BSEB Intermediate Chemistry cheat sheet

Raoult's law for a volatile solute in a volatile solvent: p_total = p_A° x_A + p_B° x_B, where x is the mole fraction in the liquid phase.

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

Elevation of boiling point: ΔT_b = K_b·m, where m is molality (mol kg⁻¹ of solvent); K_b for water is 0.512 K kg mol⁻¹.

Depression of freezing point: ΔT_f = K_f·m; K_f for water is 1.86 K kg mol⁻¹, so 1 molal aqueous solution freezes near −1.86 °C.

Osmotic pressure: π = CRT = (n/V)RT; for dilute solutions π ≈ (n₂/V)RT and is numerically equal to the gas pressure the solute would exert as a gas at that temperature.

van't Hoff factor i = observed colligative effect / calculated effect; i > 1 for dissociating solutes (NaCl → 2 ions), i < 1 for associating solutes (benzoic acid dimer 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.

Molarity depends on temperature (volume changes); molality and mole fraction do not. Convert with M = (1000·d·x_solute)/(x_solvent·M_solvent + x_solute·M_solute) style relations or via density.

Colligative properties depend only on the number of solute particles, not their identity: 0.1 m glucose ≈ 0.05 m NaCl in effect (i = 2 for NaCl).

Cell EMF: E°_cell = E°_cathode − E°_anode (reduction potentials); a positive E°_cell means ΔG° < 0 and a spontaneous reaction as written.

ΔG° = −nFE°_cell and ΔG° = −2.303RT log K; at 298 K, E°_cell = (0.0591/n) log K.

Nernst equation: E = E° − (0.0591/n) log Q at 298 K; for a concentration cell with equal electrodes E° = 0 and E = (0.0591/n) log(C_anode/C_cathode).

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

Conductance: Λ_m = κ/c (with c in mol m⁻³); Λ_m increases with dilution and levels off at Λ°_m for strong electrolytes.

Kohlrausch law: Λ°_m = ν₊λ°₊ + ν₋λ°₋; used to compute Λ°_m of weak electrolytes, e.g. CH₃COOH from HCl, NaCl and CH₃COONa.

Degree of dissociation α = Λ_m/Λ°_m for weak electrolytes; K_a = cα²/(1 − α) (Ostwald dilution law).

Faraday's laws: mass deposited m = (Q/F)(M/z) = (I·t·M)/(z·F); F = 96487 C mol⁻¹; charge on 1 mol electrons is one faraday.

In a galvanic cell oxidation occurs at the anode (negative terminal) and reduction at the cathode (positive terminal); in electrolysis the polarity is reversed but oxidation still occurs at the anode.

Product priority in aqueous electrolysis: at cathode, species with higher E°_red is discharged (Cu²⁺ before H⁺ before Na⁺); at anode, Cl⁻ or OH⁻ may oxidise before water depending on concentration and overpotential.

Rate of reaction is defined as −(1/a)d[A]/dt = (1/b)d[B]/dt for aA → bB; rate law is determined experimentally, not from stoichiometry.

Order is the sum of exponents in the experimental rate law; molecularity is the number of species colliding in an elementary step and is always a small whole number.

Zero order: [A] = [A]₀ − kt, t₁/₂ = [A]₀/2k; rate independent of concentration (e.g. some surface-catalysed reactions).

First order: ln([A]₀/[A]) = kt, k = (2.303/t) log([A]₀/[A]), t₁/₂ = 0.693/k independent of initial concentration.

Second order (single reactant): 1/[A] − 1/[A]₀ = kt, t₁/₂ = 1/(k[A]₀).

Arrhenius equation: k = A e^(−E_a/RT); log(k₂/k₁) = (E_a/2.303R)(1/T₁ − 1/T₂); a plot of ln k vs 1/T has slope −E_a/R.

Rate constant units: zero order mol L⁻¹ s⁻¹, first order s⁻¹, second order L mol⁻¹ s⁻¹, general (mol L⁻¹)^(1−n) s⁻¹.

Collision theory: rate depends on collision frequency, orientation and fraction of molecules with energy ≥ E_a; catalyst lowers E_a without changing ΔH or equilibrium position.

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

General electronic configuration: (n−1)d¹⁻¹⁰ ns¹⁻² for d-block; 4f¹⁻¹⁴ 5d⁰⁻¹ 6s² for lanthanoids, 5f¹⁻¹⁴ 6d⁰⁻¹ 7s² for actinoids.

Cr is [Ar]3d⁵4s¹ and Cu is [Ar]3d¹⁰4s¹ because half-filled and fully filled d subshells give extra exchange stability.

