European Baccalaureate Chemistry cheat sheet

Atomic notation: mass number A = protons Z + neutrons N; isotopes share Z but differ in N; relative atomic mass is the weighted mean of isotope masses by natural abundance.

Electron configuration follows the aufbau order 1s 2s 2p 3s 3p 4s 3d 4p; Cr = [Ar]3d5 4s1 and Cu = [Ar]3d10 4s1 are exceptions driven by half-filled/filled stability.

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing; the Pauli principle forbids identical quantum numbers for two electrons.

Successive ionisation energies rise steeply when a new principal shell is breached; large jumps locate the group number of the element.

Periodic trends: atomic radius decreases across a period and increases down a group; first ionisation energy and electronegativity rise across, fall down.

Effective nuclear charge increases across a period, contracting the shell; shielding by inner electrons stays roughly constant across a period but grows down a group.

s-, p-, d- and f-blocks are defined by the subshell receiving the differentiating electron; d-block elements show variable oxidation states and coloured, catalytic ions.

An orbital is a probability-density region holding at most two electrons; quantum numbers n (shell), l (subshell), m_l (orientation) and m_s (spin) define each electron.

Electronegativity difference guides bonding: ΔEN < 0.4 nonpolar covalent, 0.4–1.8 polar covalent, > 1.8 predominantly ionic (Pauling scale, approximate).

VSEPR: electron domains repel and adopt maximum separation; 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs compress angles.

Bond polarity plus molecular geometry determines the dipole moment: CO2 is linear and nonpolar despite polar bonds; H2O is bent and polar.

Formal charge = valence electrons − (nonbonding electrons + ½ bonding electrons); the dominant resonance structure minimises formal charge.

Bond order from MO theory: N2 has bond order 3 and is diamagnetic; O2 has bond order 2 and two unpaired π* electrons, hence paramagnetic.

Intermolecular forces ranked: ion–dipole > hydrogen bonding > dipole–dipole > London dispersion; dispersion grows with polarisability and electron count.

Giant covalent structures (diamond, SiO2) melt high; molecular substances melt low; metals conduct via delocalised electrons; ionic solids conduct only when molten or dissolved.

Hybridisation: sp linear (180°), sp2 trigonal planar (120°), sp3 tetrahedral (109.5°); count σ bonds plus lone pairs to assign it.

Ideal gas law pV = nRT with R = 8.314 J mol⁻¹ K⁻¹; temperature must be in kelvin (K = °C + 273.15).

Mole relations: n = m/M, n = N/N_A (N_A = 6.022 × 10²³ mol⁻¹), n = V/24.0 dm³ mol⁻¹ at standard conditions or V/22.4 dm³ mol⁻¹ at STP.

Limiting reagent: divide each reactant's amount by its stoichiometric coefficient; the smallest quotient limits and sets the theoretical yield.

Percentage yield = actual/theoretical × 100; atom economy = M(product)/ΣM(reactants) × 100.

Concentration c = n/V in mol dm⁻³; dilution obeys c1V1 = c2V2; titration at equivalence satisfies c_a V_a / ν_a = c_b V_b / ν_b.

Empirical formula from percentage composition: divide each % by atomic mass, then divide by the smallest ratio; molecular formula = empirical × n from M.

Phase changes: melting and boiling absorb energy without temperature change; the Clausius–Clapeyron relation links vapour pressure to ΔH_vap.

Real gases deviate from ideality at high pressure and low temperature where molecular volume and intermolecular attractions become significant.

Enthalpy conventions: ΔH negative = exothermic; standard conditions are 298 K and 100 kPa with all species in their standard states.

Hess's law: ΔH is path-independent, so ΔH_rxn = ΣΔH_f(products) − ΣΔH_f(reactants) or from mean bond enthalpies (bonds broken − bonds formed).

Calorimetry: q = mcΔT with c(water) = 4.18 J g⁻¹ K⁻¹; ΔH = −q/n for the amount reacting, with heat loss causing systematic error.

