

Both electrons in the shared pair come from the same atom. Once formed, identical to a covalent bond.

• NH₄⁺: lone pair from NH₃ → H⁺
• H₃O⁺: lone pair from H₂O → H⁺
• Al₂Cl₆: Cl lone pair → Al
• CO: one of three bonds is dative

🌊 van der Waals / London Forces

Temporary dipoles induced by instantaneous uneven electron distribution. Present in ALL molecules.

• Strength increases with: more electrons / larger surface area
• Weakest intermolecular force
• Explains why I₂ has higher bp than F₂

↔️ Permanent Dipole–Dipole

Electrostatic attraction between δ+ of one polar molecule and δ− of another.

• Stronger than London forces
• Example: HCl, SO₂, CH₂Cl₂
• Explains higher bp of HCl vs noble gases

🔵 Hydrogen Bonding

Strong dipole–dipole interaction between H bonded to N, O, or F and a lone pair on another N, O, or F atom.

• H₂O: up to 4 H-bonds per molecule
• Explains anomalously high bp of H₂O (100°C vs predicted −80°C)
• Explains high bp of NH₃, HF, alcohols
• Explains ice being less dense than water

🏗️ Giant Ionic Lattice

• Regular 3D array of oppositely charged ions
• High melting points (strong electrostatic forces)
• Brittle — layers shift, like charges repel
• Conducts when molten or aqueous (not solid)
• Example: NaCl (6:6 coordination), CsCl (8:8)

🔷 Giant Covalent (Macromolecular)

• Diamond: each C bonded to 4 C tetrahedrally; very hard, very high m.p., non-conductor
• Graphite: layers of hexagonal C rings; delocalised electrons within layers → conductor; soft (layers slide)
• SiO₂: giant covalent, high m.p.
• Si: semiconductor

🧊 Simple Molecular

• Discrete molecules held by weak intermolecular forces
• Low melting and boiling points
• Non-conductors (no ions or free electrons)
• Examples: H₂O, CO₂, I₂, CH₄, S₈

⚙️ Metallic Lattice

• Close-packed metal cations + delocalised electron sea
• Good conductors of heat and electricity
• Malleable, ductile, lustrous
• m.p. increases with: charge on ion, number of delocalised electrons, smaller ionic radius
• Example: Na < Mg < Al (increasing ionic charge and fewer shells)

💨 Kinetic Molecular Theory

• Gas particles in constant, random motion
• Particles have negligible volume
• No intermolecular forces (ideal gas)
• Elastic collisions (no energy lost)
• KE ∝ absolute temperature T

📐 Gas Laws Summary

• Boyle's Law: pV = constant (fixed T, n)
• Charles' Law: V/T = constant (fixed p, n)
• Pressure Law: p/T = constant (fixed V, n)
• Ideal: pV = nRT

🔥 Standard Enthalpy of Combustion ΔH°_c

Enthalpy change when 1 mole of a substance burns completely in oxygen under standard conditions (298 K, 100 kPa), with all reactants and products in standard states. Always negative (exothermic).

⚗️ Standard Enthalpy of Formation ΔH°_f

Enthalpy change when 1 mole of a compound is formed from its elements in their standard states under standard conditions. ΔH°_f of an element = 0 by definition.

💧 Enthalpy of Neutralisation ΔH°_neut

Enthalpy change when an acid and base react to form 1 mole of H₂O under standard conditions.

🧊 Enthalpy of Atomisation ΔH°_at

Enthalpy change to produce 1 mole of gaseous atoms from the element in its standard state. Always endothermic (positive).

✅ Spontaneity Conditions

• Reaction is spontaneous (feasible) when ΔG < 0
• ΔG = 0 at equilibrium
• ΔG > 0 → non-spontaneous
• If ΔH −ve and ΔS +ve → always spontaneous
• If ΔH +ve and ΔS −ve → never spontaneous

🌡️ Temperature Dependence

• ΔH −ve, ΔS −ve → spontaneous at low T
• ΔH +ve, ΔS +ve → spontaneous at high T
• Crossover temperature: T = ΔH / ΔS
• Example: CaCO₃(s) → CaO(s) + CO₂(g)
  ΔH = +178 kJ mol⁻¹, ΔS = +165 J K⁻¹ mol⁻¹
  T = 178000/165 ≈ 1079 K

⬆️ OIL RIG Mnemonic

• Oxidation Is Loss (of electrons)
• Reduction Is Gain (of electrons)
• Oxidising agent = accepts electrons (gets reduced)
• Reducing agent = donates electrons (gets oxidised)

🔢 Oxidation State Rules

• Free element = 0 (e.g. Fe, O₂, Na)
• Monatomic ion = charge (e.g. Fe²⁺ = +2)
• O in compounds = −2 (except peroxides = −1, OF₂ = +2)
• H in compounds = +1 (except metal hydrides = −1)
• Sum of OS in neutral molecule = 0
• Sum of OS in ion = charge of ion

🔑 What Each Symbol Means

• E — actual electrode potential under non-standard conditions (V)
• E° — standard electrode potential (V)
• R — gas constant = 8.314 J K⁻¹ mol⁻¹
• T — absolute temperature (K); always use K, not °C
• n — number of moles of electrons transferred in the half-equation
• F — Faraday constant = 96 485 C mol⁻¹
• Q — reaction quotient = ratio of products to reactants at the current concentrations (same form as K, but using actual concentrations)
• ln Q — natural logarithm of Q; use log₁₀ Q with the 0.0592/n form

📐 Writing the Reaction Quotient Q

Q has the same form as the equilibrium constant K, using actual (non-standard) concentrations or partial pressures instead of equilibrium values.

