Pancyprian Chemistry cheat sheet

Quantum numbers: n (shell, 1,2,3...), l (subshell, 0 to n-1 as s,p,d,f), m_l (-l to +l), m_s (±1/2); no two electrons in an atom share all four.

Orbital filling follows Aufbau order 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p; 4s fills before 3d because 4s is lower in energy for neutral atoms.

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing; explains paramagnetism of atoms with unpaired electrons.

Pauli exclusion limits each orbital to two electrons of opposite spin; an orbital holds maximum 2, a subshell 2(2l+1), a shell 2n².

Effective nuclear charge Z_eff = Z − S (screening); across a period Z_eff rises, so atomic radius falls and ionisation energy generally rises.

First ionisation energy decreases down a group as n increases and shielding grows; exceptions occur where a filled or half-filled subshell is broken (e.g. Be→B, N→O).

Electron affinity is most negative for group 17 elements; noble gases have near-zero or positive electron affinity because the added electron enters a higher shell.

Periodic trends: metallic character increases down and left; electronegativity (Pauling) increases up and right, F = 3.98 being the maximum.

An element's emission spectrum gives discrete lines from ΔE = hν = hc/λ; the convergence limit of a series yields the ionisation energy of that level.

Ionic bonding strength rises with charge product and falls with interionic distance (Coulomb, lattice energy ∝ q₁q₂/r); MgO far exceeds NaCl in lattice enthalpy.

Born–Haber cycle: ΔH_f = ΔH_atomisation(metal) + ½ΔH_dissociation(non-metal) + IE − EA − lattice enthalpy; use it to obtain lattice enthalpy from measurable quantities.

Lewis structures: total valence electrons, octet on period-2 atoms, formal charge minimised; expanded octets allowed only for period 3 and below (e.g. SF₆, PCl₅).

VSEPR: electron pairs repel; lone pair–lone pair > lone pair–bond pair > bond pair–bond pair, giving bond angles below ideal (CH₄ 109.5°, NH₃ 107°, H₂O 104.5°).

Hybridisation from steric number: 2 = sp (linear), 3 = sp² (trigonal planar), 4 = sp³ (tetrahedral), 5 = sp³d, 6 = sp³d².

Polarity requires polar bonds and an asymmetric arrangement; CO₂ (linear) is non-polar while H₂O (bent) is polar despite similar bond dipoles.

Intermolecular forces ranked: ion–dipole > hydrogen bond > dipole–dipole > London dispersion; hydrogen bonds need H bonded to N, O or F.

Hydrogen bonding raises boiling point (H₂O 100 °C vs H₂S −60 °C) and explains ice's lower density, since the open tetrahedral lattice is less dense than liquid water.

Metallic bonding: delocalised electron sea explains conductivity, malleability and lustre; band theory distinguishes conductors, semiconductors and insulators by band gap.

n = m/M; N = n·N_A with N_A = 6.022 × 10²³ mol⁻¹; molar volume of an ideal gas at STP (273 K, 1 atm) is 22.4 dm³ mol⁻¹, at 25 °C and 1 bar about 24.5 dm³ mol⁻¹.

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

Balancing redox by half-reactions: balance atoms, then O with H₂O, H with H⁺ (acidic) or OH⁻ (basic), then charge with electrons; equalise electron counts before adding.

Limiting reagent: divide moles of each reactant by its stoichiometric coefficient; the smallest quotient identifies the limiting species and sets the theoretical yield.

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

Concentration c = n/V (mol dm⁻³); dilution obeys c₁V₁ = c₂V₂; mass concentration ρ = m/V converts to molarity via c = ρ/M.

Avogadro's law: equal volumes of gases at the same T and p contain equal numbers of molecules, so gas volume ratios equal mole ratios.

Significant figures: addition/subtraction keeps the least decimal places, multiplication/division keeps the least significant figures; never round intermediate results.