Entropy S increases with temperature, phase change (solid < liquid < gas), and number of moles of gas produced; ΔS_universe = ΔS_system + ΔS_surroundings.

Gibbs free energy ΔG = ΔH − TΔS; ΔG < 0 spontaneous, ΔG = 0 at equilibrium, ΔG > 0 non-spontaneous under those conditions.

ΔG° = −RT ln K and ΔG° = −nFE°cell link thermodynamics to equilibrium constants and cell potentials.

Lattice enthalpy (Born–Haber cycle) is exothermic; hydration enthalpy is exothermic; dissolution enthalpy equals lattice plus hydration terms.

Bond enthalpy is the energy to break one mole of a given bond in the gaseous state; average values give approximate reaction enthalpies only.

Rate = −(1/a)d[A]/dt = (1/b)d[B]/dt; the rate law rate = k[A]^m[B]^n is determined experimentally, not from stoichiometry.

Order determines units of k: zero order mol dm⁻³ s⁻¹, first order s⁻¹, second order dm³ mol⁻¹ s⁻¹.

First-order half-life t½ = ln2/k is constant; concentration follows [A] = [A]0 e^(−kt).

Arrhenius equation k = A e^(−Ea/RT); a plot of ln k against 1/T has slope −Ea/R, and a catalyst lowers Ea without changing ΔH.

Collision theory requires sufficient energy (Ea) and correct orientation; increasing temperature raises the fraction of collisions exceeding Ea sharply.

Equilibrium constant K_c = [products]^coefficients/[reactants]^coefficients; K depends only on temperature, not on concentration or pressure.

Le Chatelier: raising pressure shifts toward fewer gas moles; raising temperature shifts in the endothermic direction; a catalyst changes neither K nor position.

Reaction quotient Q compared with K predicts direction: Q < K proceeds forward, Q > K proceeds reverse, Q = K at equilibrium.

Brønsted–Lowry: acid donates a proton, base accepts; conjugate pairs differ by one H⁺; Lewis acids accept electron pairs.

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

Strong acids and bases dissociate fully; weak acids obey Ka = [H⁺][A⁻]/[HA] with pH ≈ ½(pKa − log c) for a pure weak acid.

Buffer Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]); buffers resist pH change best when pH ≈ pKa and are effective within about ±1 unit.

Titration curves: strong acid–strong base equivalence pH 7; weak acid–strong base equivalence pH > 7; the half-equivalence point gives pH = pKa.

Indicators are weak acids whose colour change spans roughly pKa ± 1; the indicator's range must bracket the equivalence pH.

Salt hydrolysis: a salt of a weak acid and strong base gives alkaline solution; of a strong acid and weak base, acidic; of weak acid and weak base, pH depends on Ka and Kb.

Solubility product Ksp governs precipitation; a precipitate forms when the ion product exceeds Ksp, and common-ion addition lowers solubility.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain; an oxidising agent is itself reduced.

Oxidation-number rules: free element 0, monatomic ion equals charge, oxygen usually −2, hydrogen usually +1, sum equals overall charge.

Balance redox half-equations by mass and charge; in acidic solution add H2O and H⁺, in alkaline add H2O and OH⁻ to neutralise.

Standard electrode potential E° is measured against the standard hydrogen electrode (0.00 V) at 298 K, 1 mol dm⁻³, 100 kPa.

E°cell = E°cathode − E°anode; a positive E°cell means the reaction is spontaneous; the more positive couple is reduced.

Electrolysis: cathode attracts cations (reduction), anode attracts anions (oxidation); selective discharge depends on E° and concentration.

Quantitative electrolysis: charge Q = It, and moles of electrons n = Q/F with Faraday constant F = 96 485 C mol⁻¹.

ΔG° = −nFE°cell; Nernst equation E = E° − (RT/nF)ln Q adjusts the potential when concentrations differ from standard.

Functional groups: alcohols (OH), aldehydes (CHO), ketones (C=O), carboxylic acids (COOH), esters (COO), amines (NH2), amides (CONH2), halogenoalkanes (X).