• For: Cu²⁺(aq) + 2e⁻ → Cu(s)
  Q = 1 / [Cu²⁺]  (solid Cu omitted)
• For: Zn²⁺(aq) + 2e⁻ → Zn(s)
  Q = 1 / [Zn²⁺]
• For: Fe³⁺(aq) + e⁻ → Fe²⁺(aq)
  Q = [Fe²⁺] / [Fe³⁺]
• For: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O
  Q = [Mn²⁺] / ([MnO₄⁻][H⁺]⁸)

📊 Effect of Concentration on E — Key Rules

• Increasing [oxidised form] (e.g. more Cu²⁺) → Q decreases → E increases (more positive) → greater tendency to be reduced
• Decreasing [oxidised form] → Q increases → E decreases
• Increasing [reduced form] (e.g. more Fe²⁺) → Q increases → E decreases
• At equilibrium: E_cell = 0 and Q = K; this links E° to K: ln K = nFE°/RT

🔗 Nernst Equation & Equilibrium Constant

At equilibrium, Q = K and E_cell = 0. Substituting into the Nernst equation for the full cell:

This means a large positive E°_cell → large K → reaction strongly favours products. A negative E°_cell → K < 1 → reactants favoured.

🌡️ Effect of Temperature on E

• The Nernst equation contains T explicitly: E = E° − (RT/nF) ln Q
• Higher T → larger (RT/nF) factor → greater correction from E°
• For an exothermic cell reaction: increasing T lowers E°_cell (Le Chatelier — backward shift)
• For an endothermic cell reaction: increasing T raises E°_cell
• Fuel cells and batteries lose efficiency at low T because k is also affected

⚡ Electrolysis of Molten NaCl

• Cathode (negative): Na⁺(l) + e⁻ → Na(l)
• Anode (positive): 2Cl⁻(l) → Cl₂(g) + 2e⁻
• Overall: 2NaCl(l) → 2Na(l) + Cl₂(g)

⚡ Electrolysis of Aqueous NaCl

• Cathode: 2H⁺(aq) + 2e⁻ → H₂(g) (H⁺ from water preferentially discharged)
• Anode: 2Cl⁻(aq) → Cl₂(g) + 2e⁻
• Solution becomes NaOH(aq) — chlor-alkali process

⚡ Electrolysis of CuSO₄(aq)

• Cathode: Cu²⁺(aq) + 2e⁻ → Cu(s)
• Anode (inert): 2H₂O(l) → O₂(g) + 4H⁺(aq) + 4e⁻
• Anode (Cu): Cu(s) → Cu²⁺(aq) + 2e⁻ (used in electroplating/purification)

🏭 Haber Process (NH₃)

• Conditions: 450°C, 200 atm, Fe catalyst
• High pressure favours NH₃ (fewer moles of gas), but very expensive
• Lower T favours yield (exothermic) but rate too slow → compromise at 450°C
• Catalyst doesn't affect K but speeds equilibrium

🏭 Contact Process (H₂SO₄)

• Conditions: 450°C, 1–2 atm, V₂O₅ catalyst
• SO₃ + H₂SO₄ → H₂S₂O₇ (oleum) → then diluted
• Conversion ~99.5%

🟡 Weak Acid Calculations

Assumption: [H⁺] = [A⁻] and [HA]_eq ≈ [HA]_initial (valid when K_a << c)

📊 Buffer Solutions

Resist pH change on addition of small amounts of acid or alkali. Made from weak acid + its conjugate base (or excess weak acid + strong base).

Example: CH₃COOH / CH₃COO⁻Na⁺

🌡️ Temperature

Increasing temperature increases rate because:

• Particles have greater kinetic energy
• More particles have energy ≥ activation energy (E_a)
• Higher frequency of successful collisions
• Rule of thumb: ~10°C rise ≈ doubles rate

💊 Concentration

• Higher concentration → more particles per unit volume
• More frequent collisions
• Greater rate
• For gases: higher pressure = higher concentration

🪨 Surface Area

• Smaller particles → greater surface area
• More exposed particles → more collisions
• Increases rate
• Example: flour dust explosions, powdered vs lump zinc

🧪 Catalyst

• Provides alternative reaction pathway with lower E_a
• More particles have energy ≥ E_a
• Unchanged at end of reaction
• Does NOT shift equilibrium position but equilibrium reached faster

📊 Reaction Orders

• Zero order (m=0): rate unaffected by [A]; graph [A] vs t is straight line
• First order (m=1): rate ∝ [A]; [A] vs t is exponential decay
• Second order (m=2): rate ∝ [A]²; steeper curve
• Overall order = m + n
• Determined experimentally — NOT from stoichiometry!

⏱️ Half-Life (t_½)

• Time for concentration to halve
• First order: t_½ = constant (independent of [A])
• t_½ = 0.693 / k (first order)
• Radioactive decay is always first order
• Second order: t_½ increases as [A] decreases

📐 Units of k

• 0th order: mol dm⁻³ s⁻¹
• 1st order: s⁻¹
• 2nd order: mol⁻¹ dm³ s⁻¹
• 3rd order: mol⁻² dm⁶ s⁻¹

🔬 Rate-Determining Step

• The slowest step in a multi-step mechanism
• Determines the rate equation
• Only species in or before the RDS appear in the rate equation
• Example: SN1 vs SN2 mechanisms