RRB JE CMA — Complete CBT-2 Study Guide (Physics, Chemistry & Metallurgy)

• SI has 7 base quantities/units: length-metre(m), mass-kilogram(kg), time-second(s), electric current-ampere(A), temperature-kelvin(K), amount of substance-mole(mol), luminous intensity-candela(cd); the two former supplementary units radian(rad) & steradian(sr) are dimensionless (now classed as derived). • Dimensional formula expresses a quantity in M, L, T (e.g. Force = MLT^-2, Energy/Work = ML^2T^-2, Pressure = ML^-1T^-2, Power = ML^2T^-3). • Uses of dimensions: checking equation correctness (homogeneity principle — both sides same dimensions), unit conversion, deriving relations; cannot find dimensionless constants or trig/log/exponential terms. • Systematic errors are one-directional from a known cause (instrument/zero/personal) and are correctable; random errors fluctuate both ways and are reduced by repeated readings & averaging. • Accuracy = closeness to true value; Precision = closeness of repeated readings to each other — trap: a reading can be precise but not accurate. • Absolute error = |measured − true|; mean absolute error = average of |Δa|; relative error = Δa/a_mean; percentage error = (Δa/a_mean)×100. • In multiplication/division, relative (fractional) errors add; for x = a^p b^q/c^r, max fractional error = p(Δa/a)+q(Δb/b)+r(Δc/c). • Vernier caliper Least Count = 1 Main Scale Division − 1 Vernier Scale Division = value of 1 MSD/total no. of VSD (standard LC = 0.1 mm = 0.01 cm). • Screw gauge (micrometer) Least Count = Pitch/no. of circular-scale divisions (standard: pitch 1 mm/100 div = 0.01 mm); Pitch = distance moved by screw per one full rotation. • Zero error: positive zero error is subtracted, negative zero error is added to the observed reading; Correct reading = Observed − (zero error with sign). • Backlash error in screw gauge avoided by always rotating in one direction; ratchet ensures uniform pressure (mnemonic: positive→subtract, negative→add).

• Newton's laws: (1) Inertia — body stays at rest/uniform motion unless net force acts; (2) F = ma = rate of change of momentum (dp/dt); (3) every action has equal and opposite reaction. • Momentum p = mv (kg·m/s, vector); Impulse J = F·t = change in momentum (Δp); area under force-time graph = impulse; principle: m1u1 + m2u2 = m1v1 + m2v2 (conservation in absence of external force). • Friction: f = μN; limiting static (μs, self-adjusting up to f_max = μs·N) > kinetic (μk) > rolling friction; angle of repose θ where tanθ = μs (block just slides); trap — kinetic friction is independent of contact area and speed. • Work W = F·s·cosθ (joule); positive when force aids motion, negative for friction/opposing; zero when θ = 90° (centripetal force does no work). • Work-energy theorem: net work done = change in kinetic energy, W = ΔKE = ½mv^2 − ½mu^2. • Kinetic energy KE = ½mv^2 = p^2/2m; Potential energy PE = mgh; mechanical energy conserved if only conservative forces act. • Power P = W/t = F·v (watt); 1 HP ≈ 746 W (imperial); 1 kWh = 3.6×10^6 J; average power = total work / total time. • Circular motion: centripetal acceleration a = v^2/r = ω^2·r, directed to centre; v = ωr; time period T = 2π/ω = 2πr/v. • Centripetal force Fc = mv^2/r = mω^2·r (real inward force needed); centrifugal force is the pseudo (apparent outward) force in rotating frame. • Banking of roads: ideal angle tanθ = v^2/(rg) gives safe speed without friction; with friction max speed v = √[rg(tanθ + μ)/(1 − μ·tanθ)]; banking provides extra centripetal force, reducing tyre wear. • Common exam trap: in uniform circular motion speed is constant but velocity changes (direction varies), so acceleration ≠ 0 and net force is non-zero (centripetal).

