ACS cheat sheet

Signal-to-noise: S/N = 2 is the limit of detection, S/N = 10 is the limit of quantitation; both are defined as 3σ and 10σ of the blank for chromatographic methods.

Calibration: external standard assumes constant response factor; standard addition is required when matrix effects suppress or enhance signal; internal standard corrects for injection volume and detector drift.

Beer-Lambert law A = εbc; linearity fails above A ≈ 1.0–1.5 due to stray light and polychromatic radiation, so dilute rather than extrapolate.

Chromatography: resolution R = 2(t₂ − t₁)/(w₁ + w₂); R ≥ 1.5 is baseline separation. Efficiency N = 16(t_R/w)² and selectivity α = k₂/k₁; retention factor k = (t_R − t₀)/t₀.

Van Deemter: H = A + B/u + Cu; minimum plate height occurs where longitudinal diffusion (B) and mass-transfer (C) terms balance, typically at higher flow for small particles.

Acid-base titrations: equivalence point pH for a weak acid/strong base is > 7; buffer region pH = pKa + log([A⁻]/[HA]). Choose an indicator whose pKa lies within ±1 of the equivalence pH.

Gravimetric analysis requires a weighing form that is stable, stoichiometric, and of high molar mass relative to the analyte to minimize relative weighing error.

Atomic spectroscopy: flame AAS suits readily atomized metals at ppm; graphite furnace reaches ppb; ICP-MS offers ppb–ppt with multi-element capability but is prone to polyatomic interferences.

SN1 vs SN2: SN2 is concerted, second-order, favored by methyl/primary substrates, strong nucleophile, polar aprotic solvent; SN1 proceeds via carbocation, favored by tertiary substrates and polar protic solvents.

E1/E2: E2 requires anti-periplanar β-hydrogen and strong bulky base (e.g., tert-butoxide); E1 competes with SN1 under weak-base, ionizing conditions.

Aromaticity (Hückel): cyclic, planar, fully conjugated, 4n + 2 π electrons; 4n electrons give antiaromatic character. Pyridine is aromatic; pyrrole's lone pair participates in the sextet.

Carbonyl reactivity: aldehydes > ketones > esters > amides toward nucleophilic addition; resonance donation by N or O stabilizes the carbonyl and suppresses attack.

Grignard and organolithium reagents are strong bases and nucleophiles; they require anhydrous aprotic conditions and are destroyed by protic solvents.

Markovnikov addition: H adds to the carbon with more hydrogens; anti-Markovnikov occurs via radical (HBr/peroxide) or hydroboration-oxidation.

Chirality: a stereocenter bears four different groups; R/S assigned by CIP priorities with lowest priority pointing away. Enantiomers rotate plane-polarized light equally and oppositely.

Protecting groups: TBDMS for alcohols (cleaved by fluoride), Boc for amines (cleaved by acid), acetal for ketones (cleaved by aqueous acid).

First law: ΔU = q + w; for reversible isothermal expansion of an ideal gas, w = −nRT ln(V₂/V₁) and ΔU = 0.

Second law: ΔS_univ ≥ 0; ΔG = ΔH − TΔS determines spontaneity at constant T and P, with equilibrium at ΔG = 0.

Clausius-Clapeyron: ln(P₂/P₁) = −(ΔH_vap/R)(1/T₂ − 1/T₁); vapor pressure rises exponentially with temperature.

Arrhenius: k = A exp(−Ea/RT); the linear form ln k = ln A − Ea/RT gives Ea from the slope.

Equilibrium: K relates to ΔG° via ΔG° = −RT ln K; van't Hoff equation gives temperature dependence of K from ΔH°.

Kinetics: first-order half-life t½ = ln2/k is concentration-independent; second-order t½ = 1/(k[A]₀) depends on initial concentration.

Quantum: E = hν; particle in a box E_n = n²h²/(8mL²); the harmonic oscillator has equally spaced levels with zero-point energy ½hν.