IUPAC naming: longest chain, lowest locants, suffix for principal group, prefixes for substituents; cis/trans or E/Z for alkenes.

Isomerism: structural (chain, position, functional group) and stereoisomerism (geometric and optical, the latter requiring a chiral centre).

Nucleophilic substitution: primary halogenoalkanes favour SN2 (one step, inversion); tertiary favour SN1 (carbocation intermediate, racemisation).

Electrophilic addition to alkenes follows Markovnikov's rule; bromine water decolourises, and HBr addition can give the more stable carbocation.

Free-radical substitution of alkanes has initiation, propagation and termination steps; alkenes undergo addition rather than substitution.

Oxidation: primary alcohols → aldehydes → carboxylic acids; secondary → ketones; tertiary alcohols resist oxidation under mild conditions.

Esterification is acid-catalysed and reversible; hydrolysis of esters and amides can be acid- or base-catalysed (saponification with NaOH).

Infrared spectroscopy: O–H broad 3200–3600 cm⁻¹, C=O sharp 1680–1750 cm⁻¹, C–H 2850–3100 cm⁻¹; used to identify functional groups.

Mass spectrometry gives molecular ion M⁺ for molar mass and fragmentation patterns for structure; M+1 peaks reveal carbon count approximately.

¹H NMR: chemical shift identifies environment, integration gives relative H count, splitting follows n+1 rule from neighbouring equivalent protons.

Chromatography separates by differential affinity for mobile and stationary phases; Rf = distance travelled by solute / distance travelled by solvent front.

Retention time in gas or liquid chromatography identifies components when compared with standards; peak area allows quantitative analysis with calibration.

Atomic absorption and emission spectroscopy quantify metal ions via characteristic lines; calibration curves relate absorbance to concentration (Beer–Lambert A = εcl).

Flame tests: Li crimson, Na yellow, K lilac, Ca brick-red, Cu blue-green; these identify metal cations in simple salts.

Qualitative tests: carbonate + acid gives CO2 (limewater milky); sulfate + BaCl2 gives white precipitate; halides + AgNO3 give distinctive precipitates.

Greenhouse gases (CO2, CH4, N2O, H2O vapour) absorb infrared radiation; the enhanced greenhouse effect warms the troposphere.

Acid rain forms from SO2 and NOx oxidised to H2SO4 and HNO3; controls include flue-gas desulfurisation with CaO or CaCO3 and catalytic converters.

Ozone depletion by CFCs: UV light liberates Cl radicals that catalytically destroy O3; the Montreal Protocol phased out CFCs.

Haber–Bosch: N2 + 3H2 ⇌ 2NH3, exothermic; moderate temperature (~450 °C), high pressure (~200 atm) and iron catalyst balance rate and yield.

Contact process for H2SO4: S → SO2 → SO3 (V2O5 catalyst, ~450 °C) → H2SO4; SO3 is absorbed in concentrated acid, not water.

Materials: addition polymers (polyethene) versus condensation polymers (polyesters, polyamides); recycling and biodegradability differ.

Life-cycle assessment compares energy, raw materials, emissions and waste across extraction, manufacture, use and disposal.

Catalytic converters convert CO, unburned hydrocarbons and NOx to CO2, H2O and N2 using Pt/Pd/Rh on a support; they require stoichiometric air–fuel mixtures.

Mass number A = Z + N; isotopes differ only in neutron number, so they share chemical properties but differ in mass and nuclear stability.

Aufbau order 1s 2s 2p 3s 3p 4s 3d 4p; Cr and Cu anomalies arise from half-filled and filled d-subshell stability.

Hund's rule singly occupies degenerate orbitals before pairing; the Pauli exclusion principle limits each orbital to two electrons.

Successive ionisation energies show sharp jumps when a new shell is broken; the jump position reveals the group number.

Atomic radius falls across a period and rises down a group; ionisation energy and electronegativity show the opposite trends.

Effective nuclear charge rises across a period while shielding is roughly constant, contracting the shell and raising ionisation energy.

Block assignment follows the subshell receiving the differentiating electron; d-block ions often show variable oxidation states and colour.

