CAPE Chemistry Unit 1 cheat sheet

Mole concept: n = m/M; for gases at STP (273 K, 1.01×10^5 Pa), 1 mol occupies 22.4 dm³; at RTP (298 K, 1 atm) it occupies 24.0 dm³.

Avogadro constant N_A = 6.02×10^23 mol⁻¹; number of particles = n × N_A; molar concentration c = n/V with V in dm³.

Empirical formula from percentage composition: divide each % by atomic mass, then divide by the smallest ratio; molecular formula = (empirical formula) × n where n = M_r/mass of empirical formula.

Balanced equations conserve atoms and charge; limiting reagent is found by dividing moles of each reactant by its stoichiometric coefficient - the smallest quotient limits.

Percentage yield = (actual/theoretical) × 100; atom economy = (M_r of desired product / total M_r of all reactants) × 100.

Ideal gas equation pV = nRT with R = 8.31 J K⁻¹ mol⁻¹; convert °C to K by adding 273; p in Pa, V in m³.

Relative atomic mass A_r is the weighted mean of isotope masses on the ¹²C = 12 scale; relative molecular mass M_r is the sum of A_r values in the formula.

Titration calculation route: c₁V₁/n₁ = c₂V₂/n₂ for a balanced equation with stoichiometric coefficients n₁ and n₂.

Atomic number Z = protons; mass number A = protons + neutrons; isotopes have the same Z but different A, and identical chemical properties but different physical properties.

Electron configuration follows the Aufbau principle and Hund's rule: 1s²2s²2p⁶3s²3p⁶4s¹ for K, with 4s filling before 3d because 4s is lower in energy for K and Ca.

First ionisation energy decreases down a group (increasing shielding and atomic radius) and generally increases across a period (greater effective nuclear charge, smaller radius).

Successive ionisation energies show large jumps when a new shell is breached - evidence for shell structure.

Ionic bonding: transfer of electrons from low-ionisation-energy metal to high-electron-affinity non-metal; lattice energy increases with higher ionic charge and smaller ionic radius.

Covalent bonding: shared electron pairs; bond order and bond length relate inversely; multiple bonds are shorter and stronger than single bonds.

Electronegativity difference > 1.8 generally indicates ionic character; 0.4–1.8 polar covalent; < 0.4 nonpolar covalent.

Intermolecular forces ranked by strength: London dispersion < dipole–dipole < hydrogen bonding; hydrogen bonds require H bonded to N, O or F.

Groups are vertical columns with the same valence electron count; periods are horizontal rows with the same number of occupied shells.

Group I (alkali metals) reactivity increases down the group: ionisation energy falls and the metal loses its single valence electron more readily.

Group VII (halogens) oxidising power decreases down the group; displacement reactions show a halogen higher in the group oxidising a halide lower down.

Group 0 (noble gases) have full outer shells, very high ionisation energies and negligible reactivity; boiling points rise down the group with increasing electron count and dispersion forces.

Across Period 3, atomic radius decreases, ionisation energy rises and metallic character falls; oxides change from basic (Na, Mg) through amphoteric (Al) to acidic (P, S, Cl).

Period 3 chlorides hydrolyse: NaCl dissolves without hydrolysis; MgCl₂ and AlCl₃ hydrolyse partially; SiCl₄ and PCl₅ hydrolyse fully giving acidic solutions.

Transition metals show variable oxidation states, form coloured complex ions, act as catalysts and have partly filled d subshells in at least one common ion.

Diagonal relationships (e.g. Li–Mg, Be–Al) arise from similar charge/radius ratios giving similar polarising power and chemistry.

Enthalpy change ΔH is heat exchanged at constant pressure; exothermic reactions have ΔH negative, endothermic reactions have ΔH positive.

Standard conditions: 298 K, 100 kPa (1 bar), all substances in standard states; standard enthalpy of formation of an element in its standard state is zero.

Calorimetry: q = mcΔT; for a solution reaction with density and specific heat capacity of water, c = 4.18 J g⁻¹ K⁻¹; ΔH = −q/n (per mole).

Hess's law: the total enthalpy change of a reaction is independent of route; construct cycles using formation or combustion enthalpies.

ΔH_reaction = ΣΔH_f(products) − ΣΔH_f(reactants); alternatively ΔH = ΣΔH_c(reactants) − ΣΔH_c(products).

Bond enthalpy route: ΔH = Σ(bonds broken) − Σ(bonds formed); mean bond enthalpies give approximate results because they are averaged over compounds.

Enthalpy of atomisation, ionisation energy, electron affinity and lattice enthalpy combine in Born–Haber cycles for ionic solids.

Entropy S increases with temperature and with number of gas moles; ΔG = ΔH − TΔS determines spontaneity: negative ΔG means feasible.

Rate of reaction = change in concentration of a reactant or product per unit time; units mol dm⁻³ s⁻¹.

Rate increases with concentration, temperature, surface area and catalysts; a catalyst lowers activation energy by providing an alternative pathway.

Temperature increase raises rate mainly by increasing the fraction of molecules with energy ≥ E_a (Maxwell–Boltzmann distribution); roughly a 10 K rise doubles rate.

Rate equation: rate = k[A]^m[B]^n; m and n are orders determined experimentally, not from the stoichiometric equation.

Order determination: zero order - concentration has no effect; first order - constant half-life; second order - plot of 1/[A] against t is linear.

Collision theory requires correct orientation and energy ≥ activation energy for a successful reaction.

Le Chatelier's principle: a system at equilibrium shifts to oppose a change in concentration, pressure or temperature; catalysts do not shift the position of equilibrium.

Equilibrium constant K_c = [products]^coefficients/[reactants]^coefficients; K depends only on temperature; large K means equilibrium lies to the right.

Brønsted–Lowry: an acid is a proton donor, a base a proton acceptor; conjugate pairs differ by one H⁺.

pH = −log₁₀[H⁺]; [H⁺] = 10^(−pH); for strong monoprotic acids [H⁺] equals the acid concentration.

K_w = [H⁺][OH⁻] = 1.0×10⁻¹⁴ at 298 K; pH + pOH = 14 in aqueous solution at 298 K.

For a weak acid, K_a = [H⁺]²/[HA] approximately, so [H⁺] = √(K_a × [HA]); pK_a = −log₁₀K_a.

Buffer solutions resist pH change; Henderson–Hasselbalch: pH = pK_a + log([salt]/[acid]).

Titration curves: strong acid–strong base equivalence pH ≈ 7; weak acid–strong base equivalence pH > 7; indicator choice must match the steep region.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons (decrease in oxidation number); OIL RIG.

Standard electrode potential E° is measured against the hydrogen electrode (E° = 0.00 V); E°_cell = E°_cathode − E°_anode; positive E°_cell means the reaction is feasible.

Oxidising agents (e.g. KMnO₄, K₂Cr₂O₇) are reduced; reducing agents are oxidised; balance redox equations by the half-equation method, balancing atoms, then O with H₂O, then H with H⁺, then charge with electrons.