Ideal gas law pV = nRT with R = 8.314 J K⁻¹ mol⁻¹; combined law p₁V₁/T₁ = p₂V₂/T₂ requires absolute temperature in kelvin.

Dalton's law: total pressure equals the sum of partial pressures; p_i = x_i·p_total where x_i is the mole fraction.

Van der Waals equation (p + an²/V²)(V − nb) = nRT corrects for intermolecular attraction (a) and molecular volume (b); real gases deviate most near condensation.

Graham's law: rate of effusion ∝ 1/√M, so r₁/r₂ = √(M₂/M₁); lighter gases effuse faster.

Kinetic theory: average kinetic energy ∝ T only; root-mean-square speed u_rms = √(3RT/M), so heavier molecules move more slowly at equal T.

Phase diagram: triple point (all three phases coexist), critical point (liquid–gas boundary ends); the slope of the solid–liquid line is negative for water.

Raoult's law: p_solution = x_solvent·p°_solvent; a non-volatile solute lowers vapour pressure and raises boiling point (ΔT_b = K_b·m).

Colligative properties depend on particle count: ΔT_f = K_f·m and osmotic pressure Π = iMRT for electrolytes, where i is the van't Hoff factor.

Solubility of most solids rises with temperature; gas solubility falls as temperature rises and rises with partial pressure (Henry's law, c = k_H·p).

First law: ΔU = q + w; at constant pressure q_p = ΔH, and ΔH = ΔU + Δn_gas·RT when gas moles change.

Enthalpy of reaction from formation enthalpies: ΔH_r = ΣΔH_f(products) − ΣΔH_f(reactants); elements in standard states have ΔH_f = 0.

Hess's law: enthalpy change is path-independent, so any route summing to the overall reaction gives the same ΔH.

Calorimetry: q = mcΔT for solutions (c_water ≈ 4.18 J g⁻¹ K⁻¹); q_reaction = −q_solution, then divide by moles for molar enthalpy.

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

Second law: ΔS_universe = ΔS_system + ΔS_surroundings > 0 for a spontaneous change; ΔS_surroundings = −ΔH/T.

Gibbs energy ΔG = ΔH − TΔS; ΔG < 0 spontaneous, = 0 at equilibrium, > 0 non-spontaneous; the sign of ΔH and ΔS determines the temperature dependence.

ΔG° = −RT ln K and ΔG° = −nFE°_cell link thermodynamics to equilibrium and electrochemistry.

Standard conditions: 298 K, 1 bar, 1 mol dm⁻³; standard enthalpies of combustion and formation are tabulated per mole of substance.

Rate = −(1/a)d[A]/dt = (1/b)d[B]/dt; rate laws are determined experimentally, not from the balanced equation.

Order from initial rates: compare experiments where one concentration changes; doubling [A] doubling rate means first order, quadrupling means second order.

Integrated first-order law ln[A] = ln[A]₀ − kt; half-life t½ = ln2/k is constant and independent of concentration.

Arrhenius equation k = A·e^(−E_a/RT); ln(k₂/k₁) = (E_a/R)(1/T₁ − 1/T₂), so a plot of ln k against 1/T has slope −E_a/R.

Collision theory requires sufficient energy (E_a) and correct orientation; a catalyst lowers E_a without changing ΔH or the equilibrium position.

Rate-determining step is the slowest elementary step; the overall rate law reflects species up to and including that step.

K_c from concentrations, K_p from partial pressures; K_p = K_c(RT)^Δn where Δn is the change in gas moles.

Le Chatelier: raising pressure shifts equilibrium toward fewer gas moles; raising temperature shifts toward the endothermic direction; a catalyst changes neither K nor position.

Reaction quotient Q compared with K predicts direction: Q < K proceeds forward, Q > K proceeds reverse, Q = K at equilibrium.

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

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

Strong acid fully dissociates; weak acid obeys K_a = [H⁺][A⁻]/[HA], and for a weak monoprotic acid [H⁺] ≈ √(K_a·c).

