Physical chemistry: the formulas that recur
Almost every physical-chemistry question is a formula plus a unit conversion. Learn each with the conditions attached and the unit of every symbol.
- ✓Mole concept: n = m/M; number of particles = n × Nᴀ; molarity M = moles of solute / volume of solution in litres; molality = moles of solute / kg of solvent; mole fraction = moles of component / total moles.
- ✓Gas laws: PV = nRT with R = 8.314 J K⁻¹ mol⁻¹ = 0.0821 L atm K⁻¹ mol⁻¹. Choose R to match your pressure and volume units - this is the single most common unit slip.
- ✓Thermodynamics: ΔH = ΔU + ΔnₘRT; ΔG = ΔH − TΔS; ΔG° = −RT ln K = −2.303 RT log K; ΔG = 0 at equilibrium; w = −Pₑₓₜ ΔV for irreversible expansion; q = mcΔT.
- ✓Spontaneity: ΔG < 0 spontaneous, ΔG > 0 non-spontaneous, ΔG = 0 at equilibrium. Know which ΔH-ΔS sign combinations are temperature-dependent.
- ✓Equilibrium: Kₚ = K_c(RT)^Δn; pH = −log[H⁺]; pH + pOH = 14 at 298 K; Henderson equation pH = pKₐ + log([salt]/[acid]); for a sparingly soluble AB salt, Kₛₚ = s².
- ✓Electrochemistry: E_cell = E°_cell − (0.059/n) log Q at 298 K; ΔG° = −nFE°_cell; Λₘ = Λ°ₘ − A√C; Faraday's first law m = ZIt.
- ✓Kinetics: first order k = (2.303/t) log(a/(a−x)), half-life t½ = 0.693/k independent of concentration; zero order t½ = a/2k; Arrhenius k = Ae^(−Eₐ/RT), and log(k₂/k₁) = (Eₐ/2.303R)(1/T₁ − 1/T₂).
- ✓Solutions and colligative properties: ΔT_b = K_b m; ΔT_f = K_f m; osmotic pressure π = CRT; all four are multiplied by the van't Hoff factor i for association or dissociation.
- ✓Atomic structure: Eₙ = −13.6/n² eV for hydrogen; Rydberg 1/λ = R(1/n₁² − 1/n₂²); de Broglie λ = h/mv; Heisenberg Δx·Δp ≥ h/4π.
- ✓Solid state: density d = ZM/(a³Nᴀ); packing efficiency 74% for fcc/ccp, 68% for bcc, 52.4% for simple cubic; radius relations r = a/(2√2) for fcc and r = √3a/4 for bcc.
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Inorganic chemistry: trends and the anomalies that break them
Learn the trend, then learn the exception - because the exception is what gets asked. A question that follows the trend tests nothing.
| Trend | General rule | The exception examiners use |
|---|---|---|
| Atomic radius | Decreases across a period, increases down a group | Ga is slightly smaller than Al (d-block contraction); Zr ≈ Hf (lanthanoid contraction) |
| Ionisation enthalpy | Increases across a period | IE₁ of N > O, and Be > B, due to stable configurations |
| Electron gain enthalpy | More negative across a period | Cl is more negative than F - fluorine's small size raises electron-electron repulsion |
| Metallic character | Decreases across, increases down | Inert pair effect makes Pb²⁺ more stable than Pb⁴⁺, and Tl⁺ more stable than Tl³⁺ |
| Reducing power | Increases down group 1 | Li is the strongest reducing agent in aqueous solution, from its very high hydration enthalpy |
- ✓Anomalous first members: Li, Be, B, C, N, O and F differ from their groups because of small size, high electronegativity and the absence of d orbitals. Nitrogen forms no pentahalides for exactly this reason.
- ✓Diagonal relationships: Li-Mg, Be-Al, B-Si. BeCl₂ is covalent, and BeO and Al₂O₃ are both amphoteric.
- ✓d-block: Cr is 3d⁵4s¹ and Cu is 3d¹⁰4s¹ because half-filled and fully-filled sets are more stable. Mn²⁺ (d⁵) is the most stable +2 ion of the 3d series, while Cu²⁺ beats Cu⁺ in water thanks to hydration enthalpy.
- ✓Lanthanoid contraction explains the similarity of Zr and Hf, and the +4 state of cerium and the +2 state of europium are the standard exceptions.
- ✓Hydrogen bonding drives the anomalies: H₂O boils far above H₂S, HF is the weakest hydrohalic acid despite having the strongest bond, and NH₃ boils above PH₃.
- ✓MOT results worth knowing: O₂ is paramagnetic with two unpaired electrons, N₂ has a bond order of 3, and the bond orders of O₂⁺, O₂ and O₂⁻ rank in that order.
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Chemical bonding and coordination compounds
- ✓VSEPR shapes with lone pairs: 2 pairs linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral. Lone pairs occupy equatorial positions in a trigonal bipyramid and compress bond angles.
- ✓Hybridisation from the steric number: sp linear 180°, sp² trigonal planar 120°, sp³ tetrahedral 109.5°, sp³d, sp³d². Bond angle order NH₃ (107°) > H₂O (104.5°) because of lone-pair counts.
