KSEAB II PUC Chemistry cheat sheet

1 mole = 6.022×10²³ particles (Avogadro constant N_A); molar mass in g/mol equals formula mass in u.

Number of moles n = given mass / molar mass = N/N_A = volume of gas at STP (L) / 22.4 L.

Percentage composition of element = (mass of element in 1 mol / molar mass of compound) × 100.

Empirical formula is the simplest whole-number ratio; molecular formula = (empirical formula) × n, where n = molar mass / empirical formula mass.

Limiting reagent is the reactant that gives the least amount of product; excess reagent is left unreacted.

Molarity M = moles of solute / volume of solution in litres; molality m = moles of solute / mass of solvent in kg.

Significant figures: all non-zero digits count; zeros between non-zero digits count; leading zeros do not; trailing zeros after a decimal point do.

Law of conservation of mass, law of definite proportions, and law of multiple proportions support Dalton's atomic theory.

Bohr energy of hydrogen-like species: E_n = −13.6 Z²/n² eV; radius r_n = 0.529 n²/Z Å.

Rydberg equation: 1/λ = R_H Z² (1/n₁² − 1/n₂²), with R_H = 1.097×10⁷ m⁻¹; n₁ = 2 gives the Balmer series (visible).

de Broglie relation: λ = h/mv; Heisenberg uncertainty: Δx·Δp ≥ h/4π.

Quantum numbers: n (shell, 1,2,3…), l (0 to n−1), m_l (−l to +l), m_s (±½).

Aufbau order follows increasing (n+l); for equal (n+l) the lower n fills first.

Hund's rule: orbitals of equal energy are singly occupied with parallel spins before pairing.

Orbital shapes: s spherical, p dumbbell (two lobes), d double-dumbbell (four lobes, except d_z²).

Half-filled and fully filled subshells (d⁵, d¹⁰) have extra stability due to symmetry and exchange energy.

Formal charge = (valence electrons) − (non-bonding electrons) − ½ (bonding electrons).

Bond order = ½ (number of bonding electrons − number of antibonding electrons); higher bond order means shorter, stronger bond.

VSEPR: electron-pair repulsion order lp–lp > lp–bp > bp–bp; lone pairs reduce bond angles.

Hybridisation from steric number (σ bonds + lone pairs): 2 → sp, 3 → sp², 4 → sp³, 5 → sp³d, 6 → sp³d².

Molecular polarity: a molecule with polar bonds may be non-polar if the bond dipoles cancel by symmetry (e.g., CO₂, CCl₄).

Bond enthalpy increases with bond order and decreases down a group as atomic size increases.

Hydrogen bonding (N–H, O–H, F–H) explains the abnormally high boiling points of H₂O, HF and NH₃.

Dipole moment is a vector; net dipole is the vector sum of individual bond dipoles.

Ideal gas equation: PV = nRT; R = 8.314 J K⁻¹ mol⁻¹ = 0.0821 L atm K⁻¹ mol⁻¹.

Dalton's law: total pressure = sum of partial pressures; p_i = x_i P_total.

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

First law: ΔU = q + w; work done on the system w = −P_ext ΔV.

Enthalpy: ΔH = ΔU + Δn_g RT, where Δn_g is change in moles of gas.

Hess's law: ΔH of a reaction is independent of path; ΔH = Σ ΔH_f(products) − Σ ΔH_f(reactants).

Entropy change ΔS = q_rev/T; second law: ΔS_universe > 0 for a spontaneous process.

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

K_p = K_c (RT)^Δn_g, where Δn_g = moles of gaseous products − moles of gaseous reactants.

Le Chatelier: increasing pressure shifts equilibrium toward the side with fewer moles of gas; increasing temperature favours the endothermic direction.

For a weak acid, K_a = [H⁺][A⁻]/[HA]; pH = −log[H⁺]; pOH = 14 − pH at 25 °C.

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

K_sp of a sparingly soluble salt A_xB_y = (x s)^x (y s)^y, where s is molar solubility.

Oxidation number rules: O is usually −2, H is +1, sum of oxidation numbers in a neutral compound is zero.

Oxidising agent gains electrons and is reduced; reducing agent loses electrons and is oxidised.

Balance redox reactions by the ion–electron (half-reaction) method: balance atoms, then O with H₂O, H with H⁺, charge with electrons.

Raoult's law: p_total = p₁° x₁ + p₂° x₂; relative lowering of vapour pressure = x_solute.

Elevation of boiling point: ΔT_b = K_b m; depression of freezing point: ΔT_f = K_f m.

Osmotic pressure: π = CRT = (n/V)RT; i = van't Hoff factor = observed colligative effect / calculated value.

Colligative properties depend on the number of solute particles, not their identity.

Henry's law: p = K_H x; solubility of a gas decreases as temperature rises.

Ideal solutions obey Raoult's law and show zero enthalpy of mixing; positive deviation gives higher vapour pressure.

Molarity changes with temperature (volume changes); molality and mole fraction do not.

Cell EMF: E°_cell = E°_cathode − E°_anode; ΔG° = −nFE°_cell; E°_cell = (0.0591/n) log K at 25 °C.

Nernst equation: E = E° − (0.0591/n) log Q at 25 °C.

Faraday's laws: mass deposited m = (M I t)/(n F), with F = 96500 C mol⁻¹.

Conductivity κ = 1/ρ; molar conductivity Λ_m = κ × 1000 / M (M in mol L⁻¹).

Rate law: rate = k[A]^m[B]^n; order is the sum of exponents, determined experimentally.

First-order kinetics: k = (2.303/t) log(a/(a−x)); t₁/₂ = 0.693/k, independent of initial concentration.

