Catalonia PAU Chemistry cheat sheet

Quantum numbers: n = 1,2,3… (shell); l = 0…n−1 (s,p,d,f); m_l = −l…+l; m_s = ±½. No two electrons in an atom share all four.

Orbital filling: Aufbau (lowest n+l first; for equal n+l, lower n first), Pauli exclusion, Hund's rule (maximize parallel spins in degenerate orbitals).

Cr = [Ar]3d⁵4s¹ and Cu = [Ar]3d¹⁰4s¹ are exceptions; 4s electrons are removed first when transition metals ionize (e.g. Fe²⁺ = [Ar]3d⁶).

Periodic trends across a period: atomic radius decreases, ionization energy and electronegativity increase, electron affinity becomes more negative; down a group the reverse holds.

Ionization energy anomalies: drops at group 13 (s²p¹ after filled s²) and group 16 (p⁴ after half-filled p³) due to pairing/penetration effects.

Isotopes: same Z, different A; atomic mass = Σ(abundance × isotope mass). Mass defect Δm converts to nuclear binding energy via E = Δmc².

Isoelectronic species: more protons → smaller radius (e.g. Na⁺ < Mg²⁺ < Al³⁺ < F⁻ < O²⁻ < N³⁻).

Photoelectric/quantization: E = hν = hc/λ; Rydberg 1/λ = R(1/n₁² − 1/n₂²) for hydrogen lines.

Formal charge = valence e⁻ − nonbonding e⁻ − ½ bonding e⁻; the Lewis structure with charges closest to zero and negative charge on the more electronegative atom is preferred.

VSEPR electron-domain count (bonding + lone pairs): 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs compress angles (CH₄ 109.5° > NH₃ 107° > H₂O 104.5°).

Hybridization from steric number: 2→sp, 3→sp², 4→sp³, 5→sp³d, 6→sp³d²; π bonds use unhybridized p orbitals.

Polarity: polar bonds plus asymmetric geometry give a net dipole (CO₂ nonpolar, H₂O polar, CCl₄ nonpolar, CHCl₃ polar).

Intermolecular force strength: ion–dipole > hydrogen bond > dipole–dipole > London dispersion (dispersion grows with polarizability/molar mass).

H-bonding requires H bonded to N, O or F; it explains water's high boiling point, high ΔH_vap and ice's lower density.

Solid types: ionic (high mp, conducts molten), covalent network (very high mp, hard), metallic (malleable, conducts), molecular (low mp, soft, nonconducting).

Bond order from MO theory: (bonding e⁻ − antibonding e⁻)/2; O₂ has bond order 2 and is paramagnetic (two unpaired π* electrons).

Ideal gas: PV = nRT (R = 0.0821 L·atm·mol⁻¹·K⁻¹ = 8.314 J·mol⁻¹·K⁻¹); STP = 273.15 K, 1 atm, molar volume 22.4 L.

Dalton's law: P_total = ΣP_i, with P_i = x_i·P_total; Graham's law: rate₁/rate₂ = √(M₂/M₁).

van der Waals: (P + an²/V²)(V − nb) = nRT; a corrects attractive forces, b corrects molecular volume.

Phase diagram: triple point (all three phases), critical point (liquid–gas boundary ends); fusion curve for water slopes negatively (ice less dense than liquid).

Clausius–Clapeyron: ln(P₂/P₁) = −ΔH_vap/R (1/T₂ − 1/T₁); ΔH_sub = ΔH_fus + ΔH_vap.

Solubility: like dissolves like; gases are less soluble at higher T and more soluble at higher partial pressure (Henry's law, S = k_H·P).

Colligative properties depend on particle count: ΔT_b = i·K_b·m, ΔT_f = i·K_f·m, π = i·M·R·T; i = van't Hoff factor (i = 2 for NaCl).

Raoult's law: P_solution = x_solvent·P°_solvent; vapor pressure lowering is proportional to solute mole fraction.

For aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d/([A]^a[B]^b); pure solids and liquids are omitted (activity = 1).

Kp = Kc(RT)^Δn, where Δn = moles gaseous products − moles gaseous reactants.

Reaction quotient Q: Q < K shifts right, Q > K shifts left, Q = K at equilibrium.

Le Chatelier: adding reactant or removing product shifts right; increasing pressure (decreasing V) shifts toward fewer gas moles; heating favors the endothermic direction.

A catalyst lowers E_a and speeds both directions equally - it changes neither K nor the equilibrium position.

K reverses with the reverse reaction (K' = 1/K) and is raised to the power n when coefficients are multiplied by n.

Solubility product: Ksp = [M]^m[X]^x for M_mX_x; molar solubility s gives Ksp = (ms)^m(xs)^x. Precipitation occurs when Q > Ksp.

Common-ion effect: adding an ion already present in the equilibrium decreases solubility; a salt of a weak acid dissolves more in acidic solution.

pH = −log[H₃O⁺], pOH = −log[OH⁻], pH + pOH = 14 at 25 °C; Kw = 1.0×10⁻¹⁴.

Strong acids (HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄) ionize completely; strong bases are group 1 hydroxides and heavy group 2 hydroxides.

Weak acid: Ka = [H₃O⁺][A⁻]/[HA]; for low dissociation, [H₃O⁺] ≈ √(Ka·C₀); percent ionization = [H₃O⁺]/C₀ × 100.