Quantum numbers n, l, m_l and m_s define each electron, and an orbital is a probability-density region holding at most two electrons.

Electronegativity difference guides bond type: ΔEN < 0.4 nonpolar covalent, 0.4–1.8 polar covalent, > 1.8 predominantly ionic (approximate).

VSEPR predicts geometry from electron domains: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs compress angles.

Bond polarity plus geometry determines the molecular dipole: CO2 is linear and nonpolar while H2O is bent and polar.

Formal charge = valence electrons − (nonbonding + ½ bonding); the dominant resonance structure minimises formal charge.

MO theory: N2 has bond order 3 and is diamagnetic; O2 has bond order 2 and two unpaired π* electrons, so it is paramagnetic.

Intermolecular forces ranked ion–dipole > hydrogen bonding > dipole–dipole > London dispersion; dispersion grows with polarisability.

Giant covalent and ionic solids melt high; molecular substances melt low; metals conduct via delocalised electrons, ionic solids only when molten or dissolved.

Hybridisation sp, sp2 and sp3 correspond to 180°, 120° and 109.5°; count σ bonds plus lone pairs to assign it.

Ideal gas law pV = nRT with R = 8.314 J mol⁻¹ K⁻¹ and T in kelvin (K = °C + 273.15).

Mole relations n = m/M, n = N/N_A (N_A = 6.022 × 10²³ mol⁻¹), and n = V/24.0 dm³ mol⁻¹ at standard conditions.

Limiting reagent: divide each reactant's amount by its coefficient; the smallest quotient limits and sets the theoretical yield.

Percentage yield = actual/theoretical × 100; atom economy = M(product)/ΣM(reactants) × 100.

Concentration c = n/V in mol dm⁻³; dilution obeys c1V1 = c2V2; titration satisfies c_a V_a/ν_a = c_b V_b/ν_b.

Empirical formula: divide each percentage by atomic mass, then by the smallest ratio; molecular formula = empirical × n from M.

Phase changes absorb energy without temperature change; the Clausius–Clapeyron relation links vapour pressure to ΔH_vap.

Real gases deviate from ideality at high pressure and low temperature where molecular volume and attractions matter.

ΔH is negative for exothermic reactions; standard conditions are 298 K and 100 kPa with species in their standard states.

Hess's law: ΔH_rxn = ΣΔH_f(products) − ΣΔH_f(reactants), or from mean bond enthalpies as bonds broken minus bonds formed.

Calorimetry q = mcΔT with c(water) = 4.18 J g⁻¹ K⁻¹; heat loss causes systematic error, so ΔH = −q/n is usually underestimated in magnitude.

Entropy increases with temperature, on melting or boiling, and with more moles of gas; ΔS_universe = ΔS_system + ΔS_surroundings.

Gibbs free energy ΔG = ΔH − TΔS; ΔG < 0 spontaneous, ΔG = 0 at equilibrium, ΔG > 0 non-spontaneous.

ΔG° = −RT ln K and ΔG° = −nFE°cell link thermodynamics to equilibrium constants and cell potentials.

Born–Haber cycles combine lattice enthalpy (exothermic) and hydration enthalpy (exothermic) to give enthalpy of solution.

Bond enthalpy is the energy to break one mole of a gaseous bond; average values give only approximate reaction enthalpies.

Rate = −(1/a)d[A]/dt = (1/b)d[B]/dt; the rate law rate = k[A]^m[B]^n is found experimentally, not from stoichiometry.

Order fixes the units of k: zero order mol dm⁻³ s⁻¹, first order s⁻¹, second order dm³ mol⁻¹ s⁻¹.

First-order half-life t½ = ln2/k is constant, and concentration follows [A] = [A]0 e^(−kt).

Arrhenius k = A e^(−Ea/RT); a plot of ln k against 1/T has slope −Ea/R, and a catalyst lowers Ea without changing ΔH.

Collision theory requires energy above Ea and correct orientation; raising temperature sharply increases the fraction of successful collisions.

