UPMSP Intermediate Chemistry cheat sheet

Raoult's law for a volatile solute in a solvent: p_total = p°_A·x_A + p°_B·x_B; each partial pressure equals its pure vapour pressure times its mole fraction in the liquid.

Relative lowering of vapour pressure equals the mole fraction of solute: (p° − p)/p° = x_solute = n₂/(n₁+n₂), valid only for dilute non-dissociating, non-volatile solutes.

Colligative relations: ΔT_b = K_b·m, ΔT_f = K_f·m, π = CRT = (n/V)RT; molality m = moles solute per kg solvent, so results are temperature-independent except osmotic pressure, which changes with T.

van 't Hoff factor i = observed colligative value / calculated value; i > 1 for dissociating solutes (NaCl → i ≈ 2), i < 1 for associating solutes (benzoic acid in benzene → i ≈ 0.5).

Henry's law: p = K_H·x; solubility of a gas falls as temperature rises and rises as partial pressure rises. K_H increases with temperature.

Azeotropes: minimum-boiling (ethanol–water, positive deviation, weaker solute–solvent forces) and maximum-boiling (HNO₃–water, negative deviation, stronger solute–solvent forces) cannot be separated by fractional distillation.

Positive deviation from Raoult's law: solute–solvent attractions weaker than solvent–solvent; vapour pressure higher than predicted; ΔH_mix > 0.

Osmotic pressure is preferred for molar mass of macromolecules and proteins because it is measurable at ordinary temperature, avoiding thermal denaturation.

Nernst equation at 298 K: E = E° − (0.0591/n)·log Q. For a cell, E_cell = E°_cell − (0.0591/n)·log([products]/[reactants]).

ΔG = −nFE and ΔG° = −nFE° = −2.303RT·log K; a positive E°_cell means spontaneous reaction and K > 1.

Standard hydrogen electrode is assigned E° = 0.00 V at 1 M H⁺, 1 bar H₂, 298 K; it can act as anode or cathode.

Kohlrausch's law: Λ°_m = ν₊λ°₊ + ν₋λ°₋; used to obtain Λ°_m of weak electrolytes that cannot be extrapolated directly.

Degree of dissociation of a weak electrolyte: α = Λ_m/Λ°_m; dissociation constant K_a = Cα²/(1−α).

Faraday's laws: mass deposited m = (Q/F)·(M/z) = (I·t·M)/(96500·z); 1 F = 96485 C liberates one equivalent of substance.

Order of standard reduction potentials: Li⁺ < K⁺ < Ca²⁺ < Na⁺ < Mg²⁺ < Al³⁺ < Zn²⁺ < Fe²⁺ < H⁺ < Cu²⁺ < Ag⁺ < Au³⁺; metals above H⁺ displace hydrogen from dilute acids.

Conductivity relation: κ = (1/R)·(l/A) and Λ_m = κ·1000/M (M in mol L⁻¹); molar conductivity rises on dilution, conductivity of a strong electrolyte rises with concentration.

Rate = −d[R]/dt = k[R]^n; order is experimental, molecularity is theoretical and applies only to elementary steps.

Zero order: [R] = [R]₀ − kt, t½ = [R]₀/2k; first order: ln([R]₀/[R]) = kt, t½ = 0.693/k, independent of initial concentration.

Second order (single reactant): 1/[R] = 1/[R]₀ + kt, t½ = 1/(k[R]₀).

Arrhenius: k = A·e^(−E_a/RT); log(k₂/k₁) = (E_a/2.303R)(1/T₁ − 1/T₂). A larger E_a means stronger temperature dependence.

Temperature coefficient is often ≈ 2–3 per 10 K rise for reactions near room temperature.

Pseudo-first-order example: acid hydrolysis of ester in large excess water; rate = k'[ester], with k' = k[H₂O].

Collision theory requires correct orientation and energy ≥ E_a; catalyst lowers E_a without changing ΔH or equilibrium position.

Half-life of a first-order reaction is a direct route to k: k = 0.693/t½; radioactive decay follows the same law.

Transition metal characteristic: incompletely filled d orbitals in atom or common ions; Cr (3d⁵4s¹) and Cu (3d¹⁰4s¹) are exceptions to the aufbau filling.

Mn²⁺ is the most stable Mn ion in aqueous solution; Mn³⁺ is strongly oxidising. Cr³⁺ is stable while Cr⁶⁺ (CrO₄²⁻/Cr₂O₇²⁻) is oxidising.

