Chemistry

Atomic Structure

• Subatomic particles — proton (positive, in nucleus); neutron (neutral, in nucleus); electron (negative, in orbitals). Protons determine the element; neutrons determine the isotope.
• Atomic number (Z) — number of protons; defines element identity. Mass number (A) — protons + neutrons.
• Isotopes — atoms of the same element with different neutron counts; same Z, different A. Example: carbon-12, carbon-13, and carbon-14 are all carbon.
• Atomic mass — weighted average of naturally occurring isotope masses; measured in atomic mass units (amu), where 1 amu = 1/12 the mass of carbon-12.
• Bohr model — electrons occupy discrete circular orbits (“shells”) at fixed energies; adequate for hydrogen but not multi-electron atoms.
• Quantum mechanical model — electrons described by wave functions; occupy orbitals (probability regions). Four quantum numbers: principal (n), azimuthal (l), magnetic (mₗ), spin (mₛ).
• Orbitals — shapes: s (spherical), p (dumbbell, 3 per sublevel), d (5 per sublevel), f (7 per sublevel). Each orbital holds max 2 electrons (opposite spins).
• Aufbau principle — electrons fill orbitals from lowest to highest energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, …
• Pauli exclusion principle — no two electrons in an atom can have the same set of all four quantum numbers; each orbital holds at most 2 electrons with opposite spins.
• Hund’s rule — within a sublevel, electrons occupy separate orbitals singly before pairing; all unpaired electrons have the same spin.
• Valence electrons — outermost-shell electrons; determine chemical reactivity and bonding behavior.
• Core electrons — inner electrons that shield valence electrons from the full nuclear charge.
• Effective nuclear charge (Zeff) — net nuclear charge experienced by an electron, accounting for shielding; increases across a period.

The Periodic Table

• Mendeleev (1869) — published the first widely recognized periodic table, organized by atomic mass with gaps for undiscovered elements. Predicted properties of gallium and germanium.
• Modern arrangement — organized by increasing atomic number (Z); reflects quantum shell structure.
• Periods (rows) — 7 periods; elements in the same period have the same number of electron shells.
• Groups (columns) — 18 groups; elements in the same group have the same valence electron configuration and similar chemical properties.

Key Groups

• Group 1 — Alkali metals — Li, Na, K, Rb, Cs, Fr; one valence electron; highly reactive; form +1 ions; react vigorously with water.
• Group 2 — Alkaline earth metals — Be, Mg, Ca, Sr, Ba, Ra; two valence electrons; form +2 ions; less reactive than Group 1.
• Groups 3–12 — Transition metals — d-block; variable oxidation states; form colored compounds; good conductors; include Fe, Cu, Au, Ag, Zn.
• Group 13 — Boron group — B, Al, Ga, In, Tl; three valence electrons; Al is most abundant metal in Earth’s crust.
• Group 17 — Halogens — F, Cl, Br, I, At; seven valence electrons; highly reactive; form −1 ions; exist as diatomic molecules (F₂, Cl₂, etc.).
• Bromine (Br) — halogen, atomic number 35; one of only two elements that is liquid at room temperature (the other being mercury); deep reddish-brown; toxic and corrosive; occurs naturally as bromide salts in seawater; used in flame retardants, water purification, and formerly as the antiknock compound ethylene dibromide; bromine vapor has a pungent, suffocating odor; its compounds include HBr (hydrobromic acid) and NaBr.
• Iodine (I) — halogen, atomic number 53; a shiny black-purple solid that sublimes to a violet vapor at room temperature; essential micronutrient (thyroid hormone synthesis, T3/T4); iodine deficiency causes goiter and cretinism; found in seawater and concentrated in seaweed; used as an antiseptic (povidone-iodine/Betadine); Lugol’s iodine (KI₃) stains starch dark blue-black; radioactive ¹³¹I is used in thyroid cancer treatment and diagnostic imaging.
• Manganese (Mn) — transition metal, atomic number 25, period 4, group 7; steel-gray, brittle; essential trace element (enzymes including MnSOD/superoxide dismutase); most common oxidation state in compounds is +2, +4 (MnO₂, pyrolusite ore), and +7 (KMnO₄, a strong oxidizing agent used in titrations and water treatment); used in steel production (as an alloy to improve hardness) and dry-cell batteries; MnO₂ is the cathode material in alkaline batteries.
• Group 18 — Noble gases — He, Ne, Ar, Kr, Xe, Rn; full valence shells; generally unreactive; He has 2 valence electrons, rest have 8.
• Lanthanides and actinides — f-block elements; placed below the main table. Actinides include uranium (Z=92) and plutonium (Z=94).

Periodic Trends

• Atomic radius — increases down a group (more shells); decreases across a period left-to-right (increasing Zeff pulls electrons closer).
• Ionic radius — cations are smaller than parent atoms; anions are larger. Isoelectronic series: radius decreases with increasing Z.
• Ionization energy (IE) — energy to remove an electron; increases across a period; decreases down a group. First IE generally lower than successive IEs.
• Electron affinity — energy change when an atom gains an electron; generally more negative (more favorable) across a period; halogens have high electron affinity.
• Electronegativity — tendency to attract bonding electrons; increases across a period and up a group. Highest: F (3.98 Pauling scale); lowest: Cs/Fr.
• Metallic character — increases down a group and left across a period; metals on the left and bottom, nonmetals on the upper right.

Chemical Bonding

• Ionic bond — electron transfer from metal to nonmetal; forms cations and anions held together by electrostatic attraction; example: NaCl.
• Covalent bond — electron sharing between nonmetals; can be single, double, or triple bonds. Polar covalent if electronegativity difference is moderate (~0.4–1.7).
• Metallic bond — “sea of electrons” delocalized over a lattice of metal cations; explains electrical conductivity, malleability, and luster.
• Lewis structures — dot notation showing valence electrons and bonding pairs; used to visualize molecular connectivity.
• Octet rule — atoms tend to bond to achieve 8 valence electrons (H and He: 2). Many exceptions: expanded octets (PCl₅, SF₆), electron-deficient (BF₃).
• Formal charge — charge an atom would have if bonding electrons were split equally; used to select best Lewis structure (minimize formal charges).
• VSEPR theory — Valence Shell Electron Pair Repulsion; electron pairs arrange to minimize repulsion; predicts molecular geometry.

