ORELA Chemistry (NT321) cheat sheet

SI base units: length = meter (m), mass = kilogram (kg), amount = mole (mol), temperature = kelvin (K), time = second (s); derived units combine these (J = kg·m²/s²).

Significant figures: for multiplication/division the result carries the fewest sig figs of the factors; for addition/subtraction the result carries the fewest decimal places.

Dimensional analysis: set up conversion factors so unwanted units cancel; 1 cm³ = 1 mL, 1 L = 1 dm³, 1 cal = 4.184 J, 1 atm = 101.325 kPa = 760 mmHg.

Density d = m/V; specific gravity is dimensionless (density relative to water at 4 °C, 1.00 g/mL).

Temperature conversions: K = °C + 273.15; °F = (9/5)°C + 32; a temperature change of 1 °C equals a change of 1 K but 1.8 °F.

Classification: element (one kind of atom), compound (fixed ratio of elements, separable only chemically), homogeneous mixture (uniform, e.g., alloy or solution), heterogeneous mixture (nonuniform, e.g., sand and iron).

Atomic notation: mass number A = protons Z + neutrons N; isotopes share Z but differ in N; ions differ in electron count, so charge = Z − electrons.

Average atomic mass = Σ (isotopic mass × fractional abundance); the value on the periodic table is a weighted average, not the mass of a single atom.

Quantum numbers: n = 1,2,3… (shell); l = 0 to n−1 (s,p,d,f); m_l = −l to +l; m_s = ±1/2; orbital holds 2 electrons of opposite spin; max electrons per shell = 2n².

Periodic trends across a period (left→right): atomic radius decreases, ionization energy and electronegativity increase, metallic character decreases; down a group the trends reverse.

Ionization energy: each successive removal costs more energy; large jumps mark the emptying of a shell (e.g., jump after the valence electrons of Na or Mg).

Bond type by electronegativity difference ΔEN: <0.4 nonpolar covalent, ~0.4–1.7 polar covalent, >1.7 largely ionic (a guideline, not a law).

Lewis structures: total valence electrons minus charge adjustments; octet rule with common exceptions - BeCl₂ (4 e⁻ on Be), BF₃ (6 e⁻ on B), expanded octets for period 3+ (SF₆, PCl₅).

VSEPR shapes from steric number (bonding domains + lone pairs): 2 linear, 3 trigonal planar, 4 tetrahedral, 5 trigonal bipyramidal, 6 octahedral; lone pairs compress angles (CH₄ 109.5° > NH₃ 107° > H₂O 104.5°).

Polarity: a molecule is polar only if polar bonds are arranged asymmetrically; CO₂ is nonpolar despite polar C=O bonds, while H₂O is polar.

Intermolecular forces ranked by strength: ion–dipole > hydrogen bond (H on N, O, or F) > dipole–dipole > London dispersion; dispersion grows with polarizability and molar mass.

Bond order from molecular orbital theory: bond order = (bonding e⁻ − antibonding e⁻)/2; O₂ has bond order 2 and is paramagnetic because of two unpaired π* electrons.

Formal charge = valence e⁻ − nonbonding e⁻ − ½ bonding e⁻; the preferred resonance structure minimizes formal charges and places negative charge on the more electronegative atom.

Mole relationships: n = m/M; N = n × 6.022×10²³; at STP (0 °C, 1 atm) one mole of ideal gas occupies 22.4 L.

Balancing: conserve each element's atoms and total charge; in ionic (net ionic) equations balance atoms first, then charge.

Limiting reactant: divide each reactant's moles by its stoichiometric coefficient; the smallest quotient limits; theoretical yield follows from the limiting reactant, % yield = (actual/theoretical) × 100.

Molarity M = mol solute / L solution; dilution M₁V₁ = M₂V₂; titration at equivalence a·M_acid·V_acid = b·M_base·V_base for a H⁺ and b OH⁻ per formula unit.

Reaction types: synthesis, decomposition, single replacement (activity series decides), double replacement (driven by precipitate, gas, or weak electrolyte), combustion of hydrocarbons gives CO₂ + H₂O.

