[{"data":1,"prerenderedAt":201},["ShallowReactive",2],{"topic-review-and-capstone":3},{"topic":4,"prev":193,"next":200},{"id":5,"slug":6,"title":7,"shortTitle":8,"lesson":5,"category":9,"description":10,"metaDescription":11,"objectives":12,"conceptSections":34,"workedExample":63,"oerSources":72,"selfStudyQuestions":74,"relatedTopicSlugs":88,"relatedElements":109,"relatedReferences":120,"keyEquations":125,"howTo":162,"conceptProbe":170,"practiceTeaser":174,"gatedContent":182,"seoKeywords":185,"lastAlignmentAudit":191,"objectiveCount":192},30,"review-and-capstone","Review and Capstone","Review & Capstone","advanced","A comprehensive end-of-course review built from a 50-question practice final exam, organized into seven strands that span the whole general-chemistry sequence. Recall the key method for each strand, refresh the prerequisites, then test every skill on fresh practice problems.","Free general chemistry capstone review: seven strands covering stoichiometry, thermodynamics, kinetics, equilibrium, acid-base, electrochemistry, bonding, and coordination chemistry, with worked examples and graded practice.",[13,16,19,22,25,28,31],{"id":14,"text":15},"30.1","Apply measurement, mole/formula, stoichiometry, and solution-concentration reasoning to multi-step quantitative problems",{"id":17,"text":18},"30.2","Apply calorimetry, enthalpy/Hess, and entropy/free-energy (spontaneity) reasoning across phase changes and reactions",{"id":20,"text":21},"30.3","Determine rate laws (including integrated rates) and apply K/Q/ICE equilibrium reasoning to gas-phase and rate problems",{"id":23,"text":24},"30.4","Solve acid-base, buffer, titration, and solubility problems (pH, Ksp, hydrolysis) for aqueous systems",{"id":26,"text":27},"30.5","Balance redox reactions and apply cell-potential, Nernst, and electrolysis (Faraday) relationships",{"id":29,"text":30},"30.6","Apply atomic-structure, periodicity, bonding/VSEPR, and intermolecular-force reasoning to predict the structure and physical properties of substances",{"id":32,"text":33},"30.7","Apply coordination-chemistry and crystal-field-theory reasoning to name complexes, determine coordination and oxidation numbers, and predict d-electron count and magnetic behavior",[35,39,43,47,51,55,59],{"heading":36,"content":37,"relatedObjectives":38},"Strand 1 · Quantitative Foundations","\u003Cp>\u003Cstrong>What to recall.\u003C/strong> The whole quantitative core hangs on the mole. Convert with \u003Cstrong>mol = mass ÷ molar mass\u003C/strong>; read \u003Cstrong>mole ratios from the balanced equation\u003C/strong> to bridge any two species; track significant figures through the calculation. For solutions, \u003Cstrong>molarity = mol solute ÷ L solution\u003C/strong>, dilutions follow \u003Cstrong>M\u003Csub>1\u003C/sub>V\u003Csub>1\u003C/sub> = M\u003Csub>2\u003C/sub>V\u003Csub>2\u003C/sub>\u003C/strong>, and an ion’s concentration is the formula-unit molarity times its subscript on dissolution. Finish with limiting-reagent and density conversions when a problem mixes mass, volume, and amount.\u003C/p>\u003Cp>\u003Cstrong>Review before this strand:\u003C/strong> \u003Ca href=\"/learn/measurement-and-significant-figures\">Units & Measurement\u003C/a>, \u003Ca href=\"/learn/the-mole-and-chemical-formulas\">Moles & Composition\u003C/a>, \u003Ca href=\"/learn/predicting-and-balancing-chemical-reactions\">Predicting & Balancing\u003C/a>, \u003Ca href=\"/learn/stoichiometry\">Stoichiometry\u003C/a>, \u003Ca href=\"/learn/solutions-and-concentration\">Solutions & Molarity\u003C/a>.