BSSE Chemistry 1429 cheat sheet

Atomic number Z = protons; mass number A = protons + neutrons; isotopes differ in neutron count.

Quantum numbers: n (shell, n≥1), ℓ (0 to n−1), mℓ (−ℓ to +ℓ), ms (±1/2); orbital capacity = 2(2ℓ+1).

Electron configuration follows Aufbau (lowest energy first), Pauli exclusion, and Hund's rule (maximize unpaired spins).

Effective nuclear charge Zeff = Z − S; across a period Zeff increases, atomic radius decreases, ionization energy and electronegativity increase.

Down a group, n increases; atomic radius increases, ionization energy decreases, metallic character increases.

Periodic trends: ionization energy generally increases across a period and decreases down a group; electron affinity becomes more negative across a period.

Orbital energies: 4s fills before 3d because 4s is lower in energy for neutral atoms; Cr and Cu are exceptions (half-filled or filled d subshell stability).

Formal charge = valence electrons − (nonbonding electrons + ½ bonding electrons).

Ionic bond: electron transfer between low-ionization metal and high-electron-affinity nonmetal; lattice energy increases with higher charges and smaller ionic radii (Coulomb's law).

Covalent bond: shared electron pair; bond order = (bonding electrons − antibonding electrons)/2 in MO theory.

VSEPR: electron domains (bonding + lone pairs) arrange to minimize repulsion; lone pairs repel more than bonding pairs, compressing bond angles.

Hybridization: steric number 2 → sp (linear, 180°), 3 → sp² (trigonal planar, 120°), 4 → sp³ (tetrahedral, 109.5°).

Polarity: a molecule is polar if it has polar bonds and an asymmetric geometry so bond dipoles do not cancel.

Intermolecular forces (from strongest to weakest): ion-dipole, hydrogen bonding, dipole-dipole, London dispersion; dispersion increases with polarizability (more electrons, larger size).

Bond length decreases and bond energy increases as bond order increases (single < double < triple).

Resonance: when multiple valid Lewis structures exist, the true structure is a weighted average; formal charges should be minimized and negative charge placed on the more electronegative atom.

Ideal gas law: PV = nRT; R = 0.08206 L·atm·mol⁻¹·K⁻¹ = 8.314 J·mol⁻¹·K⁻¹.

Combined gas law: P₁V₁/T₁ = P₂V₂/T₂ (T in kelvin); Dalton's law: P_total = ΣP_i; mole fraction χ_i = n_i/n_total, P_i = χ_i P_total.

Kinetic molecular theory: average kinetic energy ∝ T (KE_avg = (3/2)kT per molecule); root-mean-square speed u_rms = √(3RT/M).

Van der Waals equation: (P + an²/V²)(V − nb) = nRT; a accounts for attractive forces, b for molecular volume.

Phase changes: melting/freezing, vaporization/condensation, sublimation/deposition; energy absorbed or released at constant temperature during a phase change.

Heating curve: q = m·c·ΔT for temperature changes; q = n·ΔH_fus or n·ΔH_vap for phase changes at constant T.

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

Phase diagram: triple point (all three phases coexist), critical point (end of liquid–vapor boundary); slope of solid–liquid line indicates whether solid is denser than liquid.

Mole concept: n = m/M; Avogadro's number N_A = 6.022×10²³ mol⁻¹.

Molarity M = moles solute / liters solution; dilution M₁V₁ = M₂V₂.

Percent yield = (actual yield / theoretical yield) × 100%; theoretical yield from limiting reactant.

Limiting reactant: the reactant that produces the least product; excess reactant remains after reaction.

Empirical formula from mass percent: divide by atomic mass, then divide by smallest ratio; molecular formula = empirical × n where n = molar mass / empirical formula mass.

Combustion analysis: moles C = moles CO₂, moles H = 2 × moles H₂O; oxygen by difference if a third element is present.

Solution stoichiometry: use M × V = moles for reactants in solution; coefficients give mole ratios.

Gas stoichiometry at STP: 1 mol ideal gas occupies 22.414 L at 0 °C and 1 atm.

First law: ΔU = q + w; work w = −PΔV (expansion does negative work on surroundings).

Enthalpy H = U + PV; at constant pressure q_p = ΔH.

Calorimetry: q = m·c·ΔT; for a bomb calorimeter q = C_cal·ΔT; heat gained by surroundings = −heat lost by system.

Hess's law: ΔH for an overall reaction is the sum of ΔH values for individual steps, independent of pathway.

Standard enthalpy of reaction: ΔH°_rxn = ΣΔH°_f(products) − ΣΔH°_f(reactants); ΔH°_f of an element in its standard state is zero.

Bond enthalpy: ΔH ≈ Σ(bonds broken) − Σ(bonds formed); breaking bonds is endothermic, forming bonds is exothermic.

Spontaneity: ΔG = ΔH − TΔS; ΔG < 0 spontaneous, ΔG = 0 at equilibrium, ΔG > 0 nonspontaneous.

