PRC Chemist cheat sheet

Mole: n = m/M; Avogadro's number N_A = 6.022×10^23 particles/mol; molar volume of ideal gas at STP (0 °C, 101.325 kPa) = 22.414 L/mol.

Ideal gas law: PV = nRT, R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K); use PV = (m/M)RT to get molar mass from density.

Limiting reagent: divide each reactant's moles by its stoichiometric coefficient; smallest quotient limits; theoretical yield = limiting moles × product coefficient ratio × M.

Equilibrium: K = products/reactants raised to coefficients (pure solids/liquids omitted); Kp = Kc(RT)^Δn; Q < K favors forward, Q > K favors reverse.

Le Chatelier: raising pressure favors the side with fewer gas moles; raising temperature favors the endothermic direction; a catalyst changes rate only, not K.

Acid-base: pH = −log[H3O+]; Kw = 1.0×10^-14 at 25 °C; Henderson–Hasselbalch pH = pKa + log([A−]/[HA]); buffer capacity peaks at pH = pKa.

Solubility: Ksp = [cation]^a[anion]^b; molar solubility s of AB = √Ksp, of AB2 = (Ksp/4)^(1/3); common ion lowers s.

Electrochemistry: ΔG° = −nFE°; E°cell = E°cathode − E°anode; Nernst E = E° − (0.0592/n)logQ at 25 °C.

Thermochemistry: ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants); Hess's law sums step enthalpies; bond breaking absorbs, bond forming releases energy.

Volumetric: at equivalence, moles titrant = moles analyte × stoichiometric ratio; for weak acid–strong base, pH at equivalence > 7; for weak base–strong acid, pH < 7.

Primary standard requirements: high purity, stable, non-hygroscopic, high molar mass (reduces weighing error); examples: KHP, Na2CO3, oxalic acid, K2Cr2O7.

Gravimetry: mass of analyte = mass of precipitate × (M_analyte / M_precipitate) × (coefficient ratio); wash and ignite to constant mass.

Beer–Lambert: A = εbc; A = −log T; linear range typically 0.1–1.0; deviations from monochromaticity, stray light, and high concentration.

Standard addition: plot signal vs added concentration; x-intercept gives original concentration; corrects for matrix effects.

Calibration: slope = sensitivity; LOD ≈ 3.3σ/slope; LOQ ≈ 10σ/slope, where σ is the standard deviation of blank measurements.

Chromatography: retention factor k = (t_R − t_0)/t_0; resolution R = 2(t_R2 − t_R1)/(w1 + w2), baseline R ≥ 1.5; N = 16(t_R/w)^2.

Redox titration: equivalent weight = M / (electrons transferred per formula unit); permanganometry is self-indicating (pink endpoint); iodometry uses starch indicator.

Statistics: confidence interval x̄ ± ts/√n; Grubbs test flags outliers; Q-test compares gap/range to a critical value.

Functional group priority for IUPAC naming: carboxylic acid > ester > amide > nitrile > aldehyde > ketone > alcohol > amine > alkene > alkyne > alkane > ether > halide.

SN1 vs SN2: SN2 is one-step, backside attack, inversion, favored by methyl/primary substrates, strong nucleophile, polar aprotic solvent; SN1 is two-step carbocation, favored by tertiary, polar protic, racemization.

E1/E2: E2 is concerted, anti-periplanar, favored by strong bulky base (t-BuOK) and heat; E1 shares carbocation intermediate with SN1, favored by heat and weak base.

Electrophilic aromatic substitution: activating groups (–OH, –NH2, –OR, –R) are ortho/para directors; deactivating groups (–NO2, –CN, –SO3H, carbonyls) are meta directors; halogens are deactivating but o/p directing.

Carbonyl reactivity order (acyl substitution): acid chloride > anhydride > ester > amide; nucleophilic addition favored for aldehydes > ketones > esters.

Aldol and Claisen: enolate formed by base at α-carbon; aldol gives β-hydroxy carbonyl (condensation to enone on heating); Claisen gives β-keto ester.

Grignard and organolithium reagents add to aldehydes (→ secondary alcohol), ketones (→ tertiary alcohol), esters (→ tertiary alcohol, two additions), CO2 (→ carboxylic acid).

Stereochemistry: R/S by CIP priority; E/Z by CIP on each alkene carbon; a molecule with n stereocenters has up to 2^n stereoisomers; meso compounds are achiral despite stereocenters.