• Newton's law: every mass attracts another with F = G m1 m2 / r^2; G = 6.67 x 10^-11 N m^2/kg^2 (universal, scalar). Trap: G is constant everywhere, g is not. • Acceleration due to gravity: g = GM/R^2 ≈ 9.8 m/s^2; g falls with altitude g_h = g(R/(R+h))^2 and with depth g_d = g(1 − d/R); at centre g = 0. • g varies with shape/spin: maximum at poles, minimum at equator (R larger + rotation); g decreases as Earth's rotation speeds up: g' = g − ω^2 R cos^2(latitude). • Orbital velocity (near surface) v_o = √(gR) = √(GM/R) ≈ 7.9 km/s; time period T = 2π√(r^3/GM) (Kepler's 3rd: T^2 ∝ r^3). • Escape velocity v_e = √(2gR) = √(2GM/R) ≈ 11.2 km/s; key relation v_e = √2 · v_o; independent of the projected body's mass and angle. • Hooke's law: within elastic limit stress ∝ strain, so stress/strain = constant (modulus of elasticity); stress = F/A (Pa), strain = change/original (no unit). • Young's modulus Y = (F·L)/(A·ΔL) = longitudinal stress/longitudinal strain; steel has higher Y than rubber, so steel is more elastic. Bulk modulus K (volume), modulus of rigidity η (shear). • Surface tension T = F/L (N/m); energy per unit area = T; arises from cohesion. Excess pressure: drop ΔP = 2T/r, soap bubble (two surfaces) ΔP = 4T/r. • Capillarity: h = 2T cosθ / (r ρ g); rise for wetting liquids (θ<90°, e.g. water), depression for mercury (θ>90°); narrower tube → greater rise. • Viscosity: F = η A (dv/dx), η = coefficient of viscosity, SI unit Pa·s (1 Pa·s = 10 poise, CGS); liquids' η falls with rising temperature, gases' η rises. • Stokes' law: viscous drag on a sphere F = 6π η r v; terminal velocity v_t = 2 r^2 (ρ − σ) g / 9η, reached when weight = buoyancy + drag (net force zero, constant speed).

• Temperature scales: conversion C/5 = (F-32)/9 = (K-273.15)/5; K = C + 273.15; -40 is equal on C and F; Kelvin is the SI absolute scale (0 K = absolute zero). • Thermal expansion: linear L = L0(1+aDT), area b = 2a, volume g = 3a (so a:b:g = 1:2:3); units of a are per °C (or per K). • Calorimetry: heat Q = mcDT (c = specific heat); principle of mixtures: heat lost = heat gained; water c = 4186 J/kg·K (1 cal/g·°C), the highest among common liquids. • Latent heat: Q = mL with no temperature change during phase change; latent heat of fusion of ice L = 334 kJ/kg (80 cal/g); latent heat of vaporization of water L ≈ 2256 kJ/kg (540 cal/g, at 100°C). • Heat transfer modes: conduction (solids, no matter movement), convection (fluids, mass movement), radiation (EM waves, no medium needed); conduction rate Q/t = kA(DT)/L. • Radiation laws: Stefan-Boltzmann E = saT^4 (s = 5.67×10^-8 W/m^2·K^4); net loss = saA(T^4 - Ts^4); Wien's law lambda_max·T = b = 2.9×10^-3 m·K (hotter body radiates at shorter wavelength). • Gas laws: Boyle's PV = constant (T fixed); Charles' V/T = constant (P fixed); Gay-Lussac's P/T = constant (V fixed); combined PV/T = constant; ideal gas PV = nRT, R = 8.314 J/mol·K. • Kinetic theory: PV = (1/3)mNc^2; average KE per molecule = (3/2)kT (k = 1.38×10^-23 J/K); rms speed v_rms = sqrt(3RT/M); pressure arises from molecular collisions on walls. • Thermodynamics laws: Zeroth = thermal equilibrium defines temperature; First Q = DU + W (energy conservation); Second = heat flows hot→cold, no engine is 100% efficient; Third = entropy →0 as T→0 K. • Carnot engine: maximum efficiency h = 1 - T2/T1 (temperatures in Kelvin; T1 source, T2 sink); efficiency rises as sink gets colder; no real engine can beat the Carnot limit. • Common trap: latent heat involves NO temperature change (energy breaks molecular bonds); always use Kelvin in gas laws and Carnot efficiency, never Celsius.

