AP Intermediate Chemistry (BIEAP) cheat sheet

Bohr model: En = -13.6 Z^2/n^2 eV for hydrogenic atoms; radius rn = 0.529 n^2/Z Å.

Rydberg equation: 1/λ = R Z^2 (1/n1^2 - 1/n2^2), R = 1.097×10^7 m^-1; Lyman n1=1 (UV), Balmer n1=2 (visible), Paschen n1=3 (IR).

de Broglie: λ = h/mv; h = 6.626×10^-34 J s. Heisenberg: Δx·Δp ≥ h/4π.

Quantum numbers: n ≥ 1; l = 0 to n-1 (s,p,d,f); ml = -l to +l; ms = ±1/2. Max electrons in shell = 2n^2.

Aufbau order follows (n+l) rule; for equal (n+l), lower n fills first. Exchange energy and symmetry decide half-filled stability (Cr 3d5 4s1, Cu 3d10 4s1).

Hund's rule: degenerate orbitals are singly occupied with parallel spins before pairing; pairing energy opposes it.

Orbital shapes: s spherical, p dumb-bell with one nodal plane, d double dumb-bell with two nodal planes; nodes = n-1 total, l angular.

Photoelectric effect: hv = hv0 + KE_max; threshold frequency ν0 = W0/h. Intensity controls electron count, frequency controls KE.

Modern periodic law: properties are periodic functions of atomic number. Long form has 7 periods and 18 groups; group 18 are noble gases.

Across a period: nuclear charge rises, atomic radius and metallic character fall, ionisation enthalpy, electron gain enthalpy (more negative) and electronegativity rise.

Down a group: shielding and size increase, so ionisation enthalpy and electronegativity decrease; metallic character increases.

Ionisation enthalpy order: IE1 < IE2 < IE3. Exceptions: Be > B and N > O in period 2; Mg > Al and P > S in period 3.

Electron gain enthalpy of Cl is more negative than F (small F has electron-electron repulsion in 2p); noble gases have positive ΔegH.

Cation radius < neutral atom < anion radius for the same element; isoelectronic species: larger nuclear charge gives smaller radius.

Diagonal relationship: Li-Mg, Be-Al, B-Si show similar chemistry because of comparable charge/radius ratio.

Lewis structures obey the octet rule with formal charge = (valence electrons) - (lone pair electrons) - ½(bonding electrons).

VSEPR: electron pairs repel in order lone pair-lone pair > lone pair-bond pair > bond pair-bond pair; count lone pairs on the central atom to predict shape.

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

Bond order = ½(Nb - Na); higher bond order means shorter, stronger bond. O2 has bond order 2 and is paramagnetic (two unpaired π* electrons).

MO energy order for O2, F2, Ne2: σ2s < σ2s < σ2pz < π2px = π2py < π2px = π2py < σ2pz; for B2, C2, N2 the π orbitals lie below σ2pz.

Polarity: μ = q × d (debye); a molecule with polar bonds can be nonpolar if dipoles cancel (CO2, CCl4, BF3).

Hydrogen bonding (F, O, N) raises boiling point and explains water's high specific heat; H-F···H-F is the strongest such interaction.

Ideal gas law: PV = nRT, R = 0.0821 L atm mol^-1 K^-1 = 8.314 J mol^-1 K^-1; STP molar volume 22.4 L.

Dalton's law: P_total = ΣPi; partial pressure Pi = xi P_total where xi is mole fraction.

Graham's law: r1/r2 = √(M2/M1); rate of effusion is inversely proportional to square root of molar mass.

van der Waals equation: (P + an^2/V^2)(V - nb) = nRT; a measures attractive forces, b measures molecular volume.

Critical temperature Tc: above it a gas cannot be liquefied by pressure alone; liquefaction is easier at low T and high P.

Kinetic molecular theory: average KE = (3/2)kT per molecule; root mean square speed = √(3RT/M).

Maxwell distribution: raising temperature broadens the curve and shifts the peak to higher speed; lighter gases have higher average speed at the same T.

Boyle temperature: at T = TB, a real gas obeys Boyle's law over a wide pressure range; TB = a/(Rb).

First law: ΔU = q + w; for expansion work w = -PΔV. Enthalpy H = U + PV, so ΔH = ΔU + ΔnRT for reactions involving gases.

Sign conventions: q positive when heat is absorbed by the system, w positive when work is done on the system.

Hess's law: ΔH of a reaction is path-independent; combine formation enthalpies ΔH°rxn = ΣΔH°f(products) - ΣΔH°f(reactants).

Standard enthalpy of formation of an element in its standard state is zero; enthalpy of neutralisation of a strong acid by a strong base is about -57.1 kJ mol^-1.

