The course map.

Public AP Chemistry reference: nine official units, eight local pathways

Verified 2026-09-28: Effective Fall 2024 CED; current public clarifications implemented June 2026. Sources: College Board course overview, current Course and Exam Description, public Course at a Glance topic IDs and current clarifications. Topic objectives below are locally paraphrased assignments, not reproduced exam questions or copied essential-knowledge statements.

The linked current topic sheet uses 7.11–7.12 for solubility/common ion, 8.11 for pH and solubility, and 9.6–9.11 for dissolution, coupling and electrochemistry. Older numbering is not interchangeable. The June 2026 notice describes front-matter, resource-location and Progress Check wording updates; it does not supply new laboratory evidence for this local pack.

Scope: This is selected AP-topic practice, not AP authorization, a complete AP syllabus, exhaustive college certification or evidence of performed lab hours. Our eight-unit navigation is intentionally not the official nine-unit sequence. Topic IDs refer to the dated public source, not local unit numbers. First-column AP labels keep the two organizations separate. Foundation/core/honors are readiness pathways, not AP designations or promises of college credit.

What the mapping means: Each link names an actual case with given inputs, explanation, a selected-level task, answer, transfer and science criterion evidence. Coverage remains partial even when a topic has a link. Source-reading assignments and synthetic calibration agreement do not establish learner mastery, breadth of independent assessment or a validated measurement method.

Separate implementation and approval: Current AP Chemistry Course Audit requirements specify at least 25% of instructional time in hands-on inquiry laboratory investigations, at least 16 labs with at least 6 guided inquiry, retained records, science practices and appropriate resources. The audit page describes supervised virtual/simulation/at-home alternatives when on-site access is unavailable; those conditions still require educator supervision and learner records. These 22 authored paper cases are not performed labs and do not by themselves meet any time, count, inquiry or authorization requirement.

Human approvals are separate from missing curriculum: An educator must review scientific accuracy, accessibility, readiness, scoring and source currency; a safety lead must approve any actual practical protocol and facilities; AP designation requires the applicable Course Audit authorization. Approving those items does not erase the substantive gaps listed above. A complete essential-knowledge audit and a broader independently assessed problem set remain curriculum work.

Use the exact-record investigation inventory and all eight student pathways. These public answers remain nonsecure practice; a summative judgment needs independent work and an educator-chosen unseen variation or oral defense.

Investigation inventory: 22 original paper/data cases

These cases add 39 labeled datasets and 89 checked numerical calibrations to the eight existing units. They complement rather than replace the shipped initial-rate practice / rate transfer and Faraday practice / Faraday transfer. No extra HTML leaf or private assessment bank is created.

Evidence convention: Bracketed case IDs label explanation, assumptions, worked model, each readiness task/answer and transfer within the student pathway. Retain the independent first attempt and corrections, not just the public calibration. Record source/date, dataset/variant, units, assumptions, uncertainty and the science criterion. Foundation support is preparation, not an automatic Mastery award. Integration cannot reduce the science grade or block practical pass.

Safety and accessible alternative: All new cases are paper/data investigations, not laboratory procedures. Any physical exercise requires prior educator and safety approval, an approved protocol, suitable facilities and accessibility provisions. Do not improvise acid/base, electrolysis, gas, high-voltage, combustion, toxic-substance or unknown-substance experiments from these tables. Supplied records do not demonstrate hands-on technique or performed lab hours. Paper ledgers, supplied spectra/tables, an accessible graph or an oral explanation can document the stated analytical objectives. Any substitute for a published hands-on criterion must be formally approved by the educator rather than silently counted as performed technique.

Proposed workload, not delivered hours: Per case, plan 15–25 minutes of reading/model discussion, 25–40 minutes of selected-level analysis, and 10–20 minutes of transfer/defense. Difficult equilibrium/kinetics cases can span meetings. Allow 15–25 minutes of educator preparation and about 5–10 minutes per selected learner defense. These are unpiloted planning estimates, not a full-year timetable or lab-hour certification.

1. Isotope abundance is a weighted population claim [isotope-pattern]

   [isotope-pattern] Unit 1. AP topic references: 1.1, 1.2, 1.5, 1.7. Science criteria: 1, 2, 3, 4.

   Question/design: How much does a population average move when one isotope fraction is replaced at fixed total atoms? Prerequisites: Fraction normalization, isotope notation, multiplication and ground-state electron configurations.

   Provided inputs / reviewed materials: Use only the isotope-pattern table, the two fraction sets in the transfer, periodic-table atomic numbers and the assigned OpenStax sections. Dataset links: isotope-pattern.

   Variables: Change the Mg-26 fraction at the expense of Mg-24; record mean mass as the response and keep Mg-25 fixed. Controls: Keep mass assignments, detector-response assumption, total atom count and charge state fixed across comparisons. Replication: Compute independently twice and compare ledgers; these are arithmetic checks, not independent physical samples.

   Paper procedure and analysis: Check fractions total one, calculate each weighted term, predict a 0.01 substitution and assess sensitivity to rounding. Uncertainty: Peak overlap, background and different detector response can bias an abundance estimate. Rounding the isotope masses to integers changes the weighted answer; it is not a new isotope. A natural-source sample need not match this constructed mixture. Radius trends need comparisons at the same charge and an explanation using shell occupancy and shielding.

   Exact record to retain: Retain case ID, both fraction ledgers, atom/electron counts, each weighted term in u, assumptions, trend explanation, source section/date and the independent transfer response.

   Observable criterion evidence: Science criteria 1–4: keep the isotope notation ledger, atom-fraction normalization, weighted calculation, ground-state diagrams and a justified two-direction periodic comparison. Label the invented sample and its transfer; a mass calculation is not a flame-test technique demonstration under criterion 5.