Lanthanoid contraction arises from poor shielding by 4f electrons; it makes Zr and Hf nearly identical in size and chemistry.

Cerium shows +4 oxidation state (Ce⁴⁺ is a good oxidant); Eu²⁺ is a reducing agent; +3 is the dominant lanthanoid state.

Nomenclature: ligands named alphabetically before the metal, anionic complex ends in -ate, oxidation state in Roman numerals in parentheses, e.g. [Co(NH₃)₄Cl₂]Cl is tetraamminedichloridocobalt(III) chloride.

Crystal field splitting: Δ_o (octahedral) > Δ_t (tetrahedral); strong-field ligands (CN⁻, CO, NO₂⁻) give low-spin, weak-field (I⁻, Br⁻, F⁻, H₂O) give high-spin complexes.

Spectrochemical series: I⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO.

Geometrical isomerism in [Ma₂b₂] octahedral gives cis and trans; [M(AA)₂b₂] type shows optical activity; tetrahedral complexes are never optically active by geometry alone.

SN1 proceeds through a carbocation: rate depends only on substrate, favoured by tertiary > secondary > primary, polar protic solvent, and gives racemisation.

SN2 is a one-step backside attack: rate = k[substrate][nucleophile], favoured by primary > secondary > tertiary, polar aprotic solvent, and gives inversion of configuration.

Reactivity order for halides in both SN1 and SN2: R–I > R–Br > R–Cl > R–F (C–X bond strength decreases down the halogen).

Aryl and vinyl halides resist nucleophilic substitution because the C–X bond has partial double-bond character and the sp² carbon blocks backside attack.

Haloarenes undergo electrophilic substitution at ortho/para positions; halogen is weakly deactivating but ortho/para directing.

Finkelstein reaction: R–X + NaI (dry acetone) → R–I; the NaCl formed precipitates, driving the equilibrium.

Swarts reaction: R–Br + AgF or Hg₂F₂ → R–F; used to prepare fluoroalkanes.

Elimination competes with substitution: alcoholic KOH favours alkene (β-elimination), aqueous KOH favours alcohol.

Lucas test: tertiary alcohol turns cloudy at once, secondary in about 5 min, primary only on heating; reagent is anhydrous ZnCl₂ in concentrated HCl.

Phenol is far more acidic than alcohols (pKa ≈ 10 vs 16) because the phenoxide is resonance-stabilised; electron-withdrawing groups like NO₂ increase phenol acidity.

Phenol + neutral FeCl₃ gives a violet colour, a test distinguishing phenols from alcohols.

Williamson ether synthesis: R–ONa + R'–X → R–O–R'; primary halides give good yields, tertiary halides give elimination instead.

Reimer–Tiemann: phenol + CHCl₃/NaOH gives salicylaldehyde (ortho). Kolbe reaction: phenol + CO₂/NaOH then H⁺ gives salicylic acid.

Alcohols react with Na to release H₂; ethers do not, and ethers are cleaved by hot concentrated HI, giving an alcohol and alkyl iodide.

Dehydration of alcohols with concentrated H₂SO₄ follows Saytzeff's rule, giving the more substituted alkene as the major product.

Boiling points: alcohols > ethers > alkanes of comparable mass because of hydrogen bonding; ethers are only weakly polar and almost insoluble in water.

Tollens' test: aldehydes give a silver mirror with ammoniacal AgNO₃; ketones do not. Fehling's solution (Cu²⁺ in alkaline tartrate) is reduced by aliphatic aldehydes only.

Iodoform test: CH₃CO– group or CH₃CH(OH)– group gives yellow CHI₃ with I₂/NaOH; ethanol and acetone are positive, methanol is not.

Aldol condensation needs an α-hydrogen; Cannizzaro reaction (disproportionation to alcohol and carboxylate) occurs only for aldehydes lacking α-hydrogen, e.g. HCHO, C₆H₅CHO.

Carboxylic acids are stronger acids than phenols; acid strength rises with electron-withdrawing substituents: HCOOH > CH₃COOH > CH₃CH₂COOH; ClCH₂COOH > CH₃COOH.

Amines are basic because of the lone pair on nitrogen; aqueous basicity order is (CH₃)₂NH > CH₃NH₂ > (CH₃)₃N > NH₃, while in the gas phase tertiary > secondary > primary > NH₃.