• Wave types: transverse (vibration perpendicular to motion, e.g. light) and longitudinal (vibration along motion, e.g. sound, made of compressions & rarefactions); relation v = fλ; sound needs a medium, light does not. • Speed of sound in air ~343 m/s at 20°C, 331 m/s at 0°C; v = 331√(T/273) with T in kelvin, so v rises ~0.6 m/s per °C; speed: solids > liquids > gases. • Resonance = forced vibration when driving frequency equals natural frequency (max amplitude); beats = periodic loudness rise/fall from two close frequencies, beat frequency = |f1 − f2| (audible if difference ≤ ~10 Hz). • Doppler effect: apparent frequency change from relative source–observer motion; f' = f(v ± vo)/(v ∓ vs); approach raises pitch, recede lowers it; used in radar and speed guns. • Reflection laws: angle of incidence = angle of reflection, both in one plane; mirror formula 1/f = 1/v + 1/u, magnification m = −v/u = h'/h; focal length f = R/2. • Sign convention (mirror): concave f negative, convex f positive (Cartesian); concave forms real/inverted or virtual/erect images, convex always virtual, erect, diminished. • Refraction & Snell's law: n1 sin i = n2 sin r; refractive index n = c/v = sin i/sin r; light bends toward normal entering denser medium; n of water ≈ 1.33, glass ≈ 1.5. • Total internal reflection: occurs when light goes denser→rarer and i > critical angle C, where sin C = 1/n; basis of optical fibres, diamond sparkle and mirage. • Lens formula 1/f = 1/v − 1/u; power P = 1/f(in metres), unit dioptre (D); convex (converging) f & P positive, concave (diverging) f & P negative; lenses in contact add: P = P1 + P2. • Dispersion: white light splits into VIBGYOR through a prism because n varies with wavelength; violet bends most (shortest λ), red least; recombination gives white light. • Rayleigh scattering: scattered intensity ∝ 1/λ^4, so blue scatters more than red — sky looks blue, while sunrise/sunset look red as blue is scattered away over the long path. • Eye defects: myopia (near-sight, image before retina) corrected by concave lens; hypermetropia (far-sight, image behind retina) by convex lens; presbyopia by bifocals; astigmatism by cylindrical lens.

• Coulomb's law: F = k·q1·q2/r^2 with k = 9×10^9 N·m^2/C^2 in vacuum; the force acts along the line joining the two charges. • Ohm's law: V = IR (at constant temperature). Resistance R = ρL/A; for metallic conductors resistivity ρ increases as temperature rises. • Series: R = R1 + R2 + … (same current through each). Parallel: 1/R = 1/R1 + 1/R2 + … (same voltage); the net parallel resistance is always smaller than the smallest resistor. • Kirchhoff's laws: KCL — the sum of currents at a junction is zero (charge conservation); KVL — the sum of EMFs and IR drops around any closed loop is zero (energy conservation). • Electric power P = VI = I^2R = V^2/R; heating effect (Joule's law) H = I^2Rt. Commercial energy unit is the kilowatt-hour: 1 kWh = 3.6×10^6 J. • Cell: terminal voltage V = EMF − I·r, where r is internal resistance. Cells in series add their EMFs; in parallel the EMF stays the same but current capacity increases. • Magnetic effect of current: a current-carrying conductor produces a magnetic field (right-hand thumb rule). Force on a conductor in a field F = BIL·sinθ — its direction is given by Fleming's Left-Hand Rule (motor rule). • Electromagnetic induction: Faraday's law — induced EMF = −N·(dΦ/dt); Lenz's law — the induced current opposes the change producing it (a consequence of energy conservation). A generator uses Fleming's Right-Hand Rule. • Transformer (works on AC only, via mutual induction): Vs/Vp = Ns/Np = Ip/Is. Step-up raises voltage and lowers current; an ideal transformer conserves power. Losses: copper (I^2R), eddy currents (cut by a laminated core) and hysteresis. • Alternating current: I_rms = I0/√2 = 0.707·I0; the average over a full cycle is zero. Impedance Z = √(R^2 + (XL − XC)^2); power factor = cosφ; resonance occurs when XL = XC.

