MDCAT Chemistry equations and key facts

Every chapter of MDCAT Chemistry on one page: the 244 equations, definitions and facts to remember, in syllabus order. Use it for a last look before a test, then check yourself.

Test yourself free About this test

Chemistry · Fundamental concepts of chemistry

The mole

moles = mass ÷ molar mass (n = m/M)
number of particles = moles × 6.02 × 10²³
volume of a gas at STP = moles × 22.4 dm³
1 amu = one-twelfth of the mass of one carbon-12 atom
% of an element = (mass of that element in 1 mol ÷ molar mass) × 100
Empirical formula: divide each % by the atomic mass, then divide every answer by the smallest one
molecular formula = (empirical formula)_n, where n = molar mass ÷ empirical formula mass

Stoichiometry

Coefficients in a balanced equation = ratio of moles
Route: mass → moles → mole ratio → moles → mass or gas volume
For gases at the same temperature and pressure, the volume ratio = the mole ratio
Limiting reagent: divide the moles of each reactant by its coefficient; the smallest answer shows the limiting reagent
Theoretical yield is calculated from the limiting reagent only
percentage yield = (actual yield ÷ theoretical yield) × 100
Mass is conserved: total mass of reactants used = total mass of products formed

Chemistry · Atomic structure

Particles, photons and the Bohr model

neutrons = A − Z; electrons = Z − charge on the ion (so a negative ion has extra electrons)
relative atomic mass = sum of (isotope mass × % abundance) ÷ 100
Charge-to-mass ratio (e/m): electron > proton > alpha particle; a neutron has no charge and is not deflected
energy of a photon = Planck's constant × frequency (E = hf = hc/λ); wave number = 1/λ
Electron jump: ΔE = E₂ − E₁ = hf
Hydrogen series: Lyman (to n = 1) ultraviolet; Balmer (to n = 2) visible; Paschen, Brackett and Pfund infrared
Bohr radius of orbit n = 0.529 Å × n²; 1 Å = 10⁻¹⁰ m = 100 pm; 1 nm = 10 Å

Orbitals and electronic configuration

n (principal) = 1, 2, 3 … gives the shell, its size and energy; l (azimuthal) = 0 to n − 1 gives the shape: s = 0, p = 1, d = 2, f = 3
m (magnetic) = −l to +l gives the orientation; s (spin) = +½ or −½
A shell has n² orbitals and holds up to 2n² electrons
Aufbau: fill the subshell with the lower (n + l) first; if equal, the lower n first. Order: 1s 2s 2p 3s 3p 4s 3d 4p 5s
Pauli: no two electrons in an atom have all four quantum numbers the same, so two electrons in one orbital have opposite spins
Hund: orbitals of equal energy are each filled singly, with parallel spins, before any pairing
Exceptions: Cr is [Ar] 3d⁵ 4s¹ and Cu is [Ar] 3d¹⁰ 4s¹

Chemistry · Gases

Gas laws

Boyle's law: at constant T, P₁V₁ = P₂V₂
Charles's law: at constant P, V₁/T₁ = V₂/T₂ (T in K); the V against T line reaches zero volume at −273 °C
Avogadro's law: at the same T and P, equal volumes of gases contain equal numbers of molecules (V ∝ n)
PV = nRT; R = 0.0821 dm³ atm K⁻¹ mol⁻¹ = 8.314 J K⁻¹ mol⁻¹; density d = PM/RT
Dalton's law: total pressure = sum of the partial pressures; partial pressure = mole fraction × total pressure
Graham's law: rate₁/rate₂ = √(M₂/M₁)
K = °C + 273; °F = (9/5 × °C) + 32; 1 atm = 760 torr = 101 325 Pa; 1 cal = 4.18 J

Kinetic theory and real gases

Postulates: the volume of the molecules is negligible; there are no forces between them; collisions are perfectly elastic; motion is random
average kinetic energy ∝ absolute temperature (in K), and it is the same for all gases at the same temperature
root mean square speed = √(3RT/M), so lighter molecules move faster at the same temperature
Real gases are most ideal at low pressure and high temperature; they deviate most at high pressure and low temperature
van der Waals equation: (P + n²a/V²)(V − nb) = nRT; a corrects for attractions, b for the volume of the molecules
PV/nRT < 1: attractions dominate; PV/nRT > 1: the volume of the molecules dominates (very high pressure)
Plasma examples: the Sun and stars, lightning, neon signs, fluorescent tubes