Transition metals show variable oxidation states because 4s and 3d electrons have similar energies; Mn shows +2 to +7, with +2 most stable and +7 strongly oxidising (MnO₄⁻).

Across the 3d series atomic radius decreases slightly then becomes nearly constant; density, melting point and enthalpy of atomisation peak near the middle (Cr, W-type maximum in 3d is Cr).

Colour of transition metal ions arises from d–d transitions; ions with d⁰ (Sc³⁺, Ti⁴⁺) or d¹⁰ (Zn²⁺, Cu⁺) are colourless.

Magnetic moment μ = √(n(n+2)) BM, where n is the number of unpaired electrons; spin-only formula.

Lanthanoid contraction: steady decrease in atomic/ionic radius from La to Lu due to poor shielding of 4f electrons; causes similarity in chemistry of lanthanoids and Zr–Hf.

Ce⁴⁺ is a good oxidising agent and Eu²⁺ a good reducing agent; Ce⁴⁺/Ce³⁺ and Eu³⁺/Eu²⁺ redox changes make these two easily separable.

KMnO₄ in acidic medium is a strong oxidant: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O (E° = +1.51 V); in neutral/alkaline medium it gives MnO₂.

Coordination number is the number of donor atoms bonded to the central metal; common values are 4 (tetrahedral or square planar) and 6 (octahedral).

Werner's theory distinguishes primary valence (ionisable, satisfies metal charge) from secondary valence (coordination number, non-ionisable).

IUPAC naming: ligands alphabetically before the metal; anionic complex ends in -ate; oxidation state of metal in Roman numerals in parentheses.

Isomerism types include ionisation, hydrate, linkage (NO₂⁻ vs ONO⁻, SCN⁻ vs NCS⁻), coordination, geometric (cis/trans in square planar and octahedral) and optical (octahedral MA₂B₂C₂, [Co(en)₃]³⁺).

Crystal field theory: Δ_o = splitting of d orbitals in an octahedral field; strong-field ligands (CN⁻, CO, NO₂⁻) give low spin, weak-field (I⁻, Br⁻, F⁻, H₂O) give high spin.

Spectrochemical series (increasing Δ): I⁻ < Br⁻ < SCN⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO.

Tetrahedral complexes have Δ_t ≈ 4/9 Δ_o and are almost always high spin, so tetrahedral Co(II) is usually blue and paramagnetic.

Magnetic moment from spin-only formula √(n(n+2)) BM; [Fe(CN)₆]³⁻ (low spin d⁵, one unpaired) has μ ≈ 1.73 BM, [Fe(H₂O)₆]³⁺ (high spin d⁵) ≈ 5.92 BM.

EAN rule: stable complexes often have 36, 54 or 86 electrons around the metal, counting metal electrons plus 2 per donor pair; [Fe(CN)₆]⁴⁻ gives 36.

SN1 proceeds via a carbocation intermediate: rate = k[RX], favoured by tertiary substrates, polar protic solvents and good leaving groups; racemisation with inversion.

SN2 is a one-step backside attack: rate = k[RX][Nu⁻], favoured by primary substrates, strong nucleophiles, polar aprotic solvents; gives inversion of configuration.

Reactivity order toward SN1: 3° > 2° > 1° > CH₃X; toward SN2: CH₃X > 1° > 2° > 3°.

Aryl and vinyl halides are inert to nucleophilic substitution because the C–X bond has partial double-bond character and the sp² carbon resists backside attack.

Finkelstein reaction: R–X + NaI in dry acetone → R–I (NaBr/NaCl precipitate, driving the equilibrium); Swarts reaction: R–X + AgF → R–F.

Haloarenes undergo electrophilic substitution at ortho/para positions because halogen is mildly deactivating but ortho/para directing.

Wurtz reaction (Na in dry ether) couples two alkyl halides to an alkane; Wurtz–Fittig uses aryl and alkyl halide to make alkylbenzene.

Bond strength C–F > C–Cl > C–Br > C–I, so RI is most reactive toward nucleophilic substitution and C–F is strongest.

Haloalkanes with a β-hydrogen undergo dehydrohalogenation with alcoholic KOH to give alkenes (Saytzeff product preferred); aqueous KOH gives the alcohol.

Classification: primary, secondary, tertiary alcohols by the carbon bearing –OH; allylic and benzylic alcohols are especially reactive toward substitution.

Boiling point order for similar molar mass: alcohol > ether > alkane, because alcohols hydrogen-bond intermolecularly; ethers do not H-bond to themselves.