• Photoelectric effect: light ejects electrons; Einstein's eqn KE_max = hf − φ, where φ = work function = hf0 (f0 = threshold frequency); stopping potential eV0 = KE_max; supports particle nature (photon energy E = hf = hc/λ); h = 6.63×10^-34 J·s. • Atomic models: Thomson "plum-pudding" (uniform positive sphere with embedded electrons); Rutherford (alpha-scattering proves tiny dense positive nucleus, electrons orbit) but fails on stability; Bohr quantizes angular momentum mvr = nh/2π. • Bohr H-atom: E_n = −13.6/n^2 eV, radius r_n ∝ n^2 (r1 = 0.529 Å); emission when electron drops n_high→n_low; 1/λ = R(1/n1^2 − 1/n2^2), Rydberg R = 1.097×10^7 m^-1 (Lyman UV, Balmer visible, Paschen IR). • Radioactivity: alpha = helium nucleus (2 protons + 2 neutrons; Z−2, A−4), low penetration; beta = electron (Z+1, A same); gamma = EM photon (no change in Z/A), most penetrating; penetration order γ > β > α, ionizing power α > β > γ. • Half-life: N = N0(1/2)^(t/T½); decay law N = N0 e^(−λt); T½ = 0.693/λ; mean life τ = 1/λ = T½/0.693; activity A = λN (unit becquerel, 1 Ci = 3.7×10^10 Bq). • Mass-energy: E = mc^2; mass defect Δm = (sum of nucleon masses − nuclear mass); binding energy BE = Δm·c^2; 1 u = 931.5 MeV; BE per nucleon peaks (~8.8 MeV) near Fe-56 = most stable nucleus. • Fission: heavy nucleus (U-235) splits on slow-neutron capture into fragments + ~2-3 neutrons + energy (~200 MeV), enables chain reaction (reactors/bombs); Fusion: light nuclei join (H→He, as in Sun), releases more energy per nucleon, needs very high temperature. • Semiconductors: Si/Ge (group IV); intrinsic pure; N-type doped with pentavalent (P, As — donors, electrons majority); P-type doped with trivalent (B, Al — acceptors, holes majority); conductivity rises with temperature (negative temp coeff of resistance). • P-N junction diode: depletion region with barrier potential (Si ≈ 0.7 V, Ge ≈ 0.3 V); forward bias (P to +) conducts, reverse bias blocks (small leakage); acts as one-way valve/rectifier. • Rectifiers: half-wave uses 1 diode (output ripple frequency = supply f, efficiency ~40.6%); full-wave/bridge uses 2/4 diodes (ripple = 2f, efficiency ~81.2%); ripple factor of HW = 1.21, FW = 0.48. • Transistors (BJT): NPN/PNP, three terminals E-B-C; current relations IE = IB + IC, α = IC/IE (<1), β = IC/IB, β = α/(1−α); used as amplifier (active region) and switch (saturation/cutoff). • Logic gates: AND Y = A·B, OR Y = A+B, NOT Y = Ā; NAND and NOR are universal gates (any circuit buildable from them); XOR Y = A⊕B = 1 when inputs differ; De Morgan: (A·B)' = A'+B', (A+B)' = A'·B'.

• Sub-atomic particles: electron (−1, 9.11×10^−31 kg), proton (+1, 1.673×10^−27 kg), neutron (0, 1.675×10^−27 kg); atomic no. Z = protons, mass no. A = protons + neutrons; isotopes (same Z), isobars (same A), isotones (same neutrons). • Four quantum numbers: principal n (shell, energy/size), azimuthal l (subshell shape, l = 0..n−1 → s,p,d,f), magnetic m_l (orientation, −l to +l), spin m_s (+½ or −½); orbitals in subshell = 2l+1, max e− in shell = 2n^2, in subshell = 2(2l+1). • Pauli exclusion: no two electrons in an atom have all four quantum numbers identical → an orbital holds max 2 electrons with opposite spins. • Aufbau: orbitals fill in increasing (n+l) energy order; for equal (n+l), lower n fills first → 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s... • Hund's rule: electrons singly occupy degenerate orbitals (parallel spins) before pairing → maximizes spin multiplicity; explains extra stability of half-filled (d^5) and fully-filled (d^10) configs, e.g. Cr [Ar]3d^5 4s^1, Cu [Ar]3d^10 4s^1. • Modern periodic law: properties are periodic functions of atomic number Z (Moseley), correcting Mendeleev's atomic-mass basis; table has 7 periods (horizontal) and 18 groups (vertical). • Blocks by last-filled subshell: s-block (Gr 1,2 + H,He), p-block (Gr 13–18), d-block/transition (Gr 3–12), f-block/inner-transition (lanthanides 4f, actinides 5f); period number = highest principal quantum number n. • Atomic radius: DECREASES across a period (rising Zeff pulls shells in), INCREASES down a group (new shells added); cation < parent atom < anion. • Ionization energy (IE = energy to remove the outermost e−): INCREASES across a period, DECREASES down a group; IE1 < IE2 < IE3...; trap — Be > B and N > O due to stable filled 2s^2 and half-filled 2p^3. • Electronegativity (tendency to attract a shared bonding pair): INCREASES across a period, DECREASES down a group; max = Fluorine (Pauling 3.98 ≈ 4.0), least = Cs/Fr; noble gases generally excluded. • Other trends: electron affinity increases across, decreases down (Cl has highest, not F, due to small size/repulsion); metallic character decreases across and increases down; non-metallic/oxidizing nature follows electronegativity.