Molecular Geometries (VSEPR)

Bonding pairs	Lone pairs	Geometry	Example
2	0	Linear	CO₂
3	0	Trigonal planar	BF₃
4	0	Tetrahedral	CH₄
3	1	Trigonal pyramidal	NH₃
2	2	Bent	H₂O
5	0	Trigonal bipyramidal	PCl₅
6	0	Octahedral	SF₆

• Hybridization — mixing of atomic orbitals to form new equivalent orbitals: sp (linear), sp² (trigonal planar), sp³ (tetrahedral), sp³d, sp³d².
• Sigma (σ) bond — head-on overlap; one per bond; can rotate freely.
• Pi (π) bond — side-to-side overlap; one in a double bond, two in a triple bond; prevents free rotation.
• Polarity — a molecule is polar if it has polar bonds AND an asymmetric geometry; dipole moment points toward more electronegative end.
• Hydronium ion (H₃O⁺) — the oxonium cation formed when a proton (H⁺) is accepted by a water molecule; the actual form of the proton in aqueous solution; responsible for acidic properties; concentration expressed as [H₃O⁺] = [H⁺]; pH = −log[H₃O⁺]; in the Brønsted-Lowry framework, water acts as the base accepting H⁺ from an acid.
• Amphoteric substance — a substance that can act as either an acid or a base depending on the reaction partner; classic examples: water (H₂O acts as base with HCl but as acid with NH₃); amino acids (zwitterionic, accepting or donating protons at different pH values); aluminum hydroxide (Al(OH)₃ dissolves in both acid and strong base); amphoteric oxides include Al₂O₃, ZnO, and PbO.
• Intermolecular forces — London dispersion (all molecules, increases with molar mass); dipole-dipole (polar molecules); hydrogen bonding (N–H, O–H, or F–H; strongest of these three).
• Resonance — when a single Lewis structure inadequately represents a molecule, two or more resonance structures are drawn; the real molecule is a hybrid (delocalization of electrons); stabilizes molecules (resonance energy); classic examples: benzene, carbonate ion (CO₃²⁻), ozone.
• Bronsted-Lowry acid-base theory — acid = proton (H⁺) donor; base = proton acceptor; every acid has a conjugate base (formed by losing H⁺) and every base has a conjugate acid; applies to non-aqueous solvents; broader than the Arrhenius definition.
• Lewis acid-base theory — Lewis acid = electron-pair acceptor; Lewis base = electron-pair donor; broadest definition; includes species like BF₃ (Lewis acid, accepts a pair) and all metal ions; subsumes Brønsted-Lowry; relevant to organometallic and coordination chemistry.

States of Matter and Gas Laws

• Kinetic molecular theory — gas particles in constant random motion; collisions elastic; volume of particles negligible; no intermolecular forces (ideal gas assumption).
• Boyle’s law — P₁V₁ = P₂V₂ at constant T and n; pressure inversely proportional to volume.
• Charles’s law — V₁/T₁ = V₂/T₂ at constant P and n; volume directly proportional to absolute temperature.
• Gay-Lussac’s law — P₁/T₁ = P₂/T₂ at constant V and n.
• Avogadro’s law — equal volumes of gas at same T and P contain equal moles of particles.
• Ideal gas law — PV = nRT; R = 8.314 J mol⁻¹ K⁻¹ (or 0.08206 L·atm mol⁻¹ K⁻¹). STP: 0°C, 1 atm; 1 mole occupies 22.4 L at STP (old definition).
• Dalton’s law of partial pressures — total pressure of a gas mixture equals the sum of partial pressures of individual components.
• Graham’s law of effusion — rate of effusion inversely proportional to the square root of molar mass.
• Real gases — deviate from ideal at high pressure and low temperature; described by the van der Waals equation, which corrects for particle volume (b) and intermolecular attraction (a).
• Phase transitions — melting, freezing, vaporization, condensation, sublimation, deposition. Enthalpy is absorbed in endothermic transitions (melting, vaporization) and released in exothermic transitions.
• Phase diagram — plot of P vs. T showing stable phases; the triple point is where all three phases coexist; above the critical point, distinct liquid and gas phases do not exist.

Stoichiometry and the Mole

• Mole — SI unit for amount of substance; 1 mol = 6.022 × 10²³ particles (Avogadro’s number).
• Molar mass — mass of one mole of a substance in g/mol; numerically equal to atomic/molecular weight in amu.
• Mole ratios — derived from balanced chemical equation coefficients; used to convert between moles of reactants and products.
• Limiting reagent — the reactant that is completely consumed first; determines the theoretical yield.
• Percent yield — (actual yield / theoretical yield) × 100%.
• Empirical vs. molecular formula — empirical is simplest whole-number ratio (CH₂O for glucose); molecular is actual number (C₆H₁₂O₆).
• Molarity (M) — moles of solute per liter of solution. Molality (m) — moles of solute per kilogram of solvent.

Acids and Bases

• Arrhenius definition — acid produces H⁺ in water; base produces OH⁻.
• Brønsted-Lowry definition — acid is a proton donor; base is a proton acceptor. Every acid-base reaction involves conjugate pairs.
• Lewis definition — acid is an electron-pair acceptor; base is an electron-pair donor. Broadest definition; includes reactions without proton transfer (e.g., BF₃ + NH₃).
• Strong acids — fully dissociate in water: HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄.
• Strong bases — fully dissociate: NaOH, KOH, Ca(OH)₂, Ba(OH)₂.
• Weak acids/bases — partially dissociate; characterized by Ka (acid dissociation constant) or Kb.
• pH — −log[H⁺]; scale 0–14 (at 25°C); pH < 7 acidic, pH = 7 neutral, pH > 7 basic. pH + pOH = 14 at 25°C.
• pKa — −log Ka; lower pKa = stronger acid.
• Autoionization of water — 2 H₂O ⇌ H₃O⁺ + OH⁻; Kw = 1.0 × 10⁻¹⁴ at 25°C.
• Buffer — solution resisting pH change; contains weak acid + conjugate base (or weak base + conjugate acid). Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]).

Thermochemistry

• System vs. surroundings — system is what is studied; surroundings is everything else.
• Enthalpy (H) — heat content at constant pressure. ΔH < 0 exothermic; ΔH > 0 endothermic.
• Hess’s law — enthalpy of a reaction is the sum of enthalpies of individual steps; path-independent; allows calculation of ΔH for reactions that cannot be measured directly.
• Standard enthalpy of formation (ΔHf°) — enthalpy change forming 1 mol of a compound from its elements in standard states. ΔHf° of any element in standard state = 0.
• Bond enthalpy — energy to break a bond in the gas phase; approximate calculation: ΔHrxn ≈ Σ(bonds broken) − Σ(bonds formed).
• Entropy (S) — measure of disorder/dispersal; increases with temperature, volume, number of moles of gas produced, and phase transitions from solid → liquid → gas.
• Gibbs free energy (G) — ΔG = ΔH − TΔS; reaction spontaneous if ΔG < 0. ΔG = 0 at equilibrium.
• Standard free energy — ΔG° = −RT ln K, where K is the equilibrium constant.
• First law of thermodynamics — energy is conserved: ΔU = q + w (heat absorbed plus work done on system).
• Second law — entropy of the universe increases for any spontaneous process.
• Third law — entropy of a perfect crystal at 0 K is exactly zero.

