Class 12 Chemistry: Solutions, Kinetics & Electrochemistry (PDF) — All Important Formulas Free
Free class 12 chemistry: solutions, kinetics & electrochemistry — all 56 key formulas on one page, downloadable as PDF for fast revision before CBSE board exams. No signup.
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Advanced chemistry: colligative properties, Raoult's law, electrochemistry, kinetics, and organic conversions. Essential for JEE/NEET and board exams.
Solutions & Colligative Properties
| Formula | Expression |
|---|---|
| Raoult's Law for ideal solutions | P_A = χ_A × P°_A — P_A = partial pressure of A, χ_A = mole fraction, P°_A = vapour pressure of pure A |
| Relative lowering of vapour pressure | ΔP/P° = χ_solute = n_solute / (n_solute + n_solvent) — Independent of identity of solute (colligative); for non-volatile solutes |
| Boiling point elevation | ΔTb = Kb × m — Kb = molal boiling point elevation constant (°C·kg/mol), m = molality |
| Freezing point depression | ΔTf = Kf × m — Kf = molal freezing point depression constant (°C·kg/mol), m = molality |
| Osmotic pressure | π = CRT = (n/V)RT — C = molarity, R = 0.0821 L·atm/(mol·K), T in Kelvin; most direct colligative property |
| van't Hoff factor | i = observed colligative effect / expected effect for 1 mol solute — i ≈ 1 for nonelectrolytes, i > 1 for electrolytes (ions); ΔTb = i·Kb·m |
| Degree of dissociation (electrolytes) | α = (initial moles − final moles) / initial moles — i = 1 + (n−1)α where n = number of ions per formula unit |
| Henry's Law for gas solubility | c = Kₕ × P_gas — c = concentration (mol/L), Kₕ = Henry's law constant, P in atm |
| Solubility and common ion effect | s = √(Ksp) (pure water); Ksp = [A⁺]^a × [B⁻]^b for AB — Adding common ion decreases solubility; Ksp independent of concentration |
Electrochemistry & Nernst Equation
| Formula | Expression |
|---|---|
| Nernst equation | E_cell = E°_cell − (0.059/n) × log Q (at 25°C) — Q = reaction quotient, n = moles of e⁻ transferred, all E in volts |
| Nernst equation (alternative form) | E_cell = E°_cell − (RT/nF) × ln Q — R = 8.314 J/(mol·K), T in Kelvin, F = 96,500 C/mol, E in volts |
| At equilibrium (Nernst) | 0 = E°_cell − (0.059/n) × log Kₑq → Kₑq = 10^(n×E°/0.059) — When E_cell = 0, system is at equilibrium |
| Electrochemical cell potential | E°_cell = E°_cathode − E°_anode — Both E° from standard reduction potential tables |
| Faraday's laws of electrolysis | W = (M/nF) × Q = (M × I × t) / (nF) — W = mass deposited (g), Q = charge (coulombs), I = current (A), t = time (s) |
| Molar conductivity | Λm = κ / c — κ = conductivity (S/cm), c = concentration (mol/L), Λm in S·cm²/mol |
| Conductivity of solution | κ = (l/A) × G — l = length between electrodes, A = cross-sectional area, G = conductance |
| Weak electrolyte molar conductivity | Λm = Λ°m − K√c — Λ°m = limiting molar conductivity, K = Kohlrausch constant |
| Mobility of ions | Λm = F(u⁺ + u⁻) — u = mobility (cm²/(V·s)), sum of cation and anion mobility |
Chemical Kinetics
| Formula | Expression |
|---|---|
| Rate of reaction | Rate = −d[A]/dt = +d[C]/dt (for aA → cC) — Negative for reactants (consumed), positive for products (formed) |
| Rate law (empirical) | Rate = k[A]^m[B]^n — k = rate constant, m & n = order (determined from experiment); overall order = m + n |
| Zero-order integrated rate law | [A] = [A]₀ − kt; t₁/₂ = [A]₀/(2k) — Half-life depends on initial concentration; straight line on [A] vs t |
