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One mole = 6.022 × 10²³ particles (Avogadro's number). It links what you can weigh (grams) to what you can count (atoms / molecules).
moles = mass / molar mass | particles = moles × 6.022 × 10²³| Step | What you do |
|---|---|
| 1 | Balance the equation |
| 2 | Convert given mass → moles (÷ molar mass) |
| 3 | Apply mole ratio from balanced eq |
| 4 | Convert moles of target → mass or particles |
% yield = (actual / theoretical) × 100. Theoretical = what stoichiometry predicts. Actual = what you measure. Real reactions are rarely 100%.2 H₂ + O₂ → 2 H₂O ratio H₂ : O₂ : H₂O = 2 : 1 : 2Empirical vs molecular formula: empirical is the simplest whole-number ratio (CH₂O); molecular is the actual count (C₆H₁₂O₆ = empirical × 6).
Mole ratios come from coefficients in the balanced equation, not the unbalanced one. Always balance first. Half the stoich problems get answered with the wrong ratio because students skipped this step.
| ΔEN range | Bond type | Example |
|---|---|---|
| < 0.4 | nonpolar covalent | H–H, C–H |
| 0.4 – 1.7 | polar covalent | O–H, N–H |
| > 1.7 | ionic | NaCl, MgO |
1. Sum valence e⁻ from all atoms (add for negative charge, subtract for positive).
2. Place least-electronegative atom in center (never H).
3. Connect with single bonds, fill octets on outer atoms first.
4. If center lacks octet, form double/triple bonds. Check formal charges.
Formal charge = valence e⁻ − lone-pair e⁻ − ½(bonded e⁻)Resonance: when one Lewis structure can't capture the real bonding (e.g. O₃, NO₃⁻), draw multiple structures with double bonds in different positions. Real molecule = average.
CO₂ has two polar C=O bonds, but the molecule is linear so dipoles cancel — nonpolar. Always check the geometry, not just the bonds. Symmetric arrangement of polar bonds = nonpolar molecule.
PV = nRT R = 0.0821 L·atm/(mol·K) = 8.314 J/(mol·K)Always convert temperature to Kelvin (TK = T°C + 273.15). Pressures: 1 atm = 760 mmHg = 101.325 kPa = 760 torr.
| Held constant | Law | Form |
|---|---|---|
| n, T | Boyle's | P₁V₁ = P₂V₂ |
| n, P | Charles's | V₁/T₁ = V₂/T₂ |
| n, V | Gay-Lussac | P₁/T₁ = P₂/T₂ |
| n | Combined | P₁V₁/T₁ = P₂V₂/T₂ |
| T, P | Avogadro's | V₁/n₁ = V₂/n₂ |
STP: 0°C (273.15 K) + 1 atm ⇒ 1 mol of gas = 22.4 LPtotal = ΣPi. Each gas exerts pressure as if alone. Mole fraction χi = ni/ntotal; Pi = χi · Ptotal.r₁/r₂ = √(M₂/M₁). He (M=4) effuses 2× faster than O₂ (M=16).Real-gas deviations: ideal-gas law breaks down at high P + low T. Use van der Waals: (P + an²/V²)(V − nb) = nRT.
Forgetting to convert °C → K is the #1 gas-law mistake. PV = nRT requires absolute temperature. Also: match R to your P units (0.0821 for atm, 8.314 for kPa or J).
| Trend | Across (L→R) | Down (T→B) | Driver |
|---|---|---|---|
| Atomic radius | ↓ decreases | ↑ increases | Zeff ↑ across; n ↑ down |
| Ionization energy | ↑ increases | ↓ decreases | harder to remove e⁻ when held tight |
| Electron affinity | ↑ (more negative) | ↓ | nonmetals 'want' e⁻ |
| Electronegativity | ↑ increases | ↓ decreases | F is the most EN element |
Zeff ≈ Z (nuclear charge) − S (shielding by inner electrons)Cation < neutral atom (lost shell or pulled tighter). Anion > neutral atom (added e⁻ → more repulsion). Isoelectronic species: more protons → smaller radius.
IE doesn't increase monotonically. Be → B dips (B's 2p e⁻ easier to lose than Be's 2s pair). N → O dips (O's paired 2p e⁻ has repulsion). Examiners love these.
| Unit | Definition | When to use |
|---|---|---|
| Molarity (M) | mol solute / L solution | most lab work |
| Molality (m) | mol solute / kg solvent | colligative props (T-dependent) |
| Mole fraction (χ) | ni / ntotal | vapor pressure, partial P |
| % by mass | (g solute / g solution) × 100 | commercial reagents |
| ppm | mg solute / kg solution | trace amounts |
Dilution: M₁V₁ = M₂V₂ (moles preserved before / after dilution)ΔTb = i · Kb · m. Sugar (i=1) raises bp less than NaCl (i≈2 — dissociates) at same molality.ΔTf = i · Kf · m. Same i factor matters. Why we salt icy roads.Van't Hoff factor i: number of particles per formula unit dissolved. NaCl → 2 (Na⁺ + Cl⁻). CaCl₂ → 3. Sugar → 1.
