Praxis Chemistry 5245 cheat sheet

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

Average atomic mass = Σ(fractional abundance × isotopic mass); abundances must sum to 1.

Quantum numbers: n (shell), l = 0…n−1 (s,p,d,f), m_l = −l…+l, m_s = ±½; no two electrons share all four.

Electron configuration follows Aufbau order, Pauli exclusion, and Hund's rule (maximize unpaired spins in degenerate orbitals).

Ionization energy increases across a period and decreases down a group; atomic radius shows the opposite trend.

Coulomb's law governs effective nuclear charge: greater Z_eff pulls electrons closer, shrinking radius and raising ionization energy.

Periodic families: alkali metals (ns1), halogens (ns2np5), noble gases (ns2np6, full octet), transition metals fill d subshells.

Moles: n = mass/molar mass; 1 mol = 6.022×10^23 particles; molar mass from periodic table in g/mol.

Percent composition = (mass of element in formula / molar mass of compound) × 100.

Balance equations by conserving atoms and charge; coefficients give mole ratios used in stoichiometry.

Limiting reactant: compute moles of product each reactant yields; the smallest value governs; excess remains unreacted.

Percent yield = (actual yield / theoretical yield) × 100.

Reaction types: synthesis, decomposition, single replacement, double replacement (metathesis), combustion, redox.

Oxidation = loss of electrons (oxidation number rises); reduction = gain of electrons; balance redox by half-reactions.

Enthalpy: ΔH_rxn = ΣΔH_f(products) − ΣΔH_f(reactants); ΔH < 0 exothermic, ΔH > 0 endothermic.

Hess's law: total ΔH is path-independent; reverse a reaction to flip the sign of ΔH, scale it to scale ΔH.

Calorimetry: q = mcΔT; for a bomb calorimeter use q = CΔT; at constant pressure q = ΔH.

Bond breaking absorbs energy; bond formation releases energy; net ΔH reflects the balance of both.

Bond type from electronegativity difference: <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic.

Lewis structures: count valence electrons, minimize formal charge, expand octets only for period 3+ elements.

VSEPR electron-domain geometries: 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral.

Lone pairs repel more than bonding pairs, compressing bond angles below the ideal (e.g., H2O ≈ 104.5°).

Hybridization: steric number 2→sp, 3→sp2, 4→sp3; multiple bonds count as one domain.

Polarity requires polar bonds AND an asymmetric geometry; symmetric molecules (CO2, CCl4) are nonpolar overall.

Intermolecular forces (weakest to strongest): London dispersion < dipole–dipole < hydrogen bonding < ion–dipole.

Hydrogen bonds require H bonded to N, O, or F; they raise boiling points and drive water's high surface tension.

Metallic bonding: delocalized electron sea explains conductivity, malleability, and luster.

Arrhenius: acids yield H+ in water, bases yield OH−; Brønsted–Lowry: acids donate protons, bases accept protons.

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

Strong acids/bases dissociate completely; weak ones reach equilibrium described by Ka or Kb.

For a weak acid: Ka = [H+][A−]/[HA]; larger Ka means stronger acid; pKa = −log Ka.

Henderson–Hasselbalch: pH = pKa + log([A−]/[HA]); buffer capacity peaks when pH = pKa.

Titration equivalence: moles H+ = moles OH−; molarity × volume gives moles of analyte or titrant.

Molarity M = mol solute / L solution; dilution: M1V1 = M2V2.

Solubility rules: most nitrates and alkali-metal salts are soluble; most Ag+, Pb2+, and Hg2+ halides are insoluble.

Colligative properties (boiling-point elevation, freezing-point depression, osmotic pressure) depend on particle count, not identity.

Rate = −Δ[reactant]/Δt = Δ[product]/Δt; units of rate are concentration per time.

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

Arrhenius equation: k = Ae^(−Ea/RT); higher temperature or lower Ea increases k.

Catalysts lower Ea by an alternate pathway; they do not change ΔH or the equilibrium position.

Equilibrium constant K = [products]^coefficients / [reactants]^coefficients; pure solids and liquids are omitted.

K > 1 favors products; K < 1 favors reactants; K depends on temperature only.

Le Châtelier's principle: shifting concentration, pressure, or temperature drives the system to restore equilibrium.

For a gas reaction, Kp = Kc(RT)^Δn, where Δn = moles gaseous products − moles gaseous reactants.

Reaction quotient Q: Q < K proceeds forward, Q > K proceeds reverse, Q = K at equilibrium.

Significant figures: all nonzero digits count; zeros between them count; leading zeros never count; trailing zeros count only with a decimal.

Addition/subtraction rounds to the fewest decimal places; multiplication/division rounds to the fewest significant figures.

SI base units: meter (length), kilogram (mass), second (time), ampere (current), kelvin (temperature), mole (amount), candela (luminous intensity).

K = °C + 273.15; density = mass/volume; percent error = |measured − accepted|/accepted × 100.

Accuracy = closeness to true value; precision = reproducibility of repeated measurements.

Always add acid to water, never water to acid, to control heat release.

Goggles and gloves are required for corrosive, toxic, or volatile reagents; no open flames near flammable solvents.

Fume hoods vent vapors; never smell or taste chemicals directly; waft toward the nose if instructed.

Report measurements with uncertainty and use appropriate glassware: graduated cylinder (coarse), burette/pipette (precise), volumetric flask (fixed volume).

Green chemistry principles: atom economy, less hazardous reagents, energy efficiency, and waste prevention.

Atom economy = (molar mass of desired product / total molar mass of reactants) × 100.

Fossil-fuel combustion releases CO2 (greenhouse gas) and SO2/NOx (acid rain precursors); catalytic converters reduce NOx and CO.

Ozone depletion is driven by CFCs releasing chlorine radicals; the Montreal Protocol phased out CFCs.

Radioactive decay follows first-order kinetics: half-life t½ = 0.693/k; used in dating and medical imaging.

Batteries convert chemical energy to electrical energy; fuel cells (e.g., H2/O2) produce water as the only byproduct.

Water treatment uses coagulation, filtration, and chlorination; hardness comes from dissolved Ca2+ and Mg2+ ions.

Renewable energy sources (solar, wind, hydro) reduce carbon emissions compared with coal or natural gas.

Risk assessment weighs hazard and exposure; dose–response relationships inform safe exposure limits.