ILTS Science: Chemistry (240) cheat sheet

Scientific inquiry cycle: question → hypothesis → controlled experiment → data analysis → conclusion → peer review and replication; a single unreplicated study is provisional evidence.

Independent variable is manipulated by the investigator; dependent variable is measured; controlled variables are held constant to isolate cause and effect.

A hypothesis must be falsifiable: it predicts a specific, testable outcome that could disconfirm it. Unfalsifiable claims fall outside empirical science.

Accuracy = closeness to the accepted/true value; precision = reproducibility among repeated measurements. Random error affects precision; systematic error shifts accuracy.

Percent error = |accepted − experimental| / accepted × 100%. Percent difference compares two experimental values without an accepted standard.

Significant figures: nonzero digits and interior zeros count; leading zeros do not; trailing zeros count only with a decimal point. Addition/subtraction keeps the least decimal places; multiplication/division keeps the least significant figures.

Scientific law describes a consistent observed relationship (e.g., conservation of mass); a theory explains why, and is supported by broad, repeated evidence. Theories do not become laws.

Peer review, replication, and independent verification distinguish science from pseudoscience; consensus can shift when new reproducible evidence appears.

Graph choice: line graph for continuous independent variables, bar chart for categorical comparisons, scatter plot with regression for correlation between two measured variables.

Classification: pure substances (elements, compounds) have fixed composition; mixtures (homogeneous, heterogeneous) do not. Physical changes alter state or form; chemical changes form new substances.

Atomic number Z = protons; mass number A = protons + neutrons; isotopes share Z but differ in neutrons; ions differ in electrons.

Average atomic mass = Σ(fractional abundance × isotopic mass). Charge of an ion = protons − electrons.

Bohr model: E = −13.6 eV/n² for hydrogen; photon energy absorbed or emitted = hf = ΔE between levels; h = 6.626 × 10⁻³⁴ J·s.

Quantum numbers: n (shell, n ≥ 1), ℓ (0 to n−1, shape), mℓ (−ℓ to +ℓ, orientation), ms (±½, spin). Pauli exclusion forbids identical sets of all four.

Electron configuration follows Aufbau order, Hund's rule (maximize unpaired spins in degenerate orbitals), and the octet/duet stability principle; Cr and Cu are exceptions.

Periodic trends: atomic radius decreases left→right and increases top→bottom; ionization energy and electronegativity increase left→right and decrease top→bottom.

Effective nuclear charge increases across a period, contracting the shell and raising ionization energy; added shells down a group shield and expand radius.

Mole concept: 1 mol = 6.022 × 10²³ particles; molar mass in g/mol; n = m/M; molar volume of ideal gas at STP (0 °C, 1 atm) = 22.4 L/mol.

Bond type by electronegativity difference: <0.4 nonpolar covalent, 0.4–1.7 polar covalent, >1.7 largely ionic; metallic bonding involves delocalized electrons.

VSEPR: electron domains repel to maximize separation; lone pairs occupy more space than bonding pairs, compressing bond angles (CH₄ 109.5°, NH₃ 107°, H₂O 104.5°).

Molecular polarity requires polar bonds plus an asymmetric geometry; CO₂ is nonpolar despite polar bonds, H₂O is polar.

Intermolecular forces ranked: ion–dipole > hydrogen bonding > dipole–dipole > London dispersion; stronger forces raise boiling point and surface tension.

Reaction types: synthesis, decomposition, single replacement, double replacement (precipitation), combustion, and acid–base neutralization.

Balance equations by conservation of atoms and charge; coefficients give mole ratios used in stoichiometric conversions.

Limiting reactant: compute moles of product from each reactant; the smallest yield identifies the limiting reagent; excess reagent remains unreacted.

Percent yield = actual/theoretical × 100%; molarity M = mol solute/L solution; dilution M₁V₁ = M₂V₂.

Net ionic equations omit spectator ions; solubility rules predict precipitate formation (e.g., most nitrates and alkali-metal salts are soluble).

First law: ΔE = q + w; enthalpy change at constant pressure q = ΔH. Exothermic ΔH < 0; endothermic ΔH > 0.

Calorimetry: q = mcΔT; Hess's law sums stepwise ΔH; ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants).

Bond breaking absorbs energy; bond formation releases energy. Entropy ΔS increases with gas production, temperature, and disorder.

Gibbs free energy: ΔG = ΔH − TΔS; spontaneous at constant T and P when ΔG < 0; ΔG° = −RT ln K.

Rate law: rate = k[A]^m[B]^n; orders determined experimentally, not from coefficients. Rate constant k depends on temperature via Arrhenius k = Ae^(−Ea/RT).

Collision theory: reaction requires sufficient energy (Ea) and correct orientation; catalysts lower Ea without changing ΔH or equilibrium position.

Equilibrium: forward and reverse rates equal; K = products^coefficients / reactants^coefficients (pure solids/liquids omitted). Q < K shifts right; Q > K shifts left.