Chemistry · Liquids

Intermolecular forces

London forces: the only force between non-polar molecules (Br₂, CH₄, noble gases); stronger with more electrons and a longer, less branched shape
Dipole–dipole forces: between polar molecules such as HCl, propanone and ethanal
Hydrogen bond: H joined to N, O or F is attracted to a lone pair on N, O or F of another molecule
For molecules of similar size: hydrogen bond > dipole–dipole > London; all are far weaker than a covalent bond
Hydrogen-bond strength: F–H···F > O–H···O > N–H···N; water still boils higher than HF because each molecule can form more hydrogen bonds
Ice: each H₂O is hydrogen bonded to 4 others in an open tetrahedral structure, so ice is less dense than water; water is densest at 4 °C
Carboxylic acids form hydrogen-bonded dimers; hydrogen bonds hold the two strands of DNA together

Properties of liquids

Vapour pressure rises with temperature along a curve; it does not depend on the amount of liquid, the surface area or the size of the container
Boiling point: the temperature at which vapour pressure = external pressure (100 °C for water at 760 torr); lower pressure gives a lower boiling point
Stronger intermolecular forces: lower vapour pressure, higher boiling point, larger heat of vaporisation
Evaporation is faster at a higher temperature, with a larger surface area and with weaker intermolecular forces
heat for a change of state = moles × molar heat of fusion (or of vaporisation); melting, boiling and sublimation absorb heat; freezing and condensation release it
Molar heat of vaporisation is larger than molar heat of fusion for the same substance
Surface tension pulls a drop into a sphere; water rises in a glass capillary (adhesion > cohesion), mercury is pushed down (cohesion > adhesion)

Chemistry · Solids

Crystalline solids

Unit cell: 6 parameters (edges a, b, c and angles α, β, γ); 7 crystal systems, e.g. cubic a = b = c, α = β = γ = 90°
Ionic (NaCl): hard, brittle, high melting point, conducts only when molten or dissolved; in NaCl each ion has 6 nearest neighbours of the other kind
Covalent network (diamond, SiO₂): very hard, very high melting point. Molecular (ice, I₂, dry ice): soft, low melting point, non-conductor
Metallic: positive ions in a sea of free electrons; conducts as a solid, malleable and ductile
Lattice energy is larger for smaller ions and for ions of higher charge
Isomorphism: different substances, same crystal form (NaF and MgO, both cubic). Polymorphism: one compound, more than one crystal form. Allotropy: the same for an element (diamond and graphite)
Radius ratio r⁺/r⁻: 0.225 to 0.414 gives coordination number 4; 0.414 to 0.732 gives 6; 0.732 to 1.0 gives 8

Chemistry · Chemical equilibrium

Equilibrium and Le Chatelier's principle

For aA + bB ⇌ cC + dD: K_c = [C]^c[D]^d ÷ [A]^a[B]^b; K_p uses partial pressures in the same way; pure solids and liquids are left out
K_p = K_c(RT)^Δn, where Δn = moles of gaseous products − moles of gaseous reactants; K_p = K_c when Δn = 0
Reaction quotient Q: if Q < K the reaction moves forward; if Q > K it moves backward
Adding a reactant or removing a product shifts the equilibrium forward; K does not change
Higher pressure shifts towards the side with fewer moles of gas; higher temperature shifts in the endothermic direction
A catalyst speeds up both directions equally: equilibrium is reached sooner, with no change in position or in K
Haber process: N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹; high pressure (about 200 atm), about 400 to 450 °C as a compromise, iron catalyst

Ionic equilibria

Arrhenius: an acid gives H⁺ in water, a base gives OH⁻. Brønsted–Lowry: an acid donates a proton, a base accepts one. Lewis: an acid accepts an electron pair, a base donates one
pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = pK_w = 14 at 25 °C (K_w = 1.0 × 10⁻¹⁴ mol² dm⁻⁶)
K_a = [H⁺][A⁻] ÷ [HA]; pK_a = −log K_a; a larger K_a (smaller pK_a) means a stronger acid
Weak acid of concentration c: [H⁺] = √(K_a × c)
K_sp for A_xB_y = [A]^x[B]^y; with solubility s: AB gives s², AB₂ or A₂B gives 4s³
A precipitate forms only when the ionic product is greater than K_sp
Buffer: pH = pK_a + log([salt] ÷ [acid]); blood is kept at pH 7.35 to 7.45, mainly by H₂CO₃ / HCO₃⁻