Hinsberg test: primary amines react with benzenesulfonyl chloride to give a soluble sulfonamide; secondary give an insoluble one; tertiary do not react.

Carbylamine test: primary amines + CHCl₃ + alcoholic KOH give an offensive isocyanide smell; secondary and tertiary amines are negative.

Amines react with nitrous acid: primary aliphatic give N₂ gas, primary aromatic give diazonium salts at 273–278 K, secondary give oily N-nitrosamines, tertiary aromatic give coloured salts.

Glucose is an aldohexose, fructose a ketohexose; both are reducing sugars. Sucrose is non-reducing because both anomeric carbons are in the glycosidic bond.

Peptide bond forms between the –COOH of one amino acid and the –NH₂ of the next with loss of water; the sequence of amino acids is the primary structure of a protein.

Denaturation destroys secondary and tertiary structure but not the primary sequence; it is caused by heat, pH change, urea, or alcohol.

Nucleotides: DNA contains deoxyribose and thymine, RNA contains ribose and uracil; base pairing is A–T (A–U in RNA) and G–C via hydrogen bonds.

Addition polymers: polyethylene, PVC, polystyrene, Teflon. Condensation polymers: nylon-6,6 (adipic acid + hexamethylenediamine), terylene (ethylene glycol + terephthalic acid), bakelite (phenol + formaldehyde).

Natural rubber is cis-polyisoprene; vulcanisation with sulfur creates cross-links that increase strength and elasticity.

Buna-S is a copolymer of butadiene and styrene; Buna-N of butadiene and acrylonitrile; neoprene from chloroprene.

Biodegradable polymers include PHBV and nylon-2-nylon-6; they are broken down by microorganisms in soil.

Unit cell counts: simple cubic 8 × 1/8 = 1 atom; body-centred 8 × 1/8 + 1 = 2; face-centred 8 × 1/8 + 6 × 1/2 = 4.

Packing efficiency: simple cubic 52.4%, bcc 68%, ccp/fcc 74%; ccp and hcp both have coordination number 12.

Density relation: ρ = (Z·M)/(a³·N_A); Z is atoms per unit cell, a in cm.

Radius relations: bcc a = 4r/√3; fcc a = 2√2·r; simple cubic a = 2r.

Schottky defect lowers density (equal numbers of cations and anions missing); Frenkel defect keeps density constant (cation displaced to interstitial site).

Bragg's law: nλ = 2d·sin θ; used to determine interplanar spacing from X-ray diffraction.

Freundlich adsorption isotherm: x/m = k·p^(1/n), with 0 < 1/n < 1; the plot of log(x/m) versus log p is linear.

Physisorption involves van der Waals forces and is reversible and non-specific; chemisorption involves chemical bonds and is usually irreversible and specific.

Dihydrogen is prepared by electrolysis of water or by the water-gas shift reaction; it is the lightest gas and forms hydrogen bonds only when attached to F, O, or N.

Hydrides: ionic (NaH, CaH₂), covalent (CH₄, NH₃, H₂O), and interstitial/metallic (PdH, LaH₂).

Group 15: N₂ is inert because of its strong triple bond; white phosphorus (P₄) is more reactive than red phosphorus; HNO₃ is a strong oxidant.

Group 16: oxygen shows anomalous behaviour; ozone is a bent paramagnetic molecule that oxidises iodide to iodine.

Group 17: oxidising power falls down the group F₂ > Cl₂ > Br₂ > I₂; fluorine is the strongest oxidising agent and reacts with water to give O₂ and O₃.

Group 18: noble gases are monatomic; ionisation enthalpy decreases down the group, and xenon forms stable compounds such as XeF₂, XeF₄, and XeO₃.

Interhalogen compounds: XY₃ (T-shaped), XY₅ (square pyramidal), XY₇ (pentagonal bipyramidal); larger halogen is the central atom.

Oxoacids of chlorine: HClO < HClO₂ < HClO₃ < HClO₄ in acid strength, because the number of terminal oxygen atoms increases.

Concentration methods: gravity separation for oxide ores, froth flotation for sulfide ores, magnetic separation for magnetic gangue, leaching for bauxite (Bayer process).

Calcination heats a carbonate or hydroxide ore in limited air; roasting heats a sulfide ore in excess air. Both remove volatile impurities.

Ellingham diagrams plot ΔG° for oxide formation versus temperature; the metal whose curve lies lower reduces the oxide above it.

