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aA + bB ⇌ cC + dD K = [C]ᶜ[D]ᵈ / ([A]ᵃ[B]ᵇ)K depends only on temperature, not concentrations. K_c uses concentrations; K_p uses partial pressures (gases). Pure solids and liquids are excluded from K expressions.
| Compare | Direction | What happens |
|---|---|---|
| Q < K | → forward | more products form |
| Q = K | at equilibrium | no net change |
| Q > K | ← reverse | products → reactants |
K_p = K_c (RT)^Δn Δn = (moles gas products) − (moles gas reactants)ICE table: set up Initial, Change, Equilibrium concentrations. Solve quadratic for x. Approximation x ≪ initial valid if K is small (typically K < 10⁻³).
Adding more reactant doesn't change K — only shifts position toward products. Adding inert gas at constant V doesn't change anything. Only temperature changes K. Many students think pressure changes the constant; it doesn't.
| Quantity | Symbol | What it captures |
|---|---|---|
| Enthalpy | ΔH | heat at const P |
| Entropy | ΔS | disorder change |
| Gibbs free energy | ΔG | spontaneity, max usable work |
ΔG = ΔH − T·ΔS spontaneous ⇔ ΔG < 0ΔG° = −RT ln K large K (favors products) ⇔ very negative ΔG°Entropy of universe: ΔS_univ = ΔS_sys + ΔS_surr ≥ 0 (2nd law). Spontaneous = ΔS_univ > 0. Notice the universe, not just system.
Diamond → graphite is spontaneous (ΔG < 0) but takes geological time (kinetics). Spontaneity says nothing about rate. ΔG only addresses thermodynamic favorability; rate needs activation energy analysis.
pH = −log[H⁺] pOH = −log[OH⁻] pH + pOH = 14 (at 25°C)Ka = [H⁺][A⁻]/[HA] pKa = −log Ka pKa + pKb = 14 (conjugate pair)| Type | Examples | Behavior |
|---|---|---|
| Strong acids | HCl, HBr, HI, HNO₃, H₂SO₄ (1st), HClO₄ | fully dissociate |
| Weak acids | CH₃COOH (pKa 4.76), HCN (9.21), HF (3.17) | partial dissociation |
| Strong bases | NaOH, KOH, Ca(OH)₂, Ba(OH)₂ | fully dissociate |
| Weak bases | NH₃ (pKb 4.75), amines | partial |
Salt hydrolysis: NH₄Cl in water → acidic (NH₄⁺ donates H⁺). NaC₂H₃O₂ → basic (acetate accepts H⁺). NaCl → neutral.
For weak acid HA at concentration C, [H⁺] ≠ C. Use ICE: x² ≈ Ka·C when x ≪ C (5% rule). pH = −log(√(Ka·C)). Common error: assuming weak acid dissociates fully like a strong one.
rate = k [A]^m [B]^n m, n = orders, found EXPERIMENTALLY (not from coefficients)Overall order = m + n. Units of k depend on order. Most reactions have small integer orders (0, 1, 2).
| Order | Integrated form | Linear plot | Half-life |
|---|---|---|---|
| 0 | [A] = [A]₀ − kt | [A] vs t | [A]₀/(2k) |
| 1 | ln[A] = ln[A]₀ − kt | ln[A] vs t | 0.693/k (const) |
| 2 | 1/[A] = 1/[A]₀ + kt | 1/[A] vs t | 1/(k[A]₀) |
k = A · e^(−Ea/RT). Higher T → higher k (exponential). Plot ln k vs 1/T → slope = −Ea/R.Mechanism: overall reaction = sum of elementary steps. Slowest step = rate-determining. Order in reactants matches the rate law of the rate-limiting step (only).
For 2NO + O₂ → 2NO₂, you might guess rate = k[NO]²[O₂]. But experiment may show rate = k[NO][O₂]² depending on the mechanism. Always determine orders empirically from data, not from balanced equation coefficients.
Spontaneous redox; chemical → electrical energy. Cathode = reduction (+), anode = oxidation (−)Memorize: Red Cat An Ox. Salt bridge maintains charge balance. e⁻ flow from anode to cathode through external wire.
| Quantity | Formula |
|---|---|
| Cell EMF (standard) | E°_cell = E°_cathode − E°_anode |
| ΔG° from EMF | ΔG° = −nFE°_cell |
| K from EMF | ln K = nFE°/(RT) |
| Nernst eq | E = E° − (RT/nF) ln Q |
F = 96485 C/mol e⁻ n = mol e⁻ transferred Q = reaction quotientSign check: spontaneous galvanic E°_cell > 0, ΔG < 0, K > 1. Electrolysis is the reverse — input energy required.