K_c = [products]^coefficients/[reactants]^coefficients depends only on temperature, not on concentration or pressure.

Le Chatelier: raising pressure shifts toward fewer gas moles; raising temperature shifts endothermically; a catalyst changes neither K nor position.

The reaction quotient Q compared with K predicts direction: Q < K forward, Q > K reverse, Q = K at equilibrium.

Brønsted–Lowry acids donate protons and bases accept them; conjugate pairs differ by one H⁺; Lewis acids accept electron pairs.

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

Strong acids dissociate fully; weak acids obey Ka = [H⁺][A⁻]/[HA] with pH ≈ ½(pKa − log c) for a pure weak acid.

Buffer Henderson–Hasselbalch pH = pKa + log([A⁻]/[HA]); buffers work best near pH = pKa, within about ±1 unit.

Titration curves: strong acid–strong base equivalence pH 7; weak acid–strong base equivalence pH > 7; half-equivalence gives pH = pKa.

Indicators are weak acids changing colour over roughly pKa ± 1; the range must bracket the equivalence pH.

Salt hydrolysis: weak acid with strong base gives alkaline solution; strong acid with weak base gives acidic; weak with weak depends on Ka and Kb.

Solubility product Ksp governs precipitation; a precipitate forms when the ion product exceeds Ksp, and a common ion lowers solubility.

Oxidation is loss of electrons (oxidation number rises); reduction is gain; the oxidising agent is itself reduced.

Oxidation-number rules: free element 0, monatomic ion equals charge, oxygen usually −2, hydrogen usually +1, sum equals overall charge.

Balance half-equations by mass and charge; in acid add H2O and H⁺, in alkali add H2O and OH⁻ to neutralise.

Standard electrode potentials are measured against the standard hydrogen electrode (0.00 V) at 298 K, 1 mol dm⁻³, 100 kPa.

E°cell = E°cathode − E°anode; positive E°cell means spontaneous reaction, and the more positive couple is reduced.

Electrolysis: cathode attracts cations and reduces them, anode attracts anions and oxidises them; discharge order depends on E° and concentration.

Quantitative electrolysis uses Q = It and n(e⁻) = Q/F with F = 96 485 C mol⁻¹.

ΔG° = −nFE°cell, and the Nernst equation E = E° − (RT/nF)ln Q corrects for non-standard concentrations.

Functional groups: alcohols OH, aldehydes CHO, ketones C=O, carboxylic acids COOH, esters COO, amines NH2, amides CONH2, halogenoalkanes X.

IUPAC naming uses the longest chain, lowest locants, a suffix for the principal group and prefixes for substituents; alkenes use cis/trans or E/Z.

Isomerism is structural (chain, position, functional group) or stereoisomerism (geometric and optical, the latter needing a chiral centre).

Nucleophilic substitution: primary halogenoalkanes favour SN2 (one step, inversion); tertiary favour SN1 (carbocation, racemisation).

Electrophilic addition to alkenes follows Markovnikov's rule; bromine water decolourises, and HBr addition can give the more stable carbocation.

Free-radical substitution of alkanes has initiation, propagation and termination steps; alkenes undergo addition rather than substitution.

Oxidation: primary alcohols → aldehyde → carboxylic acid; secondary → ketone; tertiary alcohols resist mild oxidation.

Esterification is acid-catalysed and reversible; ester and amide hydrolysis can be acid- or base-catalysed (saponification with NaOH).

Infrared spectroscopy: O–H broad 3200–3600 cm⁻¹, C=O sharp 1680–1750 cm⁻¹, C–H 2850–3100 cm⁻¹ identify functional groups.

Mass spectrometry gives the molecular ion M⁺ for molar mass and fragmentation patterns for structure; M+1 peaks indicate carbon count.

¹H NMR: chemical shift identifies environment, integration gives relative H count, and splitting follows the n+1 rule from neighbouring protons.

Chromatography separates by differential affinity for mobile and stationary phases; Rf = distance travelled by solute/distance travelled by solvent front.

Retention time identifies components against standards, and peak area allows quantitative analysis with a calibration curve.