Entropy: ΔS > 0 for solid→liquid→gas, for increasing moles of gas, and generally on heating. ΔS°rxn = ΣS°(products) - ΣS°(reactants).

Gibbs energy: ΔG = ΔH - TΔS. Spontaneous when ΔG < 0; at equilibrium ΔG = 0 and ΔG° = -RT ln K.

Calorimetry: q = mcΔT; bomb calorimeter gives ΔU (constant volume), cup calorimeter gives ΔH (constant pressure).

Second law: total entropy of the universe increases in a spontaneous process; ΔS_univ = ΔS_system + ΔS_surroundings.

Law of mass action: for aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d/([A]^a[B]^b); Kp = Kc(RT)^Δn.

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

For a reaction multiplied by n, K becomes K^n; reversing gives 1/K; adding reactions multiplies their K values.

Kw = [H+][OH-] = 1.0×10^-14 at 25 °C; pH + pOH = 14; pH = -log[H+].

Weak acid: Ka = [H+][A-]/[HA], and [H+] = √(Ka·C) for small dissociation; pKa = -log Ka.

Henderson-Hasselbalch: pH = pKa + log([salt]/[acid]) for an acidic buffer; buffers resist pH change near pKa.

Solubility product: for AB, Ksp = s^2; for AB2, Ksp = 4s^3. Precipitation occurs when the ionic product exceeds Ksp.

Salt hydrolysis: salts of weak acid and strong base give pH > 7; weak base and strong acid give pH < 7; weak acid plus weak base depends on Ka vs Kb.

Oxidation is loss of electrons and increase in oxidation number; reduction is gain. Oxidising agent is reduced, reducing agent is oxidised.

Balance redox in acidic medium with H2O and H+; in basic medium add OH- to neutralise H+ after balancing electrons.

Nernst equation at 298 K: E = E° - (0.0591/n) log Q; for a cell E°cell = E°cathode - E°anode.

Standard electrode potential of the hydrogen electrode is 0.000 V at 1 M H+, 1 bar, 298 K by convention.

ΔG° = -nFE° and E°cell = (0.0591/n) log K; positive E°cell means spontaneous cell reaction.

In a galvanic cell, oxidation occurs at the anode (negative terminal) and reduction at the cathode; electrons flow from anode to cathode in the external circuit.

Electrolysis: charge Q = It; mass deposited m = (MIt)/(nF), F = 96500 C mol^-1.

Conductivity: molar conductivity Λm = κ/c; for strong electrolytes Λm falls linearly with √c, for weak electrolytes sharply on dilution.

Rate = -d[A]/dt for a reactant; rate law rate = k[A]^x[B]^y where x and y are experimental orders, not stoichiometric coefficients.

Zero order: [A] = [A]0 - kt, t½ = [A]0/2k. First order: ln[A] = ln[A]0 - kt, t½ = 0.693/k, independent of concentration.

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). A catalyst lowers Ea without changing ΔH.

Collision theory requires proper orientation and energy ≥ activation energy; temperature raises the fraction of molecules with sufficient energy.

Physisorption: weak van der Waals forces, low enthalpy, reversible, multilayer. Chemisorption: strong bonds, high enthalpy, irreversible, monolayer.

Freundlich isotherm: x/m = k p^(1/n), with 0 < 1/n < 1; log plot gives a straight line.

Lyophilic sols are stable and reversible; lyophobic sols need electrolytes and coagulate readily. Hardy-Schulze rule: higher coagulating ion charge is more effective.

Hydrogen: isotopes protium, deuterium, tritium; ortho and para forms differ in nuclear spin. H2O2 acts as both oxidising and reducing agent.

Alkali metals: low ionisation enthalpy, form M+ ions, react vigorously with water giving H2 and hydroxide; reactivity increases down the group.

Alkaline earth metals: Be is amphoteric and covalent in bonding; Mg, Ca, Sr, Ba form ionic compounds. Group 2 hydroxides become more soluble down the group.

Diagonal pair Be-Al: both form amphoteric oxides and covalent halides; Li-Mg both form nitride on heating with N2.

Group 13: B is nonmetallic, Al amphoteric; borax Na2B4O7·10H2O and diborane B2H6 (banana bonds, 3-centre 2-electron).

Group 14: carbon shows allotropy (diamond, graphite, fullerene); CO is neutral, CO2 acidic; SiO2 is a network solid.

Group 15: N2 is inert due to triple bond; NH3 basic, HNO3 strong oxidiser; white and red phosphorus differ in structure.

Group 16 and 17: H2O > H2S > H2Se boiling point trend is broken by hydrogen bonding in water; acid strength HI > HBr > HCl > HF.