Chemistry · Reaction kinetics

Rate and rate law

rate = change in concentration ÷ time taken; unit mol dm⁻³ s⁻¹
For aA → bB: rate = −(1/a) × Δ[A]/Δt = (1/b) × Δ[B]/Δt
Rate law: rate = k[A]^x[B]^y; overall order = x + y; k is the rate when every concentration is 1 mol dm⁻³ and changes only with temperature
Units of k: zero order mol dm⁻³ s⁻¹; first order s⁻¹; second order dm³ mol⁻¹ s⁻¹
Half-life: first order t_½ = 0.693 ÷ k, constant; zero order t_½ ∝ starting concentration; second order t_½ ∝ 1 ÷ starting concentration
After n half-lives of a first-order reaction, the fraction left = (½)ⁿ
Methods: colour (spectrometry), electrical conductivity, optical rotation, volume change (dilatometry), or titration of samples; a reactant in large excess gives a pseudo-first-order reaction

Activation energy and catalysis

ΔH = E_a(forward) − E_a(reverse). Exothermic: the forward barrier is the smaller one. Endothermic: the forward barrier is the larger one.
Higher concentration (or gas pressure) and larger surface area: more collisions per second, so a faster rate.
Higher temperature: a much larger fraction of molecules have energy of at least E_a. The rate roughly doubles for each 10 °C rise.
Lower E_a means a faster reaction at the same temperature. ΔH does not decide the rate.
Arrhenius equation: k = Ae^−E_a/RT. A graph of ln k against 1/T is a straight line of slope −E_a/R.
Homogeneous catalyst: same phase as the reactants. Heterogeneous catalyst: different phase. Autocatalysis: a product catalyses the reaction (Mn²⁺ in the KMnO₄ and oxalic acid reaction).
An inhibitor (negative catalyst) slows a reaction. A catalyst never changes ΔH or the position of equilibrium.

Chemistry · Thermochemistry and energetics

Enthalpy changes

Formation, ΔH°_f: one mole of a compound is formed from its elements in their standard states. For an element in its standard state ΔH°_f = 0.
Combustion, ΔH°_c: one mole of a substance burns completely in excess oxygen. It is always negative.
Atomisation: one mole of gaseous atoms is formed from the element. It is always positive.
Neutralisation: one mole of water is formed from an acid and a base; about −57 kJ mol⁻¹ for any strong acid with a strong base.
ΔH = (sum of bond energies of bonds broken) − (sum of bond energies of bonds formed).
Heat = mass × specific heat capacity × temperature change (q = mcΔT); for a whole calorimeter q = CΔT with C in J K⁻¹. Then ΔH = −q ÷ moles, in kJ mol⁻¹.
Food energy: fat gives about 38 kJ g⁻¹, carbohydrate and protein about 17 kJ g⁻¹ each.

First law and Hess's law

ΔE = q + w. q is positive when the system absorbs heat; w is positive when work is done on the system.
Work of a gas at constant pressure: w = −PΔV. Expansion gives a negative w. 1 kPa × 1 dm³ = 1 J.
At constant volume no work is done, so q_v = ΔE. At constant pressure q_p = ΔH, where H = E + PV and ΔH = ΔE + PΔV.
Hess's law: if an equation is reversed, change the sign of ΔH; if it is multiplied, multiply ΔH by the same number; then add.
ΔH° = ΣΔH°_f(products) − ΣΔH°_f(reactants), each multiplied by its coefficient in the equation.
Born–Haber cycle: ΔH°_f = atomisation of the metal + ionisation energy + atomisation of the non-metal + electron affinity + lattice energy.
Lattice energy is the energy released when one mole of an ionic solid forms from its gaseous ions, so it is negative. Atomisation and ionisation are endothermic.

Chemistry · Electrochemistry

Oxidation numbers and redox

A free element is 0. A simple ion equals its charge. The numbers add up to 0 in a compound and to the charge in a polyatomic ion.
Group 1 metals are +1, group 2 metals +2, fluorine always −1. Hydrogen is +1, but −1 in metal hydrides such as NaH.
Oxygen is −2, except −1 in peroxides (H₂O₂), −½ in superoxides (KO₂) and +2 in OF₂.
Balancing in acid: balance the main atoms, add H₂O for oxygen, H⁺ for hydrogen and electrons for charge; then multiply the half-equations so the electrons cancel.
An element in its highest state can only be an oxidising agent (Mn in MnO₄⁻); in its lowest state only a reducing agent (I⁻); in between it can be both (H₂O₂, SO₂).
Disproportionation: the same element is oxidised and reduced in one reaction.