2. Emission and photoelectron evidence answer different questions [photons-pes]

   [photons-pes] Unit 1. AP topic references: 1.5, 1.6, 1.7, 3.11, 3.12. Science criteria: 1, 3, 4, 5.

   Question/design: Can the supplied line and corrected peak pattern support a unique identity, or only a constrained electronic model? Prerequisites: Scientific notation, unit conversion, electron configurations and the isotope-pattern distinction between atom and ion.

   Provided inputs / reviewed materials: Use photons-pes, pes-peaks, the stated 100/92 eV pair, 1 nm bandwidth and the assigned electromagnetic/PES readings. Dataset links: photons-pes, pes-peaks.

   Variables: Compare wavelength and corrected subshell area; responses are photon energy and allowed electron configurations. Controls: Keep units, ground-state assumption, photon constants and response correction identical between candidates. Replication: Have a second solver repeat the energy conversion; supplied single lines have no experimental replicate uncertainty.

   Paper procedure and analysis: Compute ν and molar energy, infer binding energy by subtraction, assign subshells and reject overconfident identity claims. Uncertainty: Two close lines may be unresolved at a stated instrument bandwidth; a matching line alone is not proof of a pure element. Calibration error in either photon or kinetic energy changes inferred binding energy. Peak areas indicate populations only under the response correction. No flame, laser, UV source or unknown salt is to be used for this paper exercise.

   Exact record to retain: Retain the two tables with IDs, units and provenance, worked dimensional chain, configuration, resolution limit, missing evidence, source/date and transfer.

   Observable criterion evidence: Criteria 1, 3 and 4 use the ion/atom distinction, orbital assignment and nuclear-attraction explanation. Criterion 5 can use the spectral reasoning component, not a claimed performed flame test. Retain nm-to-m and photon-to-mole conversions, resolution judgment and a qualified identification statement.

3. Lewis, three-dimensional shape and limited molecular evidence [molecular-structure]

   [molecular-structure] Unit 2. AP topic references: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 3.1, 3.11. Science criteria: 1, 2, 3, 4, 5.

   Question/design: Which geometric and spectral evidence distinguishes a compatible structural model from a unique molecular identification? Prerequisites: Valence-electron counts, charges, domain counting, vector cancellation and willingness to retain an inconclusive identification.

   Provided inputs / reviewed materials: Use molecular-structure, molecular-bands, Lewis drawings and paper or software models; use no chemical samples or energized instruments. Dataset links: molecular-structure, molecular-bands.

   Variables: Vary the candidate structure while keeping formula/charge fixed; compare predicted geometry, dipole and spectral compatibility. Controls: Retain the same atom count and total electrons for each resonance contributor; do not move nuclei during a resonance redraw. Replication: Two independently drawn valid contributors check counting, not physical replication; uncertainty remains in incomplete bands.

   Paper procedure and analysis: Build and label models, compute formal charges and bond-order averages, then list both supported inferences and alternatives. Uncertainty: An O-H-like band may come from water contamination; a carbonyl band does not uniquely determine a molecular structure. A nitrate resonance average is a model descriptor, not a claim that every bond is exactly 1.333 under all conditions. VSEPR does not resolve all transition-metal or delocalized geometries. Hybridization is a bonding model, not directly measured by these angle entries.

   Exact record to retain: Retain labeled electron diagrams, 3-D model or accessible description, charge sum, band compatibility table, assumptions, source/date and NO2- transfer.

   Observable criterion evidence: Criteria 1–4: preserve total-electron and formal-charge ledgers, original diagrams, dipole cancellation, energy-distance explanation and a bounded band inference. Criterion 5 may observe paper-model construction; the supplied band table does not replace an approved conductivity/solubility technique observation.

4. A calibration line is not a validated chemical method [beer-lambert]

   [beer-lambert] Unit 2. AP topic references: 3.7, 3.11, 3.13. Science criteria: 1, 4, 5.

   Question/design: Over which supplied concentration interval does a linear optical model support a defensible concentration estimate? Prerequisites: Mean, line slope/intercept, logarithm meaning, molarity, dilution factors and the difference between precision and accuracy.

   Provided inputs / reviewed materials: Use beer-lambert, the provided 0.510 ± 0.003 sample reading, fivefold dilution, 1.00/0.50 cm paths and the assigned readings. Dataset links: beer-lambert.

   Variables: Concentration is the explanatory variable and absorbance the response; the transfer changes path length deliberately. Controls: Hold wavelength, solvent, temperature, pH, matrix, optical path and blank treatment fixed within each calibration. Replication: Three supplied synthetic readings per standard model repeat-read spread; independent sample preparations are not supplied.

   Paper procedure and analysis: Calculate means, graph accepted standards with labeled axes, inspect S4 residual, invert the calibrated line and propagate the stated fixed-input bounds. Uncertainty: Synthetic triplicates illustrate spread, not independent physical preparation or method validation. Turbidity, stray light, detector response, interfering species, different path length, acid-base speciation and matrix effects can invalidate Beer-Lambert proportionality. At 0.000080 M the supplied response deviates, so extrapolation beyond the selected interval is unjustified. Replicate readouts cannot reveal all systematic errors.

   Exact record to retain: Retain raw/mean rows, fitted interval and residual, dimensional slope, blank and dilution calculations, sensitivity endpoints, rejected inference, source/date and transfer.

   Observable criterion evidence: Criteria 1 and 4: connect a molecular absorber model to measured optical response, units and a qualified concentration inference. Criterion 5 can retain the data-analysis component, but simulated readings are not evidence of operating a spectrometer or performing the published conductivity/solubility practical.

