MSCE Chemistry cheat sheet

Quantum numbers: n (1,2,3...), l (0 to n-1), m_l (-l to +l), m_s (±1/2); no two electrons in an atom share all four.

Orbital energies follow the Aufbau order 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p; (n+l) rule breaks 4s/3d and 5s/4d ties.

Hund's rule: within a degenerate set, maximize unpaired electrons with parallel spins before pairing.

Effective nuclear charge Z_eff = Z - S (Slater); across a period Z_eff rises, so atomic radius falls and ionization energy rises.

Ionization energy increases left-to-right and decreases down a group; exceptions at Group 2→13 and 15→16 due to filled/half-filled subshells.

Electron affinity is most negative for Group 17; noble gases and alkaline earths have near-zero or positive values.

Periodic anomalies: atomic radius of Ga < Al and Tl < In due to d-block contraction; lanthanide contraction explains Zr≈Hf radii.

Photoelectric/atomic spectra: E = hν = hc/λ; Rydberg 1/λ = R(1/n1² - 1/n2²) for hydrogen-like atoms.

Paramagnetism requires unpaired electrons; diamagnetic species have all electrons paired (e.g., N2 vs O2).

VSEPR electron-domain count: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs occupy equatorial positions first in TBP.

Bond order from MO theory = (bonding - antibonding)/2; O2 has bond order 2 and two unpaired π* electrons (paramagnetic).

Formal charge = valence e⁻ - nonbonding e⁻ - ½ bonding e⁻; prefer structures with formal charges closest to zero and negative charge on the more electronegative atom.

Hybridization: sp (180°), sp² (120°), sp³ (109.5°); count σ bonds + lone pairs on the central atom.

Bond polarity follows ΔEN; a molecule is polar only if bond dipoles do not cancel by symmetry (CO2 nonpolar, H2O polar).

Bond length decreases and bond energy increases with bond order: C-C > C=C > C≡C in length; reverse in energy.

Dipole-dipole < hydrogen bonding < ion-dipole in strength; London dispersion grows with polarizability/molecular size.

Resonance structures differ only in electron placement; the real structure is a weighted hybrid, with bond orders between the contributing forms.

Metallic bonding: delocalized electron sea explains conductivity, malleability, and lustre; band gap distinguishes conductors, semiconductors, insulators.

Mole conversions: n = m/M, n = N/N_A (6.022×10²³), n = V/22.414 L at STP for ideal gases.

Limiting reagent: divide moles of each reactant by its stoichiometric coefficient; the smallest quotient limits.

Percent yield = (actual/theoretical) × 100; theoretical yield derives from the limiting reagent.

Combustion analysis: all C → CO2, all H → H2O; mass fractions give empirical formula, molar mass gives molecular formula.

Solution concentration: M = mol/L; dilution M1V1 = M2V2; molality m = mol solute/kg solvent.

Redox balancing: split into half-reactions, balance atoms then O with H2O and H with H⁺ (acidic) or OH⁻ (basic), then charge with e⁻.

Oxidizing agent is reduced (gains electrons); reducing agent is oxidized (loses electrons); oxidation number rules assign O = -2, H = +1 except hydrides/peroxides.

Percent composition by mass = (mass of element in formula/molar mass) × 100; used to verify purity and empirical formulas.

Gravimetric and volumetric stoichiometry: use reaction ratios consistently through moles, never directly between masses.

Ideal gas law PV = nRT; R = 0.08206 L·atm/mol·K = 8.314 J/mol·K; combined gas law P1V1/T1 = P2V2/T2.

Dalton's law: total pressure equals sum of partial pressures; P_i = X_i·P_total.

van der Waals equation (P + an²/V²)(V - nb) = nRT corrects for intermolecular attraction (a) and molecular volume (b).

Phase diagram: triple point where all three phases coexist; critical point above which liquid and gas are indistinguishable; slope of solid-liquid line reflects density change on melting.

First law: ΔU = q + w; at constant pressure q_p = ΔH; at constant volume q_v = ΔU.

Calorimetry: q = mcΔT; for a bomb calorimeter q = C_cal·ΔT; sign conventions: exothermic ΔH < 0.

Hess's law: ΔH_total equals the sum of step enthalpies regardless of pathway; use standard enthalpies of formation: ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants).

Entropy: ΔS > 0 for increasing disorder (gas > liquid > solid); ΔS°rxn from standard entropies; Gibbs free energy ΔG = ΔH − TΔS; spontaneous when ΔG < 0.

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

Equilibrium constant K for aA + bB ⇌ cC + dD: K = [C]^c[D]^d/([A]^a[B]^b); pure solids/liquids excluded.

Reaction quotient Q compared to K: Q < K shifts right, Q > K shifts left, Q = K at equilibrium.

Le Chatelier: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; heating favors the endothermic direction.

K_p = K_c(RT)^Δn, where Δn = moles gaseous products − reactants.

Acid dissociation: K_a = [H⁺][A⁻]/[HA]; pK_a = −log K_a; smaller pK_a means stronger acid.

pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = 14 at 25 °C; K_w = 1.0×10⁻¹⁴.

Henderson-Hasselbalch: pH = pK_a + log([A⁻]/[HA]); buffer capacity is highest when pH = pK_a.

Salt hydrolysis: strong acid-strong base salts are neutral; weak acid-strong base salts are basic; weak base-strong acid salts are acidic.

Solubility product K_sp = [cation]^m[anion]^n; compare ion product Q to K_sp to predict precipitation; common-ion effect lowers solubility.

Rate law: rate = k[A]^m[B]^n; orders determined experimentally, not from stoichiometry; overall order = m + n.