Electrode potentials and cells

SHE: hydrogen gas at 1 atm bubbles over platinum coated with platinum black, in 1 M H⁺ at 298 K. Its E° is 0.00 V by convention.
Standard conditions: ion concentration 1 M, temperature 298 K, gases at 1 atm.
E°_cell = E°(cathode) − E°(anode), using reduction potentials. A positive value means the reaction is feasible.
In both kinds of cell, oxidation is at the anode and reduction is at the cathode. Galvanic: anode is negative. Electrolytic: anode is positive.
A metal with a negative E° displaces hydrogen from dilute acid, and a metal displaces from solution the ions of any metal with a more positive E°.
The salt bridge (|| in cell notation) lets ions move between the half-cells, keeping the solutions neutral and completing the circuit.
Lead accumulator: anode Pb, cathode PbO₂, electrolyte dilute H₂SO₄. Electrolysis is used to refine copper, extract aluminium and electroplate.

Chemistry · Chemical bonding

Ionic and covalent bonding

An ionic bond forms most easily between a metal of low ionisation energy and a non-metal that releases much energy on gaining an electron.
Coordinate bond: the donor needs a lone pair and the acceptor an empty orbital, as in NH₄⁺, H₃O⁺ and Al₂Cl₆.
Electronegativity difference: 0 is non-polar covalent; up to about 1.7 is polar covalent; above 1.7 is mainly ionic.
Dipole moment = charge × distance between the charges (μ = q × r), unit debye (D). In symmetrical molecules (CO₂, BF₃, CH₄, CCl₄) the bond dipoles cancel, so μ = 0.
Bond energy: the energy needed to break one mole of a bond in gaseous molecules, in kJ mol⁻¹.
More shared pairs give a shorter, stronger bond: C–C is longer and weaker than C=C, which is longer and weaker than C≡C. Bond length ≈ sum of the two covalent radii.
Fajans' rules: a small, highly charged cation with a large anion gives more covalent character (AlCl₃ > MgCl₂ > NaCl).

Shapes of molecules

Repulsion: lone pair–lone pair > lone pair–bond pair > bond pair–bond pair.
2 regions: linear, 180°, sp (BeCl₂, CO₂). 3 regions: trigonal planar, 120°, sp² (BF₃). 4 regions: tetrahedral, 109.5°, sp³ (CH₄).
5 bond pairs: trigonal bipyramidal, 90° and 120° (PCl₅). 6 bond pairs: octahedral, 90° (SF₆).
Four pairs with lone pairs: NH₃ (one lone pair) is trigonal pyramidal, 107.5°; H₂O (two lone pairs) is bent, 104.5°.
s-character: sp 50%, sp² 33%, sp³ 25%.
Single bond = 1σ; double bond = 1σ + 1π; triple bond = 1σ + 2π. A σ bond is stronger because head-on overlap is greater; π electron density lies above and below the line joining the nuclei.
Molecular orbital theory: O₂ has two unpaired electrons in antibonding π orbitals, so it is paramagnetic, with bond order 2.

Chemistry · s and p block elements

Periodic trends and the s block

Across a period: atomic radius decreases; ionisation energy, electronegativity and the energy released on gaining an electron generally increase. Down a group: the opposite.
Exceptions: first ionisation energy Al < Mg (3p electron, shielded by 3s) and S < P (paired 3p electron is repelled). Cl releases more energy than F on gaining an electron. Adding a second electron (O⁻ → O²⁻) absorbs energy.
Period 3 melting points: rise Na < Mg < Al (more delocalised electrons), highest at Si (giant covalent), then low for the small molecules: S₈ > P₄ > Cl₂ > Ar.
A positive ion is smaller than its atom and a negative ion is larger. For ions with the same number of electrons, more protons means a smaller ion.
Burning in excess oxygen: Li gives Li₂O, Na gives Na₂O₂ (peroxide), K gives KO₂ (superoxide). Only Li in group 1 forms a nitride, Li₃N.
Down group 2: hydroxides become more soluble and more basic; sulphates become less soluble (BaSO₄ least); carbonates, nitrates and hydroxides need stronger heating to decompose. BeO is amphoteric.
Flame colours: Li crimson, Na golden yellow, K lilac, Ca brick red, Sr crimson, Ba apple green. Be and Mg give no colour.