When you reverse a half-reaction (oxidation instead of reduction), flip the sign of E°. But when adding two half-cells to get cell EMF: don't multiply E° by stoichiometric coefficient — E° is intensive. Multiply ΔG, not E°.
Henderson–Hasselbalch: pH = pKa + log([A⁻] / [HA])A buffer resists pH changes. Best buffering when [A⁻] ≈ [HA] (pH ≈ pKa). Buffer capacity scales with absolute concentrations.
| Region | What dominates | pH calc |
|---|---|---|
| Initial | weak acid only | x² ≈ Ka·C |
| Pre-equiv | buffer (HA + A⁻) | HH equation |
| Half-equiv | [HA] = [A⁻] | pH = pKa |
| Equivalence | only A⁻ | pH from Kb hydrolysis |
| Post-equiv | excess strong base | just OH⁻ |
Equivalence ≠ neutralization to pH 7. For weak acid + strong base, equivalence pH > 7 (basic salt left over). Strong + strong: pH = 7. Strong acid + weak base: pH < 7.
Titrating CH₃COOH with NaOH gives equivalence at pH ≈ 8.7 (acetate is basic). Indicator must turn around there, not at pH 7. Universal-indicator pH 7 endpoint loses you the experiment.
AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq) Ksp = [Ag⁺][Cl⁻]Solid AgCl excluded from K. Smaller Ksp = less soluble. Ksp values vary across many orders of magnitude (10⁻¹⁰ to 10⁻³⁵).
s = √Ksp.s = ∛(Ksp/4). Be careful with the stoichiometric factors.| Common Ksp values | Ksp |
|---|---|
| AgCl | 1.8 × 10⁻¹⁰ |
| BaSO₄ | 1.1 × 10⁻¹⁰ |
| CaCO₃ | 4.5 × 10⁻⁹ |
| Mg(OH)₂ | 5.6 × 10⁻¹² |
Common-ion effect: adding a shared ion decreases solubility. Add Cl⁻ to AgCl saturated solution → [Ag⁺] drops to maintain Ksp. Le Chatelier in action.
Q vs Ksp: Q < Ksp = unsaturated (more dissolves). Q > Ksp = supersaturated (precipitates). Q = Ksp = saturated.
For Ag₂CrO₄: 2 Ag⁺ + 1 CrO₄²⁻. Solubility s gives [Ag⁺] = 2s, [CrO₄²⁻] = s. Ksp = (2s)²s = 4s³. Forgetting the (2s)² costs the entire problem. Always write the dissolution equation first.
| Question says… | Use § from | Approach |
|---|---|---|
| 'find K' or 'eq concentrations' | § ① | ICE table; small-x approx if K<10⁻³ |
| 'shift in equilibrium' | § ① | Le Chatelier: oppose the stress |
| 'pressure / volume change' | § ① | Δn(gas) tells direction |
| 'pH of strong acid/base' | § ② | full dissociation, direct log |
| 'pH of weak acid' | § ② | x² ≈ Ka·C; check 5% rule |
| polyprotic acid | § ② | treat each Ka step; usually Ka1 dominates |
| salt acidity (NH₄Cl, NaOAc) | § ② | hydrolysis: cation acid, anion base |
| 'buffer pH' / Henderson | § ③ | pH = pKa + log([A⁻]/[HA]) |
| 'titration midpoint / equiv' | § ③ | identify region: HH or weak hydrolysis |
| 'will it precipitate?' | § ④ | compute Q, compare to Ksp |
| solubility from Ksp | § ④ | watch stoichiometry: 4s³ for 1:2 etc. |
| 'find rate law from data' | § ⑤ | compare runs, find orders, then k |
| 'half-life of 1st order' | § ⑤ | t½ = 0.693/k (constant only for 1st order) |
| 'find Ea' | § ⑤ | Arrhenius: ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂) |
| 'mechanism + RDS' | § ⑤ | slow step rate law = overall rate law |
| 'is rxn spontaneous?' | § ⑥ | ΔG = ΔH − TΔS; sign analysis |
| 'find ΔG° from K' | § ⑥ | ΔG° = −RT ln K |
| 'galvanic cell EMF' | § ⑦ | E°_cell = E°_cath − E°_anode |
| 'electrolysis: how much deposited' | § ⑦ | Q = It; mol = Q/(nF) |
| 'Nernst non-standard E' | § ⑦ | E = E° − (RT/nF) ln Q |
R = 8.314 J/(mol·K) — match J or convert to kJ for ΔH. F = 96485 C/mol e⁻. Always confirm units when mixing equations. Off-by-1000 errors cascade through the whole problem.
'If Q < K, reaction shifts toward products' — this is the universal direction-check. Use it for: equilibrium shifts, solubility (Q vs Ksp), galvanic cell direction (ΔG = ΔG° + RT ln Q). One framework, many applications.