LC Chemistry cheat sheet

Atomic number Z = number of protons; mass number A = protons + neutrons; isotopes differ only in neutron count.

Electron configuration follows Aufbau order 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p; 4s fills before 3d because its energy is lower.

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

Energy of a photon is E = hf = hc/λ, with h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.

Atomic radius decreases across a period (increasing effective nuclear charge) and increases down a group (extra shells).

First ionisation energy increases across a period and decreases down a group; exceptions occur at filled or half-filled subshells, e.g. Mg > Al and N > O.

Electronegativity rises across a period and falls down a group; the most electronegative element is fluorine.

The ideal gas equation is pV = nRT, with R = 8.314 J K⁻¹ mol⁻¹; temperature must be in kelvin.

Percent abundance of an isotope = (number of atoms of that isotope ÷ total atoms) × 100; relative atomic mass is the abundance-weighted average of isotope masses.

Ionic bonding: electron transfer from a metal to a non-metal, giving a lattice held by electrostatic attraction; lattice energy increases with higher charges and smaller ion radii.

Covalent bonding: shared electron pairs; a single bond is one sigma bond, a double bond is one sigma plus one pi bond, a triple bond is one sigma plus two pi bonds.

Bond polarity depends on electronegativity difference; a difference greater than about 1.7 usually gives predominantly ionic character.

VSEPR shapes: 2 electron domains linear (180°), 3 trigonal planar (120°), 4 tetrahedral (109.5°), 5 trigonal bipyramidal, 6 octahedral (90°).

Lone pairs repel more strongly than bonding pairs, compressing bond angles: CH₄ 109.5° > NH₃ 107° > H₂O 104.5°.

Polar bonds do not guarantee a polar molecule; symmetric geometries such as CO₂ (linear) and CCl₄ (tetrahedral) are non-polar overall.

Intermolecular forces in increasing strength: London dispersion < dipole–dipole < hydrogen bonding; hydrogen bonds occur with H bonded to N, O or F.

Sigma bonds form by end-on orbital overlap and are stronger than side-on pi bonds; pi bonds restrict rotation.

A coordinate (dative) bond forms when one atom donates both electrons of the shared pair, as in the ammonium ion.

Amount of substance: n = m ÷ M, where m is mass in grams and M is molar mass in g mol⁻¹.

Avogadro constant N_A = 6.02 × 10²³ mol⁻¹; number of particles = n × N_A.

Moles of gas at STP (273 K, 1 × 10⁵ Pa): n = V ÷ 22.7 dm³ mol⁻¹; at s.t.p. (273 K, 101.3 kPa) the molar volume is 22.4 dm³ mol⁻¹.

A balanced equation gives mole ratios; convert masses or volumes to moles, apply the ratio, then convert back.

Limiting reagent: divide moles of each reactant by its stoichiometric coefficient; the smallest quotient is limiting.

Percentage yield = (actual yield ÷ theoretical yield) × 100; percentage atom economy = (mass of desired product ÷ total mass of reactants) × 100.

Empirical formula from percentage composition: divide each percentage by the atomic mass, then divide by the smallest value to get the simplest ratio.

Molecular formula = empirical formula × n, where n = molar mass ÷ empirical formula mass.

Water of crystallisation is found by heating to constant mass and using the mass loss as moles of water.

Balance equations by changing coefficients only, never subscripts; conserve atoms of each element and total charge.

Combustion of a hydrocarbon CₓHᵧ: CₓHᵧ + (x + y/4) O₂ → x CO₂ + (y/2) H₂O.

Acid + base → salt + water; acid + carbonate → salt + water + CO₂; acid + metal → salt + hydrogen.

State symbols (s), (l), (g), (aq) are required in full ionic equations; spectator ions are cancelled.

Solubility rules: all nitrates and sodium, potassium and ammonium salts are soluble; most chlorides are soluble except AgCl and PbCl₂; most sulfates are soluble except BaSO₄, PbSO₄ and CaSO₄.

Oxidation is loss of electrons and increase in oxidation number; reduction is gain of electrons and decrease in oxidation number.

Oxidation numbers: elements are 0; oxygen is usually −2 (peroxides −1); hydrogen is +1 with non-metals and −1 with metals; sum equals the overall charge.

Precipitation: two soluble salts react to give an insoluble product, e.g. Ag⁺(aq) + Cl⁻(aq) → AgCl(s).