Reaction Types and Kinetics

• Synthesis — A + B → AB.
• Decomposition — AB → A + B.
• Single displacement — A + BC → AC + B; more reactive element displaces less reactive one.
• Double displacement (metathesis) — AB + CD → AD + CB; includes precipitation, neutralization, and gas-forming reactions.
• Combustion — hydrocarbon + O₂ → CO₂ + H₂O (complete combustion); exothermic.
• Reaction rate — change in concentration per unit time; increases with temperature, concentration, surface area, catalysts.
• Rate law — rate = k[A]^m[B]^n; orders m, n determined experimentally, not from stoichiometry.
• Rate constant (k) — depends on temperature; units vary with reaction order.
• Zero order — rate independent of concentration; rate = k.
• First order — rate = k[A]; half-life = ln 2 / k (constant, independent of concentration); used in radioactive decay.
• Second order — rate = k[A]²; half-life = 1/(k[A]₀), increases as reactant is consumed.
• Activation energy (Ea) — minimum energy for a reaction to occur; the energy barrier at the transition state.
• Arrhenius equation — k = Ae^(−Ea/RT); higher temperature → larger k → faster reaction.
• Catalyst — lowers Ea without being consumed; does not affect ΔH or equilibrium position; enzymes are biological catalysts.
• Reaction mechanism — step-by-step sequence; elementary steps sum to overall reaction; the slowest step is the rate-determining step.

Equilibrium

• Chemical equilibrium — forward and reverse reaction rates are equal; concentrations constant but not necessarily equal.
• Equilibrium constant (K) — for aA + bB ⇌ cC + dD: K = [C]^c[D]^d / [A]^a[B]^b; pure solids and liquids excluded.
• Kc vs Kp — Kc uses molar concentrations; Kp uses partial pressures; Kp = Kc(RT)^Δn where Δn = moles of gas products − moles of gas reactants.
• Le Chatelier’s principle — a system at equilibrium shifts to counteract a stress (concentration change, pressure change, temperature change).
• Temperature effect — increasing T shifts equilibrium toward endothermic direction (the one that absorbs heat). This is the only stress that changes K.
• Reaction quotient (Q) — same expression as K but using current concentrations; Q < K → reaction proceeds forward; Q > K → proceeds reverse.
• Solubility product (Ksp) — equilibrium constant for dissolution of a slightly soluble salt; used to predict precipitation.
• Common ion effect — presence of a common ion decreases solubility of a sparingly soluble salt; shifts equilibrium left.

Redox and Electrochemistry

• Oxidation — loss of electrons; mnemonic: OIL (Oxidation Is Loss). Oxidation state increases.
• Reduction — gain of electrons; mnemonic: RIG (Reduction Is Gain). Oxidation state decreases.
• Oxidizing agent — causes oxidation in another species; is itself reduced.
• Reducing agent — causes reduction in another species; is itself oxidized.
• Balancing redox reactions — half-reaction method: balance atoms, balance O with H₂O, balance H with H⁺, balance charge with electrons; then equalize electrons between half-reactions.
• Oxidation states — rules: elements = 0; monatomic ions = charge; O = −2 (−1 in peroxides); H = +1 (−1 in metal hydrides); sum equals overall charge.
• Galvanic (voltaic) cell — spontaneous redox reaction generates electrical current; anode (oxidation) and cathode (reduction) connected by salt bridge. ΔG < 0.
• Standard cell potential (E°cell) — E°cell = E°cathode − E°anode; positive E°cell indicates spontaneous reaction.
• Standard hydrogen electrode (SHE) — reference electrode with E° = 0.00 V by definition.
• Relationship to Gibbs energy — ΔG° = −nFE°; where n = moles of electrons transferred, F = Faraday constant (96,485 C/mol).
• Nernst equation — E = E° − (RT/nF) ln Q; at 25°C: E = E° − (0.0592/n) log Q; relates cell potential to nonstandard conditions.
• Electrolytic cell — uses external current to drive a nonspontaneous redox reaction; used in electroplating and electrolysis of water.
• Faraday’s laws of electrolysis — mass of substance deposited proportional to charge passed; proportional to molar mass divided by electrons transferred.

Organic Chemistry Basics

• Carbon’s versatility — forms 4 bonds; can chain, branch, and ring; basis of all organic chemistry.
• Hydrocarbons — compounds of C and H only. Alkanes (C–C single bonds, CₙH₂ₙ₊₂, saturated); alkenes (C=C double bond, CₙH₂ₙ, unsaturated); alkynes (C≡C triple bond, CₙH₂ₙ₋₂).
• Benzene — aromatic ring, C₆H₆; delocalized π electrons; unusually stable; electrophilic aromatic substitution.
• Isomers — same molecular formula, different structure. Constitutional (structural) isomers: different connectivity. Stereoisomers: same connectivity, different spatial arrangement.
• Chirality — a carbon bonded to four different groups is a chiral center (stereocenter); non-superimposable mirror images are enantiomers; opposite optical rotation (+/−).

Functional Groups

• Thiol — –SH functional group; the sulfur analog of an alcohol; also called mercaptans; the –SH group can form disulfide bonds (–S–S–) by oxidation, which are critical for protein structure (e.g., cysteine disulfide bridges in antibodies); thiols have a strong, unpleasant odor (methanethiol, ethanethiol used as odorants in natural gas); biologically, the thiol group of glutathione (GSH) is a key cellular antioxidant; characterized by the -thiol suffix (e.g., ethanethiol) or “mercapto-“ prefix.
• Alcohol — –OH; suffix -ol; hydrogen bonding raises boiling point.
• Aldehyde — –CHO (carbonyl at chain end); suffix -al; oxidized to carboxylic acid.
• Ketone — C=O within the carbon chain; suffix -one.
• Carboxylic acid — –COOH; suffix -oic acid; weak acids; form esters and amides.
• Ester — –COOR (from acid + alcohol + esterification); suffix -oate; found in fats and fragrances.
• Amine — –NH₂; Brønsted-Lowry bases; suffix -amine.
• Amide — –CONH₂; bond between carboxylic acid and amine; backbone of proteins (peptide bond).
• Ether — R–O–R; relatively inert; diethyl ether is a classic solvent/anesthetic.
• Halide (alkyl halide) — –X (F, Cl, Br, I attached to carbon); reactive in substitution and elimination reactions.

Key Reaction Types

• Substitution — one group replaces another; SN1 (two-step, carbocation intermediate, favored by tertiary carbon and polar protic solvents) vs SN2 (one-step, backside attack, favored by primary carbon and polar aprotic solvents).
• Elimination — removal of atoms to form double bond; E1 (two-step) and E2 (one-step, anti-periplanar).
• Addition — atoms add across a double or triple bond; Markovnikov’s rule: H adds to the less substituted carbon (more substituted carbon gets the other group).
• Condensation/dehydration — two molecules join with loss of a small molecule (usually water); ester formation, peptide bond formation.
• Polymerization — monomers link to form polymers; addition polymerization (alkenes) and condensation polymerization (nylons, polyesters).