Arrhenius equation: k = A e^(−E_a/RT); log(k₂/k₁) = (E_a/2.303R)(1/T₁ − 1/T₂).

Collision theory: rate depends on collision frequency and the fraction of molecules with energy ≥ E_a; a catalyst lowers E_a.

Group 15 hydrides: NH₃ > PH₃ > AsH₃ > SbH₃ > BiH₃ in basicity; thermal stability decreases down the group.

Group 16: H₂O is liquid due to hydrogen bonding; H₂S, H₂Se, H₂Te are gases.

Group 17: oxidising power F₂ > Cl₂ > Br₂ > I₂; bond dissociation enthalpy is highest for Cl₂.

Group 18: noble gases are monatomic with very low boiling points; Xe forms compounds such as XeF₂, XeF₄, XeF₆.

Transition metals show variable oxidation states due to small energy gap between (n−1)d and ns orbitals.

Cr³⁺ and Mn²⁺ are coloured and paramagnetic due to unpaired d electrons; Sc³⁺ and Zn²⁺ are colourless and diamagnetic.

Lanthanoid contraction: atomic and ionic radii decrease across the series due to poor shielding by 4f electrons.

Interstitial compounds of transition metals are hard and have high melting points; alloy formation is common.

Coordination number is the number of donor atoms bonded to the central metal ion.

Ligand names: NH₃ ammine, H₂O aqua, CN⁻ cyano, Cl⁻ chloro, OH⁻ hydroxo, CO carbonyl, en ethylenediamine.

IUPAC naming: name ligands alphabetically, then the metal with its oxidation state in Roman numerals in parentheses.

EAN = atomic number of metal − oxidation state + 2 × coordination number.

Crystal field splitting: Δ_o determines colour; strong-field ligands (CN⁻, CO) give low-spin complexes.

Spectrochemical series: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻ < CO.

Geometries: coordination number 4 gives tetrahedral or square planar; 6 gives octahedral.

Isomerism types: ionisation, hydrate, linkage, coordination, geometrical and optical isomerism.

SN1 proceeds via a carbocation intermediate and is favoured by tertiary halides and polar protic solvents; SN2 is a one-step backside attack favoured by primary halides.

Reactivity toward nucleophilic substitution: tertiary > secondary > primary for SN1; primary > secondary > tertiary for SN2.

Aryl halides are less reactive toward nucleophilic substitution because of partial double-bond character and sp² hybridisation.

Alcohols react with HX to form haloalkanes; tertiary alcohols react fastest via carbocation stability.

Lucas test: tertiary alcohol gives immediate turbidity, secondary on heating, primary does not react at room temperature.

Phenols are acidic because the phenoxide ion is resonance-stabilised; electron-withdrawing groups increase acidity.

Williamson synthesis: alkoxide + alkyl halide → ether; primary halides give the best yield.

Ethers are cleaved by concentrated HI; the iodide goes to the smaller alkyl group.

Aldehydes are oxidised by Tollens' reagent (silver mirror) and Fehling's solution; ketones are not.

Iodoform test is positive for methyl ketones and acetaldehyde (CH₃CO– group).

Aldol condensation requires an α-hydrogen; Cannizzaro reaction occurs for aldehydes without α-hydrogen.

Carboxylic acids are stronger acids than phenols and alcohols because the carboxylate ion is resonance-stabilised.

Acid strength increases with electron-withdrawing groups: CCl₃COOH > CHCl₂COOH > CH₂ClCOOH > CH₃COOH.

Amines are basic due to the lone pair on nitrogen; basicity in water: secondary > primary > tertiary > NH₃ for alkylamines.

Hinsberg test: primary amines form a soluble sulfonamide, secondary an insoluble one, tertiary no reaction.

Carbylamine test is positive for primary amines, giving an offensive smell with CHCl₃ and KOH.

Monosaccharides: glucose and fructose are C₆H₁₂O₆; glucose is an aldohexose, fructose a ketohexose.

Sucrose is a non-reducing disaccharide; maltose and lactose are reducing.

Amino acids are zwitterionic near neutral pH; the peptide bond forms between –COOH and –NH₂ with loss of water.

Nucleic acids: DNA contains deoxyribose and thymine; RNA contains ribose and uracil.

Addition polymers: polyethylene, PVC, polystyrene, Teflon; condensation polymers: nylon-6,6, terylene, bakelite.

Natural rubber is cis-polyisoprene; vulcanisation with sulphur creates cross-links.

Antacids neutralise stomach acid; antihistamines block histamine receptors; antibiotics inhibit bacterial growth.

Soaps are sodium or potassium salts of long-chain fatty acids; hard water reduces their cleansing action.

Flame test colours: Na golden yellow, K lilac, Ca brick red, Ba apple green, Cu blue-green, Sr crimson.

Cation group reagents: dilute HCl (group I), H₂S in acidic medium (group II), NH₄OH (group III), H₂S in basic medium (group IV), (NH₄)₂CO₃ (group V).

Anion tests: CO₃²⁻ gives effervescence with dilute acid; SO₄²⁻ gives a white precipitate with BaCl₂ insoluble in dilute HCl; Cl⁻ gives a white precipitate with AgNO₃ soluble in ammonia.

Acid–base titration: use phenolphthalein for strong acid–strong base and methyl orange for strong acid–weak base.

Burette readings are taken at eye level with the meniscus bottom; the reading is recorded to two decimal places.

Precipitates are washed with distilled water and dried before weighing in gravimetric analysis.

A pH meter is calibrated with buffer solutions before use; the electrode is rinsed with distilled water between measurements.