Moles of solute: n = c × V, with c in mol dm⁻³ and V in dm³ (cm³ ÷ 1000).

Titration calculation: c_a × V_a ÷ a = c_b × V_b ÷ b, where a and b are the stoichiometric coefficients in the balanced equation.

Brønsted–Lowry: an acid is a proton donor and a base is a proton acceptor; a conjugate pair differs by one H⁺.

Strong acids (HCl, HNO₃, H₂SO₄) dissociate completely; weak acids (CH₃COOH) dissociate partially and have K_a expressions.

pH = −log₁₀[H⁺]; [H⁺] = 10^(−pH); at 25 °C pH + pOH = 14 and K_w = 1 × 10⁻¹⁴.

For a weak acid, K_a = [H⁺]² ÷ [HA] when dissociation is small, so pH ≈ ½(pK_a − log c).

At the equivalence point of a strong acid–strong base titration the pH is 7; for a weak acid titrated with a strong base it is above 7.

An indicator changes colour when pH ≈ pK_a; phenolphthalein (8.3–10.0) suits strong base titrations, methyl orange (3.1–4.4) suits strong acid titrations.

A buffer resists pH change on adding small amounts of acid or base; it consists of a weak acid and its conjugate base, with pH = pK_a + log([A⁻] ÷ [HA]).

Ideal gas equation: pV = nRT; use p in Pa, V in m³, T in K and R = 8.314 J K⁻¹ mol⁻¹.

Boyle's law: p₁V₁ = p₂V₂ at constant temperature.

Charles's law: V₁ ÷ T₁ = V₂ ÷ T₂ at constant pressure; temperature must be in kelvin.

Combined gas law: p₁V₁ ÷ T₁ = p₂V₂ ÷ T₂.

Dalton's law of partial pressures: total pressure equals the sum of partial pressures; partial pressure = mole fraction × total pressure.

Absolute temperature T(K) = θ(°C) + 273.

At the same temperature and pressure, equal volumes of gases contain equal numbers of molecules (Avogadro's law).

Graham's law: the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

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

Concentration: molarity = moles of solute ÷ volume of solution in dm³; molality = moles of solute ÷ mass of solvent in kg.

Dilution: c₁V₁ = c₂V₂, because the number of moles of solute is unchanged.

Mass percentage = (mass of solute ÷ mass of solution) × 100; ppm = (mass of solute ÷ mass of solution) × 10⁶.

Solubility of most solids increases with temperature; solubility of gases in liquids decreases as temperature rises and increases with pressure (Henry's law).

Raoult's law: vapour pressure of a solution equals the sum of the partial vapour pressures of its components; a non-volatile solute lowers vapour pressure.

Boiling point elevation ΔT_b = K_b × m and freezing point depression ΔT_f = K_f × m, where m is the molality of all dissolved particles.

Osmotic pressure π = iMRT, where i is the van 't Hoff factor (number of ions per formula unit).

Colligative properties depend on the number of dissolved particles, not their identity: 0.1 mol dm⁻³ NaCl gives about twice the effect of 0.1 mol dm⁻³ glucose.

A saturated solution is in dynamic equilibrium with undissolved solute; solubility product K_sp for a sparingly soluble salt is the product of ion concentrations.

Enthalpy change q = mcΔT, where c is the specific heat capacity (water 4.18 J g⁻¹ K⁻¹).

ΔH is negative for exothermic reactions and positive for endothermic reactions; bond breaking absorbs energy and bond formation releases it.

Hess's law: the enthalpy change of a reaction is independent of the route taken, so ΔH values can be summed over steps.

Standard enthalpy of formation ΔH_f° is the enthalpy change when one mole of a compound forms from its elements in standard states; ΔH_r° = ΣΔH_f°(products) − ΣΔH_f°(reactants).

Mean bond enthalpy method: ΔH = Σ(bonds broken) − Σ(bonds formed); results are approximate because average bond enthalpies are used.

Average rate = change in concentration ÷ change in time; units mol dm⁻³ s⁻¹.

Rate increases with concentration, temperature, surface area and catalysts; a catalyst lowers activation energy without changing ΔH.

Collision theory: only collisions with energy ≥ activation energy and correct orientation lead to reaction; the Maxwell–Boltzmann distribution shifts to higher energies as temperature rises.