\u003C/p>",[14],{"heading":40,"content":41,"relatedObjectives":42},"Strand 2 · Thermochemistry & Thermodynamics","\u003Cp>\u003Cstrong>What to recall.\u003C/strong> Heat tracks with \u003Cstrong>q = mcΔT\u003C/strong>, and calorimetry is conservation: \u003Cstrong>q\u003Csub>rxn\u003C/sub> = −q\u003Csub>surroundings\u003C/sub>\u003C/strong> (a bomb gives q\u003Csub>rxn\u003C/sub> = −C\u003Csub>cal\u003C/sub>ΔT). Build reaction enthalpies by \u003Cstrong>Hess’s law\u003C/strong> or \u003Cstrong>ΔH°\u003Csub>rxn\u003C/sub> = ∑nΔH°\u003Csub>f\u003C/sub>(products) − ∑nΔH°\u003Csub>f\u003C/sub>(reactants)\u003C/strong>; entropies the same way with \u003Cstrong>ΔS°\u003Csub>rxn\u003C/sub> = ∑nS°(products) − ∑nS°(reactants)\u003C/strong> (watch J vs kJ). Spontaneity is \u003Cstrong>ΔG = ΔH − TΔS\u003C/strong>: negative-ΔH/positive-ΔS always favorable, the reverse never, and the two mixed cases switch at \u003Cstrong>T = ΔH ÷ ΔS\u003C/strong>.\u003C/p>\u003Cp>\u003Cstrong>Review before this strand:\u003C/strong> \u003Ca href=\"/learn/thermochemistry\">Thermochemistry\u003C/a>, \u003Ca href=\"/learn/intermolecular-forces-and-phase-changes\">IMFs & Phases\u003C/a>, \u003Ca href=\"/learn/entropy-and-free-energy\">Thermodynamics\u003C/a>.\u003C/p>",[17],{"heading":44,"content":45,"relatedObjectives":46},"Strand 3 · Kinetics & Equilibrium","\u003Cp>\u003Cstrong>What to recall.\u003C/strong> Get rate-law orders from the \u003Cstrong>ratio of initial rates\u003C/strong> when one concentration changes at a time; first-order decay obeys \u003Cstrong>ln([A]\u003Csub>0\u003C/sub>/[A]) = kt\u003C/strong> with \u003Cstrong>t\u003Csub>1/2\u003C/sub> = ln 2 ÷ k\u003C/strong>. Write the equilibrium expression as products over reactants, each raised to its coefficient; compare \u003Cstrong>Q to K\u003C/strong> for direction; solve concentrations with an \u003Cstrong>ICE table\u003C/strong>. Shift predictions come from \u003Cstrong>Le Châtelier\u003C/strong> — concentration, pressure/volume through moles of gas, and temperature through endo/exo. Gas mixtures partition by \u003Cstrong>Dalton’s partial pressures\u003C/strong>.\u003C/p>\u003Cp>\u003Cstrong>Review before this strand:\u003C/strong> \u003Ca href=\"/learn/gases-and-gas-laws\">Gas Laws\u003C/a>, \u003Ca href=\"/learn/chemical-kinetics\">Kinetics\u003C/a>, \u003Ca href=\"/learn/chemical-equilibrium\">Equilibrium\u003C/a>.\u003C/p>",[20],{"heading":48,"content":49,"relatedObjectives":50},"Strand 4 · Aqueous Equilibria","\u003Cp>\u003Cstrong>What to recall.\u003C/strong> Strong acids and bases give pH straight from concentration. A weak acid needs an ICE table: \u003Cstrong>K\u003Csub>a\u003C/sub> = x\u003Csup>2\u003C/sup> ÷ (C − x)\u003C/strong> — drop the −x only when ionization is small (a few percent), otherwise solve the quadratic. Buffers follow \u003Cstrong>Henderson–Hasselbalch: pH = pK\u003Csub>a\u003C/sub> + log([A\u003Csup>−\u003C/sup>] ÷ [HA])\u003C/strong>. Get \u003Cstrong>K\u003Csub>sp\u003C/sub> from molar solubility\u003C/strong> (mind the stoichiometric powers), salt pH from hydrolysis with \u003Cstrong>K\u003Csub>a\u003C/sub>·K\u003Csub>b\u003C/sub> = K\u003Csub>w\u003C/sub>\u003C/strong>, and titration results from neutralization stoichiometry to the equivalence point.