5. Stoichiometric extent, limiting reagent and a yield claim [limiting-yield]

   [limiting-yield] Unit 3. AP topic references: 1.1, 1.3, 4.1, 4.3, 4.5. Science criteria: 1, 2, 3, 4, 5.

   Question/design: Which reagent limits the written reaction, and how much can a recovered-mass record actually establish about process performance? Prerequisites: Balancing by coefficients, mole/mass conversion, proportional reasoning and empirical formula ratios.

   Provided inputs / reviewed materials: Use limiting-yield, elemental-composition, the 8.000 g challenge and the assigned textbook sections; no reagents are required. Dataset links: limiting-yield, elemental-composition.

   Variables: Change available Al in the transfer; calculate limiting extent, Cu yield and leftover reagent as dependent quantities. Controls: Hold reaction stoichiometry, anhydrous identity and molar-mass conventions fixed; keep inferred product purity explicit. Replication: Independent balance and dimensional checks are analytical repeats; the single synthetic yield is not a replicate experiment.

   Paper procedure and analysis: Build an atom ledger, compute both extent limits, calculate theoretical and recovered fractions, then list non-unique loss explanations. Uncertainty: Hydrated copper salt would have a different molar mass and invalidate an anhydrous calculation. Incomplete reaction, product loss and wet product bias yield differently. The table does not establish actual purity or observed completion. Report the assumed dry-pure condition and do not infer the cause of a yield deficit from mass alone.

   Exact record to retain: Save equation, supplied identities, mole chains, limiting comparison, excess and percent yield, empirical/molecular formulas, alternative explanations and transfer.

   Observable criterion evidence: Criteria 1–4: retain atom ledger, canceled-unit mole chains, extent comparison, excess amount and elemental formula distinction. Criterion 5 receives the yield calculation with an explicit dry/pure assumption; a synthetic recovered mass is not evidence of measuring actual product yield.

6. Net ionic equations, solution denominators and spectators [solution-reactions]

   [solution-reactions] Unit 3. AP topic references: 1.4, 3.7, 3.8, 4.2, 4.3, 4.4, 4.5, 4.7. Science criteria: 1, 2, 3, 4.

   Question/design: How do stoichiometry and final volume together determine residual-ion concentrations in the ideal precipitation model? Prerequisites: Molarity, strong-electrolyte particle representations, ionic charges and coefficient-based limiting-reagent reasoning.

   Provided inputs / reviewed materials: Use solution-reactions, a paper ion ledger and the assigned net-ionic/molarity readings; do not obtain or mix the named substances. Dataset links: solution-reactions.

   Variables: Change calcium-solution volume; observe calculated product, excess-ion amount and final concentration. Controls: Keep formula-unit concentrations and the ideal speciation assumption fixed; recompute total volume rather than treating it as fixed. Replication: Have a second calculation verify material and charge closure; no physical replication or conversion measurement is supplied.

   Paper procedure and analysis: Convert volumes to moles, cancel spectators, calculate extent and final ions, then check charge closure and alternate speciation. Uncertainty: Real phosphate speciation depends strongly on pH and finite solubility, so the ideal record is not a recipe or a solubility measurement. Concentration errors and nonadditive volumes alter ion amounts. A visual cloud does not uniquely identify a precipitate. No physical trial is implied by this supplied dataset.

   Exact record to retain: Save reaction and charge ledgers, before/after particle representation, initial/final volumes, remaining-ion concentrations, assumptions, source/date and halved-volume transfer.

   Observable criterion evidence: Science criteria 1–4: retain molecular/net ionic equations, charge ledger, particle-count model, limiting calculation and final-volume concentrations. Label the equilibrium and speciation assumptions; the paper record cannot certify a precipitation practical or identify an actual unknown.

7. Partial pressure, Kelvin and the limits of the ideal gas model [gas-mixtures]

   [gas-mixtures] Unit 4. AP topic references: 3.3, 3.4, 3.5, 3.6. Science criteria: 1, 2, 4, 5.

   Question/design: Does an ideal-mixture calculation remain internally consistent after water correction, unit changes and a volume/temperature transfer? Prerequisites: Absolute temperature, mole fraction, dimensional analysis and the difference between pressure and amount.

   Provided inputs / reviewed materials: Use gas-mixtures, gas-deviation and the supplied transfer; no gas collection, heating, pressurization or vacuum apparatus is required. Dataset links: gas-mixtures, gas-deviation.

   Variables: Compare units and model density; in the transfer change volume and absolute temperature while keeping dry amount fixed. Controls: Use the same R convention consistently, account for water only in the wet record, and preserve stated gas composition. Replication: Recompute n in two compatible unit systems as an arithmetic check; density cases are not replicated measurements.

   Paper procedure and analysis: Calculate dry pressure, n, nitrogen partial pressure and Z; separate a residual from a proven physical cause. Uncertainty: A leak, incomplete water saturation, temperature gradient or pressure offset changes the inferred gas amount. Using 25 rather than 298.15 in PV/nRT gives a major scale error. Attractions can lower observed pressure relative to ideal while finite particle volume matters at high density; one residual alone cannot identify a unique non-ideal cause.

   Exact record to retain: Retain original and converted units, dry/wet labels, PV/RT chains, Z residuals, model limitations, source/date and transfer prediction.

   Observable criterion evidence: Criteria 1, 2 and 4: retain the particle-motion explanation, dry/wet distinction, unit-canceling Kelvin calculation, partial pressures and non-ideal limit. Criterion 5 may use model evaluation only; a table is not evidence of taking an actual gas or pressure measurement.