Oxidation/reduction: PCC or DMP oxidizes primary alcohol to aldehyde; KMnO4/H2CrO4 to carboxylic acid; NaBH4 reduces aldehydes/ketones only; LiAlH4 reduces esters and acids too.

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

Entropy: ΔS = q_rev/T; ΔS_universe ≥ 0 for spontaneity; ΔG = ΔH − TΔS; ΔG < 0 spontaneous at constant T, P.

Clausius–Clapeyron: ln(P2/P1) = −(ΔH_vap/R)(1/T2 − 1/T1); use to get vapor pressure or enthalpy of vaporization.

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

First-order kinetics: t½ = ln2/k = 0.693/k; [A] = [A]0 e^(−kt); second-order t½ = 1/(k[A]0).

Colligative properties: ΔTb = i·Kb·m; ΔTf = i·Kf·m; π = iMRT; i = van't Hoff factor (number of ions per formula unit for strong electrolytes).

Quantum: E = hν; λ = h/(mv) (de Broglie); Δx·Δp ≥ ħ/2; Rydberg 1/λ = R(1/n1² − 1/n2²).

Electrochemistry/thermodynamics link: ΔG° = −RT ln K = −nFE°; Nernst slope 0.0592/n V per decade at 25 °C.

Phase rule: F = C − P + 2; a pure substance at the triple point has F = 0; at the critical point liquid and gas become indistinguishable.

Michaelis–Menten: v = Vmax[S]/(Km + [S]); Km = [S] at v = Vmax/2; Lineweaver–Burk 1/v = (Km/Vmax)(1/[S]) + 1/Vmax.

Inhibition: competitive raises apparent Km, Vmax unchanged; noncompetitive lowers Vmax, Km unchanged; uncompetitive lowers both Km and Vmax.

Glycolysis: glucose → 2 pyruvate, net 2 ATP, 2 NADH; committed step phosphofructokinase-1 (PFK-1), regulated by ATP (inhibits) and AMP/F-2,6-BP (activate).

TCA cycle per acetyl-CoA: 3 NADH, 1 FADH2, 1 GTP; oxidative phosphorylation yields ~2.5 ATP/NADH and ~1.5 ATP/FADH2 (modern P/O ratios).

Central dogma: DNA → RNA (transcription) → protein (translation); codons are triplet, degenerate, non-overlapping; start AUG (Met), stop UAA/UAG/UGA.

Nucleic acid structure: A–T two H-bonds, G–C three H-bonds; Chargaff's rule A = T, G = C; DNA melting temperature rises with GC content.

Protein structure: primary (sequence), secondary (α-helix, β-sheet via H-bonds), tertiary (3D fold), quaternary (subunits); denaturation disrupts noncovalent bonds, not peptide bonds.

Lipids and membranes: fatty acid β-oxidation yields acetyl-CoA + FADH2 + NADH; ketone bodies form when acetyl-CoA exceeds TCA capacity; cholesterol is a steroid precursor.

Enzyme kinetics with pH/temperature: activity peaks at optimum; temperature above optimum denatures; allosteric enzymes show sigmoidal v vs [S] kinetics.

Haber–Bosch: N2 + 3H2 ⇌ 2NH3, exothermic (ΔH ≈ −92 kJ/mol); high pressure (~200 atm), moderate temperature (~450 °C), Fe catalyst with K2O/Al2O3 promoters; Le Chatelier favors low T, high P.

Contact process (H2SO4): S → SO2 → SO3 (V2O5 catalyst, ~450 °C); SO3 absorbed in concentrated H2SO4, not water, to avoid acid mist.

Ostwald process (HNO3): NH3 oxidized over Pt-Rh gauze (~800–900 °C) to NO, then NO → NO2 → HNO3 by absorption in water.

Solvay process (Na2CO3): NaCl + NH3 + CO2 → NaHCO3 precipitate + NH4Cl; NaHCO3 calcined to Na2CO3; NH3 recovered by lime.

Chlor-alkali: electrolysis of brine yields Cl2 at anode, H2 and NaOH at cathode; membrane cell avoids mercury and asbestos hazards.

Petroleum refining: fractional distillation by boiling point; cracking (thermal/catalytic) breaks large alkanes; reforming raises octane; alkylation and isomerization improve fuel quality.

Yield and economics: percent yield = (actual/theoretical) × 100; atom economy = (M of desired product / ΣM of reactants) × 100; E-factor = mass waste / mass product.

Safety and environment: exothermic reactors need cooling and relief systems; NOx and SO2 emissions controlled by scrubbers and catalytic converters; CO2 capture targets cement and ammonia plants.