Transition metals: partly filled d orbitals, variable oxidation states, coloured ions, catalytic activity and paramagnetism.

Ligand types: monodentate (NH3, Cl-), bidentate (en, oxalate), polydentate (EDTA is hexadentate); coordination number is the number of donor atoms bonded to the metal.

Nomenclature: name ligands alphabetically before the metal; anionic complex ends in -ate; oxidation state shown in Roman numerals.

Isomerism: ionisation, hydrate, linkage (NO2 vs ONO), coordination, geometric (cis/trans) and optical isomers in octahedral complexes.

Crystal field: Δo splitting; strong-field ligands (CN-, CO) give low-spin and large Δo, weak-field (Cl-, H2O) give high-spin.

Colour arises from d-d transitions; [Cu(NH3)4]^2+ is deep blue, [Cu(H2O)4]^2+ is pale blue. Spectrochemical series orders ligand field strength.

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

EAN rule and stability: chelate complexes are extra stable (chelate effect) because of favourable entropy of formation.

IUPAC naming: longest chain, lowest locants, suffix for principal functional group; priority -COOH > -CHO > -OH > -NH2 > alkene > alkyne.

Isomerism: chain, position, functional group, tautomerism (keto-enol), geometric (cis/trans, E/Z) and optical (chiral centre with four different groups).

Homolytic fission gives radicals (initiators, light, heat); heterolytic fission gives carbocations and carbanions.

Carbocation stability: 3° > 2° > 1° > CH3+; allyl and benzyl cations are resonance-stabilised. Carbanion stability is the reverse.

SN1: two steps, carbocation intermediate, racemisation, favoured by polar protic solvents and 3° halides. SN2: one step, backside attack, inversion, favoured by 1° halides and polar aprotic solvents.

E1 and E2 compete with substitution; strong bulky base and heat favour elimination; Saytzeff rule predicts the more substituted alkene.

Electrophilic aromatic substitution: halogenation, nitration, sulphonation, Friedel-Crafts; -NO2 deactivates and is meta-directing, -OH and -NH2 activate and are ortho/para-directing.

Markovnikov's rule: H adds to the carbon with more hydrogens; peroxide effect (anti-Markovnikov) occurs with HBr only.

Alkanes: sp3 carbons, free-radical halogenation with order of reactivity F2 > Cl2 > Br2 > I2; combustion is highly exothermic.

Alkenes: sp2 carbons, planar; undergo electrophilic addition with HX, H2O, Br2 and KMnO4; Baeyer's test decolourises cold dilute KMnO4.

Alkynes: sp carbons, linear; terminal alkynes are acidic and react with Na to give acetylides; hydration gives acetaldehyde (ethyne) or ketones.

Benzene: aromatic, planar, delocalised 6π electrons; substitution rather than addition; undergoes nitration, sulphonation, Friedel-Crafts alkylation and acylation.

Haloalkanes: C-X bond polar; reactivity to nucleophilic substitution RI > RBr > RCl > RF. Haloarenes are far less reactive because of partial double-bond character and sp2 carbon.

Grignard reagent RMgX reacts with water, aldehydes, ketones and CO2; must be prepared in dry ether.

Haloarenes undergo nucleophilic substitution only with strong nucleophiles at activated positions (e.g., 2,4-dinitrochlorobenzene).

Chloroform (CHCl3) is oxidised to phosgene COCl2 on exposure to air and light; stored in dark bottles with ethanol.

Alcohols: primary, secondary, tertiary; oxidised to aldehydes (primary, with K2Cr2O7), ketones (secondary); tertiary alcohols resist oxidation. Lucas test distinguishes them.

Phenols: acidic because the phenoxide ion is resonance-stabilised; give violet colour with neutral FeCl3; undergo electrophilic substitution readily.

Ethers: relatively inert, cleaved by HI to give alcohol and iodoalkane; Williamson synthesis uses alkoxide plus alkyl halide.

Aldehydes and ketones: nucleophilic addition with HCN, NaHSO3, alcohols; Tollens' and Fehling's tests are positive for aldehydes only; iodoform test for CH3CO- group.

Carboxylic acids: pKa about 4-5; electron-withdrawing groups increase acidity (ClCH2COOH > CH3COOH); react with NaHCO3 giving CO2.

Amines: basicity 2° > 1° > 3° in water for methylamines; aniline is less basic than ammonia because the lone pair is delocalised into the ring.

Diazonium salt: benzene diazonium chloride prepared at 273-278 K; couples with phenol to give azo dyes and is replaced by OH, Cl, CN or I.

Amides and nitro compounds: nitrobenzene is reduced to aniline; amides are hydrolysed by acid or base and show hydrogen bonding.