8. A plateau is an energy transfer, not no energy transfer [phase-energy]

   [phase-energy] Unit 4. AP topic references: 3.1, 3.2, 3.3, 6.3, 6.5. Science criteria: 1, 3, 4, 5.

   Question/design: Which phase proportions, rather than temperatures alone, account for energy during a constructed melting plateau? Prerequisites: Heat versus temperature, specific heat, latent heat, grams and joule/kilojoule conversion.

   Provided inputs / reviewed materials: Use phase-energy and the stated constants; draw a graph and particle diagrams on paper or in a spreadsheet. Dataset links: phase-energy.

   Variables: Added energy varies; temperature and melted fraction are distinct response variables in each phase interval. Controls: Fix total mass, pressure, purity and the zero-loss/zero-vessel-heat-capacity model assumptions. Replication: Check the piecewise sum independently; the four constructed stages are sequential states, not replicate experiments.

   Paper procedure and analysis: Separate latent and sensible terms, graph the plateau, calculate phase proportions and evaluate the effect of ignored heat sinks. Uncertainty: Real heat inputs also warm the vessel and may be lost to surroundings; impure materials can melt over a range. A thermometer lag can make a plateau appear sloped. Supplied exact segments do not establish a sensor response or a measured latent heat. Distinguish nominal model energy from actual supplied electrical energy.

   Exact record to retain: Save stage labels, graph axes and units, phase fractions, heat sums, particle explanation, model limitations, source/date and incomplete-melting transfer.

   Observable criterion evidence: Criteria 1, 3 and 4: retain the particle model, labeled piecewise graph, phase and temperature-difference reasoning and the latent/sensible energy sum. Criterion 5 may record data interpretation, not a performed gas or heating practical.

9. Valence electrons, common ions and neutral formula ratios [ionic-formulas]

   [ionic-formulas] Unit 1. AP topic references: 1.8. Science criteria: 1, 3, 4.

   Question/design: What can common valence occupation and explicitly supplied ion charges establish about a neutral ionic formula? Prerequisites: Understand atomic number, signed integers, valence electrons, factors and the difference between subscripts and ion charges.

   Provided inputs / reviewed materials: Use the two reference ledgers, periodic-table proton counts, the specified iron/phosphate ions and assigned textbook sections only. Dataset links: valence-ion-ledger, ionic-formula-inputs.

   Variables: Change the cation/anion charge pair and calculate electron counts or smallest formula ratios as distinct outputs. Controls: Keep each ion identity, signed charge and intact polyatomic group fixed while reducing the formula ratio. Replication: Check neutrality and common-factor reduction independently; repeated arithmetic is not replicate chemical synthesis.

   Paper procedure and analysis: Subtract signed charge from proton count, find the smallest balanced ion counts, then evaluate the variable-charge counterexample. Uncertainty: No measured composition or lattice structure is provided. Variable-charge metals, covalent compounds and atypical ions require more evidence than a group-number rule. Charge neutrality is necessary for the stated bulk formulas but does not prove solubility, synthesis conditions, energetic favorability or a unique solid structure.

   Exact record to retain: Retain source/date, each input charge, electron counts, neutral sums, reduced formulas, the limits of the shell heuristic and the fresh phosphate transfer.

   Observable criterion evidence: Science criteria 1, 3 and 4: retain signed charge/electron ledgers, three reduced neutral formulas, a valence-shell explanation and the variable-charge/polyatomic transfer. Neither a correct formula nor a paper electron count demonstrates flame-test or sample-identification technique.

10. Separation choices, component recovery and product purity [mixture-separation]

    [mixture-separation] Unit 3. AP topic references: 3.9. Science criteria: 5.

    Question/design: How can a larger isolated fraction have lower target recovery and purity, and what measurements would establish those claims? Prerequisites: Read additive component masses, percentages with different denominators, physical versus chemical change, and distance ratios.

    Provided inputs / reviewed materials: Use separation-streams, chromatogram-distances, the new 9.0 g fraction and the assigned conceptual reading sections; no substances or apparatus. Dataset links: separation-streams, chromatogram-distances.

    Variables: Compare output stream compositions and chromatographic migration while retaining the stated initial component masses and common origin. Controls: Keep chemical identities, ledger boundaries and the chromatographic solvent/stationary-phase system fixed in each comparison. Replication: Independently sum each component and recalculate ratios; these analytic checks are not independently repeated laboratory separations.

    Paper procedure and analysis: Sum output columns, compare with feed, name both percentage denominators, calculate Rf and challenge the larger-product claim. Uncertainty: Real composition would require independent assay and moisture evidence. The synthetic ledger closes exactly by construction and does not validate a method. Product lost into another stream can reduce recovery without changing the identity of the target. A chromatographic spot can contain co-migrating substances; equal retention factors are not unique identity or purity evidence.

    Exact record to retain: Retain separation goals and properties, labeled balances, recovery/purity calculations, chromatographic distances, source/date, limitations and the new-fraction response.

    Observable criterion evidence: Science criterion 5: justify a property-based separation choice, retain the complete component ledger, distinguish recovery/purity from reaction yield, calculate Rf and evaluate the fresh fraction. These supplied-data results do not certify a performed filtration, distillation or chromatography technique.

11. Proton-transfer reactions before equilibrium shortcuts [acid-base-intro]

    [acid-base-intro] Unit 7. AP topic references: 4.8. Science criteria: 1, 2, 3.

    Question/design: When does a proton-transfer mixture leave acid or base in excess, and what evidence distinguishes it from precipitation or weak equilibrium? Prerequisites: Understand mole concentration, mL-to-L conversion, signed ionic charge and acid/base definitions; logarithms are used only after the amount ledger.