| First-order integrated rate law | ln[A] = ln[A]₀ − kt; t₁/₂ = 0.693/k — Half-life constant; ln[A] vs t is linear; k in s⁻¹ typically |
| Second-order integrated rate law | 1/[A] = 1/[A]₀ + kt; t₁/₂ = 1/(k[A]₀) — Half-life depends on initial concentration; 1/[A] vs t is linear |
| Arrhenius equation | k = A·e^(−Ea/RT); ln(k₂/k₁) = (Ea/R)(T₂−T₁)/(T₁T₂) — A = frequency factor, Ea = activation energy (J/mol), R = 8.314 J/(mol·K) |
| Temperature dependence rule of thumb | Rate doubles for every ~10°C rise (rough estimate) — Exact value from Arrhenius; depends on Ea |
| Reaction mechanism and rate | Rate-determining step controls overall rate law — Elementary steps must sum to give overall equation |
| Collision theory | Rate = Z·p·e^(−Ea/RT) — Z = collision frequency, p = steric factor (orientation), Ea = activation energy |
Organic Chemistry: Key Conversions & Reactions
| Formula | Expression |
|---|---|
| Esterification (Fischer) | RCOOH + R'OH → RCOOR' + H₂O (acid catalyst H₂SO₄, heat) — Reversible; equilibrium favors products if water removed |
| Saponification | RCOOR' + NaOH → RCOONa + R'OH (ester + strong base) — Irreversible soap formation; R can be long chain alkyl |
| Aldol condensation | 2 CH₃CHO → CH₃CH(OH)CH₂CHO (base catalyst) → CH₃CH=CHCHO + H₂O (heat) — Enolate attacks carbonyl; forms C−C bond |
| Grignard reaction | RMgX + R'CHO → R−CH(OH)−R' (SN2-like); followed by acid workup — Highly nucleophilic; reacts with any C=O or C≡N |
| Williamson ether synthesis | R−O⁻ + R'−X → R−O−R' + X⁻ (SN2, X = Br, I, Cl) — R−O⁻ from alcohol + base (KOH); X on primary/secondary alkyl best |
| Elimination (E2 mechanism) | R₃C−H + Base → C=C + alkene (1° substrate poor, 3° excellent) — Zaitsev's rule: major product is more substituted (more stable) alkene |
| Nucleophilic aromatic substitution | Ar−NO₂ + Nu⁻ → Ar−Nu + NO₂⁻ (activated by NO₂, CN, F at ortho/para) — Requires electron-withdrawing group; rare for Ar−H |
| Oxidation (Jones, permanganate, chromic) | RCH₂OH → RCHO (primary alcohol to aldehyde); RCHO → RCOOH (aldehyde to carboxylic acid) — KMnO₄ strong; Jones quick; final product depends on conditions |
| Reduction (LiAlH₄, NaBH₄) | RCOOH → RCH₂OH (carboxylic acid to 1° alcohol); RCOR' → RCHOHC'H₃ (ketone to 2° alcohol) — LiAlH₄ powerful (all carbonyls); NaBH₄ mild (aldehydes, ketones only) |
| Friedel-Crafts acylation | Ar−H + R−CO−Cl → Ar−CO−R (AlCl₃ catalyst) — Creates aryl ketone; Lewis acid required; para isomer major |
Polymer Chemistry & Condensation
| Formula | Expression |
|---|---|
| Addition polymerization | n CH₂=CH₂ → (−CH₂−CH₂−)n (ethylene → polyethylene) — Alkene monomers; chain grows by repeated addition |
| Condensation polymerization | n HOOC−R−COOH + n HO−R'−OH → polyester + 2n H₂O — Bifunctional monomers; water or small molecule eliminated per link |
| Nylon 6,6 synthesis | n H₂N−(CH₂)₆−NH₂ + n HOOC−(CH₂)₄−COOH → nylon + 2n H₂O — Adipic acid + hexamethylenediamine; amide linkage |
| Degree of polymerization | Degree of polymerization = number of monomer units in chain — n in (−C−C−)n formula; typically 100s to 1000s |
| Molar mass of polymer | M_polymer = (degree of polymerization) × (molar mass of monomer unit) — Approximate for long chains; end groups negligible |
Surface Chemistry & Adsorption
| Formula | Expression |
|---|---|
| Adsorption isotherm (Freundlich) | x/m = k·P^(1/n) (at constant T) — x = mass adsorbed, m = mass adsorbent, P = pressure, k & n constants |