\u003C/p>\u003Cp>\u003Cstrong>Review before this strand:\u003C/strong> \u003Ca href=\"/learn/acids-bases-and-ph\">Acids & Bases\u003C/a>, \u003Ca href=\"/learn/buffers-and-titration-curves\">Buffers\u003C/a>, \u003Ca href=\"/learn/solubility-and-complex-ion-equilibria\">Solubility Equilibria\u003C/a>.\u003C/p>",[23],{"heading":52,"content":53,"relatedObjectives":54},"Strand 5 · Electrochemistry & Redox","\u003Cp>\u003Cstrong>What to recall.\u003C/strong> Balance redox by \u003Cstrong>half-reactions\u003C/strong> — atoms first, then O with H\u003Csub>2\u003C/sub>O, H with H\u003Csup>+\u003C/sup>, charge with e\u003Csup>−\u003C/sup>; in base, neutralize H\u003Csup>+\u003C/sup> with OH\u003Csup>−\u003C/sup>. A galvanic cell’s standard potential is \u003Cstrong>E°\u003Csub>cell\u003C/sub> = E°\u003Csub>cathode\u003C/sub> − E°\u003Csub>anode\u003C/sub>\u003C/strong>, spontaneous when \u003Cstrong>E°\u003Csub>cell\u003C/sub> > 0\u003C/strong> (since ΔG° = −nFE°); the Nernst equation handles nonstandard concentrations. Electrolysis is bookkeeping with \u003Cstrong>Faraday: moles e\u003Csup>−\u003C/sup> = (I·t) ÷ F\u003C/strong>. The stronger oxidizing agent has the more positive E°.\u003C/p>\u003Cp>\u003Cstrong>Review before this strand:\u003C/strong> \u003Ca href=\"/learn/redox-reactions-and-redox-balancing\">Redox & Balancing\u003C/a>, \u003Ca href=\"/learn/electrochemistry\">Electrochemistry\u003C/a>.\u003C/p>",[26],{"heading":56,"content":57,"relatedObjectives":58},"Strand 6 · Atomic Structure, Bonding & IMF","\u003Cp>\u003Cstrong>What to recall.\u003C/strong> Write ground-state \u003Cstrong>electron configurations\u003C/strong>, including the Cr/Cu exceptions and the remove-4s-before-3d rule for transition-metal ions; count valence and d electrons from them. Predict \u003Cstrong>VSEPR geometry\u003C/strong> from electron domains and the \u003Cstrong>predominant intermolecular force\u003C/strong> (hydrogen bonding > dipole–dipole > dispersion, scaled by size). Periodic trends rank radius, ionization energy, and electronegativity. A cubic unit cell gives density by \u003Cstrong>ρ = (Z · M) ÷ (N\u003Csub>A\u003C/sub> · a\u003Csup>3\u003C/sup>)\u003C/strong>.\u003C/p>\u003Cp>\u003Cstrong>Review before this strand:\u003C/strong> \u003Ca href=\"/learn/atomic-structure-and-isotopes\">Atomic Structure\u003C/a>, \u003Ca href=\"/learn/electron-structure-and-light\">Electron Structure\u003C/a>, \u003Ca href=\"/learn/molecular-geometry-and-bonding-theories\">Molecular Shape\u003C/a>, \u003Ca href=\"/learn/intermolecular-forces-and-phase-changes\">IMFs & Phases\u003C/a>.\u003C/p>",[29],{"heading":60,"content":61,"relatedObjectives":62},"Strand 7 · Coordination Chemistry & Crystal-Field Theory","\u003Cp>\u003Cstrong>What to recall.\u003C/strong> Name complexes by IUPAC rules — ligand prefixes in alphabetical order, the \u003Cstrong>−ate\u003C/strong> suffix for an anionic complex, and the metal’s oxidation state in Roman numerals. The \u003Cstrong>coordination number\u003C/strong> is the count of donor atoms; the metal’s \u003Cstrong>oxidation number\u003C/strong> comes from charge balance against the ligands and counter-ions. From the d-electron count and the field strength, crystal-field theory fixes the spin state — \u003Cstrong>strong field → low spin, weak field → high spin\u003C/strong> — which sets the number of unpaired electrons and whether the complex is paramagnetic or diamagnetic.