Electrochemistry: ΔG° = −nFE°cell and Nernst E = E° − (RT/nF) ln Q; at 298 K the factor RT/F ≈ 0.0257 V.

Crystal field splitting: Δo increases with higher metal oxidation state and with stronger-field ligands following the spectrochemical series (I⁻ < Br⁻ < Cl⁻ < F⁻ < H₂O < NH₃ < CN⁻ < CO).

High-spin vs low-spin: weak-field ligands give high-spin configurations with unpaired electrons and paramagnetism; strong-field ligands give low-spin, often diamagnetic complexes.

18-electron rule predicts stability for transition-metal carbonyls and organometallics; count metal d electrons plus electrons donated by each ligand.

Lanthanide contraction: ionic radius decreases across the 4f series because poorly shielding 4f electrons increase effective nuclear charge.

Hard/soft acid-base (HSAB): hard acids pair with hard bases (e.g., Al³⁺ with F⁻, O-donors); soft acids pair with soft bases (e.g., Hg²⁺, Ag⁺ with S-donors, I⁻).

Periodic trends: ionization energy and electronegativity increase across a period and decrease down a group; atomic radius follows the reverse pattern.

Coordination number and geometry: CN 4 gives tetrahedral or square planar; CN 6 gives octahedral. Square planar is favored by d⁸ ions such as Pt(II) and Pd(II).

Jahn-Teller distortion is pronounced for orbitally degenerate ground states, notably high-spin d⁴ and d⁹ octahedral complexes, which elongate along one axis.

Michaelis-Menten: v = Vmax[S]/(Km + [S]); Km is the substrate concentration at half Vmax and approximates substrate affinity (lower Km means higher affinity).

Lineweaver-Burk plot (1/v vs 1/[S]): slope = Km/Vmax, y-intercept = 1/Vmax. Competitive inhibition raises apparent Km; noncompetitive lowers Vmax.

Glycolysis yields net 2 ATP and 2 NADH per glucose; complete oxidation to CO₂ gives about 30–32 ATP including oxidative phosphorylation.

Enzyme catalysis lowers activation energy without changing ΔG of the reaction; the transition state is stabilized, and the enzyme is not consumed.

DNA base pairing: A pairs with T via two hydrogen bonds; G pairs with C via three, giving higher melting temperature for GC-rich duplexes.

Protein structure: primary is sequence; secondary is α-helix and β-sheet stabilized by backbone hydrogen bonds; tertiary is overall 3D fold; quaternary is subunit assembly.

ATP hydrolysis releases about 30.5 kJ/mol under standard conditions; phosphorylation by kinases and dephosphorylation by phosphatases regulate enzyme activity.

Central dogma: DNA is transcribed to mRNA by RNA polymerase, then translated to protein by ribosomes using the genetic code, with three-base codons.

Number-average and weight-average molecular weight: Mn = ΣNiMi/ΣNi, Mw = ΣNiMi²/ΣNiMi; polydispersity index PDI = Mw/Mn ≥ 1, equal to 1 for a monodisperse sample.

Step-growth polymerization requires high conversion for high molecular weight (Carothers equation); chain-growth polymerization gives high molecular weight even at low conversion.

Free-radical polymerization has initiation, propagation, and termination (combination or disproportionation) steps; chain transfer limits molecular weight.

Tg (glass transition) rises with increasing chain stiffness, crystallinity, and crosslink density; plasticizers lower Tg by increasing free volume.

Copolymer types: random, alternating, block, and graft. The monomer reactivity ratios r₁ and r₂ determine composition drift and sequence distribution.

Ziegler-Natta and metallocene catalysts give stereoregular polyolefins; isotactic polypropylene is crystalline, whereas atactic material is amorphous.

Degradation mechanisms include hydrolysis (polyesters, polyamides), oxidation, and photodegradation; crosslinking generally improves solvent resistance and thermal stability.

Thermosets are irreversibly crosslinked (epoxies, phenolics); thermoplastics soften reversibly on heating and can be reprocessed.