Common Organic Compounds and Reagents

• Acetic acid (ethanoic acid) — CH₃COOH; the simplest carboxylic acid with biological and industrial importance; the active component of vinegar (~4–8% acetic acid in water); a weak acid (pKa ~4.76); produced industrially by the Monsanto/Cativa process (carbonylation of methanol); the acetyl group (CH₃CO–) is central to biochemistry (acetyl-CoA in the Krebs cycle; acetylation of histones; aspirin = acetylsalicylic acid); glacial acetic acid is the pure anhydrous form.
• Acetone (propanone) — (CH₃)₂C=O; the simplest ketone; a colorless, highly volatile liquid with a distinctive sweet odor; completely miscible with water; widely used as a solvent (nail polish remover, laboratory solvent); produced industrially by the cumene process; a metabolic product of fatty acid oxidation — acetone, acetoacetate, and β-hydroxybutyrate are the three ketone bodies elevated in diabetic ketoacidosis (DKA) and starvation; its smell on a patient’s breath is a clinical sign of DKA.
• Toluene (methylbenzene) — C₆H₅CH₃; a monosubstituted benzene (methyl group on the ring); colorless, insoluble liquid with a distinctive aromatic odor; less reactive than benzene in electrophilic aromatic substitution (the methyl group is electron-donating and ortho/para-directing); important industrial solvent and precursor to TNT (2,4,6-trinitrotoluene via nitration), benzene (by dealkylation), and polyurethanes (via TDI); neurotoxic at high exposure; named for the Tolu balsam from which it was first isolated.
• Diols (glycols) — organic compounds bearing two hydroxyl (–OH) groups; ethylene glycol (1,2-ethanediol; the most common diol) is the main component of automotive antifreeze/coolant and is metabolized to oxalic acid (toxic); propylene glycol is used in food, pharmaceuticals, and cosmetics; 1,3-diols are less strained; pinacol and 1,2-diols are produced by vicinal dihydroxylation of alkenes (OsO₄ or KMnO₄/cold); they can be cyclized to form epoxides or used in acetonide protection of adjacent diols.
• Carbene — a highly reactive neutral intermediate containing a divalent carbon with only six valence electrons (no charge, no radical); two classes: singlet carbene (both electrons in the same orbital, spin-paired; electrophilic; adds in a concerted, stereospecific manner) and triplet carbene (electrons in separate orbitals; diradical; adds in a stepwise manner, loses stereochemistry); the simplest carbene is :CH₂ (methylene); carbenes insert into C–H bonds, add to double bonds forming cyclopropanes, and can undergo Wolff rearrangement; generated from diazo compounds or via alpha-elimination; N-heterocyclic carbenes (NHCs) are stable carbenes used as ligands in organometallic catalysis.

Named Reactions

• Diels-Alder reaction — [4+2] cycloaddition between a conjugated diene and a dienophile; forms a six-membered ring; stereospecific (syn addition, endo rule for kinetic product); widely used in total synthesis.
• Grignard reaction — organomagnesium reagent (RMgX) acts as a carbanion nucleophile; adds to carbonyls (aldehydes, ketones, esters) to give alcohols after aqueous workup; sensitive to water and air.
• Friedel-Crafts reactions — electrophilic aromatic substitution using a Lewis acid catalyst (AlCl₃): alkylation adds an alkyl group (R–Cl + ArH → Ar–R); acylation adds an acyl group (RCOCl + ArH → Ar–COR); acylation preferred because product not hyperactivated.
• Aldol condensation — base or acid catalysis; enolate of a carbonyl attacks the carbonyl carbon of another to give a β-hydroxy carbonyl (aldol); heating eliminates water to give an α,β-unsaturated carbonyl (the condensation product).
• Esterification / saponification — Fischer esterification: carboxylic acid + alcohol ⇌ ester + H₂O, acid-catalyzed, reversible. Saponification: ester + NaOH → carboxylate salt + alcohol; irreversible; the basis of soap-making from triglycerides.
• Wittig reaction — phosphonium ylide (Ph₃P=CHR) reacts with an aldehyde or ketone to give an alkene with loss of triphenylphosphine oxide; provides precise control over double-bond position; Georg Wittig won the 1979 Nobel Prize in Chemistry.
• Claisen condensation — base-catalyzed condensation of two ester molecules (or an ester and a carbonyl compound) via enolate attack on a carbonyl; product is a β-ketoester; intramolecular version is the Dieckmann condensation.
• Michael addition — 1,4-conjugate addition of a nucleophile (Michael donor, typically an enolate) to an α,β-unsaturated carbonyl compound (Michael acceptor); combined with an aldol step it constitutes the Robinson annulation.
• Suzuki coupling — palladium-catalyzed cross-coupling of an aryl or vinyl boronic acid with an aryl or vinyl halide; forms C–C bonds with mild conditions and functional-group tolerance; Akira Suzuki, Ei-ichi Negishi, and Richard Heck shared the 2010 Nobel Prize.
• Heck reaction — palladium-catalyzed coupling of an aryl or vinyl halide with an alkene in the presence of a base; produces a substituted alkene; one of the original C–C cross-coupling reactions.
• Sonogashira coupling — palladium/copper-catalyzed coupling of a terminal alkyne with an aryl or vinyl halide; efficient route to conjugated enynes; copper co-catalyst distinguishes it from Suzuki and Heck.
• Birch reduction — aromatic rings reduced to 1,4-cyclohexadienes using alkali metal (Na or Li) dissolved in liquid ammonia with an alcohol proton source; electron-withdrawing substituents give unconjugated products, electron-donating substituents give conjugated products.
• Sandmeyer reaction — diazonium salts (ArN₂⁺) converted to aryl halides, nitriles, or other groups using cuprous salt catalysts (CuCl, CuBr, CuCN); useful for introducing substituents that cannot be placed directly by electrophilic aromatic substitution.
• Mannich reaction — three-component condensation of an aldehyde (often formaldehyde), a primary or secondary amine, and an enolizable carbonyl compound; product is a β-amino carbonyl (Mannich base); important in pharmaceutical synthesis.
• Cannizzaro reaction — disproportionation of an aldehyde lacking α-hydrogens in concentrated base; one molecule is oxidized to a carboxylate, another reduced to an alcohol; classic example: benzaldehyde → benzoate + benzyl alcohol.
• Hofmann elimination — exhaustive methylation of an amine followed by silver oxide treatment and heating; produces the less substituted alkene (anti-Markovnikov, Hofmann product) in contrast to Zaitsev elimination; used to degrade nitrogen-containing natural products.
• Williamson ether synthesis — S_N2 reaction of an alkoxide (RO⁻) with a primary alkyl halide to give an unsymmetrical ether; requires a primary halide to avoid elimination; classic method for mixed ethers.
• Markovnikov’s rule — in addition reactions to alkenes, the electrophile (H⁺) adds to the carbon with more hydrogen atoms, so the nucleophile ends up on the more substituted carbon; rationalized by preferential formation of the more stable (more substituted) carbocation; anti-Markovnikov products arise with radical initiation (HBr + peroxides) or hydroboration-oxidation.
• Ozonolysis — cleavage of an alkene (or alkyne) C=C double bond using ozone (O₃); proceeds via a molozonide intermediate that rearranges to an ozonide, then cleaved in a second step: reductive workup (e.g., Zn/AcOH or Me₂S) gives aldehydes (from CH=) and ketones (from CR₂=); oxidative workup (e.g., H₂O₂) converts aldehydes to carboxylic acids while ketones remain unchanged; used in synthesis to identify double-bond positions (by identifying the cleavage fragments) and to prepare carbonyl compounds; internal alkynes give carboxylic acids.
• Hückel’s rule — an aromatic compound must be planar, cyclic, fully conjugated, and contain 4n + 2 π electrons (n = 0, 1, 2, …); benzene (6 π e⁻, n=1), naphthalene (10, n=2), and pyridine are aromatic; cyclooctatetraene (8 π e⁻) is antiaromatic (4n rule, n=2) and adopts a tub shape to avoid it; heterocyclic aromatics include pyrrole (6 π e⁻, lone pair on N donated), furan, and thiophene; proposed by Erich Hückel in 1931 based on molecular orbital calculations; the rule also predicts antiaromaticity (4n π electrons in a planar cyclic conjugated system: destabilized).
• Zaitsev’s rule — in elimination reactions, the major product is the more substituted (thermodynamically more stable) alkene; applies when a small, unhindered base is used in E2; bulky bases (t-BuO⁻) favor the less substituted Hofmann product.
• Haber-Bosch process — industrial synthesis of ammonia: N₂ + 3H₂ ⇌ 2NH₃; iron catalyst promoted with K₂O and Al₂O₃, ~400–500°C, ~150–300 atm; Fritz Haber developed the chemistry, Carl Bosch engineered the industrial scale; estimated to feed roughly half the current human population through synthetic fertilizers.
• Ostwald process — industrial synthesis of nitric acid: ammonia catalytically oxidized over a platinum-rhodium gauze to NO (then oxidized to NO₂), absorbed in water to give HNO₃; integral to fertilizer and explosives production; complements Haber-Bosch.
• Solvay process — industrial production of sodium carbonate (soda ash): NaCl brine ammoniated, carbonated with CO₂ → NaHCO₃ precipitate, heated to give Na₂CO₃; ammonia is recycled via ammonia-soda cycle; replaced the more polluting Leblanc process in the late 19th century.
• Contact process — industrial production of sulfuric acid: SO₂ oxidized to SO₃ over vanadium(V) oxide catalyst at ~450°C, absorbed in oleum, diluted to H₂SO₄; the most-produced industrial chemical by mass worldwide.