\u003C/p>\u003Cp>\u003Cstrong>Review before this strand:\u003C/strong> \u003Ca href=\"/learn/coordination-chemistry\">Coordination Chemistry\u003C/a>.\u003C/p>",[32],{"title":64,"problem":65,"steps":66,"answer":71},"A worked capstone item: combustion stoichiometry","What mass of oxygen gas is needed for the complete combustion of 76.6 g of ethylene (C₂H₄) to form carbon dioxide and water?",[67,68,69,70],"Balance the combustion equation: C₂H₄ + 3 O₂ → 2 CO₂ + 2 H₂O.","Moles C₂H₄ = 76.6 g ÷ 28.05 g/mol = 2.731 mol.","Mole ratio O₂ : C₂H₄ = 3 : 1, so moles O₂ = 3 × 2.731 = 8.192 mol.","Mass O₂ = 8.192 mol × 32.00 g/mol = 262 g.","262 g O₂.",[73],"General Chemistry Workbook (Beryllium Edition) — Practice Final Exam (50 questions).",[75,77,79,82,84,86],{"question":76},"Which of the seven strands does a given exam question belong to, and what is the single key relationship that strand turns on?",{"question":78},"For a multi-step stoichiometry problem, how do you chain mass → moles → mole ratio → moles → mass without losing units?",{"question":80,"hint":81},"Given ΔH and ΔS, how do you decide whether a reaction is spontaneous, and at what temperature spontaneity changes?","ΔG = ΔH − TΔS; the crossover is T = ΔH ÷ ΔS when ΔH and ΔS share a sign.",{"question":83},"When is the small-x approximation safe in a weak-acid ICE table, and what do you do when it is not?",{"question":85},"How do you assemble a balanced redox equation from half-reactions in acidic versus basic solution?",{"question":87},"From a transition-metal ion's d-electron count and the ligand field strength, how do you predict the number of unpaired electrons?",[89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108],"measurement-and-significant-figures","the-mole-and-chemical-formulas","predicting-and-balancing-chemical-reactions","stoichiometry","solutions-and-concentration","thermochemistry","intermolecular-forces-and-phase-changes","entropy-and-free-energy","gases-and-gas-laws","chemical-kinetics","chemical-equilibrium","acids-bases-and-ph","buffers-and-titration-curves","solubility-and-complex-ion-equilibria","redox-reactions-and-redox-balancing","electrochemistry","atomic-structure-and-isotopes","electron-structure-and-light","molecular-geometry-and-bonding-theories","coordination-chemistry",[110,111,112,113,114,115,116,117,118,119],"H","O","C","N","S","Cl","Na","Fe","Co","Cu",[121,122,123,124],"weak-acid-base-constants","solubility-product-constants","standard-enthalpies-of-formation","standard-reduction-potentials",[126,130,134,138,142,146,150,154,158],{"label":127,"equation":128,"note":129},"Molarity","M = mol solute ÷ L solution","Dilutions: M₁V₁ = M₂V₂",{"label":131,"equation":132,"note":133},"Gibbs Free Energy","ΔG = ΔH − TΔS","T in kelvins; spontaneous when ΔG \u003C 0; crossover at T = ΔH ÷ ΔS",{"label":135,"equation":136,"note":137},"Free Energy and Equilibrium","ΔG° = −RT ln K","R = 8.314 J/(mol·K); K > 1 ⇒ ΔG° \u003C 0",{"label":139,"equation":140,"note":141},"First-Order Half-Life","t₁/₂ = ln 2 ÷ k","Integrated first-order