ΔG° = −RT ln K; a larger equilibrium constant corresponds to a more negative ΔG°.

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

Reaction quotient Q: Q < K → reaction proceeds forward; Q > K → reverse; Q = K → equilibrium.

Le Chatelier's principle: increasing concentration of a reactant shifts right; increasing pressure shifts toward fewer gas moles; increasing temperature favors the endothermic direction.

K_p = K_c(RT)^Δn_gas; Δn_gas = moles gaseous products − moles gaseous reactants.

Acid dissociation: HA ⇌ H⁺ + A⁻, K_a = [H⁺][A⁻]/[HA]; larger K_a means stronger acid.

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

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

Titration: equivalence point occurs when moles acid = moles base (adjusted by stoichiometry); strong acid–strong base equivalence pH = 7 at 25 °C.

Rate = −Δ[reactant]/Δt = Δ[product]/Δt (divided by stoichiometric coefficient).

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

Zero order: [A] = [A]₀ − kt, half-life t₁/₂ = [A]₀/(2k).

First order: ln[A] = ln[A]₀ − kt, half-life t₁/₂ = 0.693/k (independent of concentration).

Second order: 1/[A] = 1/[A]₀ + kt, half-life t₁/₂ = 1/(k[A]₀).

Arrhenius equation: k = A e^(−E_a/RT); ln(k₂/k₁) = (E_a/R)(1/T₁ − 1/T₂).

Collision theory: reaction requires sufficient energy (E_a) and proper orientation; catalyst lowers E_a and increases k without changing ΔH or K.

Rate-determining step: the slowest elementary step controls the overall reaction rate; intermediates do not appear in the overall rate law.

Oxidation is loss of electrons (anode); reduction is gain of electrons (cathode); mnemonic: An Ox, Red Cat.

Oxidation number rules: free element = 0; monatomic ion = charge; O usually −2; H usually +1; sum of oxidation numbers equals overall charge.

Galvanic cell: spontaneous reaction produces electrical energy; E°_cell = E°_cathode − E°_anode (both reduction potentials).

Standard reduction potentials: more positive E° means greater tendency to be reduced (stronger oxidizing agent).

ΔG° = −nFE°_cell; F = 96,485 C/mol; n = moles electrons transferred.

Nernst equation: E = E° − (RT/nF) ln Q; at 25 °C, E = E° − (0.0592/n) log Q.

Electrolysis: nonspontaneous reaction driven by external voltage; amount of substance deposited related to charge by Faraday's law (moles e⁻ = It/F).

Balance redox reactions in acidic solution with H₂O and H⁺; in basic solution, add OH⁻ to neutralize H⁺.

Functional groups: alcohol (–OH), ether (–O–), aldehyde (–CHO), ketone (>C=O), carboxylic acid (–COOH), ester (–COO–), amine (–NH₂), amide (–CONH–).

IUPAC naming: longest carbon chain containing the principal functional group; number to give the principal group the lowest locant; substituents alphabetical.

Isomers: structural (different connectivity), geometric (cis/trans or E/Z around double bond), optical (non-superimposable mirror images, chiral center with four different groups).

Alkanes: C_nH_{2n+2}; alkenes: C_nH_{2n} (one double bond); alkynes: C_nH_{2n−2} (one triple bond); aromatic benzene ring C₆H₆.

Addition reactions occur at double/triple bonds (e.g., H₂, HX, halogens); substitution occurs at saturated carbons or aromatic rings.

Alcohols can be oxidized to aldehydes/ketones then carboxylic acids; primary alcohols → aldehyde → acid; secondary → ketone; tertiary alcohols resist oxidation.

Carboxylic acid + alcohol ⇌ ester + water (Fischer esterification, acid-catalyzed, reversible).

Boiling point order for similar molar mass: carboxylic acid > alcohol > ketone/aldehyde > ether > alkane, due to hydrogen bonding and dipole strength.

Significant figures: multiplication/division result has the same number of sig figs as the factor with the fewest; addition/subtraction result has the same number of decimal places as the term with the fewest.

Precision describes reproducibility; accuracy describes closeness to the true value; random error affects precision, systematic error affects accuracy.

Percent error = |experimental − accepted| / accepted × 100%.

Volumetric glassware: burette and pipette are precise to ±0.01–0.05 mL; graduated cylinder is less precise; read bottom of meniscus at eye level.

Standard solution preparation: weigh solute, dissolve, transfer quantitatively to volumetric flask, dilute to the mark, mix.

Titration endpoint is the observed color change; equivalence point is the stoichiometric point; indicator should change near the equivalence pH.

Drying and weighing: cool heated crucible in a desiccator before weighing to avoid moisture pickup; weigh to constant mass when determining water of hydration.

Safety: know SDS hazards, use fume hood for volatile or toxic substances, never pipette by mouth, add acid to water (not water to acid) when diluting.