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

Half-life first order: t½ = 0.693/k; concentration decays as [A] = [A]₀e^(−kt).

Solution concentration: molarity M = mol/L; molality m = mol solute/kg solvent; mole fraction and mass percent are temperature-independent alternatives.

Colligative properties depend on particle count: ΔTb = iKb·m and ΔTf = iKf·m; van't Hoff factor i accounts for dissociation (NaCl → i ≈ 2).

Solubility of most solids rises with temperature; gas solubility falls with temperature and rises with partial pressure (Henry's law).

Brønsted–Lowry: acid donates a proton, base accepts one; conjugate pairs differ by one H⁺. Lewis acid accepts an electron pair.

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

Strong acids/bases ionize completely; weak acids use Ka: Ka·Kb = Kw for a conjugate pair; pKa = −log Ka.

Buffer: weak acid plus conjugate base resists pH change; Henderson–Hasselbalch pH = pKa + log([A⁻]/[HA]).

Titration equivalence: moles acid = moles base adjusted by stoichiometric coefficients; strong–strong equivalence pH = 7 at 25 °C.

Electrochemistry: oxidation at anode, reduction at cathode (An Ox, Red Cat); E°cell = E°cathode − E°anode; ΔG° = −nFE°cell; positive E°cell means spontaneous galvanic cell.

Hydrocarbon families: alkanes (single bonds, CnH2n+2), alkenes (one double, CnH2n), alkynes (one triple, CnH2n−2); IUPAC naming uses the longest chain and lowest locants.

Functional groups: hydroxyl (alcohol), carbonyl (aldehyde/ketone), carboxyl (acid), amino, ester, amide, ether, and phosphate; each dictates characteristic reactivity.

Isomers share molecular formula but differ in connectivity (structural) or spatial arrangement (cis–trans, enantiomers).

Common reaction patterns: substitution (alkanes, aromatics), addition (alkenes/alkynes), elimination, oxidation of alcohols, esterification, and polymerization.

Biomolecules: carbohydrates (monosaccharides → polysaccharides), proteins (amino acids linked by peptide bonds), lipids (fatty acids, triglycerides), nucleic acids (nucleotides with sugar, phosphate, base).

Enzymes are biological catalysts that lower activation energy and are specific to substrates; denaturation disrupts tertiary structure and activity.

Nuclear notation: mass number A = protons + neutrons; alpha decay reduces A by 4 and Z by 2; beta-minus decay raises Z by 1; gamma emission changes neither.

Nuclear stability: neutron-to-proton ratio; band of stability; half-life and radioactive decay follow first-order kinetics.

Fission splits a heavy nucleus releasing energy; fusion combines light nuclei; both convert mass to energy via E = mc².

Safety priority order: protect people, then contain the hazard, then clean up; know eyewash, shower, fire extinguisher, and spill kit locations before starting.

Goggles and appropriate PPE are required whenever chemicals, heat, or glassware under pressure are used; never taste or directly smell chemicals.

Acid spill on skin: flush with copious water for at least 15 minutes; add acid to water (never water to acid) when diluting.

Heating: use a water bath or heating mantle for flammable solvents; never heat a closed system; point test-tube mouths away from people.

Glassware: volumetric flasks and pipettes are for measuring; graduated cylinders for approximate volumes; never use graduated cylinders for accurate volumetric work.

Separation techniques: filtration (insoluble solid), distillation (boiling-point difference), chromatography (differential affinity), extraction (solubility difference).

Data analysis: identify outliers, calculate mean and standard deviation, plot calibration curves, and report units with correct significant figures.

Experimental design: include a control group, replicate trials, randomize or standardize conditions, and record raw data before processing.

Waste disposal follows local and institutional rules; never pour chemicals down the drain unless explicitly authorized.

5E model (Engage, Explore, Explain, Elaborate, Evaluate) sequences inquiry: exploration precedes formal explanation to build concepts from evidence.

Three levels of chemistry representation: macroscopic (observable), symbolic (formulas, equations), and particulate (atoms, molecules); instruction should connect all three.

Common misconceptions to target: conservation of mass in open systems, mole as a mass rather than a count, equilibrium as a static state, and bonds releasing energy when broken.

Assessment alignment: formative checks (exit tickets, concept inventories) guide instruction; summative assessments match stated learning objectives and cognitive demand.

Laboratory pedagogy: pre-lab planning, explicit safety instruction, and post-lab analysis develop inquiry and data-literacy skills; modeling and simulations supplement hands-on work.

Differentiation: tiered tasks, multiple representations, and scaffolds (graphic organizers, worked examples) support diverse learners, including English learners.

Argumentation from evidence: students should construct claims supported by data and reasoning, and critique peer explanations using scientific criteria.

Disciplinary literacy: teach reading of procedures, data tables, and chemical notation explicitly; use precise vocabulary and sentence frames for explanation.