Solubility rules: most nitrates, acetates, and alkali-metal salts are soluble; most chlorides soluble except Ag⁺, Pb²⁺, Hg₂²⁺; most carbonates, phosphates, and hydroxides insoluble except with alkali metals or NH₄⁺.

Equilibrium constant K: for aA + bB ⇌ cC + dD, K = [C]^c[D]^d/([A]^a[B]^b); pure solids and liquids are omitted; K > 1 favors products.

Le Châtelier: adding reactant shifts right; removing product shifts right; compressing a gas equilibrium shifts toward fewer gas moles; heating shifts in the endothermic direction; a catalyst changes rate, not K.

Acid–base: pH = −log[H₃O⁺], pOH = −log[OH⁻], pH + pOH = 14 at 25 °C; K_w = 1.0×10⁻¹⁴; strong acids/bases dissociate completely, weak ones follow K_a or K_b.

First law: ΔE = q + w; for constant-pressure processes q_p = ΔH; w = −PΔV, so work is done by the system when gas expands.

Calorimetry: q = mcΔT for a single phase; q = nΔH for a phase change or reaction; in a bomb calorimeter q_rxn = −C_calΔT.

Hess's law: ΔH for an overall reaction equals the sum of the steps' enthalpies; ΔH°_rxn = Σ ΔH°_f(products) − Σ ΔH°_f(reactants), with elements in standard state = 0.

Bond energies: breaking bonds absorbs energy (positive), forming bonds releases energy; ΔH ≈ Σ bonds broken − Σ bonds formed.

Spontaneity: ΔG = ΔH − TΔS; spontaneous when ΔG < 0; ΔG° = −RT ln K; ΔG° = −nFE°_cell.

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

Integrated kinetics: zero order [A] = [A]₀ − kt; first order ln[A] = ln[A]₀ − kt with t₁/₂ = 0.693/k; second order 1/[A] = 1/[A]₀ + kt.

Arrhenius: k = Ae^(−E_a/RT); raising temperature or lowering E_a (catalyst) increases k; a catalyst provides an alternate lower-energy path.

Electrochemistry: oxidation at the anode, reduction at the cathode (AnOx/RedCat); E°_cell = E°_cathode − E°_anode; in galvanic cells E°_cell > 0 and ΔG° < 0; in electrolysis an external voltage drives the nonspontaneous reaction.

Hydrocarbon families: alkanes CₙH₂ₙ₊₂ (single bonds), alkenes CₙH₂ₙ (one C=C), alkynes CₙH₂ₙ₋₂ (one C≡C), arenes such as benzene C₆H₆ (aromatic).

Functional groups: alcohol –OH, ether –O–, aldehyde –CHO, ketone –C(=O)–, carboxylic acid –COOH, ester –COO–, amine –NH₂, amide –CONH₂.

Isomerism: structural isomers differ in connectivity; cis/trans (geometric) isomers require restricted rotation (C=C or ring); enantiomers are nonsuperimposable mirror images with a chiral carbon bearing four different groups.

Reaction patterns: alkenes undergo addition; alkanes and arenes undergo substitution; alcohols oxidize to aldehydes/ketones then carboxylic acids; carboxylic acid + alcohol (acid catalyst) gives an ester plus water.

IUPAC naming: longest carbon chain, number from the end nearest the first substituent, name substituents alphabetically, and give the principal functional group the lowest number.

Nuclear notation: alpha decay lowers A by 4 and Z by 2; beta-minus decay raises Z by 1 with A unchanged; positron emission lowers Z by 1; gamma emission changes neither A nor Z.

Half-life: after n half-lives the fraction remaining is (1/2)ⁿ; activity A = A₀(1/2)^(t/t₁/₂); mass defect converts to energy by E = mc².

Fission splits a heavy nucleus (chain reaction, needs critical mass); fusion combines light nuclei (requires extremely high temperature, powers stars).

Lab safety: read SDS before use; add acid to water, never water to acid; fume hood for volatile or toxic vapors; know eyewash, shower, and fire extinguisher locations; never pipette by mouth; report spills and injuries immediately.