    Provided inputs / reviewed materials: Use the two supplied symbolic/data tables, the replacement volumes and concentrations, and the assigned classification/pH sections only. Dataset links: acid-base-reactants, proton-transfer-models.

    Variables: Change acid and base equivalent amounts; record limiting species, excess concentration and conditional final pH. Controls: Keep monoprotic/monohydroxide stoichiometry, full dissociation, final 25 C and additive-volume assumptions explicit. Replication: Independently check moles, charge and the limiting comparison; recalculation is not a replicate titration or sensor reading.

    Paper procedure and analysis: Write the net ionic equation, calculate both amounts, subtract the limiting equivalent, divide by total volume and apply the appropriate pH relation. Uncertainty: These are synthetic solution records, not a titration or a validated concentration assay. Actual thermal/volume changes, concentration uncertainty and activity effects require separate evidence. The simple excess model fails near very low concentrations or when a weak reagent controls equilibrium; a color endpoint is not supplied and must not be invented.

    Exact record to retain: Retain equations, proton donor/acceptor labels, spectator and excess ledgers, units, final volume, assumptions, source/date, weak-base critique and transfer.

    Observable criterion evidence: Science criteria 1, 2 and 3: classify proton transfer, balance atoms/charge, retain molarity-to-amount and final-volume steps, distinguish spectators from excess, and solve the fresh base-excess case. A calculated mixture does not demonstrate a performed titration or an observed endpoint.

12. An energy ledger includes the cup, signs and the written reaction [calorimetry-hess]

    [calorimetry-hess] Unit 5. AP topic references: 6.1, 6.2, 6.3, 6.4, 6.6, 6.7, 6.8, 6.9. Science criteria: 1, 2, 3, 4, 5.

    Question/design: How do cup heat, amount basis and reading bounds alter a defensible calorimetric enthalpy inference? Prerequisites: q = mcΔT, total heat capacity, signs, reaction extent, joule/kilojoule conversion and balanced equations.

    Provided inputs / reviewed materials: Use calorimetry-hess, hess-records, bond-records and the supplied ±0.1 K endpoint bounds; there is no heating or combustion procedure. Dataset links: calorimetry-hess, hess-records, bond-records.

    Variables: Compare trial ΔT and change cup heat capacity in the transfer; inferred molar ΔH is the response. Controls: Keep solution mass/c, constant-pressure condition and reaction extent fixed while explicitly tracking all modeled heat sinks. Replication: Three invented trials model repeat results; they do not establish physical reproducibility or remove systematic bias.

    Paper procedure and analysis: Compute each heat ledger, mean and worst-case bound, then independently close the Hess equation and distinguish a bond-energy estimate. Uncertainty: Temperature endpoints have a specified possible ±0.1 K reading offset each. Independent random errors and shared calibration bias are different; a mean of repeated readings does not eliminate a common offset. Escaping heat tends to underestimate the magnitude of an exothermic reaction. A larger product mass or temperature change alone does not establish an actual reaction enthalpy without amount and heat-sink accounting.

    Exact record to retain: Retain raw endpoints, trial calculations, cup/solution terms, amount and phase labels, interval assumptions, Hess cancellation, source/date and transfer.

    Observable criterion evidence: Criteria 1–4: keep the signed system/surroundings ledger, amount basis, trial comparison, Hess cancellation and bond estimate with phases. Criterion 5 uses the uncertainty/analysis component only; invented temperatures cannot demonstrate actual thermometer technique, insulation control or a performed calorimetry investigation.

13. Entropy, Gibbs energy and direction under actual conditions [entropy-gibbs]

    [entropy-gibbs] Unit 5. AP topic references: 9.1, 9.2, 9.3, 9.4, 9.5. Science criteria: 1, 2, 3.

    Question/design: Can changing composition reverse the favored direction without changing temperature or the standard reaction properties? Prerequisites: Kelvin, logarithms/exponentials, J versus kJ, system/surroundings and stoichiometric activity quotients.

    Provided inputs / reviewed materials: Use entropy-gibbs, gibbs-signs and the assigned entropy/free-energy sections; work with symbolic gas states on paper only. Dataset links: entropy-gibbs, gibbs-signs.

    Variables: First change Q at fixed 298 K; then change T at fixed standard activities in the transfer. Treat these as distinct interventions. Controls: Keep the reaction direction, standard-state definition, energy basis and stated constant-H/S approximation explicit. Replication: Check direction independently using ΔG and Q/K; agreement is algebraic consistency, not independent empirical validation.

    Paper procedure and analysis: Compute entropy difference, standard Gibbs energy, actual logarithm term, K and crossover; compare signs and model limits. Uncertainty: A tiny ΔG near a crossover is sensitive to uncertainties in ΔH, ΔS and T. Heat capacities can make temperature-independent values inaccurate across a wide range. A supplied entropy difference does not measure reaction speed or a transition-state barrier. At equilibrium actual ΔG is zero even if ΔG° is not zero; calling every exothermic reaction favorable ignores the entropy and condition terms.

    Exact record to retain: Retain the chosen reaction direction, absolute/reference units, Q and standard-state definitions, dimensional calculations, sign table, limitations and transfer.

    Observable criterion evidence: Science criterion 1 includes entropy, standard versus actual Gibbs direction and rate/favorability separation. Criteria 2–3 retain the energy-unit ledger and state-function/condition reasoning. Save Q/K sign checks, source interpretation and the changed-temperature transfer; these are science evidence, not a requirement to adopt an integration viewpoint.

14. Coupling and dissolution need a complete thermodynamic system [coupling-dissolution]

    [coupling-dissolution] Unit 5. AP topic references: 3.10, 9.3, 9.6, 9.7. Science criteria: 1, 3.

