01 • Solutions (Class 12 — 3 to 4 Qs / 12–16 Marks)
| Concept | Core Equation | Units / Constants | Boundary Condition (Fails When...) |
|---|---|---|---|
| Raoult's Law | P_total = P°A·xA + P°B·xB yA = (P°A·xA) / P_total |
P in atm/torr/bar x: liquid mole frac y: vapor mole frac |
Fails for non-ideal solutions! If ΔH_mix ≠ 0 or ΔV_mix ≠ 0, solution shows +ve or -ve deviation. |
| RLVP | (P° - Ps)/P° = i · xB ≈ i · (wB·MA) / (MB·wA) |
Dilute solution limit: nB << nA |
Fails for concentrated solutions! For exact work, use: (P° - Ps)/Ps = i · (nB/nA). |
| Boiling & Freezing | ΔTb = i · Kb · m ΔTf = i · Kf · m |
m = molality (mol/kg) Kb, Kf in K·kg/mol |
Fails if i is omitted! For NaCl: i=2. For BaCl2: i=3. For acetic acid in benzene: i < 1 (dimerization). |
| Osmotic Pressure | Π = i · C · R · T | R = 0.0821 L·atm/mol·K T strictly in Kelvin! |
Isotonic solutions have equal Π: i1·C1 = i2·C2 (Not just C1 = C2 if one solute dissociates!). |
| van 't Hoff Factor | i = 1 + (n - 1)α (Dissoc.) i = 1 + (1/n - 1)β (Assoc.) |
α, β = deg of dissoc/assoc n = ions produced |
For strong electrolytes at infinite dilution, α → 1, so i = n. For weak electrolytes, α must be calculated. |
02 • Electrochemistry (Class 12 — 3 to 4 Qs / 12–16 Marks)
| Concept | Core Equation | Units / Constants | Boundary Condition (Fails When...) |
|---|---|---|---|
| Nernst Equation | E = E° - (0.0591/n) log Q (at 298 K) |
E, E° in Volts n = moles of e⁻ transferred |
Fails if T ≠ 298 K! Pure solids and liquids have activity = 1 (do NOT include solid Zn, Cu in Q). |
| Equilibrium & ΔG° | ΔG° = -n F E°cell E°cell = (0.0591/n) log Kc |
F = 96,500 C/mol ΔG° in Joules (divide by 1000 for kJ) |
At equilibrium: E_cell = 0 (Not E°cell!). Reaction is spontaneous if E°cell > 0 and ΔG° < 0. |
| Conductivity (κ & Λm) | R = ρ(l/A) • G = κ(A/l) Λm = (κ × 1000) / M |
κ in S·cm⁻¹ M in mol/L (Molarity) Λm in S·cm²·mol⁻¹ |
Unit Trap! If κ is given in S·m⁻¹, the formula is: Λm = κ / (1000 × M). Always check cm vs m! |
| Kohlrausch's Law | Λ°m = ν+ λ°+ + ν- λ°- α = Λm / Λ°m |
ν+, ν- = stoichiometry Ka = Cα² / (1 - α) |
Applies at infinite dilution. For weak electrolytes (acetic acid), calculate Λ°m using strong electrolyte combinations. |
03 • Chemical Kinetics (Class 12 — 3 Qs / 12 Marks)
| Concept | Core Equation | Units / Constants | Boundary Condition (Fails When...) |
|---|---|---|---|
| First-Order Rate | k = (2.303/t) log([A]₀/[A]t) t₁/₂ = 0.693 / k |
Unit of k: s⁻¹ or min⁻¹ [A]₀ = initial conc [A]t = remaining at t |
Fails for Zero Order! Zero order: [A]t = [A]₀ - kt, and t₁/₂ = [A]₀ / 2k (half-life depends on [A]₀!). |
| Arrhenius Equation | log(k₂/k₁) = (Ea/2.303R) × [(T₂ - T₁) / (T₁·T₂)] |
R = 8.314 J/mol·K Ea must be in Joules! T in Kelvin! |
Units Mismatch Trap! If Ea is given in kJ/mol, either multiply Ea by 1000 or divide R by 1000. |