- ✓Bond parameters: bond length falls and bond energy rises as bond order rises. Polarity follows electronegativity difference; a molecule can hold polar bonds and still be non-polar if symmetric, as in CO₂ and CCl₄.
- ✓Coordination: coordination number, oxidation state, and IUPAC naming (ligands alphabetically, then the metal with its oxidation state in Roman numerals).
- ✓Crystal field theory: octahedral splitting gives t₂g below e_g, tetrahedral is the reverse and smaller. Strong-field ligands give low-spin complexes, weak-field ligands high-spin.
- ✓Spectrochemical series (weak to strong): I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO.
- ✓Magnetic moment μ = √(n(n+2)) BM where n is the number of unpaired electrons - a standard numerical question.
- ✓Isomerism in complexes: ionisation, hydrate, linkage and coordination isomerism for structural forms, plus geometrical and optical isomerism for stereo forms.
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Organic chemistry: reason it out, do not memorise it
Organic questions become predictable once you can rank stability, because nearly every mechanism goes toward the more stable intermediate or product. Four rankings carry most of the subject.
- ✓Electronic effects: the inductive effect works through sigma bonds and weakens with distance; resonance delocalises electrons and is stronger; hyperconjugation stabilises carbocations and alkenes through adjacent C-H sigma bonds.
- ✓Carbocation stability: tertiary > secondary > primary > methyl, with allylic and benzylic cations stabilised further by resonance. This ranking predicts rearrangements and Markovnikov addition.
- ✓Acidity: carboxylic acid > phenol > water > alcohol > alkyne > ammonia > alkene > alkane. Electron-withdrawing groups increase acidity by stabilising the conjugate base; electron-donating groups decrease it.
- ✓Basicity of amines in water: secondary ≈ tertiary > primary > ammonia for aliphatic amines, with the order disturbed by solvation and steric effects. Aromatic amines are far weaker because the lone pair is delocalised into the ring.
- ✓Aromaticity requires a planar, cyclic, fully conjugated system with (4n + 2) π electrons - Hückel's rule.
- ✓Substitution: SN1 goes through a carbocation, favours tertiary substrates and polar protic solvents, and racemises. SN2 is a single-step backside attack, favours methyl and primary substrates and polar aprotic solvents, and inverts configuration.
- ✓Elimination: E1 parallels SN1, E2 needs an anti-periplanar arrangement, and Zaitsev's rule predicts the more substituted alkene while Hofmann elimination gives the less substituted one with bulky bases.
- ✓Aromatic substitution: −OH, −NH₂, −OR and alkyl groups activate the ring and direct ortho and para; −NO₂, −CN, −COOH and −SO₃H deactivate and direct meta; halogens deactivate yet still direct ortho and para.
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Related reading
Biomolecules, polymers and everyday chemistry
The short chapters at the end of the syllabus are pure recall and are frequently the difference between a good score and a great one, because most students under-revise them.
- ✓Carbohydrates: aldoses versus ketoses; glucose and fructose structures; reducing versus non-reducing sugars (sucrose is non-reducing, maltose and lactose are reducing); starch, glycogen and cellulose linkages.
- ✓Proteins: the peptide bond, primary through quaternary structure, denaturation, essential versus non-essential amino acids, the zwitterion and isoelectric point.
- ✓Nucleic acids: DNA versus RNA in sugar, bases and strandedness; the base-pairing rules.
- ✓Vitamins: fat-soluble A, D, E and K versus water-soluble B and C, and the deficiency disease for each.
- ✓Polymers: addition versus condensation; chain-growth versus step-growth; the monomers of nylon-6,6, terylene, bakelite, teflon and buna-S; biodegradable polymers PHBV and nylon-2-nylon-6.
- ✓Chemistry in everyday life: analgesics, antibiotics, antiseptics versus disinfectants, antacids, antihistamines, artificial sweeteners, soaps versus detergents and how each behaves in hard water.
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The mistakes that cost chemistry marks
- ✓Unit mismatches - using R = 0.0821 with pressure in pascals, or forgetting that molality uses kilograms of solvent while molarity uses litres of solution.
- ✓Ignoring the van't Hoff factor in colligative-property problems involving electrolytes.
- ✓Applying the first-order half-life formula to a zero-order reaction, or vice versa.
- ✓Learning periodic trends without their exceptions, which is precisely the half that gets tested.
- ✓Memorising organic reactions as input-output pairs, so an unfamiliar substrate becomes unanswerable. Learn the intermediate instead.
- ✓Skipping biomolecules, polymers and everyday chemistry because they feel trivial. They are the cheapest marks in the paper.
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How to use these notes
One-shot notes work as a testing instrument, not a reading one. Read a section, close it, and write out what you remember on a blank page - then reopen and mark only the gaps. The gaps are your actual revision list; everything else was already secure and did not need your time.
- ✓Pass 1 - read the whole page in one sitting to re-map the subject.
- ✓Pass 2 - next day, blank-page recall per section, marking hesitations.
- ✓Pass 3 - only the marked items, plus 20 MCQs on each of those topics.
- ✓Then repeat pass 3 weekly. The marked list shrinks, and that shrinking list is your final-week material.
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