Stereochemistry

• R/S nomenclature (Cahn-Ingold-Prelog) — assign priority 1–4 to substituents by atomic number; view with lowest-priority group pointing away; if 1→2→3 is clockwise, the center is R (rectus); counterclockwise is S (sinister).
• Fischer projection — 2D representation of a chiral molecule; horizontal bonds project toward the viewer, vertical bonds away; used to compare sugar stereoisomers systematically.
• Meso compound — molecule with chiral centers that is achiral overall because an internal plane of symmetry makes the two halves mirror images of each other; identical physical properties to neither enantiomer.

Biochemistry Molecules

Carbohydrates

• Monosaccharides — simplest sugars (e.g., glucose C₆H₁₂O₆, fructose, galactose); aldoses have an aldehyde group, ketoses have a ketone; in solution mostly exist as cyclic hemiacetals (pyranose or furanose rings).
• Disaccharides — two monosaccharides linked by a glycosidic bond with loss of water; examples: sucrose (glucose + fructose), lactose (glucose + galactose), maltose (glucose + glucose).
• Polysaccharides — long chains of monosaccharides; starch and glycogen (α-1,4 and α-1,6 glycosidic bonds, energy storage in plants and animals respectively); cellulose (β-1,4 bonds, structural in plants; not digestible by humans).

Lipids

• Triglycerides — glycerol backbone esterified to three fatty acids; primary form of energy storage; saturated fatty acids (no double bonds, solid at room temperature, e.g., lard); unsaturated (one or more double bonds, liquid at room temperature, e.g., olive oil).
• Phospholipids — glycerol + two fatty acids + phosphate head group; amphipathic; form lipid bilayers (cell membranes) with hydrophilic heads outward and hydrophobic tails inward.
• Micelle — a spherical aggregate of amphipathic molecules (such as soaps or detergents) in aqueous solution; hydrophobic tails face inward and hydrophilic heads face the water; form above the critical micelle concentration (CMC); the mechanism by which soaps solubilize grease (the fatty tail associates with the oil, the polar head faces water); bile salts form micelles to solubilize dietary fats in the intestine; distinct from a lipid bilayer in that micelles are spherical monolayers.
• Steroids — four fused carbon rings; cholesterol is the backbone; derivatives include cortisol, testosterone, estrogen, and bile acids.

Amino Acids and Proteins

• Amino acids — 20 standard; each has an amino group (–NH₂), carboxyl group (–COOH), and a unique side chain (R group) on the α-carbon; classified by side-chain polarity, charge, and aromaticity.
• Peptide bond — amide bond formed between the carboxyl of one amino acid and the amino of the next, with loss of water; the backbone is rigid and planar due to partial double-bond character.
• Four levels of protein structure — primary: sequence of amino acids; secondary: local regular structures (α-helix, β-sheet) stabilized by backbone hydrogen bonds; tertiary: overall 3D fold of the polypeptide, stabilized by side-chain interactions (hydrophobic core, disulfide bridges, salt bridges); quaternary: assembly of multiple polypeptide subunits (e.g., hemoglobin has four subunits).

Nucleic Acids

• Nucleotide structure — nucleobase + pentose sugar + one or more phosphate groups; DNA uses deoxyribose and bases A, T, G, C; RNA uses ribose and replaces T with U.
• Watson-Crick base pairing — A pairs with T (or U in RNA) via two hydrogen bonds; G pairs with C via three hydrogen bonds; complementarity underlies replication and transcription.
• DNA double helix — two antiparallel strands wound around each other; right-handed B-form helix is the predominant physiological form; backbone is sugar-phosphate; bases face inward.