law: ln([A]₀/[A]) = kt",{"label":143,"equation":144,"note":145},"Buffer pH (Henderson–Hasselbalch)","pH = pKa + log([A⁻] ÷ [HA])","Valid in the buffering region near pH ≈ pKa",{"label":147,"equation":148,"note":149},"Weak-Acid Equilibrium","Ka = x² ÷ (C − x)","Drop −x only when ionization is small; otherwise solve the quadratic",{"label":151,"equation":152,"note":153},"Standard Cell Potential","E°cell = E°cathode − E°anode","Spontaneous when E°cell > 0; ΔG° = −nFE°",{"label":155,"equation":156,"note":157},"Electrolysis (Faraday)","moles e⁻ = (I · t) ÷ F","F = 96485 C/mol e⁻",{"label":159,"equation":160,"note":161},"Cubic Unit-Cell Density","ρ = (Z · M) ÷ (N_A · a³)","Z = atoms per cell (2 for BCC, 4 for FCC); a = edge length",{"title":163,"steps":164},"How to Use This Capstone",[165,166,167,168,169],"Work one strand at a time — each strand bundles the skills the final exam tests together, so you review in the way the exam asks.","Start from the strand's \"What to recall\" summary. If any relationship is unfamiliar, follow the \"Review before this strand\" links back to the original topic before going on.","Study the worked example and follow the full method from identifying the relationships through checking the final result.","Then attempt the related practice problems with fresh values, checking the chemistry, setup, units, and final result.","Don't memorize specific numbers. Practice recognizing which strand and method a question belongs to, then apply the key relationship — that is what transfers to the exam.",{"question":171,"answer":172,"type":173},"A final-exam question gives a 0.0349 M solution of a weak acid and asks for the pH. Before doing any arithmetic, how do you decide which method to use, and what tells you whether the simple approximation is safe?","Identify the species first: a weak acid means an equilibrium problem, so set up an ICE table with Ka = x²/(C − x), where x = [H⁺]. The method follows from recognizing the strand (aqueous equilibria), not from the numbers. The approximation x ≪ C is safe only when ionization is small — roughly when Ka is small relative to C (a few percent ionized); if the acid ionizes appreciably, keep the −x and solve the quadratic. Choosing the method by recognizing the question type is the capstone skill.","conceptual",[175,179],{"id":176,"problem":177,"type":178},"pt-30-1","What mass of oxygen gas is needed for the complete combustion of 50.0 g of propane (C₃H₈) to form carbon dioxide and water?","calculation",{"id":180,"problem":181,"type":178},"pt-30-2","Calculate the pH of a buffer solution prepared from a weak acid and its conjugate base, given the concentrations and pKa.",{"workedExampleCount":183,"hasWorksheets":184},50,true,[186,187,188,189,190],"general chemistry review","final exam practice","chemistry capstone","comprehensive chemistry review","gen chem final","2026-07-17",7,{"id":194,"slug":195,"lesson":194,"title":196,"shortTitle":196,"description":197,"category":9,"objectiveCount":198,"problemCount":199},29,"main-group-chemistry","Main Group Chemistry","Predict the properties and reactions of the representative (main-group) elements from periodic trends, compare their allotropes, and learn the major industrial processes that make ammonia, nitric acid, sulfuric acid, and the metals.",5,18,null,1785108608245]