Castilla y León PAU Chemistry cheat sheet

Bohr model: E_n = -13.6 Z²/n² eV for hydrogen-like atoms; photon energy of a transition is |E_final − E_initial| = hν = hc/λ.

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

Orbital filling: Aufbau order 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p; (n+l) rule, lower n first when sums tie.

Cr = [Ar]3d⁵4s¹ and Cu = [Ar]3d¹⁰4s¹ are exceptions because half-filled and filled d subshells are more stable.

Cations lose the highest-n electrons first: Fe²⁺ = [Ar]3d⁶, not 4s²3d⁴.

Periodic trends across a period: atomic radius decreases, ionization energy and electronegativity increase, metallic character decreases.

Down a group: radius increases (added shells), ionization energy decreases, electronegativity decreases, metallic character increases.

Anomalies: IE drops at group 13 (np electron shielded by ns²) and at group 16 (np⁴ pairing repulsion); F has lower electron affinity than Cl.

Lewis structures: total valence electrons, octet rule (duet for H), formal charge = valence e⁻ − nonbonding e⁻ − ½ bonding e⁻; minimize formal charges.

VSEPR electron-pair geometries by steric number: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs compress angles.

Hybridization from steric number: 2 → sp, 3 → sp², 4 → sp³; a lone pair on the central atom still occupies a hybrid orbital (H₂O is sp³, bent).

Molecular polarity: polar bonds plus asymmetric geometry give a net dipole; CO₂ (linear) is nonpolar, H₂O (bent) is polar.

Intermolecular forces in increasing strength: London dispersion < dipole–dipole < hydrogen bond (N–H, O–H, F–H) < ion–dipole.

Hydrogen bonding raises boiling points: H₂O 100 °C vs H₂S −60 °C; HF 20 °C vs HCl −85 °C.

Ionic solids: high melting points, conduct only when molten or dissolved; molecular solids: low melting points, generally non-conducting.

Metallic bonding: delocalized electron sea explains conductivity, malleability, and ductility.

First law: ΔU = q + w; for work against constant external pressure w = −PΔV, so at constant P, q_p = ΔH = ΔU + Δ(PV).

Hess's law: ΔH of a reaction is path-independent; reverse a step to change the sign of its ΔH, multiply a step to scale its ΔH.

Standard enthalpy of formation ΔH_f° of an element in its standard state is zero; ΔH_r° = ΣνΔH_f°(products) − ΣνΔH_f°(reactants).

Bond enthalpy estimate: ΔH_r° = Σ(bonds broken) − Σ(bonds formed); always positive for bond breaking.

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

Gibbs free energy: ΔG = ΔH − TΔS; spontaneous when ΔG < 0, at equilibrium ΔG = 0.

Sign rules: ΔH<0, ΔS>0 always spontaneous; ΔH>0, ΔS<0 never; mixed signs depend on T = ΔH/ΔS.

ΔG° = −RT ln K, so ΔG°<0 means K>1; ΔG° = −nFE°cell for electrochemical cells.

Rate = −(1/a)d[A]/dt = (1/b)d[B]/dt; average rate uses finite concentration changes, instantaneous rate uses the tangent at t.

Rate law is determined experimentally: rate = k[A]^m[B]^n; orders are not taken from stoichiometric coefficients.

Integrated forms: 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, t½ = 1/(k[A]₀).

Arrhenius: k = A·e^(−Ea/RT); ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂), so higher Ea means stronger temperature dependence.

Collision theory: rate rises with concentration, temperature, and surface area; a catalyst lowers Ea without changing ΔH or K.

Equilibrium constant: for aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d/([A]^a[B]^b); Kp = Kc(RT)^Δn with Δn = gas product moles − gas reactant moles.

Le Chatelier: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; heating shifts in the endothermic direction; a catalyst changes neither K nor position.

Reaction quotient Q: Q < K shifts right, Q > K shifts left, Q = K at equilibrium; K depends only on temperature.

Brønsted–Lowry: acid donates a proton, base accepts one; conjugate pairs differ by one H⁺ (NH₄⁺/NH₃, HCO₃⁻/CO₃²⁻).

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; pH of 0.01 M HCl = 2.

Weak acid: Ka = [H₃O⁺][A⁻]/[HA]; for a monoprotic acid [H₃O⁺] ≈ √(Ka·C₀); pKa = −log Ka.