    Question/design: When does a matched thermodynamic sum change sign, and what does that leave unproven about coupling or dissolution? Prerequisites: Hess-style cancellation, Gibbs energy, entropy units, activity quotient and the distinction between standard and actual state.

    Provided inputs / reviewed materials: Use coupling-dissolution and dissolution-terms with the specified revised coupling ratio and assigned readings. Dataset links: coupling-dissolution, dissolution-terms.

    Variables: Change the cost-to-driving stoichiometric ratio; separately evaluate standard versus nonstandard dissolution conditions. Controls: Match temperature, pressure, activity convention and the written reaction basis before adding step energies. Replication: A second cancellation/energy ledger is a check of bookkeeping, not mechanistic replication or a solubility measurement.

    Paper procedure and analysis: Cancel the intermediate, sum compatible ΔG values, compute dissolution ΔG° and list conditions for changing Q. Uncertainty: A proposed shared intermediate needs mechanistic evidence, not just a negative arithmetic sum. Using free energies measured at different activities breaks a simple sum unless conditions are reconciled. At nonstandard concentrations dissolution can approach equilibrium or reverse; strongly concentrated solutions may require activity coefficients. No real salt’s solubility or environmental safety follows from this synthetic model.

    Exact record to retain: Retain written net equations, coefficient-weighted sums, J/kJ conversion, standard/actual labels, mechanistic limits, source/date and changed-ratio transfer.

    Observable criterion evidence: Criteria 1 and 3 retain compatible-condition free-energy sums, canceled intermediates, dissolution enthalpy/entropy reasoning and a limitation on solubility inference. This is an original symbolic science argument, not a claim of measured mechanism, bond-energy calculation, performed experiment or an integration grading requirement.

15. Concentration over time, half-life and temperature sensitivity [kinetic-time]

    [kinetic-time] Unit 6. AP topic references: 5.1, 5.3, 5.5, 5.6. Science criteria: 1, 2, 5.

    Question/design: Which time law is consistent with the given depletion pattern, and which extra records would be needed to test its limitations? Prerequisites: Concentration, rate versus amount, logarithms, inverse concentration and Kelvin/J/kJ conventions.

    Provided inputs / reviewed materials: Use kinetic-time, arrhenius-pair and the explicitly different transfer law; retain existing rate-practice as a separate prerequisite. Dataset links: kinetic-time, arrhenius-pair.

    Variables: Time varies within the first model; temperature varies only in the separate k pair. Concentration and apparent k are responses. Controls: Hold volume, initial state and other-reactant/catalyst status fixed within each model; do not pool the distinct datasets. Replication: Exact supplied points are not replicates. A proposed real study would require independent runs and background controls under a separately approved procedure.

    Paper procedure and analysis: Compute ratios and transformed slopes, predict held-out points, calculate Ea and list residual patterns that would undermine the model. Uncertainty: Exact exponential values are generated inputs, not high-precision observations. Real late-time background and relative concentration error can distort logarithmic fits. Two temperatures always determine an Arrhenius slope but cannot test curvature or establish that the mechanism is unchanged. A pseudo-first-order law can also arise from holding another reactant in excess, so order alone does not identify an elementary step.

    Exact record to retain: Retain raw/transformed data with axes and units, k/half-life/Ea chains, fit limitations, proposed replicate design, source/date and the second-order transfer.

    Observable criterion evidence: Criteria 1–2: keep initial-rate work already assigned, then add time-law selection, dimensional k, half-life, Arrhenius energy and a qualified fit inference. Criterion 5 receives analysis planning only; the constructed curve is not evidence of measuring a reaction rate.

16. A pre-equilibrium approximation must earn its use [mechanism-energy]

    [mechanism-energy] Unit 6. AP topic references: 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11. Science criteria: 1, 2, 3.

    Question/design: How large is the error from eliminating an intermediate before checking the competing removal timescales? Prerequisites: Elementary versus overall reaction, rate-constant units, intermediates, reversible rates and reading energy profiles.

    Provided inputs / reviewed materials: Use mechanism-energy and reaction-profile with both stated algebraic hypotheses; all NO labels are symbolic inputs, not substances to obtain. Dataset links: mechanism-energy, reaction-profile.

    Variables: Vary the reverse loss constant in the transfer and compare predicted intermediate concentration/rate under two hypotheses. Controls: Keep forward/slow constants, starting concentrations and reaction direction fixed; maintain unchanged thermodynamic endpoints in the profile. Replication: Compare independent derivations and a proposed simulated timescale sweep; supplied single records do not validate a mechanism.

    Paper procedure and analysis: Cancel steps, derive pre-equilibrium and quasi-steady expressions, compare loss rates and relative errors, then calculate local barriers. Uncertainty: Here kr = 0.200 s^-1 while ks[O2] = 0.100 s^-1, only a factor of two smaller. “Fast reversible” is therefore not adequately justified. If a quasi-steady intermediate is instead assumed, [I] = kf[NO]^2/(kr + ks[O2]); even that requires a timescale check. A fitted overall rate law does not prove a unique mechanism. Energy-barrier heights without prefactors and concentrations do not uniquely identify the rate-controlling step.

    Exact record to retain: Keep the elementary steps, units, two predictions, competing loss ratio, error denominator, energy diagram, assumption verdict, source/date and transfer.

    Observable criterion evidence: Science criteria 1–3: retain elementary-step cancellation, rate-law derivation with dimensions, the failed-approximation comparison and energy-profile barriers. These supplement existing rate-practice; do not claim a kinetic fit establishes causation, mechanism uniqueness or a changed equilibrium constant.

17. Q predicts direction; a material balance predicts the new state [equilibrium-response]

    [equilibrium-response] Unit 6. AP topic references: 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9, 7.10. Science criteria: 3, 4, 5.