| Adsorption isotherm (Langmuir) | x/m = (abP) / (1 + bP) — a = monolayer capacity, b = affinity constant; more realistic than Freundlich |
| Colloidal stability (zeta potential) | High |ζ| > stability (similar charges repel); low |ζ| → coagulation — ζ = zeta potential; electrostatic stabilization; salt can cause coagulation |
| Hardy-Schulze rule | Coagulating power of ions ∝ charge; +3 > +2 > +1 — Higher charge density = faster coagulation of opposite colloid |
Coordination Chemistry & Crystal Field Theory
| Formula | Expression |
|---|---|
| Coordination number | Number of ligands bonded to central metal ion — Typically 4 (square planar, tetrahedral) or 6 (octahedral) |
| IUPAC naming (coordination compounds) | Ligands named first (alphabetical) + central metal + oxidation state in () — e.g. [Co(NH₃)₆]³⁺ = hexaamminecobalt(III) |
| Crystal field splitting (octahedral) | d_xy, d_xz, d_yz (lower) | Δ | d_x²−y², d_z² (higher) — Δ = Δ₀ (crystal field splitting energy); weak field vs strong field determines spin |
| High spin vs low spin | High spin: Δ small → electrons occupy all d orbitals singly first (Hund's rule) — Low spin: Δ large → electrons pair in lower orbitals (strong field ligands like CN⁻) |
| Magnetic moment (spin only) | μ = √[n(n+2)] B.M. (Bohr magnetons) — n = number of unpaired electrons; stronger field → more pairing → lower μ |
Quantitative Practice Reminders
| Formula | Expression |
|---|---|
| Percentage by mass | % by mass = (mass of element/total mass) × 100 — Use molar masses and stoichiometry; sum should = 100% |
| Simplest mole ratio | Divide all moles by smallest; multiply by whole number if fraction — This gives the empirical formula subscripts |
| Limiting reagent identification | Divide each reactant moles by its stoichiometric coefficient; smallest = limiting — Controls theoretical yield; others are in excess |
| Normality arithmetic | N₁V₁ = N₂V₂ (for titrations); relates to concentration for redox — N = equivalents/L; for polyprotic acid, N = M × (number of H⁺/OH⁻) |
| Energy per mole | ΔH_rxn = ΔH_reaction per balanced equation (not per mole of single reactant) — Always specify 'per mole' or clarify reaction stoichiometry |
FAQs
What is the difference between Kc and Kp, and when should I use the Nernst equation?
Kc uses concentrations (mol/L); Kp uses partial pressures. Use Nernst (E_cell = E°_cell − 0.059/n × log Q) to find cell potential at non-standard conditions (any concentration/pressure, any temperature). At equilibrium, E_cell = 0 and Q = Kₑq. Always ensure n matches the moles of electrons in the balanced equation.
How do colligative properties like boiling point elevation depend on solute?
They don't depend on the identity of the solute, only on the number of solute particles. ΔTb = Kb × m and osmotic pressure π = CRT are colligative, so they work for any non-volatile solute. For electrolytes that dissociate (like NaCl), multiply by van't Hoff factor i to get the observed effect.
For reaction kinetics, how do I determine reaction order from experimental data?
Plot [A] vs t (zero-order = straight line), ln[A] vs t (first-order = straight line), and 1/[A] vs t (second-order = straight line). The one that gives a linear plot reveals the order. Then calculate k from the slope. For complex rate laws, use the method of initial rates (vary one reactant concentration, keep others constant, measure how rate changes).