Integrated forms: zero order [A] = [A]0 − kt; first order ln[A] = ln[A]0 − kt; second order 1/[A] = 1/[A]0 + kt.

Half-life: first order t½ = 0.693/k (independent of concentration); zero order t½ = [A]0/2k; second order t½ = 1/(k[A]0).

Arrhenius: k = Ae^(−Ea/RT); ln(k2/k1) = (Ea/R)(1/T1 − 1/T2).

Catalysts lower Ea and speed both forward and reverse reactions without changing K or ΔG.

Rate-determining step controls overall rate; the reaction order equals the molecularity of that step for elementary steps.

Cell potential: E°cell = E°cathode − E°anode; positive E°cell means spontaneous (galvanic).

Nernst equation: E = E° − (0.0592/n) log Q at 25 °C; ΔG = −nFE and ΔG° = −nFE°.

Faraday's law: moles of electrons = It/F; F = 96485 C/mol; mass deposited = (M·It)/(nF).

IUPAC naming: longest carbon chain, lowest locants for substituents, suffix by highest-priority functional group (acid > ester > amide > aldehyde > ketone > alcohol > amine).

SN1: carbocation intermediate, first-order, racemization, favored by tertiary substrates and polar protic solvents.

SN2: backside attack, second-order, inversion of configuration, favored by primary substrates and polar aprotic solvents.

E1 competes with SN1 (heat favors elimination); E2 is anti-periplanar, second-order, favored by strong bulky bases.

Markovnikov addition of HX to alkenes gives the more substituted carbocation; anti-Markovnikov occurs with HBr/peroxides or hydroboration.

Aromaticity: cyclic, planar, fully conjugated, 4n+2 π electrons (Hückel); benzene (6 π) aromatic, cyclooctatetraene (8 π) not.

EAS directing: -NH2, -OH, -OR, -R activate ortho/para; -NO2, -CN, -SO3H, carbonyl deactivate meta; halogens deactivate but direct ortho/para.

Aldehydes oxidize to carboxylic acids; ketones resist oxidation; Tollens' and Fehling's distinguish aldehydes from ketones.

Chirality requires a stereocenter with four different groups; R/S assigned by Cahn-Ingold-Prelog priority (higher atomic number first).

Beer-Lambert: A = εbc; absorbance linear with concentration; deviations occur at high concentration or with polychromatic light.

UV-Vis quantitation uses a calibration curve and blank; λ_max identifies chromophores (conjugated systems absorb at longer wavelengths).

Atomic absorption (AAS) uses a hollow cathode lamp and atomization; atomic emission (ICP-OES) measures excited-state emission and is multi-element.

Chromatography: retention time identifies, peak area quantifies; resolution depends on selectivity, efficiency (N), and retention factor.

GC requires volatile analytes; HPLC with reversed-phase C18 is suited to polar and nonvolatile compounds; gradient elution shortens run time.

Mass spectrometry: molecular ion gives molar mass; fragmentation pattern provides structural information; isotope patterns (M, M+2) reveal halogens.

NMR: chemical shift reflects electronic environment; integration gives proton count; n+1 splitting from neighboring equivalent protons.

IR: O-H broad ~3300 cm⁻¹, C=O sharp ~1700 cm⁻¹, C-H ~2900 cm⁻¹; used to identify functional groups.

Acid-base titration: equivalence point from stoichiometry; indicator pK_a should match the equivalence-point pH; standardize titrants before use.

Coordination number and geometry: 2 linear, 4 tetrahedral or square planar, 6 octahedral; common ligands NH3, H2O, Cl⁻, CN⁻, EDTA⁴⁻.

Oxidation state of metal = total charge − sum of ligand charges; e.g., [Fe(CN)6]⁴⁻ gives Fe²⁺.

Naming: ligands alphabetically, then metal with oxidation state in Roman numerals; anionic complexes end in -ate.

Crystal field theory: Δo splits d orbitals; strong-field ligands (CN⁻, CO) give low-spin, weak-field (H2O, Cl⁻) give high-spin complexes.

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

d-d transitions give color; Δo corresponds to absorbed wavelength; complementary color is observed.

Magnetic moment μ ≈ √(n(n+2)) B.M., where n = unpaired d electrons; distinguishes high- from low-spin.

Chelate effect: multidentate ligands (EDTA, en) increase stability due to favorable entropy of complexation.

Isomerism: geometric (cis/trans), optical (Δ/Λ), and linkage isomerism (e.g., NO2⁻ vs ONO⁻) occur in coordination compounds.

SDS sections: 1 identification, 2 hazards, 4 first aid, 6 accidental release, 7 handling/storage, 8 exposure controls, 9 physical properties.

GHS pictograms include flame, skull and crossbones, corrosion, health hazard, exclamation mark, and environment; labels carry signal word, hazard statements, and precautionary statements.

Chemical hygiene plan (OSHA 29 CFR 1910.1450) covers SOPs, engineering controls, PPE, training, and medical consultation.

Fume hood face velocity is typically 80-120 ft/min; verify with a flow meter and never store chemicals in the hood.

Incompatible storage: oxidizers separate from organics; acids separate from bases; water-reactive metals in dry, inert areas.

Waste segregation: halogenated vs nonhalogenated organic, aqueous heavy-metal, and corrosive waste streams kept separate.

Quality assurance tools: control charts, calibration verification, blanks, duplicates, matrix spikes, and proficiency testing.

Chain of custody and recordkeeping: document sample collection, transfers, and analysis with dates, initials, and instrument IDs.

Spill response: evacuate, alert, contain with absorbent, neutralize only if trained; consult SDS Section 6 for specific spill procedures.