    Question/design: How does a volume perturbation change an equilibrium composition while preserving the same temperature-dependent equilibrium constant? Prerequisites: Balanced reaction coefficients, concentrations, quadratic roots, closed-system material balance and normalized quotients.

    Provided inputs / reviewed materials: Use equilibrium-response and equilibrium-interventions with a paper ICE table; no gas production, compression or handling is assigned. Dataset links: equilibrium-response, equilibrium-interventions.

    Variables: Volume and initial concentration change in separate scenarios; Qc and final species concentrations are the calculated responses. Controls: Fix temperature, gas-model convention, total species-equivalent amount and catalyst-independent Kc during the compression case. Replication: Check substitution into Kc and atom balance independently; synthetic roots are not observed replicate equilibria.

    Paper procedure and analysis: Distinguish initial, immediate-perturbation and re-equilibrated states; solve the quadratic and check physical bounds/approximation size. Uncertainty: With initial 0.200 M, assuming x negligible compared with the initial amount fails; solve the quadratic. Temperature drift during compression would also change K, invalidating the isothermal prediction. Real gas nonideality changes activity relationships. A catalyst changes the equilibration time, not the fixed-temperature K. The model states endothermic forward dissociation, so raising temperature increases K for this direction, not for all reactions.

    Exact record to retain: Retain all three state ledgers, volume/temperature conditions, Qc/Kc comparisons, physical-root checks, atom balance, source/date and dilution transfer.

    Observable criterion evidence: Criteria 3–4: retain Q/K expressions with state conventions, ICE table, root selection, material balance and quantitative perturbation. Criterion 5 receives prediction/analysis evidence but a supplied gas calculation is not a performed equilibrium-shift or rate observation.

18. Weak does not mean dilute, and a square-root shortcut can fail [weak-acid]

    [weak-acid] Unit 7. AP topic references: 8.1, 8.2, 8.3, 8.6, 8.7. Science criteria: 1, 2, 4.

    Question/design: At what dilution does a convenient weak-acid approximation contradict material balance, and when must water be included? Prerequisites: Conjugate pairs, logarithms, Ka/Kb/Kw, molarity, quadratic roots and material/charge balance.

    Provided inputs / reviewed materials: Use weak-acid, acid-structure, the 1e-8 M strong-acid challenge and the dilution transfer; all work is on paper. Dataset links: weak-acid, acid-structure.

    Variables: Change analytical concentration while holding Ka and temperature fixed; calculate free H3O+, pH and percent ionization. Controls: State the activity approximation, initial conjugate-base amount and when water autoionization is negligible. Replication: Verify physical roots by substitution and compare two solution methods; no actual solution or repeated pH measurement is supplied.

    Paper procedure and analysis: Solve the equilibrium, compare sqrt and exact roots, test depletion and autoionization, and distinguish structural strength from concentration. Uncertainty: A 5% depletion screen is a convenience rule, not a universal error guarantee. At C = 1e-5 M the square-root estimate exceeds total available acid and must be rejected. Temperature or solvent changes alter constants; ionic-strength effects limit the activity approximation. Molecular comparisons need bond strength and conjugate-base stabilization, not a rule that electronegativity alone always decides acid strength.

    Exact record to retain: Retain C/Ka/Kw, both roots or rejected root explanation, units, pH/percent chains, approximation checks, structure argument, source/date and transfer.

    Observable criterion evidence: Science criteria 1, 2 and 4: retain the equilibrium equation, analytical-versus-free concentration labels, positive quadratic root, depletion check, molecular explanation and water-correction challenge. No calculation establishes safe preparation or actual acid/base handling.

19. Neutralize first; a pH ratio is not a capacity reserve [buffer-capacity]

    [buffer-capacity] Unit 7. AP topic references: 8.4, 8.7, 8.8, 8.9, 8.10. Science criteria: 1, 2, 3, 4.

    Question/design: Can two buffers with the same starting ratio respond very differently to the same acid-equivalent challenge? Prerequisites: Moles, strong neutralization, conjugate pairs, logarithms and the weak-acid equilibrium assumptions.

    Provided inputs / reviewed materials: Use buffer-capacity and its fixed final-volume model plus the given base transfer; no real acid, base or buffer preparation is required. Dataset links: buffer-capacity.

    Variables: Vary total conjugate-pair reserve or sign of added equivalents; compare residual amounts and calculated pH. Controls: Keep Ka, temperature, final volume and ratio-model assumptions explicit; do not confuse matched pH with matched capacity. Replication: Compare independent mole ledgers; four scenarios are not replicate titrations and supply no laboratory repeatability claim.

    Paper procedure and analysis: Neutralize, check whether both partners remain, select ratio or excess-strong-ion model and assess the neglected weak contribution. Uncertainty: A tenfold-diluted buffer can have nearly the same initial pH but one tenth of the neutralization reserve. pH near pKa does not imply unlimited capacity or a guaranteed safe solution. Activity effects, inaccurate amounts and added volume can shift actual pH. “Within about one pH unit of pKa” is a useful operating heuristic, not a sharp universal capacity boundary.

    Exact record to retain: Retain initial/change/final moles, final volume, pKa and pH, exhaustion verdict, approximation assessment, source/date and reversed-challenge transfer.

    Observable criterion evidence: Science criteria 1–4: retain neutralization stoichiometry before equilibrium, pKa/ratio calculation, explicit remaining amounts, capacity comparison and the rejected exhausted-buffer shortcut. This reasoning is separate from integration and does not show hands-on solution preparation.