The p block

F₂ pale yellow gas, Cl₂ greenish-yellow gas, Br₂ red-brown liquid, I₂ grey-black solid. Oxidising power: F₂ > Cl₂ > Br₂ > I₂.
A halogen displaces a less reactive halogen from its halide: Cl₂ + 2KBr → 2KCl + Br₂.
Acid strength: HF < HCl < HBr < HI (the H–X bond gets weaker), and HOCl < HClO₂ < HClO₃ < HClO₄ (more oxygen atoms).
Cold dilute alkali: Cl₂ + 2NaOH → NaCl + NaOCl + H₂O. Hot concentrated alkali: 3Cl₂ + 6NaOH → 5NaCl + NaClO₃ + 3H₂O.
Period 3 oxides: Na₂O and MgO basic; Al₂O₃ amphoteric; SiO₂, P₄O₁₀, SO₃ and Cl₂O₇ acidic. Chlorides: NaCl neutral; AlCl₃, SiCl₄ and PCl₅ are hydrolysed, giving acidic solutions with HCl.
Concentrated HNO₃ turns yellow in light: 4HNO₃ → 4NO₂ + 2H₂O + O₂. Concentrated H₂SO₄ (oil of vitriol) is a dehydrating and oxidising agent. Blue vitriol is CuSO₄·5H₂O.
Aluminium: bauxite (Al₂O₃·2H₂O) is purified to alumina, dissolved in molten cryolite (Na₃AlF₆) to lower the working temperature, and electrolysed.

Chemistry · Transition elements

Properties of transition elements

General configuration: (n−1)d^1–10 ns^1–2. Exceptions: Cr is [Ar] 3d⁵ 4s¹ and Cu is [Ar] 3d¹⁰ 4s¹, because half-filled and full d subshells are extra stable.
Zn and Zn²⁺ both have a full 3d¹⁰ subshell, so zinc is not a typical transition element: its ion is colourless and diamagnetic.
Highest oxidation state from Sc to Mn = number of 4s + 3d electrons: Cr +6, Mn +7.
More unpaired electrons means stronger paramagnetism: Mn²⁺ and Fe³⁺ (3d⁵) have five. Ions with no unpaired electron (Sc³⁺, Cu⁺, Zn²⁺) are diamagnetic and colourless.
Catalysts: Fe in the Haber process, V₂O₅ in the Contact process, Ni for hydrogenation of oils.
Brass = Cu + Zn; bronze = Cu + Sn. Interstitial compounds (C in Fe) are harder and stronger than the pure metal. Binding energy rises to the middle of the 3d series, then falls to its lowest at Zn.
2CrO₄²⁻ (yellow) + 2H⁺ ⇌ Cr₂O₇²⁻ (orange) + H₂O. Acid gives orange, alkali gives yellow. Cr is +6 in both, so it is not redox.

Complexes

Monodentate ligands (one donor atom): H₂O, NH₃, Cl⁻, CN⁻, OH⁻. Bidentate (two): ethylenediamine (en), oxalate C₂O₄²⁻.
Coordination number = number of donor atoms bonded to the metal, not the number of ligands: [Co(en)₃]³⁺ has 6.
Oxidation number of the metal = charge on the complex ion − total charge of the ligands.
Naming: cation before anion; ligands in alphabetical order with di, tri, tetra, hexa (aqua, ammine, chloro, cyano, hydroxo); then the metal with its oxidation state in Roman numerals. In a complex anion the metal ends in -ate (ferrate, cuprate).
Shapes: coordination number 2 linear; 4 tetrahedral (sp³) or square planar (dsp²); 6 octahedral (d²sp³ or sp³d²).
In an octahedral complex the five d orbitals split into three of lower energy and two of higher energy. Ions with d⁰ or d¹⁰ are colourless.
Stability is greater for a smaller, more highly charged metal ion (Co³⁺ > Co²⁺) and for chelating ligands; for 3d ions Mn²⁺ < Fe²⁺ < Co²⁺ < Ni²⁺ < Cu²⁺.

