OAE Chemistry cheat sheet

Scientific method: observation → hypothesis → experiment → analysis → conclusion → communication; hypotheses must be falsifiable and testable.

Independent variable is manipulated; dependent variable is measured; controlled variables are held constant to prevent confounding.

Accuracy = closeness to true value; precision = reproducibility of repeated measurements; random errors affect precision, systematic errors affect accuracy.

Significant figures: nonzero digits and zeros between them are significant; leading zeros are not; trailing zeros after a decimal point are significant; multiplication/division keep the least number of sig figs, addition/subtraction keep the least decimal places.

Scientific notation: a × 10^n where 1 ≤ |a| < 10; used to express very large or small numbers and to clarify significant figures.

Dimensional analysis: multiply by conversion factors so unwanted units cancel; e.g., 1 in = 2.54 cm, 1 kg = 2.2046 lb, 1 L = 1.0567 qt.

A theory is a well-substantiated explanation supported by repeated evidence; a law describes a consistent relationship, often mathematically.

Peer review and reproducibility are hallmarks of valid science; anecdotal evidence and non-falsifiable claims are not scientific evidence.

Classification of matter: pure substances (elements, compounds) have fixed composition; mixtures (homogeneous, heterogeneous) do not; physical changes alter state but not composition; chemical changes alter composition.

Atomic number Z = number of protons; mass number A = protons + neutrons; isotopes have same Z but different A; ions have unequal protons and electrons.

Average atomic mass = Σ (isotope mass × fractional abundance); e.g., Cl-35 (75.78%) and Cl-37 (24.22%) give 35.45 amu.

Bohr model: electrons occupy quantized energy levels; transition from n=3 to n=2 emits a photon with energy ΔE = hν = hc/λ.

Quantum mechanical model: orbitals are probability distributions; s, p, d, f subshells hold 2, 6, 10, 14 electrons; Pauli exclusion, Aufbau, and Hund's rules govern electron configuration.

Periodic trends: atomic radius decreases across a period and increases down a group; ionization energy increases across a period and decreases down a group; electronegativity generally increases across and decreases down.

Mole concept: 1 mol = 6.022×10^23 particles; molar mass in g/mol numerically equals atomic/molecular mass in amu.

Nuclear notation: alpha decay emits He-4 (A decreases by 4, Z by 2); beta-minus decay converts neutron to proton (Z increases by 1); gamma emission changes neither A nor Z.

Ionic bonds form between metals and nonmetals via electron transfer; lattice energy increases with higher charges and smaller ionic radii (Coulomb's law).

Covalent bonds form by sharing electrons; bond polarity depends on electronegativity difference: 0–0.4 nonpolar, 0.4–1.7 polar covalent, >1.7 mostly ionic (guideline).

Lewis structures: count valence electrons, form octets (H duet), minimize formal charge; resonance structures differ only in electron placement.

VSEPR geometry: electron domains (bonding + lone pairs) determine shape; lone pairs repel more than bonds, compressing bond angles (e.g., CH4 109.5°, NH3 107°, H2O 104.5°).

Hybridization: steric number 2 → sp (linear, 180°), 3 → sp² (trigonal planar, 120°), 4 → sp³ (tetrahedral, 109.5°); multiple bonds count as one domain.

Intermolecular forces strength: ion-dipole > hydrogen bonding > dipole-dipole > London dispersion; hydrogen bonds occur when H is bonded to N, O, or F.

Molecular polarity depends on both bond dipoles and geometry; symmetrical molecules (CO2, CCl4) can be nonpolar despite polar bonds.

Metallic bonding: delocalized valence electrons explain conductivity, malleability, and ductility; alloys are mixtures of metals with altered properties.

Balance chemical equations by adjusting coefficients, never subscripts; total atoms of each element and total charge must be conserved.

Mole ratio from balanced equation converts moles of one substance to moles of another: n_B = n_A × (coefficient_B / coefficient_A).

Limiting reactant is the one that produces the least product; excess reactant remains after reaction; theoretical yield is based on limiting reactant.

Percent yield = (actual yield / theoretical yield) × 100%; actual yield is measured experimentally and is usually less than theoretical.

Solution stoichiometry: moles = molarity × volume (in liters); dilution M1V1 = M2V2; titration equivalence point depends on stoichiometric ratio.

Reaction types: synthesis (A+B→AB), decomposition (AB→A+B), single replacement (A+BC→AC+B), double replacement (AB+CD→AD+CB), combustion (hydrocarbon + O2 → CO2 + H2O).

Net ionic equations show only species that change; spectator ions are omitted; solubility rules help predict precipitates (e.g., most nitrates and alkali metal salts are soluble).

Empirical formula from percent composition: convert % to grams, divide by molar mass, divide by smallest mole ratio; molecular formula = empirical formula × integer factor from molar mass.

First law: ΔE = q + w; at constant pressure q = ΔH; exothermic reactions release heat (ΔH < 0), endothermic absorb heat (ΔH > 0).

Calorimetry: q = mcΔT; for a reaction in solution, q_rxn = –q_solution; use specific heat of water 4.184 J/(g·°C).

Hess's law: ΔH for an overall reaction is the sum of ΔH values for individual steps; ΔH_rxn = Σ ΔH_f(products) – Σ ΔH_f(reactants).

Gibbs free energy: ΔG = ΔH – TΔS; spontaneous if ΔG < 0; ΔG = 0 at equilibrium; ΔG° = –RT ln K.

Entropy increases with more gas moles, higher temperature, and greater disorder; ΔS > 0 favors spontaneity at high T when ΔH > 0.

Reaction rate depends on concentration, temperature, surface area, and catalysts; rate law is determined experimentally, not from stoichiometry.

Arrhenius equation: k = A e^(–Ea/RT); higher Ea slows reaction; catalyst lowers Ea without changing ΔH or equilibrium position.

Le Chatelier's principle: stress (concentration, pressure, temperature) shifts equilibrium to counteract the change; K changes only with temperature.

Molarity M = moles solute / liters solution; molality m = moles solute / kg solvent; mole fraction X_A = n_A / total moles; ppm = (mass solute / mass solution) × 10^6.

Dilution and mixing: M1V1 = M2V2 for dilution; for mixing solutions of same solute, M_final = (M1V1 + M2V2) / (V1 + V2).

Solubility depends on temperature and pressure (Henry's law: S = kP for gases); like dissolves like; electrolytes dissociate into ions, nonelectrolytes do not.

Colligative properties depend on number of solute particles: boiling point elevation ΔTb = iKb m; freezing point depression ΔTf = iKf m; osmotic pressure π = iMRT.

Acid-base definitions: Arrhenius produces H+ or OH– in water; Brønsted-Lowry proton donor/acceptor; Lewis electron-pair acceptor/donor.

pH = –log[H3O+]; pOH = –log[OH–]; pH + pOH = 14 at 25°C; [H3O+][OH–] = 1.0×10^–14.

Strong acids (HCl, HNO3, H2SO4, HBr, HI, HClO4) and strong bases (Group 1 hydroxides, Ba(OH)2) ionize completely; weak acids/bases use Ka or Kb and ICE tables.

Buffer: weak acid + conjugate base resists pH change; Henderson–Hasselbalch pH = pKa + log([A–]/[HA]); equivalence point in strong acid–strong base titration is pH 7.