• Ionic bond: transfer of electrons (metal to non-metal), e.g. NaCl; high melting point, conducts in molten/aqueous state, soluble in water. Covalent bond: sharing of electron pairs (non-metals), e.g. H2O, CH4; low m.p., poor conductors. • Metallic bond: lattice of cations in a "sea" of delocalised electrons — explains conductivity, malleability, ductility, lustre. Strength: primary bonds (ionic, covalent, metallic) are strong; H-bond and van der Waals are weak intermolecular forces (H-bond > van der Waals). • Hydrogen bonding: weak attraction when H is bonded to highly electronegative F, O, N; intermolecular type raises boiling point (H2O, HF, NH3); intramolecular in o-nitrophenol. Trap: HF higher b.p. than HCl due to H-bonding. • Hybridization mixes atomic orbitals into equal hybrids: sp (50% s, linear, 180°), sp2 (33% s, trigonal planar, 120°), sp3 (25% s, tetrahedral, 109.5°). Examples: BeCl2 (sp), BF3 (sp2), CH4 (sp3). • Expanded hybrids: sp3d → trigonal bipyramidal (PCl5, 90° & 120°); sp3d2 → octahedral (SF6, 90°). Steric number (bond pairs + lone pairs) decides geometry. • VSEPR: electron pairs arrange to minimise repulsion; repulsion order lp–lp > lp–bp > bp–bp. Lone pairs distort shape: H2O bent (104.5°), NH3 pyramidal (107°), CH4 tetrahedral (109.5°). • Ideal gas equation: PV = nRT; R = 0.0821 L·atm·K⁻¹·mol⁻¹ = 8.314 J·mol⁻¹·K⁻¹. Boyle's law: PV = constant (const T); Charles' law: V/T = constant (const P); Gay-Lussac: P/T = constant (const V). • Avogadro's law: equal volumes of gases at same T,P contain equal molecules; 1 mole gas = 22.4 L at STP (0°C, 1 atm). Combined gas law: P1V1/T1 = P2V2/T2. Always convert T to Kelvin (K = °C + 273). • Crystalline solid types: ionic (NaCl — hard, brittle), covalent/network (diamond, SiO2 — very hard, high m.p.), molecular (ice, dry ice — soft, low m.p.), metallic (Cu, Fe — conducting). Amorphous solids (glass) lack long-range order. • Unit cell = smallest repeating unit of a lattice. Atoms per cell Z: simple cubic = 1, BCC = 2, FCC = 4. Packing efficiency: SC 52%, BCC 68%, FCC/HCP 74%. Coordination number: SC 6, BCC 8, FCC 12.

• Reaction types: combination (A+B→AB), decomposition (AB→A+B), displacement (more reactive metal displaces less reactive), double displacement/metathesis, redox, neutralization (acid+base→salt+water); precipitation gives insoluble salt. • Oxidation number rules: free element=0, monatomic ion=its charge, O=−2 (peroxide −1, OF2 +2), H=+1 (metal hydride −1); sum of O.N.=net charge. Oxidation=loss of e−/↑O.N.; reduction=gain of e−/↓O.N. (OIL RIG). Oxidizing agent gets reduced. • Balancing redox (ion-electron/half-reaction): balance atoms, then O with H2O, H with H+; in basic medium add OH− to neutralize H+; balance charge with e−; equalize e− and add half-reactions. • Stoichiometry: moles=mass/molar mass; for a gas at STP moles=volume(L)/22.4 (22.4 L/mol at 0°C, 1 atm). Limiting reagent = reactant giving least product (lowest mole/coefficient ratio); excess reagent left over. % yield=(actual/theoretical)×100. • Acid-base theories: Arrhenius—acid gives H+, base gives OH− in water; Bronsted-Lowry—acid is proton donor, base proton acceptor (conjugate pairs differ by one H+); Lewis—acid is electron-pair acceptor, base electron-pair donor. • pH=−log[H+], pOH=−log[OH−], pH+pOH=14 at 25°C; Kw=[H+][OH−]=1×10^−14 at 25°C. Neutral pH=7, acidic <7, basic >7. Strong acid fully ionizes; weak acid Ka=[H+][A−]/[HA], pKa=−logKa. • Buffer = weak acid+its salt (or weak base+its salt); resists pH change. Henderson-Hasselbalch: pH=pKa+log([salt]/[acid]); for basic buffer pOH=pKb+log([salt]/[base]). • Concentration terms: Molarity M=mol solute/L solution (temp-dependent); Molality m=mol solute/kg solvent (temp-independent); Normality N=gram-equivalents/L; N=M×n-factor. Mole fraction x=moles component/total moles. ppm=parts per million (mg/L for dilute aqueous solutions where density≈1 g/mL). • Colligative properties depend on number of solute particles, not nature: relative lowering of vapour pressure (Raoult), boiling point elevation ΔTb=Kb·m, freezing point depression ΔTf=Kf·m, osmotic pressure π=CRT (π=(n/V)RT). • Van't Hoff factor i = observed particles/expected; for electrolytes i>1 (NaCl i≈2, CaCl2 i≈3); colligative formulas become ΔT=i·K·m, π=i·CRT. Association gives i<1. • Common traps: molarity changes with temperature (use molality for ΔTb/ΔTf problems); n-factor of H2SO4=2, of Na2CO3=2 (eq. wt=53); equivalent weight = molar mass/n-factor; salt of strong acid+weak base is acidic, weak acid+strong base is basic.

