PAU Chemistry (Cantabria) cheat sheet

Rydberg/Bohr: 1/λ = R(1/n₁² − 1/n₂²), R = 1.097×10⁷ m⁻¹; ΔE = hν = −2.18×10⁻¹⁸ Z²(1/n₂² − 1/n₁²) J per electron (H, Z=1).

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

Aufbau + Madelung: fill by increasing (n+l); for equal (n+l), lower n first (4s before 3d, 5s before 4d, 6s before 4f).

Exceptions to memorize: Cr [Ar]3d⁵4s¹, Cu [Ar]3d¹⁰4s¹; cations lose ns electrons first (Fe²⁺ = [Ar]3d⁶, not 3d⁴4s²).

Periodic trends across a period (left→right): Z_eff rises, atomic radius falls, ionization energy and electronegativity rise, metallic character falls.

Down a group: n increases, radius increases, ionization energy decreases, metallic character increases; electron affinity is irregular (F < Cl).

Anomalies: IE(Be) > IE(B) and IE(N) > IE(O) due to filled 2s² or half-filled 2p³ stability.

Hund's rule: maximize unpaired electrons with parallel spins in degenerate orbitals; paramagnetic = unpaired electrons, diamagnetic = all paired.

Lewis structures: count valence e⁻, form octets; formal charge = (valence e⁻) − (nonbonding e⁻) − ½(bonding e⁻); minimize formal charges.

VSEPR geometry from steric number (bonding pairs + lone pairs): 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral.

Lone-pair repulsion order: LP–LP > LP–BP > BP–BP; H₂O bond angle ≈104.5°, NH₃ ≈107°, CH₄ 109.5°.

Hybridization: sp (linear, 180°), sp² (trigonal planar, 120°), sp³ (tetrahedral, 109.5°); count σ bonds + lone pairs on the central atom.

Polarity: polar bonds plus an asymmetric geometry give a polar molecule (CO₂ nonpolar, H₂O polar); dipole moment is a vector sum.

Intermolecular forces in increasing strength: London dispersion < dipole–dipole < hydrogen bond << ionic/covalent. H-bonds need H attached to N, O, or F.

Properties: stronger intermolecular forces raise boiling point and surface tension; hydrogen bonding in H₂O, HF, NH₃ gives anomalously high boiling points.

Lattice energy (Born–Haber): increases with higher ionic charge and smaller ionic radius; compare via Kapustinskii-style q₁q₂/r reasoning.

First law: ΔU = q + w; at constant pressure q_p = ΔH, and ΔH = ΔU + ΔnRT with Δn = moles of gaseous products − reactants.

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

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

Bond enthalpies: ΔH°rxn = Σ(bonds broken) − Σ(bonds formed); values are averages, so results are approximate.

Entropy: ΔS°rxn = ΣνS°(products) − ΣνS°(reactants); ΔS > 0 when gas moles increase, solid dissolves, or temperature rises.

Gibbs: ΔG = ΔH − TΔS. Spontaneous when ΔG < 0; equilibrium when ΔG = 0; T = ΔH/ΔS is the crossover temperature.

Sign cases: ΔH<0,ΔS>0 always spontaneous; ΔH>0,ΔS<0 never; ΔH<0,ΔS<0 spontaneous at low T; ΔH>0,ΔS>0 spontaneous at high T.

ΔG° = −RT ln K, so K > 1 ⇔ ΔG° < 0; also ΔG = ΔG° + RT ln Q for nonstandard conditions.

Rate = −(1/a)d[A]/dt = (1/b)d[B]/dt; average vs instantaneous rate from a concentration–time graph (slope of tangent).

Rate law v = k[A]ᵐ[B]ⁿ; orders determined experimentally, not from stoichiometry; overall order = m + n.

Zero order: [A] = [A]₀ − kt; first order: ln[A] = ln[A]₀ − kt, t½ = ln2/k; second order: 1/[A] = 1/[A]₀ + kt.

Arrhenius: k = A·e^(−Ea/RT); ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂); catalysts lower Ea without changing ΔH or K.

Factors affecting rate: concentration, temperature, surface area, catalyst, and nature of reactants; temperature raises k, not just collision frequency.

Kc = Π[products]^coeff / Π[reactants]^coeff for gases in solution; Kp = Kc(RT)^Δn with Δn = gas moles products − reactants.

Le Chatelier: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; raising T shifts toward the endothermic direction; catalysts do not shift K.

For an exothermic reaction, increasing T decreases K; for endothermic, increases K. Q vs K: Q < K shifts right, Q > K shifts left.