Buffer (Henderson–Hasselbalch): pH = pK_a + log([A⁻]/[HA]); maximum buffer capacity occurs at pH = pK_a.

Titration curve: equivalence point pH depends on salt hydrolysis - strong acid/strong base pH 7, weak acid/strong base > 7, weak base/strong acid < 7.

Salt hydrolysis rules: cation of a weak base or anion of a weak acid hydrolyses; salts of strong acid and strong base are neutral.

Solubility product K_sp = [cation]^m[anion]^n; precipitation occurs when the ion product exceeds K_sp, and common ions lower solubility.

Indicator choice: the indicator's pK_a range (roughly ±1) must bracket the equivalence-point pH; phenolphthalein suits weak acid/strong base titrations.

Amphoteric species such as HCO₃⁻ and water can act as acid or base; polyprotic acids dissociate in successive steps with decreasing K_a values.

Oxidation is loss of electrons (oxidation number rises), reduction is gain; the oxidising agent is reduced, the reducing agent is oxidised.

Oxidation number rules: free element 0, monatomic ion = charge, oxygen usually −2 (peroxides −1), hydrogen +1 with non-metals, sum equals overall charge.

Galvanic cell: anode is negative and oxidises, cathode is positive and reduces; electrons flow anode→cathode in the external circuit, conventional current the opposite way.

E°_cell = E°_cathode − E°_anode using standard reduction potentials; a positive E°_cell means the reaction is spontaneous.

Standard hydrogen electrode is the reference (E° = 0.00 V); potentials are intensive and not multiplied when a half-equation is scaled.

Electrolysis: cathode attracts cations (reduction), anode attracts anions (oxidation); the more easily discharged species wins, with water competing in aqueous solutions.

Quantitative electrolysis: charge Q = It, moles of electrons = Q/F with F = 96 485 C mol⁻¹; mass deposited = (M·It)/(nF).

Disproportionation is simultaneous oxidation and reduction of the same element, e.g. Cl₂ + 2OH⁻ → Cl⁻ + ClO⁻ + H₂O.

Corrosion of iron is an electrochemical process requiring oxygen and water; sacrificial anodes (Zn, Mg) protect steel because they are more easily oxidised.

Group 1 metals react with water giving hydroxide and hydrogen, reactivity increasing down the group; oxides are basic and become more basic down the group.

Group 2: oxides and hydroxides are basic; solubility of hydroxides increases down the group while sulfates decrease (BaSO₄ insoluble, used in barium meals).

Group 17: oxidising power decreases down the group (Cl₂ > Br₂ > I₂); a halogen displaces a halide lower in the group from solution.

Group 17 trends: boiling point and van der Waals forces increase down the group; hydrogen halides are acidic, HF weakest due to strong H–F bond.

Group 16 and nitrogen/phosphorus: ammonia is a weak base via lone pair; nitric acid is a strong oxidising acid; phosphorus shows +3 and +5 oxidation states.

Transition metals show variable oxidation states (Mn: +2 to +7), form coloured ions from d–d transitions, act as catalysts, and form complex ions.

Ligand substitution and colour: [Cu(H₂O)₆]²⁺ is pale blue, [Cu(NH₃)₄(H₂O)₂]²⁺ deep blue; ligand strength follows the spectrochemical series.

Tests: flame tests (Na yellow, K lilac, Ca brick-red, Cu blue-green); NH₃ turns damp red litmus blue; CO₂ turns limewater milky; Cl⁻ gives white AgCl soluble in ammonia.

d-block ion electron configurations: Cr [Ar]3d⁵4s¹ and Cu [Ar]3d¹⁰4s¹ are exceptions because half-filled and filled d subshells are more stable.

IUPAC naming: longest carbon chain, lowest locants for principal functional group, then alphabetical substituent prefixes; suffix priority carboxylic acid > ester > amide > aldehyde > ketone > alcohol > amine > alkene > alkyne.