Rate equation rate = k[A]^m[B]^n; order is determined experimentally, not from the stoichiometric coefficients.

Dynamic equilibrium: forward and reverse rates are equal and concentrations remain constant, but both reactions continue.

Equilibrium constant K_c = [C]^c[D]^d ÷ [A]^a[B]^b for aA + bB ⇌ cC + dD; pure solids and liquids are omitted.

Le Chatelier's principle: a system at equilibrium shifts to oppose a change in concentration, pressure, volume or temperature.

Increasing pressure (decreasing volume) shifts equilibrium toward the side with fewer moles of gas.

Increasing temperature shifts equilibrium in the endothermic direction; K changes with temperature only.

A catalyst speeds attainment of equilibrium but does not change the position of equilibrium or the value of K.

Reaction quotient Q compared with K: Q < K the reaction proceeds forward, Q > K it proceeds in reverse, Q = K the system is at equilibrium.

For gases, K_p uses partial pressures; K_p = K_c(RT)^Δn, where Δn is the change in moles of gas.

The Haber process (N₂ + 3H₂ ⇌ 2NH₃, exothermic) is favoured by high pressure and moderate temperature with an iron catalyst.

Homologous series members share a general formula and similar chemical properties, differing by CH₂ units.

General formulas: alkanes CₙH₂ₙ₊₂, alkenes CₙH₂ₙ, alkynes CₙH₂ₙ₋₂, alcohols CₙH₂ₙ₊₁OH, carboxylic acids CₙH₂ₙ₊₁COOH.

IUPAC naming: longest carbon chain, lowest locants to substituents, suffix for the principal functional group.

Structural isomers have the same molecular formula but different connectivity; alkenes also show cis–trans (E/Z) isomerism.

Alkanes undergo free-radical substitution with halogens under UV light: initiation, propagation, termination.

Alkenes undergo electrophilic addition with H₂, HBr, Br₂ and water; bromine water is decolourised, a test for unsaturation.

Primary alcohols are oxidised to aldehydes then carboxylic acids; secondary alcohols to ketones; tertiary alcohols resist oxidation.

Carboxylic acids react with alcohols in esterification, catalysed by concentrated sulfuric acid, giving an ester and water.

Addition polymerisation of alkenes gives saturated chains; condensation polymerisation (e.g. nylon, polyester) releases a small molecule such as water or HCl.

Oxidation occurs at the anode and reduction at the cathode; in a galvanic cell the anode is negative and the cathode positive.

Cell potential E°_cell = E°_cathode − E°_anode using standard reduction potentials; a positive value indicates a spontaneous reaction.

Electron flow in the external circuit is from anode to cathode; conventional current flows in the opposite direction.

In electrolysis the cathode attracts cations and the anode attracts anions; the more easily reduced or oxidised species reacts preferentially.

Quantity of charge Q = I × t in coulombs, and moles of electrons = Q ÷ F, where F = 96 500 C mol⁻¹.

Mass deposited at an electrode: m = (M × I × t) ÷ (n × F), where n is the number of electrons per ion.

In a galvanic cell the salt bridge completes the circuit and maintains electrical neutrality by allowing ion migration.

Standard conditions for E° values: 298 K, 1 mol dm⁻³ solutions and 100 kPa gas pressure.

Disproportionation is simultaneous oxidation and reduction of the same element, e.g. chlorine in cold dilute alkali.

Burette readings are taken to the bottom of the meniscus and recorded to ±0.05 cm³; the burette is rinsed with the titrant.

A conical flask is rinsed with distilled water only; rinsing with the solution being titrated would add extra moles and give a high result.

A pipette is rinsed with the solution it will deliver; a white tile under the flask helps detect the endpoint colour change.

Titres are repeated until concordant results agree to within 0.10 cm³, and the mean excludes the rough titre.

Filtration separates an insoluble solid from a liquid; recrystallisation purifies a solid using a hot saturated solution cooled slowly.

Distillation separates liquids by boiling point; fractional distillation is used when boiling points are close.

A desiccator or heating to constant mass removes water of crystallisation; weighing by difference reduces transfer error.

Flame tests: lithium crimson, sodium yellow, potassium lilac, calcium brick-red, copper blue-green.

Tests: CO₂ turns limewater milky; H₂ gives a squeaky pop; O₂ relights a glowing splint; Cl₂ bleaches damp litmus paper; water turns anhydrous copper(II) sulfate blue.