Chemistry · Fundamental principles of organic chemistry

Classification and isomerism

Skeleton: open chain (aliphatic) or cyclic. Cyclic compounds are alicyclic (cyclohexane), aromatic (benzene, naphthalene) or heterocyclic, with N, O or S in the ring (pyridine, furan, thiophene).
Functional groups: alcohol –OH, aldehyde –CHO, ketone >C=O, carboxylic acid –COOH, ester –COOR, ether R–O–R, amine –NH₂, thiol –SH.
Members of a homologous series differ by CH₂. A carbon atom is primary, secondary, tertiary or quaternary when it is bonded to 1, 2, 3 or 4 other carbon atoms.
Structural isomerism: chain, position, functional group (ethanol and dimethyl ether), metamerism (different alkyl groups on each side of the same group) and tautomerism (shift of an H atom, keto and enol forms).
Cis-trans isomerism needs a C=C bond (no free rotation) with two different groups on each of its carbon atoms.
Optical isomerism needs a chiral carbon: one bonded to four different groups. The two mirror-image forms rotate plane-polarised light in opposite directions.
Fullerene C₆₀: a hollow cage of 20 hexagons and 12 pentagons; each carbon is bonded to three others. It is a molecular form (allotrope) of carbon.

Bonding and reactivity in carbon compounds

sp³ carbon: 4 σ bonds, tetrahedral, 109.5° (methane, ethane)
sp² carbon: 3 σ bonds + 1 π bond, trigonal planar, 120° (ethene, benzene, C=O)
sp carbon: 2 σ bonds + 2 π bonds, linear, 180° (ethyne, the carbon of C≡N)
Homolytic fission: A–B → A• + B•. It is favoured by non-polar bonds, ultraviolet light or heat
Heterolytic fission: A–B → A⁺ + B⁻. It is favoured by polar bonds and polar solvents; the more electronegative atom takes both electrons
Electrophiles are positive or electron-deficient: H⁺, NO₂⁺, Br⁺, AlCl₃, BF₃, SO₃
Nucleophiles have a lone pair to give: OH⁻, CN⁻, Cl⁻, NH₃, H₂O

Chemistry · Hydrocarbons

Alkanes and alkenes

Initiation: Cl₂ → 2Cl• (light). Propagation: Cl• + CH₄ → •CH₃ + HCl, then •CH₃ + Cl₂ → CH₃Cl + Cl•. Termination: two radicals join
Reactivity of halogens with alkanes: F₂ > Cl₂ > Br₂ > I₂
Markovnikov's rule: when HX adds to an unsymmetrical alkene, H goes to the carbon that already has more H atoms, because the more stable carbocation forms
Reactivity of HX with alkenes: HI > HBr > HCl (the weakest H–X bond breaks most easily)
Tests for C=C: bromine turns from red-brown to colourless; cold, dilute, alkaline KMnO₄ (Baeyer's reagent) loses its purple colour and a diol forms
Alkenes are made by dehydrating alcohols (concentrated H₂SO₄ at about 170 °C, or hot Al₂O₃), by heating alkyl halides with alcoholic KOH, or from vicinal dihalides with zinc dust
More branching gives a lower boiling point; a cycloalkane boils higher than the straight-chain alkane with the same number of carbon atoms

Alkynes and benzene

Terminal alkynes give a white precipitate with ammoniacal AgNO₃ and a reddish-brown precipitate with ammoniacal Cu₂Cl₂; they also react with Na or NaNH₂
Hydration of an alkyne (dilute H₂SO₄, HgSO₄): ethyne gives ethanal, all other alkynes give ketones
Benzene: all C–C bonds 139 pm (between C–C and C=C), bond angle 120°, resonance energy about 150 kJ mol⁻¹
Nitration: concentrated HNO₃ + concentrated H₂SO₄, electrophile NO₂⁺. Sulphonation: fuming H₂SO₄, electrophile SO₃
Halogenation: Cl₂ or Br₂ with FeCl₃, FeBr₃ or AlCl₃. Friedel–Crafts: RCl or RCOCl with anhydrous AlCl₃ (a Lewis acid that makes R⁺ or RCO⁺)
–CH₃ and –OH activate the ring and direct to positions 2 and 4; –NO₂ deactivates the ring and directs to position 3
Faraday discovered benzene in 1825; Kekulé proposed the ring structure in 1865. Toluene = methylbenzene, cumene = (1-methylethyl)benzene

