IB Chemistry SL cheat sheet

Amount of substance: n = N/N_A = m/M; N_A = 6.02 × 10^23 mol−1; M has units g mol−1 and m is mass in g.

Concentration: c = n/V; V in dm3; dilution obeys c1V1 = c2V2 for the same amount of solute.

Ideal gas: PV = nRT; P in Pa, V in m3, T in K, R = 8.314 J K−1 mol−1.

Empirical formula is the simplest whole-number atom ratio; molecular formula = empirical formula × integer n, with n = M_molecular/M_empirical.

Mass spectrum: m/z gives ion mass/charge; tallest peaks indicate abundance; molecular ion M+ gives relative molecular mass; fragments identify structure.

Electron configuration: fill 1s 2s 2p 3s 3p 4s 3d 4p; orbital capacities s2, p6, d10, f14; Pauli allows two opposite-spin electrons per orbital; Hund fills degenerate orbitals singly first.

Ionisation energy: first IE = energy to remove one mole of electrons from one mole of gaseous atoms; across a period it generally increases; down a group it decreases.

Emission spectrum: discrete lines arise from electron transitions between quantised energy levels; ΔE = hν, with h = 6.63 × 10−34 J s.

Ionic bonding: electrostatic attraction between oppositely charged ions in a giant lattice; typical of metal with non-metal; high melting point; conducts when molten or aqueous, not solid.

Covalent bond: shared pair of electrons; bond polarity increases with electronegativity difference; nonpolar when difference is zero or very small.

VSEPR: electron domains repel; two domains linear 180°; three trigonal planar 120°; four tetrahedral 109.5°.

Lone-pair repulsion: four domains with one lone pair gives trigonal pyramidal (~107°); with two lone pairs gives bent (~104.5°).

Intermolecular forces: London dispersion in all molecules; dipole–dipole in polar molecules; hydrogen bonding when H bonded to N/O/F interacts with lone pair on N/O/F.

Metallic bonding: positive ion lattice in delocalised electrons; explains conductivity, malleability and ductility.

Giant covalent: diamond, graphite, silicon dioxide; high melting points; graphite conducts because delocalised electrons move within layers.

Bond enthalpy: ΔH ≈ Σ bonds broken − Σ bonds formed using mean gaseous bond enthalpies; bond breaking is endothermic and bond forming exothermic.

Periodic table: groups are vertical columns with similar valence electron configurations; periods are horizontal rows; elements are ordered by increasing atomic number.

Blocks: s-block groups 1–2; p-block groups 13–18; d-block transition metals; f-block lanthanides and actinides.

Group 1 alkali metals: one valence electron, form +1 ions, reactivity increases down the group; react with water to give hydroxide and hydrogen.

Group 17 halogens: diatomic, form −1 ions, reactivity decreases down the group; a more reactive halogen displaces a less reactive halide.

Transition metals: variable oxidation states, coloured compounds, catalytic activity, and formation of complex ions.

Oxides: metal oxides are generally basic; non-metal oxides are generally acidic; amphoteric oxides such as Al2O3 and ZnO react with both acids and bases.

Organic families: alkanes CnH2n+2; alkenes CnH2n; alcohols CnH2n+1OH; carboxylic acids CnH2n+1COOH; same functional group implies similar reactions.

Matter classification: element = one type of atom; compound = chemically combined elements; mixture = substances not chemically combined; separation by filtration, distillation or chromatography.

Enthalpy change: ΔH is negative for exothermic and positive for endothermic; q = mcΔT for a calorimetry experiment, with m mass of solution and c specific heat capacity.

Bond breaking absorbs energy; bond forming releases energy; ΔH ≈ Σ bonds broken − Σ bonds formed.

Hess's law: ΔH is route-independent; ΔH reaction = Σ ΔHf(products) − Σ ΔHf(reactants) using standard enthalpies of formation.

Combustion enthalpy: ΔHc = Σ ΔHc(reactants) − Σ ΔHc(products) when using standard enthalpies of combustion.

Entropy S: gas > liquid > solid generally; entropy increases when number of gaseous particles increases or temperature rises.

Gibbs free energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0; if ΔH negative and ΔS positive, spontaneous at all temperatures.

If ΔH positive and ΔS negative, ΔG is positive at all temperatures; if signs are opposite, temperature determines spontaneity.

Catalyst lowers activation energy without changing ΔH; energy profile shows reactants, products, Ea and ΔH.

Rate = change in concentration/change in time; typical units mol dm−3 s−1; rates usually decrease as reactants are consumed.

Collision theory: reaction requires collisions with E ≥ Ea and correct orientation; increasing concentration, pressure, surface area or temperature raises collision frequency/energy.

Maxwell–Boltzmann distribution: temperature increases the fraction of molecules with energy ≥ Ea; catalyst lowers Ea; total area under curve remains constant.

Dynamic equilibrium: forward and reverse rates equal in closed system; concentrations constant; equilibrium can be reached from either direction.

Kc for aA + bB ⇌ cC + dD is [C]^c[D]^d/([A]^a[B]^b); pure solids and liquids are omitted; Kc depends only on temperature.

Le Chatelier: increasing reactant concentration shifts right; increasing pressure shifts toward fewer gas moles; increasing temperature favours the endothermic direction.

Limiting reactant determines theoretical yield; percentage yield = actual/theoretical × 100; atom economy = molar mass desired product/total molar mass reactants × 100.

Reaction quotient Q compared with Kc: Q < Kc favours forward reaction; Q > Kc favours reverse; Q = Kc at equilibrium.

Brønsted–Lowry acid donates H+; base accepts H+; conjugate acid–base pair differs by one H+.

pH = −log[H+]; [H+] = 10^−pH; at 298 K Kw = [H+][OH−] = 1.0 × 10−14 and pH + pOH = 14.

Strong acid fully ionises; weak acid partially ionises; larger Ka or smaller pKa means stronger acid; pKa = −log Ka.

Neutralisation: H+ + OH− → H2O; titration equivalence point depends on stoichiometry; indicator must change colour near equivalence pH.

Oxidation is loss of electrons/increase in oxidation number; reduction is gain of electrons/decrease in oxidation number; oxidising agent is reduced, reducing agent is oxidised.

Oxidation-number rules: free element 0; monatomic ion equals charge; O usually −2; H usually +1; sum equals overall charge.

Voltaic cell: anode oxidation, cathode reduction; Ecell = E°cathode − E°anode; positive Ecell indicates spontaneous reaction.

Organic mechanism types: electrophilic addition to alkenes; nucleophilic substitution of haloalkanes; addition polymerisation; oxidation of alcohols; condensation to esters.

Variable types: independent variable is changed; dependent variable is measured; controlled variables held constant to make comparisons valid.

Accuracy is closeness to true value; precision is closeness of repeated measurements; random errors reduce precision, systematic errors reduce accuracy.

Absolute uncertainty from instrument resolution; percentage uncertainty = (absolute uncertainty/measurement) × 100; add absolute uncertainties for addition/subtraction and percentage uncertainties for multiplication/division.

Significant figures in a result should match the least precise measurement; carry extra digits during calculation and round at the end.

Repeats improve reliability; mean of concordant results; anomalous results identified and excluded only with justification.

Tables: headings include quantity and unit; graphs: labelled axes with units, suitable scale, line of best fit; gradient and intercept may carry physical meaning.

Titration technique: rinse burette with titrant, use conical flask with indicator, read meniscus at eye level, add dropwise near endpoint, record concordant titres.

Chromatography: Rf = distance travelled by spot/distance travelled by solvent front; colorimetry uses absorbance proportional to concentration via calibration.