Atomic absorption and emission quantify metal ions using characteristic lines; Beer–Lambert A = εcl links absorbance to concentration.

Flame tests: Li crimson, Na yellow, K lilac, Ca brick-red, Cu blue-green identify metal cations in simple salts.

Qualitative tests: carbonate + acid gives CO2 (limewater milky); sulfate + BaCl2 gives white precipitate; halides + AgNO3 give distinctive precipitates.

Greenhouse gases CO2, CH4, N2O and water vapour absorb infrared radiation, and the enhanced greenhouse effect warms the troposphere.

Acid rain forms from SO2 and NOx oxidised to H2SO4 and HNO3; controls include flue-gas desulfurisation with CaO or CaCO3 and catalytic converters.

Ozone depletion by CFCs: UV light liberates Cl radicals that catalytically destroy O3; the Montreal Protocol phased out CFCs.

Haber–Bosch N2 + 3H2 ⇌ 2NH3 is exothermic; moderate temperature (~450 °C), high pressure (~200 atm) and an iron catalyst balance rate and yield.

Contact process: S → SO2 → SO3 (V2O5 catalyst, ~450 °C) → H2SO4; SO3 is absorbed in concentrated acid, not water.

Materials: addition polymers such as polyethene versus condensation polymers such as polyesters and polyamides; recycling and biodegradability differ.

Life-cycle assessment compares energy, raw materials, emissions and waste across extraction, manufacture, use and disposal.

Catalytic converters convert CO, hydrocarbons and NOx to CO2, H2O and N2 using Pt/Pd/Rh on a support, requiring near-stoichiometric air–fuel mixtures.

Mass number A = Z + N; isotopes differ only in neutron number, so they share chemical properties but differ in mass and nuclear stability.

Aufbau order 1s 2s 2p 3s 3p 4s 3d 4p; Cr and Cu anomalies arise from half-filled and filled d-subshell stability.

Hund's rule singly occupies degenerate orbitals before pairing; the Pauli exclusion principle limits each orbital to two electrons.

Successive ionisation energies show sharp jumps when a new shell is broken; the jump position reveals the group number.

Atomic radius falls across a period and rises down a group; ionisation energy and electronegativity show the opposite trends.

Effective nuclear charge rises across a period while shielding is roughly constant, contracting the shell and raising ionisation energy.

Block assignment follows the subshell receiving the differentiating electron; d-block ions often show variable oxidation states and colour.

Quantum numbers n, l, m_l and m_s define each electron, and an orbital is a probability-density region holding at most two electrons.

Electronegativity difference guides bond type: ΔEN < 0.4 nonpolar covalent, 0.4–1.8 polar covalent, > 1.8 predominantly ionic (approximate).

VSEPR predicts geometry from electron domains: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs compress angles.

Bond polarity plus geometry determines the molecular dipole: CO2 is linear and nonpolar while H2O is bent and polar.

Formal charge = valence electrons − (nonbonding + ½ bonding); the dominant resonance structure minimises formal charge.

MO theory: N2 has bond order 3 and is diamagnetic; O2 has bond order 2 and two unpaired π* electrons, so it is paramagnetic.

Intermolecular forces ranked ion–dipole > hydrogen bonding > dipole–dipole > London dispersion; dispersion grows with polarisability.

Giant covalent and ionic solids melt high; molecular substances melt low; metals conduct via delocalised electrons, ionic solids only when molten or dissolved.

Hybridisation sp, sp2 and sp3 correspond to 180°, 120° and 109.5°; count σ bonds plus lone pairs to assign it.

Ideal gas law pV = nRT with R = 8.314 J mol⁻¹ K⁻¹ and T in kelvin (K = °C + 273.15).

Mole relations n = m/M, n = N/N_A (N_A = 6.022 × 10²³ mol⁻¹), and n = V/24.0 dm³ mol⁻¹ at standard conditions.

Limiting reagent: divide each reactant's amount by its coefficient; the smallest quotient limits and sets the theoretical yield.