Chemistry · Alkyl halides

Alkyl halides

Reactivity: R–I > R–Br > R–Cl > R–F (C–F is the strongest bond)
S_N2: one step, rate = k[RX][Nu⁻], attack from the back, inversion of configuration. Order: primary > secondary > tertiary
S_N1: two steps, slow step forms a carbocation, rate = k[RX], product is mostly racemic. Order: tertiary > secondary > primary
E2: one step, rate depends on both halide and base. E1: two steps through a carbocation, rate depends on the halide only
Aqueous KOH favours substitution (alcohol); hot concentrated alcoholic KOH favours elimination (alkene). Tertiary halides eliminate most easily
R–X + Mg in dry ether → R–Mg–X (Grignard reagent); with water it gives the alkane R–H. Wurtz: 2R–X + 2Na → R–R + 2NaX
Boiling points: R–I > R–Br > R–Cl for the same R, and branching lowers them. Freons (CFCs) were refrigerants and aerosol propellants; their Cl atoms destroy ozone

Chemistry · Alcohols and phenols

Alcohols

Oxidation with acidified K₂Cr₂O₇ (orange to green): primary → aldehyde → carboxylic acid; secondary → ketone; tertiary → no oxidation
Lucas reagent (concentrated HCl + anhydrous ZnCl₂): tertiary turns cloudy at once, secondary in 5 to 10 minutes, primary stays clear at room temperature
Concentrated H₂SO₄: about 170 °C with excess acid gives an alkene; about 140 °C with excess alcohol gives an ether
Esterification: RCOOH + R′OH ⇌ RCOOR′ + H₂O (concentrated H₂SO₄). The acid loses –OH and the alcohol loses H
2ROH + 2Na → 2RONa + H₂. ROH + SOCl₂ → RCl + SO₂ + HCl. ROH + PCl₅ → RCl + POCl₃ + HCl
Iodoform test (I₂ + NaOH, yellow precipitate of CHI₃): positive for CH₃CH(OH)–, so ethanol and propan-2-ol react but methanol does not
Made by: hydration of alkenes, hydrolysis of alkyl halides with aqueous NaOH, Grignard reagent + carbonyl compound, reduction of aldehydes, ketones and acids, fermentation (ethanol)

Phenols and ethers

Acid strength: carboxylic acid > phenol > water > alcohol. K_a of phenol is about 1 × 10⁻¹⁰
Phenol reacts with NaOH to give sodium phenoxide and water, but it gives no CO₂ with Na₂CO₃ or NaHCO₃
Electron-withdrawing groups (–NO₂) make a phenol more acidic; electron-donating groups (–CH₃) make it less acidic
Bromine water at room temperature: white precipitate of 2,4,6-tribromophenol. Dilute HNO₃: 2- and 4-nitrophenol. Concentrated HNO₃ + H₂SO₄: 2,4,6-trinitrophenol (picric acid)
Phenol + zinc dust (heat) → benzene + ZnO. Phenol + methanal → Bakelite. Phenol + CH₃COCl → phenyl ethanoate + HCl
Phenol (carbolic acid): colourless crystals, melting point 41 °C, absorbs moisture from air, turns pink in air by oxidation. Catechol, resorcinol and quinol are benzene-1,2-, 1,3- and 1,4-diol
Ethers are named alkoxyalkanes, with the smaller group as alkoxy: CH₃OC₂H₅ is methoxyethane. Oxygen is sp³, so C–O–C is bent, about 110°. Williamson: RONa + R′X → ROR′ + NaX

Chemistry · Aldehydes and ketones

Aldehydes and ketones

General formula C_nH_2nO. An aldehyde and a ketone with the same formula are functional group isomers (propanal and propanone)
2,4-DNPH: yellow or orange precipitate with both aldehydes and ketones (test for C=O)
Tollens' reagent: silver mirror with aldehydes only. Fehling's solution: brick-red Cu₂O with aliphatic aldehydes only (not benzaldehyde, not ketones)
Iodoform test (I₂ + NaOH, yellow CHI₃): positive for CH₃CO–, so ethanal and methyl ketones. Alkaline sodium nitroprusside: red colour with ketones
HCN (with a little NaCN) adds to give a hydroxynitrile (cyanohydrin); the attacking species is CN⁻. Saturated NaHSO₃ gives white crystals with aldehydes and small methyl ketones
Reduction (NaBH₄, LiAlH₄ or H₂/Ni): aldehyde → primary alcohol, ketone → secondary alcohol. Zn/Hg + concentrated HCl (Clemmensen) changes C=O to CH₂
Dilute NaOH: aldol condensation if there is an α-hydrogen. Concentrated NaOH: Cannizzaro reaction if there is no α-hydrogen (methanal, benzaldehyde)