• Faraday's 1st law: mass deposited m = Z·I·t, where Z = electrochemical equivalent; 2nd law: masses of substances are proportional to their equivalent weights; 1 Faraday = 96500 C (≈96485) deposits 1 gram-equivalent. • Moles of electrons n = It/96500; m = (E·I·t)/96500 where E = equivalent weight = atomic mass / valency. • Galvanic (voltaic) cell converts chemical energy to electrical; oxidation at anode (−), reduction at cathode (+); salt bridge keeps neutrality; Daniell cell: Zn|Zn2+||Cu2+|Cu. • Cell EMF: E°cell = E°cathode − E°anode; Nernst: Ecell = E°cell − (0.0591/n)·log Q at 298 K; positive E°cell means spontaneous reaction. • Electrochemical series ranks electrodes by standard reduction potential (SHE = 0 V); higher (more +ve) E° → stronger oxidising agent/easily reduced; lower → stronger reducing agent (K, Na top as reducers). • Corrosion is electrochemical oxidation; rusting = Fe2O3·xH2O needs O2 + moisture; prevention: galvanising (Zn coat), painting, alloying (stainless steel), sacrificial anode (Zn/Mg), cathodic protection. • Primary cells (dry/Leclanché) non-rechargeable; secondary (lead-acid, Ni-Cd, Li-ion) rechargeable; fuel cell (H2-O2) converts fuel energy directly to electricity with high efficiency, product = water. • Rate = −d[R]/dt = +d[P]/dt; order = sum of exponents in rate law; molecularity is whole-number for elementary steps; first-order: k has unit s^−1, t½ = 0.693/k (independent of concentration). • Arrhenius: k = A·e^(−Ea/RT); higher T or lower activation energy Ea raises rate; ln(k2/k1) = (Ea/R)(1/T1 − 1/T2); catalyst lowers Ea (does not change ΔH). • Enthalpy ΔH: exothermic ΔH negative, endothermic positive; Hess's law: total ΔH is path-independent (sum of step enthalpies); ΔH = ΣH(products) − ΣH(reactants). • Gibbs free energy: ΔG = ΔH − TΔS; ΔG < 0 spontaneous, = 0 equilibrium, > 0 non-spontaneous; ΔG° = −nFE°cell = −RT·ln K (trap: spontaneity decided by ΔG, not ΔH alone).