Homologous series: alkanes C_nH_(2n+2), alkenes C_nH_2n, alkynes C_nH_(2n−2), alcohols C_nH_(2n+2)O; each differs by CH₂.

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

Alkanes undergo free-radical substitution with halogens (initiation, propagation, termination); combustion is highly exothermic.

Alkenes undergo electrophilic addition: with HBr gives Markovnikov product, with Br₂ in CCl₄ decolourises (test for unsaturation), and with acidified KMnO₄ gives diols.

Alcohols: primary oxidise to aldehydes then carboxylic acids, secondary to ketones, tertiary resist oxidation; dehydration with concentrated H₂SO₄ gives alkenes.

Nucleophilic substitution: primary haloalkanes favour SN2 (one step, inversion), tertiary favour SN1 (carbocation intermediate, racemisation).

Carboxylic acids react with alcohols under acid catalysis to give esters (Fischer esterification, reversible, water removed to shift equilibrium); esters hydrolyse to acid and alcohol.

Aromatic substitution: benzene undergoes electrophilic substitution (nitration with HNO₃/H₂SO₄, halogenation with a Lewis acid catalyst) rather than addition, preserving aromaticity.

Volumetric glassware: burette and pipette deliver variable/fixed volumes to ±0.05 cm³ and ±0.10 cm³ respectively; read the bottom of the meniscus at eye level.

Titration procedure: rinse burette with the titrant, pipette with the analyte, add indicator, swirl, and take concordant results within 0.10 cm³ for the mean.

Weighing by difference avoids transfer error; record to the balance's precision (typically 0.001 g or 0.0001 g) and never weigh hot objects.

Heating to constant mass confirms complete drying or decomposition; a desiccator prevents reabsorption of moisture before weighing.

Percentage error = (uncertainty/measurement) × 100; the largest percentage error dominates overall uncertainty, so improve that measurement first.

Qualitative tests: flame test for metal cations, dilute acid for carbonates (CO₂), BaCl₂ for sulfate, AgNO₃ for halide, and NaOH for NH₄⁺ (damp red litmus).

Safety and waste: fume cupboard for halogens and concentrated acids, eye protection throughout, and labelled waste containers for heavy-metal and organic residues.

Graphical analysis: plot the dependent variable on the y-axis, draw a line of best fit, and use its gradient and intercept to extract constants (e.g. slope −E_a/R from ln k vs 1/T).

Reliability is improved by repeat measurements and averaging; accuracy concerns systematic error (calibration), precision concerns random scatter between repeats.

IUPAC naming: longest carbon chain, lowest locants for principal functional group, then alphabetical substituent prefixes; suffix priority carboxylic acid > ester > amide > aldehyde > ketone > alcohol > amine > alkene > alkyne.

Homologous series: alkanes C_nH_(2n+2), alkenes C_nH_2n, alkynes C_nH_(2n−2), alcohols C_nH_(2n+2)O; each differs by CH₂.

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

Alkanes undergo free-radical substitution with halogens (initiation, propagation, termination); combustion is highly exothermic.

Alkenes undergo electrophilic addition: with HBr gives Markovnikov product, with Br₂ in CCl₄ decolourises (test for unsaturation), and with acidified KMnO₄ gives diols.

Alcohols: primary oxidise to aldehydes then carboxylic acids, secondary to ketones, tertiary resist oxidation; dehydration with concentrated H₂SO₄ gives alkenes.

Nucleophilic substitution: primary haloalkanes favour SN2 (one step, inversion), tertiary favour SN1 (carbocation intermediate, racemisation).

Carboxylic acids react with alcohols under acid catalysis to give esters (Fischer esterification, reversible, water removed to shift equilibrium); esters hydrolyse to acid and alcohol.

Aromatic substitution: benzene undergoes electrophilic substitution (nitration with HNO₃/H₂SO₄, halogenation with a Lewis acid catalyst) rather than addition, preserving aromaticity.