Chemistry · Carboxylic acids

Carboxylic acids and derivatives

Acid strength: ClCH₂COOH > HCOOH > C₆H₅COOH > CH₃COOH > CH₃CH₂COOH. A larger K_a (smaller pK_a) means a stronger acid
Made by: oxidising primary alcohols or aldehydes; hydrolysing nitriles (RCN → RCOOH); Grignard reagent + CO₂, then dilute acid; oxidising the side chain of an alkylbenzene to benzoic acid
Acids react with metals, alkalis and carbonates; CO₂ from Na₂CO₃ or NaHCO₃ is the test for –COOH
RCOOH + PCl₅ → RCOCl + POCl₃ + HCl. RCOOH + SOCl₂ → RCOCl + SO₂ + HCl. 3RCOOH + PCl₃ → 3RCOCl + H₃PO₃
Reactivity towards nucleophiles: acid chloride > anhydride > ester > amide
Ester hydrolysis: with dilute acid it is reversible; with NaOH it goes to completion, giving the sodium salt of the acid and the alcohol
LiAlH₄ reduces RCOOH to RCH₂OH. Decarboxylation: RCOONa + NaOH (soda lime, heat) → RH + Na₂CO₃

Chemistry · Macromolecules

Polymers

Addition polymers: polyethene from CH₂=CH₂; PVC from CH₂=CHCl; polystyrene from C₆H₅CH=CH₂; Teflon (PTFE) from CF₂=CF₂; polyacrylonitrile from CH₂=CHCN
To find the monomer of an addition polymer, take the two-carbon repeating unit and put the double bond back between the two chain carbons
Nylon-6,6 (a polyamide): hexanedioic acid + hexane-1,6-diamine, joined by amide links –CO–NH–, water lost
Terylene or Dacron (a polyester): benzene-1,4-dicarboxylic acid + ethane-1,2-diol, joined by ester links –CO–O–, water lost
Bakelite: phenol + methanal, a condensation polymer with cross-links between chains
Thermoplastics (polyethene, PVC, nylon) soften on heating and can be remoulded; thermosetting plastics (Bakelite) are cross-linked and cannot be remoulded
Number of monomer units in an addition polymer chain = M_r of polymer ÷ M_r of monomer

Biological macromolecules

Fibrous proteins are insoluble and structural (collagen, keratin). Globular proteins are folded and soluble (enzymes, haemoglobin, insulin, albumin)
Simple proteins give only amino acids on hydrolysis; conjugated proteins also have a non-protein part (haemoglobin has haem)
Primary structure = sequence of amino acids, held by peptide bonds. The α-helix is held by hydrogen bonds between C=O and N–H groups
Competitive inhibitor: looks like the substrate, blocks the active site, overcome by adding more substrate. Non-competitive inhibitor: binds elsewhere, not overcome by more substrate
Cofactors: metal ions or organic coenzymes such as NAD⁺. A zymogen is an inactive form of an enzyme (pepsinogen, trypsinogen) that becomes active when part of its chain is cut off
Reducing sugars (glucose, fructose, maltose, lactose) reduce Fehling's solution; sucrose does not. Starch and cellulose are polymers of glucose
Iodine number = grams of iodine taken up by 100 g of fat; a high value means many C=C bonds. A nucleotide = pentose sugar + phosphate group + nitrogenous base

Chemistry · Industrial chemistry

Industrial chemistry

Urea: 2NH₃ + CO₂ → NH₂COONH₄ (ammonium carbamate), then NH₂COONH₄ → CO(NH₂)₂ + H₂O. Urea is about 46 to 47% nitrogen by mass (28 ÷ 60)
Ammonium nitrate: NH₃ + HNO₃ → NH₄NO₃
Single superphosphate: Ca₃(PO₄)₂ + 2H₂SO₄ → Ca(H₂PO₄)₂ + 2CaSO₄
Triple superphosphate: Ca₃(PO₄)₂ + 4H₃PO₄ → 3Ca(H₂PO₄)₂ (no CaSO₄, so more phosphorus per kg)
Cracking: a large alkane → a smaller alkane + an alkene, for example C₁₀H₂₂ → C₈H₁₈ + C₂H₄
Octane number: 2,2,4-trimethylpentane (iso-octane) = 100, heptane = 0. Reforming changes straight chains into branched, ring and aromatic molecules to raise it
Ethene from cracking gives polyethene, ethanol and ethane-1,2-diol