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

Strong acids/bases dissociate completely: pH from initial concentration (e.g., 0.01 M HCl → pH 2; 0.01 M NaOH → pH 12).

Weak acid: Ka = [H₃O⁺][A⁻]/[HA]; [H₃O⁺] ≈ √(Ka·C₀) if C₀/Ka > 100; degree of dissociation α = [H₃O⁺]/C₀.

pKa + pKb = 14 for a conjugate pair; stronger acid ⇔ weaker conjugate base (HClO₄ > HCl > CH₃COOH > H₂CO₃).

Buffer (Henderson–Hasselbalch): pH = pKa + log([base]/[acid]); maximum buffer capacity when pH = pKa.

Salt hydrolysis: salt of strong acid + weak base → acidic; weak acid + strong base → basic; strong + strong → neutral; weak + weak depends on Ka vs Kb.

Titration of weak acid with strong base: initial pH from Ka, half-equivalence pH = pKa, equivalence pH > 7 (basic conjugate base).

Titration of strong acid with strong base: equivalence pH = 7; indicator chosen so pKa_indicator ≈ pH at equivalence.

For MₐX_b(s) ⇌ aMᵇ⁺ + bXᵃ⁻, Ksp = [Mᵇ⁺]ᵃ[Xᵃ⁻]ᵇ; pure solid does not appear in the expression.

Solubility s relates to Ksp: for MX, Ksp = s²; MX₂ or M₂X, Ksp = 4s³; M₂X₃, Ksp = 108s⁵.

Common-ion effect: adding an ion common to the salt decreases solubility; solubility in pure water > solubility in a common-ion solution.

Q (ion product) vs Ksp: Q < Ksp unsaturated (no precipitate), Q = Ksp saturated, Q > Ksp supersaturated → precipitation.

pH dependence: salts of basic anions (CO₃²⁻, PO₄³⁻, OH⁻, S²⁻) dissolve more in acid; salts of acidic cations dissolve more in base.

Ksp is temperature-dependent only; adding water dilutes but does not change Ksp.

Selective precipitation: the salt whose Q first exceeds its Ksp precipitates first when ions are added gradually.

Complex formation (e.g., Ag⁺ + 2NH₃ → [Ag(NH₃)₂]⁺) increases solubility by consuming the free cation.

Oxidation = loss of electrons (oxidation number increases); reduction = gain of electrons; the oxidizing agent is reduced.

Oxidation number rules: O = −2 (except peroxides −1, OF₂ +2); H = +1 (except hydrides −1); sum equals the ion/compound charge.

Balance in acidic medium with H⁺/H₂O; in basic medium add OH⁻ to neutralize H⁺; equalize electrons between half-reactions.

Standard cell: E°cell = E°cathode − E°anode; spontaneous when E°cell > 0 and ΔG° = −nFE° < 0.

Nernst: E = E° − (0.0592/n)log Q at 25 °C; for a concentration cell E° = 0 and E depends on the ion ratio.

E°cell = (0.0592/n)log K at 25 °C, linking cell potential to the equilibrium constant.

Electrolysis: moles of product from Q = It and Faraday's law m = (M·I·t)/(n·F), F = 96485 C/mol.

Electrode conventions: oxidation at the anode, reduction at the cathode in both galvanic cells and electrolytic cells; signs differ between the two.

Homologous series suffixes: -ane (alkane), -ene/-yne (alkene/alkyne), -ol (alcohol), -al (aldehyde), -one (ketone), -oic acid (carboxylic acid), -amine.

IUPAC priority: carboxylic acid > ester > amide > nitrile > aldehyde > ketone > alcohol > amine > alkene/alkyne > alkane; number to give the lowest locants.

Isomerism: structural (chain, position, functional group) vs stereoisomerism (geometric cis/trans, optical with a chiral carbon bearing four different groups).

Alkane halogenation: free-radical substitution (initiation/UV, propagation, termination); alkene addition is electrophilic (H₂, HX, X₂, H₂O/H⁺).

Markovnikov: in HX addition to an alkene, H adds to the carbon with more H; anti-Markovnikov occurs with HBr/peroxides (radical mechanism).

Aromatic electrophilic substitution: nitration (HNO₃/H₂SO₄), halogenation (X₂/FeX₃), Friedel–Crafts alkylation (RX/AlCl₃).

Alcohols: oxidation of primary → aldehyde → carboxylic acid, secondary → ketone, tertiary resists; dehydration with H₂SO₄ gives alkenes.

Polymers: addition polymerization of alkenes (polyethylene from ethene) vs condensation polymerization with loss of small molecules (nylon, PET, polyester).