Acidity of alcohols in water: CH₃OH > primary > secondary > tertiary, because alkyl groups destabilise the alkoxide and solvation favours smaller ions.

Phenol is much more acidic than ethanol (pKa ≈ 10 vs 16) because the phenoxide ion is resonance-stabilised; electron-withdrawing groups (NO₂) increase phenol acidity, especially at ortho/para.

Phenol with neutral FeCl₃ gives a violet/blue/green colour; used as a test distinguishing phenols from alcohols.

Reimer–Tiemann: phenol + CHCl₃/NaOH → salicylaldehyde (ortho); Kolbe: phenol + NaOH then CO₂ then H⁺ → salicylic acid; Williamson: RONa + R′X → R–O–R′.

Lucas reagent (conc. HCl + anhydrous ZnCl₂): tertiary alcohol turns cloudy immediately, secondary within about 5 min, primary only on heating.

Ethers are cleaved by conc. HBr/HI: with excess HI, R–O–R′ gives R–I + R′–I; the smaller alkyl group generally forms the iodide first.

Oxidation: primary alcohol → aldehyde → carboxylic acid; secondary → ketone; tertiary resists oxidation under mild conditions. PCC stops at aldehyde; acidic KMnO₄ goes to acid.

Nucleophilic addition is the characteristic reaction of carbonyls; aldehydes are more reactive than ketones because of less steric hindrance and less electron donation by alkyl groups.

Tollens' reagent (ammoniacal AgNO₃) gives a silver mirror with aldehydes, not with ketones except α-hydroxy ketones.

Fehling's solution gives a red Cu₂O precipitate with aliphatic aldehydes; benzaldehyde does not respond (aromatic aldehydes fail Fehling's).

Iodoform test (I₂/NaOH) is positive for CH₃CO– groups and for CH₃CH(OH)– groups, e.g. acetaldehyde, acetone, ethanol, isopropanol.

Aldol condensation requires an α-hydrogen; benzaldehyde has none, so it undergoes Cannizzaro reaction (disproportionation to benzoate and benzyl alcohol) with conc. alkali.

Clemmensen reduction (Zn–Hg/HCl) and Wolff–Kishner (NH₂NH₂/KOH) convert C=O to CH₂; NaBH₄ reduces only carbonyl, not C=C or –COOH.

Carboxylic acids are stronger acids than alcohols and phenols; formic acid is the strongest of the simple monocarboxylic acids and also reduces Tollens' reagent.

Acid strength falls with electron-donating alkyl groups: HCOOH > CH₃COOH > CH₃CH₂COOH; chloroacetic acids are much stronger (ClCH₂COOH, Cl₂CHCOOH, Cl₃CCOOH increasing).

HVZ reaction: carboxylic acid with X₂/red P gives α-halo acid; used to build amino acids.

Classification: primary (R–NH₂), secondary (R₂NH), tertiary (R₃N); quaternary ammonium salts have four alkyl groups and a permanent positive charge.

Basicity in water: aliphatic amines > ammonia > aromatic amines (aniline pKb ≈ 9.4); aryl amines are weaker because the lone pair is delocalised into the ring.

In aqueous solution, secondary aliphatic amines are often the strongest base because of a balance between inductive electron release and solvation of the conjugate acid.

Hofmann bromamide degradation: RCONH₂ + Br₂ + 4KOH → RNH₂ (one carbon fewer); used to prepare pure primary amines.

Gabriel phthalimide synthesis gives primary amines only, and fails for aryl amines because aryl halides do not undergo SN2.

Hinsberg test: primary amine reacts with benzenesulphonyl chloride to give a soluble product; secondary gives an insoluble sulphonamide; tertiary does not react.

Carbylamine test: primary amines + CHCl₃ + alcoholic KOH give foul-smelling isocyanides; a specific test for primary amines.

Diazonium salt chemistry: aniline + NaNO₂/HCl at 0–5 °C → benzenediazonium chloride; coupling with phenol gives azo dye, with H₃PO₂ gives benzene.

Amines are more nucleophilic than alcohols and react with acid chlorides to give amides; tertiary amines are basic but do not form amides.

Carbohydrates: monosaccharides (glucose, fructose) cannot be hydrolysed; disaccharides (sucrose, lactose, maltose) give two monosaccharide units; polysaccharides give many.

Glucose is an aldohexose with a straight chain of six carbons; fructose is a ketohexose and is a structural isomer of glucose.

Reducing sugars (glucose, fructose, maltose, lactose) reduce Tollens' and Fehling's reagents; sucrose is non-reducing because its glycosidic link joins both anomeric carbons.