Enzymes and Metabolism

• Enzymes — biological catalysts (mostly proteins); lower activation energy without being consumed; specificity determined by the active site; classified by reaction type: oxidoreductases, transferases, hydrolases, lyases, isomerases, ligases.
• Michaelis-Menten kinetics — model for enzyme kinetics: v = V_max[S] / (K_m + [S]); K_m (Michaelis constant) = substrate concentration at half-maximal velocity; V_max is the maximum rate at saturating substrate; Lineweaver-Burk double-reciprocal plot linearizes the data.
• Competitive inhibition — inhibitor resembles the substrate and competes for the active site; increases apparent K_m but leaves V_max unchanged; can be overcome with excess substrate.
• ATP (adenosine triphosphate) — the universal energy currency of cells; hydrolysis of each phosphoanhydride bond releases ~30.5 kJ/mol under standard conditions; synthesized by ATP synthase using a proton gradient (chemiosmosis); structure: adenine + ribose + three phosphate groups.
• Citric acid cycle (Krebs cycle / TCA cycle) — eight-step cyclic pathway in the mitochondrial matrix; acetyl-CoA (2C) condenses with oxaloacetate (4C) to form citrate (6C); each turn produces 3 NADH, 1 FADH₂, 1 GTP, and 2 CO₂; discovered by Hans Krebs (1937), for which he shared the 1953 Nobel Prize.
• Oxidative phosphorylation — electron transport chain (Complexes I–IV) passes electrons from NADH/FADH₂ to O₂, pumping protons across the inner mitochondrial membrane; the proton gradient drives ATP synthase (Complex V); yields ~32–34 ATP per glucose molecule.
• The 20 standard amino acids — grouped by side chain: nonpolar/aliphatic (Gly, Ala, Val, Leu, Ile, Pro, Met); aromatic (Phe, Trp, Tyr); polar uncharged (Ser, Thr, Cys, Asn, Gln); positively charged at pH 7 (Lys, Arg, His); negatively charged at pH 7 (Asp, Glu); only Gly lacks a chiral center; Pro is an imino acid that introduces kinks in polypeptide chains.
• Proline — a unique cyclic amino acid in which the side chain loops back to bond the alpha-nitrogen, forming a pyrrolidine ring; this makes proline an imino acid (secondary amine) rather than a primary amine; its ring structure restricts the phi dihedral angle and introduces a rigid kink in polypeptide chains, disrupting alpha-helices and beta-sheets; found at turns and loop regions; hydroxyproline (formed by post-translational hydroxylation of proline by vitamin C-dependent prolyl hydroxylase) is abundant in collagen triple helices; vitamin C deficiency (scurvy) impairs collagen synthesis because hydroxylation fails.
• Disulfide bonds — covalent –S–S– linkages formed by oxidation of two cysteine residues; stabilize tertiary/quaternary structure; important in extracellular proteins and antibodies; broken by reducing agents (β-mercaptoethanol, DTT).

Coordination Chemistry

• Coordination complex — central metal ion (usually a transition metal) surrounded by ligands that donate electron pairs to the metal; written as [metal(ligand)ₙ]^charge.
• Ligand — Lewis base that donates one or more electron pairs to the metal; monodentate (one donor atom, e.g., NH₃, Cl⁻) or polydentate (multiple donor atoms).
• Chelate — complex in which a polydentate ligand binds through two or more donor atoms simultaneously, forming a ring; chelates are thermodynamically more stable than analogous monodentate complexes (chelate effect); EDTA is a classic hexadentate chelating agent.
• Crystal field theory — the electrostatic effect of ligands splits d-orbital energies; the magnitude of splitting (Δ) determines whether a complex is high-spin (small Δ, weak-field ligands) or low-spin (large Δ, strong-field ligands); explains color and magnetic properties of complexes.
• Ligand field theory — a more quantum-mechanical extension of crystal field theory that incorporates covalent (orbital overlap) interactions between metal d-orbitals and ligand orbitals; better accounts for bond lengths, spectra, and electron delocalization.
• Spectrochemical series — ranks ligands by field strength (weak to strong): I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO; strong-field ligands cause large Δ, favor low-spin complexes, and generally shift absorption to shorter wavelengths (higher energy).
• 18-electron rule — transition metal complexes are most stable when the metal has 18 valence electrons (filling d, s, and p orbitals); analogous to the octet rule for main-group elements; widely obeyed by organometallic compounds such as Cr(CO)₆ and ferrocene; square-planar Pd/Pt(II) complexes are common 16-electron exceptions.
• HSAB theory (Hard-Soft Acid-Base) — Pearson’s principle: hard acids prefer hard bases, soft acids prefer soft bases; hard species are small, highly charged, not polarizable (e.g., Fe³⁺ is hard); soft species are large, low charge, polarizable (e.g., Hg²⁺ is soft); guides prediction of stability and reaction outcome in coordination and organic chemistry.
• Cyanide — the ion CN⁻ (cyanide ion) or the neutral HCN (hydrogen cyanide; a volatile liquid, bp 25.6°C, smells of bitter almonds); potent toxin that binds the ferric iron (Fe³⁺) in cytochrome c oxidase (Complex IV of the mitochondrial electron transport chain), blocking electron transfer to O₂ and halting aerobic respiration; antidotes include hydroxocobalamin (binds CN⁻ to form cyanocobalamin) and thiosulfate (converts CN⁻ to less toxic thiocyanate); CN⁻ is a strong-field ligand (end of the spectrochemical series), forming very stable complexes with transition metals (e.g., [Fe(CN)₆]³⁻ ferricyanide); used industrially in gold extraction (cyanide leaching) and electroplating.
• Molecular orbital (MO) theory — atomic orbitals on different atoms combine to form bonding (lower energy), antibonding (higher energy, starred, σ* or π*), and nonbonding MOs; electrons fill MOs by the Aufbau principle; explains O₂ paramagnetism, the stability of aromatic systems, and band theory in solids.
• Woodward-Hoffmann rules — orbital symmetry rules governing the stereochemistry of pericyclic reactions (electrocyclics, cycloadditions, sigmatropic); thermal and photochemical pathways proceed with opposite facial selectivity because the symmetry of the HOMO changes; Robert Woodward and Roald Hoffmann formulated them in 1965; Hoffmann shared the 1981 Nobel Prize in Chemistry.
• Raoult’s law — vapor pressure of a component in an ideal solution equals its mole fraction times its pure vapor pressure (P_A = x_A P°_A); applies to ideal mixtures; positive deviations indicate weaker solute-solvent interactions than in pure components.
• Henry’s law — at constant temperature, the amount of a gas dissolved in a liquid is proportional to the partial pressure of the gas above the liquid: C = k_H P; applies at low concentrations and for sparingly soluble gases; contrasts with Raoult’s law (which applies to the solvent).

Nuclear Chemistry

• Nuclear fission — heavy nucleus (e.g., ²³⁵U) absorbs a neutron and splits into smaller nuclei, releasing energy (~200 MeV per event) and 2–3 neutrons; basis of nuclear reactors and atomic bombs.
• Nuclear fusion — two light nuclei (e.g., deuterium + tritium) merge to form a heavier nucleus; releases more energy per unit mass than fission; powers the Sun; requires extreme temperature and pressure to overcome Coulomb repulsion.
• Chain reaction — neutrons released by fission trigger further fission events; self-sustaining if a critical mass is present; controlled in reactors (with moderators and control rods), uncontrolled in weapons.
• Radiometric dating — uses known half-lives to date materials; carbon-14 (t½ ≈ 5,730 yr) dates organic material up to ~50,000 yr; potassium-40/argon-40 (t½ ≈ 1.25 Gyr) and uranium-lead systems date rocks over millions to billions of years.
• Cyclotron — particle accelerator using alternating electric fields and a static magnetic field to accelerate charged particles in a spiral path; invented by Ernest O. Lawrence (~1930); used to produce radioactive isotopes for medical imaging (e.g., ¹⁸F for PET scans).