Thermite reaction: Fe₂O₃ + 2Al → 2Fe + Al₂O₃; the very negative ΔG makes it self-sustaining and useful for welding.

Zone refining purifies semiconductors; vant Hoff–Mond process purifies nickel via Ni(CO)₄; electrolytic refining uses the impure metal as anode.

Group 1 hydroxides are strong bases; basicity and solubility of hydroxides increase down the group. Li₂CO₃ is the least soluble carbonate.

Alkali metals are stored in kerosene, show flame colours (Li crimson, Na yellow, K lilac), and react with water to give H₂ and hydroxide.

Group 2: Be forms covalent, amphoteric Be(OH)₂; Mg, Ca, Sr, Ba form ionic basic hydroxides, and solubility of sulfates falls down the group (BaSO₄ insoluble).

Inductive effect: electron-withdrawing groups (–NO₂, –CN, –COOH, –X) stabilise carboxylate anions and increase acidity; electron-releasing alkyl groups decrease it.

Resonance requires planar, conjugated p orbitals; a structure with more covalent bonds and fewer formal charges contributes more.

Carbocation stability: tertiary > secondary > primary > methyl, with allylic and benzylic stabilised by resonance; carbanions show the reverse order.

Markovnikov's rule: in HX addition to an unsymmetrical alkene, H goes to the carbon with more hydrogens, giving the more stable carbocation intermediate.

Peroxide effect (anti-Markovnikov) operates through free radicals and is observed with HBr but not HCl or HI.

Alkenes decolourise bromine water; alkynes decolourise it too and give a red precipitate of copper acetylide with ammoniacal CuCl (terminal alkynes only).

Aromaticity: cyclic, planar, fully conjugated, with (4n + 2) π electrons; benzene (6) and naphthalene (10) are aromatic, cyclobutadiene (4) is antiaromatic.

Electrophilic aromatic substitution: –NO₂, –CN, –COOH are meta-directing and deactivating; –OH, –NH₂, –CH₃, –X are ortho/para-directing (halogens deactivate but direct ortho/para).

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

Qualitative cations: Group I (Pb²⁺, Ag⁺, Hg₂²⁺) as chlorides; Group II (Cu²⁺, Cd²⁺, Bi³⁺) as sulfides in acidic medium; Group III (Al³⁺, Fe³⁺, Cr³⁺) as hydroxides in NH₄OH/NH₄Cl.

Anion tests: carbonate gives effervescence with dilute acid, sulfate gives white BaSO₄ insoluble in acid, chloride gives white AgCl soluble in ammonia, iodide gives yellow AgI insoluble in ammonia.

Chromyl chloride test confirms chloride: red vapours with K₂Cr₂O₇ and concentrated H₂SO₄, which turn NaOH yellow (chromate).

Burette is rinsed with the titrant; pipette with the solution it will deliver. Read the meniscus at eye level, and record the lower meniscus for colourless solutions.

Standard titration formula: M₁V₁/n₁ = M₂V₂/n₂, where n is the stoichiometric coefficient from the balanced equation.

In the Lassaigne test, sodium fusion converts N to NaCN, S to Na₂S, and halogens to NaX; NaCN gives Prussian blue with FeSO₄ and FeCl₃.

Safety rules: never heat a closed system, add concentrated acid to water (not the reverse), and point test tubes away from the face when heating.

First law: ΔU = q + w; for a gas at constant pressure, w = −pΔV and ΔH = ΔU + Δn_gRT.

ΔG = ΔH − TΔS; a reaction is spontaneous when ΔG < 0, at equilibrium ΔG = 0, and ΔG° = −RT ln K.

Le Chatelier: raising pressure shifts equilibrium toward fewer gas moles; raising temperature shifts an endothermic reaction forward.

Hess's law: the enthalpy change is path-independent, so ΔH can be summed over any set of steps that add to the overall reaction.

Entropy increases with phase changes solid → liquid → gas and with an increase in the number of gas molecules.

For a weak acid, K_a·K_b = K_w = 1.0 × 10⁻¹⁴ at 298 K; a buffer obeys pH = pK_a + log([salt]/[acid]).

Solubility product: K_sp = [A⁺]^m[B⁻]^n; precipitation occurs when the ionic product exceeds K_sp.

Bond enthalpy route: ΔH_reaction = Σ(bond enthalpies broken) − Σ(bond enthalpies formed).