Percentage yield = actual/theoretical × 100; atom economy = M(product)/ΣM(reactants) × 100.

Concentration c = n/V in mol dm⁻³; dilution obeys c1V1 = c2V2; titration satisfies c_a V_a/ν_a = c_b V_b/ν_b.

Empirical formula: divide each percentage by atomic mass, then by the smallest ratio; molecular formula = empirical × n from M.

Phase changes absorb energy without temperature change; the Clausius–Clapeyron relation links vapour pressure to ΔH_vap.

Real gases deviate from ideality at high pressure and low temperature where molecular volume and attractions matter.

ΔH is negative for exothermic reactions; standard conditions are 298 K and 100 kPa with species in their standard states.

Hess's law: ΔH_rxn = ΣΔH_f(products) − ΣΔH_f(reactants), or from mean bond enthalpies as bonds broken minus bonds formed.

Calorimetry q = mcΔT with c(water) = 4.18 J g⁻¹ K⁻¹; heat loss causes systematic error, so ΔH = −q/n is usually underestimated in magnitude.

Entropy increases with temperature, on melting or boiling, and with more moles of gas; ΔS_universe = ΔS_system + ΔS_surroundings.

Gibbs free energy ΔG = ΔH − TΔS; ΔG < 0 spontaneous, ΔG = 0 at equilibrium, ΔG > 0 non-spontaneous.

ΔG° = −RT ln K and ΔG° = −nFE°cell link thermodynamics to equilibrium constants and cell potentials.

Born–Haber cycles combine lattice enthalpy (exothermic) and hydration enthalpy (exothermic) to give enthalpy of solution.

Bond enthalpy is the energy to break one mole of a gaseous bond; average values give only approximate reaction enthalpies.

Rate = −(1/a)d[A]/dt = (1/b)d[B]/dt; the rate law rate = k[A]^m[B]^n is found experimentally, not from stoichiometry.

Order fixes the units of k: zero order mol dm⁻³ s⁻¹, first order s⁻¹, second order dm³ mol⁻¹ s⁻¹.

First-order half-life t½ = ln2/k is constant, and concentration follows [A] = [A]0 e^(−kt).

Arrhenius k = A e^(−Ea/RT); a plot of ln k against 1/T has slope −Ea/R, and a catalyst lowers Ea without changing ΔH.

Collision theory requires energy above Ea and correct orientation; raising temperature sharply increases the fraction of successful collisions.

K_c = [products]^coefficients/[reactants]^coefficients depends only on temperature, not on concentration or pressure.

Le Chatelier: raising pressure shifts toward fewer gas moles; raising temperature shifts endothermically; a catalyst changes neither K nor position.

The reaction quotient Q compared with K predicts direction: Q < K forward, Q > K reverse, Q = K at equilibrium.

Brønsted–Lowry acids donate protons and bases accept them; conjugate pairs differ by one H⁺; Lewis acids accept electron pairs.

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

Strong acids dissociate fully; weak acids obey Ka = [H⁺][A⁻]/[HA] with pH ≈ ½(pKa − log c) for a pure weak acid.

Buffer Henderson–Hasselbalch pH = pKa + log([A⁻]/[HA]); buffers work best near pH = pKa, within about ±1 unit.

Titration curves: strong acid–strong base equivalence pH 7; weak acid–strong base equivalence pH > 7; half-equivalence gives pH = pKa.

Indicators are weak acids changing colour over roughly pKa ± 1; the range must bracket the equivalence pH.

Salt hydrolysis: weak acid with strong base gives alkaline solution; strong acid with weak base gives acidic; weak with weak depends on Ka and Kb.

Solubility product Ksp governs precipitation; a precipitate forms when the ion product exceeds Ksp, and a common ion lowers solubility.

Oxidation is loss of electrons (oxidation number rises); reduction is gain; the oxidising agent is itself reduced.

Oxidation-number rules: free element 0, monatomic ion equals charge, oxygen usually −2, hydrogen usually +1, sum equals overall charge.

Balance half-equations by mass and charge; in acid add H2O and H⁺, in alkali add H2O and OH⁻ to neutralise.