Metallurgy

• Blast furnace / steelmaking — iron ore (Fe₂O₃) reduced by coke (carbon) at ~1500°C: Fe₂O₃ + 3CO → 2Fe + 3CO₂; produces pig iron (~4% C); converted to steel by reducing carbon content (basic oxygen furnace) and adding alloying elements (Mn, Ni, Cr).
• Hall-Héroult process — industrial production of aluminum via electrolysis; alumina (Al₂O₃) dissolved in molten cryolite (Na₃AlF₆) at ~960°C; electricity reduces Al³⁺ to molten aluminum at the cathode; energy-intensive (~14 kWh/kg Al), which is why aluminum recycling saves ~95% of energy.

Carbon Allotropes and Nanomaterials

• Carbon nanotube (CNT) — cylindrical allotropes of carbon consisting of one or more rolled graphene sheets; single-walled (SWCNT) or multi-walled (MWCNT); discovered by Sumio Iijima (1991); can be metallic or semiconducting depending on the chiral angle (chirality) of rolling; extraordinarily high tensile strength (~100× stronger than steel at 1/6 the weight) and excellent electrical and thermal conductivity; synthesized by arc discharge, laser ablation, or chemical vapor deposition (CVD); potential applications in electronics, composites, and drug delivery; related allotropes: graphene (single-atom-thick hexagonal sheet; Geim and Novoselov, 2010 Nobel), buckminsterfullerene (C₆₀, “buckyball”; Kroto, Curl, Smalley, 1985 discovery; 1996 Nobel), and diamond (sp³-hybridized carbon, hardest natural substance).

Spectroscopy and Analysis

• IR spectroscopy — infrared radiation excites molecular bond vibrations (stretching, bending); each functional group absorbs at characteristic wavenumbers (cm⁻¹): O–H ~3200–3550, C=O (carbonyl) ~1700–1750, C–H ~2850–3000; used to identify functional groups.
• NMR spectroscopy — nuclear magnetic resonance; most commonly ¹H and ¹³C; nuclei in a magnetic field absorb radiofrequency energy at frequencies proportional to their chemical environment; chemical shift (δ, ppm) identifies chemical environment; coupling (J) reveals neighboring protons; the most powerful tool for determining organic structures.
• Mass spectrometry — molecules are ionized, fragmented, and separated by mass-to-charge ratio (m/z); the molecular ion peak gives molecular weight; fragmentation pattern reveals structure; high-resolution MS can determine molecular formula exactly.
• Beer-Lambert law — A = εlc; absorbance (A) is proportional to molar absorptivity (ε), path length (l), and concentration (c); basis of UV-Vis quantitation; linear only at low absorbance (~0.1–1.0 A units).
• UV-Vis spectroscopy — measures absorption of ultraviolet (200–400 nm) and visible (400–700 nm) light; electronic transitions in π systems, aromatic rings, and metal d-orbitals; λ_max shifts with conjugation length; used for protein quantitation (A₂₈₀), DNA (A₂₆₀), enzyme assays, and concentration measurements.
• Fluorescence (vs. phosphorescence) — both are forms of photoluminescence (re-emission of light after absorption); fluorescence: a molecule absorbs a photon, undergoes rapid internal conversion to the lowest excited singlet state (S₁), then emits a photon and returns to the ground state; emission is nearly instantaneous (~10⁻⁹–10⁻⁶ s); emitted light is always red-shifted relative to excitation (Stokes shift); phosphorescence: involves intersystem crossing from S₁ to a triplet excited state (T₁), which has a longer lifetime (ms to s) before emission; the delay distinguishes it from fluorescence; GFP (green fluorescent protein), fluorescein, and rhodamine are widely used fluorescent reporters in biology; fluorescence is exploited in FRET, flow cytometry, and confocal microscopy.
• X-ray crystallography — X-rays diffracted by electrons in a crystal lattice; the diffraction pattern (Bragg’s law: nλ = 2d sinθ) is Fourier-transformed to give electron density maps from which atomic positions are determined; used to solve protein and small-molecule structures; Dorothy Hodgkin determined structures of penicillin, vitamin B₁₂, and insulin.
• Chromatography — separation based on differential migration between a stationary phase and a mobile phase; HPLC (high-performance liquid chromatography) uses high-pressure liquid mobile phase for small molecules and biomolecules; GC (gas chromatography) uses a carrier gas and is limited to volatile compounds; TLC (thin-layer chromatography) uses silica plates, quick and qualitative; R_f = distance traveled by spot / distance traveled by solvent front.
• Titration — quantitative addition of a standardized titrant to an analyte solution; the equivalence point is where stoichiometric amounts have reacted; detected by indicators (phenolphthalein for strong base titrations) or by pH meter; back titration used when the endpoint is not sharp.
• Flame test — volatile metal salts introduced into a flame emit characteristic colors from excited electron transitions: lithium (crimson red), sodium (bright yellow), potassium (lilac/violet), calcium (brick red), strontium (scarlet), barium (green), copper (blue-green); non-quantitative but diagnostic for cation identity.
• Cryo-EM (cryo-electron microscopy) — a form of electron microscopy in which biological specimens are frozen in vitreous (non-crystalline) ice and imaged at cryogenic temperatures (near −180°C); avoids chemical fixation and staining artifacts; single-particle cryo-EM averages images of many identical particles to reconstruct 3D structures; resolution has improved dramatically since 2012 (“resolution revolution”) due to direct electron detectors and software advances; now routinely achieves near-atomic (<3 Å) resolution for large macromolecules without requiring crystals; Nobel Prize in Chemistry 2017 (Jacques Dubochet, Joachim Frank, and Richard Henderson); has revealed structures of membrane proteins, ribosomes, ion channels, and SARS-CoV-2 spike protein.
• Electrophoresis — separation of charged molecules (proteins, DNA, RNA) in a gel matrix (agarose for DNA; polyacrylamide/SDS-PAGE for proteins) under an electric field; smaller or more charged molecules migrate faster; SDS denatures proteins so migration reflects molecular weight; gel stained with ethidium bromide (DNA) or Coomassie/silver (proteins).

Physical Chemistry Concepts

• Clausius-Clapeyron equation — relates the rate of change of vapor pressure with temperature to the enthalpy of vaporization: d(ln P)/dT = ΔH_vap/(RT²); in its integrated form: ln(P₂/P₁) = −(ΔH_vap/R)(1/T₂ − 1/T₁); used to determine ΔH_vap from vapor pressure measurements at two temperatures; derived by Clausius and Clapeyron; the Clapeyron equation is the more general form for any phase transition: dP/dT = ΔS/ΔV = ΔH/(TΔV).