20. Titration regions and solubility require different balances [titration-solubility]

    [titration-solubility] Unit 7. AP topic references: 4.6, 8.5, 7.11, 7.12, 8.11. Science criteria: 1, 2, 3, 4, 5.

    Question/design: Which equilibrium model applies in each titration region, and how do endpoint bias and common ions change the interpretation? Prerequisites: Moles, balanced acid/base stoichiometry, Ka/Kb, buffer conditions, hydrolysis, molarity after mixing and solubility powers.

    Provided inputs / reviewed materials: Use titration-solubility, endpoint-records and solubility-records plus the given monoprotic and diprotic equations; no chemicals or apparatus are assigned. Dataset links: titration-solubility, endpoint-records, solubility-records.

    Variables: Base-equivalent amount varies in the curve; added common ion varies separately in the solubility comparison. Controls: Keep temperature, initial acid amount, base concentration and stated activity/speciation approximations explicit; compute each final volume. Replication: Three constructed endpoint volumes illustrate repeatability only. Their mean remains biased relative to the supplied stoichiometric reference.

    Paper procedure and analysis: Build a mole ledger for each volume, select its pH model, graph labeled regions, compute endpoint bias and diluted Qsp, then evaluate assumption failures. Uncertainty: Indicator range and sensor calibration can shift the endpoint systematically; repeated nearby endpoints do not prove equivalence accuracy. Near equivalence the validity of a simple buffer approximation must be rechecked. A Ksp model that ignores complexes, ionic strength or protonation may miss real solubility. A paper curve cannot demonstrate controlled drops, safe handling or a reproducible physical titration.

    Exact record to retain: Retain curve points with regime labels, neutralization/hydrolysis work, volumes, endpoint mean/range and bias, solubility/Qsp chains, source/date and MX2 transfer.

    Observable criterion evidence: Criteria 1–4: preserve regime selection, balanced neutralization, all final volumes, endpoint bias and Qsp/Ksp with approximation checks. Criterion 5 may retain repeatability analysis but still needs a separate educator-approved observed titration or formally approved assessment alternative; synthetic endpoints are not performed technique.

21. Cell potential is intensive; its free-energy consequence is not [nonstandard-cell]

    [nonstandard-cell] Unit 8. AP topic references: 9.5, 9.8, 9.9, 9.10. Science criteria: 1, 2, 3, 4.

    Question/design: When can composition reverse a predicted cell direction even though its standard potential is positive? Prerequisites: Balanced redox equations, n, galvanic/electrolytic roles, Gibbs energy, natural logarithms and activities.

    Provided inputs / reviewed materials: Use nonstandard-cell and the existing Faraday practice as complementary paper records; no electrodes, voltages or electrolytes are assigned. Dataset links: nonstandard-cell.

    Variables: Vary Q at fixed T and compare cell types; E and ΔG are calculated responses tied to a specified reaction direction. Controls: Hold reference conventions, n, T, R and F consistent; omit pure solids from Q only when their pure phases are present. Replication: Cross-check the energy result using two algebraic routes; this is not a replicated voltage measurement or performance test.

    Paper procedure and analysis: Compute Nernst E, both Gibbs routes and log K; assess open-circuit limits and preserve separate current-efficiency reasoning. Uncertainty: Nernst E is a reversible/open-circuit prediction. It does not supply a safe operating voltage or predict current, product selectivity, resistance or electrode kinetics. Concentrations can be poor activity estimates at higher ionic strength. Liquid-junction potentials and temperature uncertainty are absent from the ideal record. This supplements, rather than replaces, the previously assigned Faraday current-efficiency practice.

    Exact record to retain: Retain reaction, electron number, Q construction, electrode labels, both energy chains, equilibrium limit, uncertainty, source/date and sign-changing transfer.

    Observable criterion evidence: Science criteria 1–4: retain oxidation/electron ledgers, actual versus standard conditions, electrode polarity, intensive-potential reasoning and independent ΔG/Q checks. Keep the existing faraday-practice and faraday-transfer charge/efficiency evidence too; neither set alone demonstrates constructing or operating a cell under criterion 5.

22. Mass and charge must both close in acidic and basic ledgers [redox-balance]

    [redox-balance] Unit 8. AP topic references: 4.9, 9.8. Science criteria: 1, 2, 3.

    Question/design: Which independent conservation checks expose a redox equation that looks plausible but is chemically impossible? Prerequisites: Ion charge, oxidation-number conventions, atom counting, half-reaction algebra and acid/base balancing species.

    Provided inputs / reviewed materials: Use redox-balance and the assigned redox section, with a blank paper ledger for an independent reconstruction. Dataset links: redox-balance.

    Variables: Compare acidic versus basic assigned products and deliberately remove one balancing species to test sensitivity. Controls: Keep atom identities, net charges and stated products fixed while adjusting coefficients and canceling shared species. Replication: Separate atom and charge tallies are independent bookkeeping checks, not experimental confirmation of the modeled reaction.

    Paper procedure and analysis: Derive halves, find a common electron count, combine and cancel, then check every elemental column and total charge. Uncertainty: Balanced equations prove conservation, not actual kinetics, selectivity or product identity. A different medium can change the manganese product and electron ratio. Water and H+/OH- are balancing species, not permission to combine the named substances. An oxidation-state argument does not predict a cell potential without thermodynamic data.

    Exact record to retain: Retain both half-reaction derivations, coefficient ledger, atom/charge sums, corrected missing-water example, assumptions, source/date and mole-ratio transfer.

    Observable criterion evidence: Science criteria 1–3: keep oxidation-state assignments, agent roles, both complete half-reaction derivations, canceled electrons and every atom/charge check. Label medium and assigned products. This does not replace the criterion-4 cell or Faraday evidence and does not demonstrate laboratory cell construction.