Glucose with Br₂ water gives gluconic acid, with HNO₃ gives saccharic acid, and with excess phenylhydrazine gives a glucosazone - evidence for the open-chain structure.

Amino acids are zwitterionic near neutral pH; the pH at which the zwitterion dominates is the isoelectric point (e.g. glycine ≈ 5.97).

Peptide bond is formed between the –COOH of one amino acid and the –NH₂ of another with loss of water; primary structure is the amino acid sequence.

Nucleic acids: DNA contains deoxyribose and bases A, G, C, T; RNA contains ribose and uracil instead of thymine.

DNA double helix is held by hydrogen bonds between complementary base pairs (A–T, G–C) and base stacking; G–C pairs have three hydrogen bonds, A–T have two.

Enzymes are proteins that act as highly specific biological catalysts; a competitive inhibitor binds the active site and raises apparent K_m, a non-competitive inhibitor does not.

Group 15: nitrogen is a gas (N₂) with a strong triple bond; phosphorus exists as white P₄ (tetrahedral, reactive) and red phosphorus (polymeric, less reactive).

Group 16: oxygen shows –2 in most compounds but –1 in peroxides (H₂O₂) and –1/2 in superoxides (KO₂); ozone is bent with a bond angle near 117°.

Group 17: oxidising power falls down the group F₂ > Cl₂ > Br₂ > I₂; fluorine is the strongest oxidising agent because of low bond dissociation energy and high hydration energy.

Interhalogen compounds (ClF, ClF₃, BrF₅, IF₇) form because halogen–halogen bonds are weaker than halogen–halogen bonds of the heavier partner; larger halogens show higher fluorides.

Group 18: noble gases are monatomic and have very high ionisation energies; Xe forms XeF₂, XeF₄, XeF₆, while He, Ne and Ar form essentially no stable compounds.

Group 15 hydrides: NH₃ > PH₃ > AsH₃ > SbH₃ > BiH₃ in decreasing thermal stability and basicity; NH₃ has the highest boiling point due to hydrogen bonding.

Allotropes of carbon: diamond (sp³, hard, non-conducting), graphite (sp², layered, conducts), fullerene C₆₀ (molecular, 12 pentagons and 20 hexagons).

Oxides of nitrogen: N₂O (laughing gas), NO (colourless radical), NO₂ (brown, dimerises to N₂O₄), N₂O₅ (anhydride of HNO₃), N₂O₃ (anhydride of HNO₂).

Bleaching powder is Ca(OCl)Cl (calcium hypochlorite + calcium chloride); with dilute acid it liberates Cl₂, and it is used to disinfect water.

Cation flame colours: Na⁺ golden yellow, K⁺ lilac (violet), Ca²⁺ brick red, Sr²⁺ crimson, Ba²⁺ apple green, Cu²⁺ blue-green.

Group reagents: dilute HCl gives group I (Pb²⁺, Ag⁺, Hg₂²⁺); H₂S in acidic medium gives group II (Cu²⁺, Cd²⁺, Bi³⁺, Sn²⁺); NH₄OH + H₂S gives group III (Fe³⁺, Al³⁺, Cr³⁺); (NH₄)₂CO₃ gives group IV (Ca²⁺, Ba²⁺, Sr²⁺); group V is Mg²⁺.

Anion tests: CO₃²⁻ gives effervescence with dilute acid (CO₂ turns limewater milky); SO₃²⁻ gives SO₂ (decolourises KMnO₄); SO₄²⁻ gives white BaSO₄ insoluble in conc. HCl; Cl⁻ gives white AgCl soluble in NH₄OH.

Nitrate test (brown ring): add FeSO₄ then conc. H₂SO₄ slowly down the side of the tube - a brown ring of FeSO₄·NO forms at the junction.

Chromyl chloride test for chloride: solid + K₂Cr₂O₇ + conc. H₂SO₄ gives red vapours of CrO₂Cl₂, which turn NaOH yellow (chromate).

Ammonium test: heat the salt with NaOH; a gas that turns moist red litmus blue and gives white fumes with a glass rod dipped in HCl confirms NH₄⁺.

Purity of an organic solid is checked by sharp melting point; impurities lower and broaden the melting range.

Sodium fusion test: Na metal converts N, S and halogens in an organic compound to NaCN, Na₂S and NaX; then test the extract with FeSO₄/FeCl₃ (Prussian blue for N+S), lead acetate (black PbS for S) and AgNO₃ (halide).

Titration of oxalic acid against KMnO₄ is self-indicating (pink end point) and is carried out warm (about 60 °C) in acidic medium; H₂SO₄ is used, not HCl, which KMnO₄ would oxidise.