• Debye-Hückel theory — a limiting law (Peter Debye and Erich Hückel, 1923) that accounts for the non-ideal behavior of dilute electrolyte solutions by treating ions as point charges surrounded by an ionic atmosphere of opposite charge; predicts how the mean activity coefficient (γ±) decreases with increasing ionic strength (I): log γ± = −A

  z₊z₋

  √I; valid only at low ionic strength (<~0.01 M); the basis for understanding why real electrolyte solutions deviate from ideal behavior.

• Adsorption — the adhesion of atoms, ions, or molecules from a gas, liquid, or dissolved solid to a surface, forming a thin film; distinguished from absorption (in which the substance is taken into the bulk); physisorption involves weak van der Waals forces (reversible); chemisorption involves covalent or ionic bonding (stronger, often irreversible); the Langmuir adsorption isotherm describes monolayer coverage; the BET isotherm (Brunauer-Emmett-Teller) extends this to multilayer adsorption and is used to measure surface area of porous materials; catalysis, chromatography, and air purification (activated carbon) rely on adsorption.
• Colloid — a mixture in which one substance is dispersed in another at a particle size (~1–1,000 nm) intermediate between a solution (molecular, <1 nm) and a suspension (>1,000 nm, settles by gravity); colloidal particles are large enough to scatter light (Tyndall effect); types include sols (solid in liquid, e.g., paint), gels (liquid in solid, e.g., gelatin), emulsions (liquid in liquid, e.g., milk), aerosols (solid or liquid in gas, e.g., fog, smoke), and foams (gas in liquid); colloids are stabilized against aggregation by charge repulsion or adsorbed surfactants; coagulation can be induced by adding electrolytes (salting out).
• Maxwell-Boltzmann distribution — probability distribution of molecular speeds in an ideal gas at a given temperature; the most probable speed, mean speed, and root-mean-square speed are distinct; the distribution broadens and shifts to higher speeds with increasing temperature; underpins kinetic molecular theory and explains why only high-energy molecules react.
• Carnot cycle — idealized heat engine operating between two reservoirs (T_hot, T_cold); four reversible steps (isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression); maximum possible efficiency = 1 − T_cold/T_hot (Kelvin); establishes the upper bound for any real heat engine.
• Colligative properties — properties that depend on the number of solute particles, not their identity; include boiling-point elevation (ΔT_b = K_b·m), freezing-point depression (ΔT_f = K_f·m), osmotic pressure (π = MRT), and vapor-pressure lowering (Raoult’s law); used to determine molar mass of solutes.
• Chemical potential (μ) — partial molar Gibbs free energy; the tendency of a substance to leave a phase or react; at equilibrium, chemical potential of each component is equal in all phases; drives diffusion, phase transitions, and chemical reactions.

Notable Chemists and Discoveries

• Antoine Lavoisier — “father of modern chemistry”; established conservation of mass; named oxygen and hydrogen; debunked phlogiston theory; Traité Élémentaire de Chimie (1789).
• John Dalton — atomic theory (~1803): matter composed of atoms; atoms of an element are identical; compounds are fixed ratios of different atoms.
• Dmitri Mendeleev — published the periodic table in 1869, organized by atomic mass, leaving gaps for undiscovered elements; predicted properties of gallium, scandium, and germanium.
• Marie Curie — discovered polonium and radium; first woman to win a Nobel Prize; only person to win Nobel Prizes in two different sciences (Physics 1903, Chemistry 1911).
• Linus Pauling — developed the electronegativity scale; described the nature of the chemical bond; won Nobel Prize in Chemistry (1954) and Nobel Peace Prize (1962).
• Fritz Haber — developed the Haber-Bosch process for nitrogen fixation (N₂ + 3H₂ ⇌ 2NH₃); Nobel Prize in Chemistry 1918; enabled mass production of fertilizers.
• Gilbert Lewis — introduced the electron-pair theory of bonding; Lewis dot structures; Lewis acid-base concept.
• Svante Arrhenius — dissociation theory of electrolytes; Arrhenius definition of acids and bases; Nobel Prize in Chemistry 1903.
• August Kekulé — proposed the ring structure of benzene (1865).
• Ernest Rutherford — gold foil experiment revealed the nuclear model of the atom (1911); discovered alpha and beta radiation.
• Niels Bohr — proposed the quantum model with discrete electron energy levels for hydrogen (1913).
• Henry Moseley — showed atomic number (not mass) is the fundamental ordering principle of the periodic table (1913).
• Glenn Seaborg — synthesized and discovered 10 transuranic elements; proposed the actinide concept; element 106 (seaborgium) named in his honor.
• Jöns Jacob Berzelius — determined the atomic masses of nearly 40 elements; introduced the modern chemical symbols (letters) for elements; discovered cerium, selenium, and thorium; coined the terms “protein,” “isomer,” and “catalyst.”
• Amedeo Avogadro — proposed in 1811 that equal volumes of gases at the same T and P contain equal numbers of molecules (Avogadro’s hypothesis); his name attached to Avogadro’s number (6.022 × 10²³); concept was not widely accepted until after his death.
• Pierre and Marie Curie — isolated polonium (named after Marie’s homeland Poland) and radium; showed that radioactivity was an atomic property, not a molecular one; Marie Curie remains the only person to win Nobel Prizes in two different sciences.
• Dorothy Hodgkin — pioneered X-ray crystallography of biological molecules; determined structures of penicillin (1945), vitamin B₁₂ (1956), and insulin (1969); Nobel Prize in Chemistry 1964; only British woman to win a science Nobel.
• Robert Burns Woodward — preeminent 20th-century synthetic chemist; total syntheses of cholesterol, cortisone, strychnine, reserpine, chlorophyll, cephalosporin C, and vitamin B₁₂; Nobel Prize in Chemistry 1965; co-formulated the Woodward-Hoffmann rules.
• Frederick Sanger — developed methods for sequencing biological polymers; determined the amino acid sequence of insulin (first protein sequenced, 1955, Nobel 1958); developed the dideoxy chain-termination method for DNA sequencing (Sanger sequencing, Nobel 1980); one of four people to win two Nobel Prizes.
• Roald Hoffmann — theoretical chemist who co-developed the Woodward-Hoffmann rules for pericyclic reactions; Nobel Prize in Chemistry 1981 (shared with Kenichi Fukui); also a published poet and playwright.
• Jacobus van’t Hoff — first Nobel Prize in Chemistry (1901); developed the laws of osmotic pressure and thermodynamic treatment of chemical equilibria; stereochemistry of carbon (tetrahedral model independent of Le Bel).
• August von Hofmann — organic chemist who trained many notable chemists at the Royal College of Chemistry, London; described the Hofmann elimination and Hofmann rearrangement (conversion of amide to amine, one carbon shorter, using halogen and base).