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

Salt hydrolysis: salt of strong acid + weak base is acidic (NH₄Cl); strong base + weak acid is basic (CH₃COONa); strong–strong is neutral.

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

Ka·Kb = Kw for a conjugate pair; a stronger acid has a weaker conjugate base.

For MₐX_b(s) ⇌ aM^(b+) + bX^(a−), Ksp = [M]^a[X]^b; solid concentration is excluded.

Molar solubility s from Ksp: for AB, s = √Ksp; for AB₂, Ksp = 4s³; for AB₃, Ksp = 27s⁴.

Common-ion effect: adding a shared ion lowers solubility; recompute s from Ksp with the common ion treated as a constant.

Compare Qsp with Ksp: Qsp < Ksp unsaturated (no precipitate); Qsp = Ksp saturated; Qsp > Ksp supersaturated, precipitate forms.

Selective precipitation: the salt whose ion product reaches Ksp at the lower added-ion concentration precipitates first.

Dissolving precipitates: add acid to remove the anion (CaCO₃ + HCl) or a complexing agent (NH₃ with AgCl) to lower free cation concentration.

pH-dependent solubility: salts of basic anions (CO₃²⁻, OH⁻, PO₄³⁻) dissolve in acid; salts of strong-acid anions do not.

Oxidation state rules: element 0; monatomic ion = charge; O usually −2 (peroxide −1); H usually +1 (hydride −1); sum equals overall charge.

Oxidation is loss of electrons (anode); reduction is gain (cathode); the oxidizing agent is reduced.

Balance in acidic medium: split into half-reactions, balance atoms, add H₂O for O and H⁺ for H, add electrons, equalize, add, cancel.

In basic medium, after balancing as acidic, add OH⁻ to both sides for each H⁺ and combine into H₂O.

Cell EMF: E°cell = E°cathode − E°anode; a positive E°cell means a spontaneous galvanic cell.

ΔG° = −nFE°cell and E°cell = (RT/nF)ln K; with F = 96485 C/mol.

Nernst equation at 25 °C: E = E° − (0.0592/n)log Q, using concentrations or partial pressures in Q.

Electrolysis: charge Q = I·t; moles of product = Q/(nF); the minimum voltage is the reverse of E°cell.

IUPAC naming: longest chain containing the principal group, number to give it the lowest locant, name substituents alphabetically.

Homologous series: alkane CₙH₂ₙ₊₂, alkene/cycloalkane CₙH₂ₙ, alkyne/diene CₙH₂ₙ₋₂, alcohol CₙH₂ₙ₊₂O.

Isomerism: structural (chain, position, functional group) and stereoisomerism (geometric cis/trans, optical enantiomers with a chiral carbon).

Substitution (alkanes, alcohols with HX, halogenoalkanes with OH⁻/CN⁻) competes with elimination (alkoxide or concentrated H₂SO₄ gives alkene).

Addition to C=C: H₂/Ni, HX (Markovnikov), H₂O/H⁺ (Markovnikov), X₂ (anti addition, bromine water decolorized).

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

Condensation: esterification (acid + alcohol, H⁺ catalyst, water lost), amide formation, and peptide bonds from amino acids.

Polymers: addition polymers from alkenes (polyethene, PVC, polystyrene); condensation polymers lose water, e.g. PET from diol + diacid, nylon from diamine + diacid.

IUPAC naming: longest chain containing the principal group, number to give it the lowest locant, name substituents alphabetically.

Homologous series: alkane CₙH₂ₙ₊₂, alkene/cycloalkane CₙH₂ₙ, alkyne/diene CₙH₂ₙ₋₂, alcohol CₙH₂ₙ₊₂O.

Isomerism: structural (chain, position, functional group) and stereoisomerism (geometric cis/trans, optical enantiomers with a chiral carbon).

Substitution (alkanes, alcohols with HX, halogenoalkanes with OH⁻/CN⁻) competes with elimination (alkoxide or concentrated H₂SO₄ gives alkene).

Addition to C=C: H₂/Ni, HX (Markovnikov), H₂O/H⁺ (Markovnikov), X₂ (anti addition, bromine water decolorized).

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

Condensation: esterification (acid + alcohol, H⁺ catalyst, water lost), amide formation, and peptide bonds from amino acids.

Polymers: addition polymers from alkenes (polyethene, PVC, polystyrene); condensation polymers lose water, e.g. PET from diol + diacid, nylon from diamine + diacid.