Henderson–Hasselbalch: pH = pKa + log([base]/[acid]); a buffer works best when pH ≈ pKa (ratio within 0.1–10).

Titration: strong acid–strong base equivalence pH = 7; weak acid–strong base equivalence pH > 7; weak base–strong acid equivalence pH < 7.

Salt hydrolysis: cation of weak base or anion of weak acid hydrolyzes (e.g. NH₄Cl acidic, CH₃COONa basic, NaCl neutral).

Ka·Kb = Kw for a conjugate pair; stronger acid → weaker conjugate base (HCl strong, Cl⁻ negligible base).

Buffer capacity depends on absolute concentrations of the pair; adding strong acid converts base to acid, shifting the ratio but pH only slightly.

Oxidation = loss of electrons (anode); reduction = gain of electrons (cathode); oxidation numbers track electron transfer.

Balance redox in acid: separate half-reactions, balance atoms, then O with H₂O, H with H⁺, charge with e⁻; in base add OH⁻ to neutralize H⁺.

Standard cell potential: E°cell = E°cathode − E°anode; positive E°cell means spontaneous reaction; ΔG° = −nFE°cell (F = 96485 C/mol).

Galvanic cell: anode negative, cathode positive; electron flow anode → cathode through the wire, cations migrate to the cathode in the salt bridge.

Nernst equation: E = E° − (0.0592/n)·log Q at 25 °C; at equilibrium E = 0 and log K = nE°/0.0592.

Electrolysis: moles of product from charge Q = I·t and Faraday's law (n·F coulombs per mole of electrons).

Species oxidized/reduced: the stronger oxidizing agent has the higher (more positive) reduction potential; a species can disproportionate if its potential lies between the two product couples.

Corrosion of iron is an electrochemical process; sacrificial anodes (Zn, Mg) protect steel because they are more easily oxidized.

Rate = −(1/a)d[A]/dt = (1/c)d[C]/dt; average vs instantaneous rate differ as concentration changes.

Rate law rate = k[A]^m[B]^n; m and n are determined experimentally, not from stoichiometry.

Integrated laws: zero order [A] = [A]₀ − kt; first order ln[A] = ln[A]₀ − kt (t½ = 0.693/k); second order 1/[A] = 1/[A]₀ + kt.

Arrhenius: k = A·e^(−Ea/RT); ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁); a plot of ln k vs 1/T has slope −Ea/R.

Collision theory: rate depends on collision frequency, orientation and fraction of molecules with E ≥ Ea; catalysts lower Ea, raising k.

Mechanism: the slow (rate-determining) step controls the rate; intermediates appear in steps but not in the overall equation.

Molecularity: elementary steps are unimolecular, bimolecular or termolecular; the rate law of an elementary step follows its stoichiometry.

Half-life of a first-order reaction is constant; for second order t½ = 1/(k[A]₀), so it lengthens as concentration falls.

ΔH = q_p at constant pressure; q = mcΔT; sign convention: exothermic ΔH < 0, endothermic ΔH > 0.

Hess's law: ΔH is path-independent; combine reactions by reversing (change sign) and scaling (multiply ΔH).

Standard enthalpy of formation: ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants); ΔH°f of an element in its standard state = 0.

Bond energy: ΔH ≈ Σ(bonds broken) − Σ(bonds formed); bond breaking is endothermic, bond making exothermic.

Entropy: ΔS = q_rev/T; ΔS > 0 for gas formation, increased moles of gas, and greater disorder; ΔS_universe ≥ 0 for spontaneity.

Gibbs energy: ΔG = ΔH − TΔS; ΔG < 0 spontaneous, ΔG = 0 at equilibrium; ΔG° = −RT ln K.

Temperature switch: if ΔH > 0 and ΔS > 0, reaction is spontaneous only above T = ΔH/ΔS (reverse if both negative).

Calorimetry: bomb calorimeter gives ΔU (constant V); q_solution = −q_reaction for coffee-cup measurements at constant pressure.

Functional group priority for naming: carboxylic acid > ester > amide > nitrile > aldehyde > ketone > alcohol > amine > alkene > alkyne > ether/halide.

Isomerism: chain, position and functional-group isomers (structural); cis–trans and optical isomers (chiral carbon with four different groups) are stereoisomers.

Alkanes undergo free-radical substitution (initiation, propagation, termination); alkenes undergo electrophilic addition (Markovnikov's rule) and addition polymerization.

Aromatic substitution is electrophilic; substituents direct ortho/para if electron-donating (OH, NH₂, alkyl) and meta if electron-withdrawing (NO₂, COOH, SO₃H).

Alcohols: oxidation to aldehyde then carboxylic acid (primary), to ketone (secondary); tertiary alcohols resist oxidation. Esterification is acid-catalyzed with water loss.

Nucleophilic substitution: SN1 (tertiary, carbocation intermediate, racemization) vs SN2 (primary, backside attack, inversion).

Carbonyl reactivity: aldehydes oxidize (Tollens, Fehling); ketones resist; nucleophilic addition of HCN or Grignard reagents extends the carbon chain.

Polymers: addition (polyethylene, polystyrene) vs condensation (polyester, polyamide, nylon); biomolecules: amino acids → proteins via peptide bonds, sugars → polysaccharides via glycosidic bonds.