Standard electrode potentials are measured against the standard hydrogen electrode (0.00 V) at 298 K, 1 mol dm⁻³, 100 kPa.

E°cell = E°cathode − E°anode; positive E°cell means spontaneous reaction, and the more positive couple is reduced.

Electrolysis: cathode attracts cations and reduces them, anode attracts anions and oxidises them; discharge order depends on E° and concentration.

Quantitative electrolysis uses Q = It and n(e⁻) = Q/F with F = 96 485 C mol⁻¹.

ΔG° = −nFE°cell, and the Nernst equation E = E° − (RT/nF)ln Q corrects for non-standard concentrations.

Functional groups: alcohols OH, aldehydes CHO, ketones C=O, carboxylic acids COOH, esters COO, amines NH2, amides CONH2, halogenoalkanes X.

IUPAC naming uses the longest chain, lowest locants, a suffix for the principal group and prefixes for substituents; alkenes use cis/trans or E/Z.

Isomerism is structural (chain, position, functional group) or stereoisomerism (geometric and optical, the latter needing a chiral centre).

Nucleophilic substitution: primary halogenoalkanes favour SN2 (one step, inversion); tertiary favour SN1 (carbocation, racemisation).

Electrophilic addition to alkenes follows Markovnikov's rule; bromine water decolourises, and HBr addition can give the more stable carbocation.

Free-radical substitution of alkanes has initiation, propagation and termination steps; alkenes undergo addition rather than substitution.

Oxidation: primary alcohols → aldehyde → carboxylic acid; secondary → ketone; tertiary alcohols resist mild oxidation.

Esterification is acid-catalysed and reversible; ester and amide hydrolysis can be acid- or base-catalysed (saponification with NaOH).

Infrared spectroscopy: O–H broad 3200–3600 cm⁻¹, C=O sharp 1680–1750 cm⁻¹, C–H 2850–3100 cm⁻¹ identify functional groups.

Mass spectrometry gives the molecular ion M⁺ for molar mass and fragmentation patterns for structure; M+1 peaks indicate carbon count.

¹H NMR: chemical shift identifies environment, integration gives relative H count, and splitting follows the n+1 rule from neighbouring protons.

Chromatography separates by differential affinity for mobile and stationary phases; Rf = distance travelled by solute/distance travelled by solvent front.

Retention time identifies components against standards, and peak area allows quantitative analysis with a calibration curve.

Atomic absorption and emission quantify metal ions using characteristic lines; Beer–Lambert A = εcl links absorbance to concentration.

Flame tests: Li crimson, Na yellow, K lilac, Ca brick-red, Cu blue-green identify metal cations in simple salts.

Qualitative tests: carbonate + acid gives CO2 (limewater milky); sulfate + BaCl2 gives white precipitate; halides + AgNO3 give distinctive precipitates.

Greenhouse gases CO2, CH4, N2O and water vapour absorb infrared radiation, and the enhanced greenhouse effect warms the troposphere.

Acid rain forms from SO2 and NOx oxidised to H2SO4 and HNO3; controls include flue-gas desulfurisation with CaO or CaCO3 and catalytic converters.

Ozone depletion by CFCs: UV light liberates Cl radicals that catalytically destroy O3; the Montreal Protocol phased out CFCs.

Haber–Bosch N2 + 3H2 ⇌ 2NH3 is exothermic; moderate temperature (~450 °C), high pressure (~200 atm) and an iron catalyst balance rate and yield.

Contact process: S → SO2 → SO3 (V2O5 catalyst, ~450 °C) → H2SO4; SO3 is absorbed in concentrated acid, not water.

Materials: addition polymers such as polyethene versus condensation polymers such as polyesters and polyamides; recycling and biodegradability differ.

Life-cycle assessment compares energy, raw materials, emissions and waste across extraction, manufacture, use and disposal.

Catalytic converters convert CO, hydrocarbons and NOx to CO2, H2O and N2 using Pt/Pd/Rh on a support, requiring near-stoichiometric air–fuel mixtures.