Osmotic pressure: Π = iMRT Raoult's law: P = χsolvent · P°pureMolarity uses liters of solution. Molality uses kg of solvent. Different denominators! Mixing the two costs problems. ppm and % by mass use mass of solution.
Heat (q) = energy transferred. Temperature = average KE. Same heat warms different masses by different amounts.
q = m · c · ΔT c = specific heat capacity (J/g·°C)ΔH = q at constant P. Exothermic ΔH < 0 (releases heat); endothermic ΔH > 0 (absorbs).
| Method | Formula | Use when |
|---|---|---|
| Hess's law | ΔHrxn = Σ ΔHsteps | given step ΔHs |
| Formation enthalpies | ΔH = ΣnΔHf(prod) − ΣnΔHf(reac) | ΔH°f table |
| Bond energies | ΔH = Σ BEbroken − Σ BEformed | only bond data |
| Calorimetry | qrxn = −qsolution = −mcΔT | experimental |
1st law of thermodynamics: ΔU = q + w. At const P: ΔH = ΔU + PΔV.
q < 0 means system loses heat (exothermic). qsystem = −qsurroundings. In calorimetry, qrxn = −qwater — the negative sign is mandatory.
| n | ℓ | mℓ | ms |
|---|---|---|---|
| shell (1, 2, 3...) | subshell (s=0, p=1, d=2, f=3) | orbital (−ℓ to +ℓ) | spin (±½) |
Orbitals per subshell: s=1, p=3, d=5, f=7 e⁻ per shell n: max 2n²Electron config: O = 1s² 2s² 2p⁴ Noble-gas core: O = [He] 2s² 2p⁴Anomalies (memorize): Cr = [Ar] 4s¹ 3d⁵, Cu = [Ar] 4s¹ 3d¹⁰. Half- and fully-filled d are extra stable — one electron 'promoted' from 4s.
Transition metals losing e⁻ to form cations remove from 4s before 3d (despite filling order being opposite). Fe → Fe²⁺ = [Ar] 3d⁶ (not 3d⁴ 4s²). This breaks intuition; mark it now.
| Keyword | Use § from | Move |
|---|---|---|
| 'how much produced from' | § ① | balance, mole ratio, convert |
| two reactants given | § ① | limiting reagent comparison |
| '% yield' | § ① | actual / theoretical × 100 |
| 'empirical formula from %' | § ① | assume 100 g, divide by molar mass, scale to whole numbers |
| given P, V, n, T (any 3) | § ② | PV = nRT (T in K!) |
| changing conditions | § ② | combined: P₁V₁/T₁ = P₂V₂/T₂ |
| gas mixture, partial pressure | § ② | Dalton's: Pi = χi · Ptot |
| 'rate of effusion' | § ② | Graham's: r₁/r₂ = √(M₂/M₁) |
| 'q to heat from T₁ to T₂' | § ③ | q = mcΔT |
| 'ΔH from steps' | § ③ | Hess's law (flip sign on reverse, scale on multiply) |
| given ΔHf° table | § ③ | Σ ΔHf(prod) − Σ ΔHf(reac) |
| 'electron config' | § ④ | Aufbau, Pauli, Hund; cation? remove 4s first |
| 'unpaired electrons' | § ④ | fill degenerate orbitals singly per Hund's rule |
| 'rank by atomic radius / IE / EN' | § ⑤ | periodic trends — across vs down |
| 'draw Lewis structure' | § ⑥ | Σ valence e⁻, central atom, octet, formal charges |
| 'molecular geometry / bond angle' | § ⑥ | steric number → VSEPR shape |
| 'molarity / dilution' | § ⑦ | M = mol/L; M₁V₁ = M₂V₂ |
| 'freezing/boiling pt change' | § ⑦ | ΔT = i · K · m (don't forget i!) |
Mixed units kill problems. PV=nRT: must match R. Calorimetry: J vs kJ. Concentrations: M vs m. Always write units after every number — graders give partial credit if your method is right even when arithmetic is off, but only if units are tracked.
'How many moles' vs 'how many grams' — answer to the right one. 'STP' = 1 atm, 0°C (not 25°C, that's 'standard conditions'). Re-read the prompt before you submit.