• Carbon is tetravalent (4 valence electrons, forms 4 covalent bonds) and shows catenation — self-linking into long chains/rings/branches; strong C–C bonds give huge number of compounds; atomic no. 6, config 2,4. • Allotropes: Diamond (sp^3, 3-D tetrahedral, hardest natural substance, non-conductor); Graphite (sp^2 layered hexagons, soft, conducts electricity, lubricant); Fullerene (C60, "Buckyball", spherical); also graphene & carbon nanotubes. • Isomerism = same molecular formula, different structure/properties; types: chain, position, functional; e.g. C4H10 has 2 isomers (n-butane, isobutane), C5H12 has 3. • Alkanes CnH2n+2 (saturated, single bonds, paraffins, give substitution reactions); Alkenes CnH2n (one C=C, unsaturated); Alkynes CnH2n-2 (one C≡C); first members: CH4, C2H4, C2H2. • Homologous series: members differ by –CH2– (mass 14 u); same general formula & functional group, gradual change in physical properties, similar chemical behaviour. • Functional groups: Alcohol –OH (e.g. C2H5OH); Aldehyde –CHO; Ketone >C=O (–CO–); Carboxylic acid –COOH (e.g. CH3COOH, acetic acid); Amine –NH2; ether –O–, halo –X. • Saturation test: Bromine water (orange-brown→colourless) and alkaline KMnO4 (purple decolourised) are decolourised by alkenes/alkynes, not by alkanes — trap: alkanes do NOT decolourise them. • Ethanol → ethanoic acid on oxidation (alk. KMnO4 / acidified K2Cr2O7); esterification: acid + alcohol → ester + water (sweet smell), reversible with conc. H2SO4 catalyst. • Polymers = large molecules from repeating monomers; addition (polythene from ethene, PVC, Teflon) and condensation (nylon, terylene, with elimination of small molecule). • Soaps = sodium/potassium salts of long-chain fatty acids (made by saponification: fat + NaOH); fail in hard water forming scum. Detergents = sodium salts of long-chain alkylbenzene sulphonic acids or alkyl hydrogen sulphates; work in hard water too. • Micelle: cleansing action — hydrophilic ionic head in water, hydrophobic hydrocarbon tail traps oil/grease, forming a colloidal cluster washed away with water.

• Mineral = naturally occurring substance containing a metal (as a compound or sometimes native/free); ore = mineral from which a metal can be extracted profitably; every ore is a mineral but not vice-versa. Gangue/matrix = unwanted earthy/rocky impurities mixed with ore. • Concentration (ore dressing): Gravity separation (hydraulic washing) — for dense oxide ores using water/density difference; Froth flotation — for sulphide ores (pine oil collector, makes ore hydrophobic, floats on froth); Magnetic separation — when ore or gangue is magnetic (e.g. magnetite Fe3O4, wolframite); Leaching — chemical dissolution (bauxite by hot NaOH, gold/silver by dilute NaCN in air). • Roasting = heating sulphide ore strongly below m.p. in excess air to convert to oxide + SO2 (e.g. 2ZnS + 3O2 → 2ZnO + 2SO2); done for sulphides. Calcination = heating carbonate/hydroxide ore in limited/no air to drive off CO2/H2O giving oxide (CaCO3 → CaO + CO2). Trap: roasting needs air, calcination does not. • Smelting = reduction of metal oxide to molten metal with a reducing agent (C/CO) plus a flux that combines with gangue to form fusible slag (acidic gangue SiO2 + basic flux CaO → CaSiO3 slag). • Activity (reactivity) series → method: highly reactive metals (K, Na, Ca, Mg, Al) by electrolysis of molten salt; moderately reactive (Zn, Fe, Pb, Cu) by reduction of oxide with C/CO/Al; least reactive (Ag, Au, Pt) found native, extracted by simple roasting/heating or displacement. • Blast furnace (iron): charge = haematite Fe2O3 + coke + limestone (CaCO3). Reactions: C + O2 → CO2; CO2 + C → 2CO; Fe2O3 + 3CO → 2Fe + 3CO2; flux CaO + SiO2 → CaSiO3 (slag). Hot blast enters near base; bottom hottest (~2000°C), top coolest; molten pig iron (~4% C) tapped at bottom with lighter slag floating above it. • Hall–Héroult (aluminium): electrolysis of pure alumina Al2O3 dissolved in molten cryolite Na3AlF6 (lowers m.p. to ~950°C, increases conductivity) with fluorspar CaF2. Cathode (carbon lining): Al3+ + 3e^– → Al; anode (carbon): liberated O2 burns electrode forming CO/CO2 so anodes wear out. Alumina from bauxite via Bayer process. • Copper extraction (from copper pyrites CuFeS2): froth flotation → roasting → smelting gives matte (Cu2S + FeS); in Bessemer converter 2Cu2S + 3O2 → 2Cu2O + 2SO2, then 2Cu2O + Cu2S → 6Cu + SO2 (self/auto-reduction) → blister copper (~98%). • Refining: Electrolytic refining — impure metal = anode, pure metal = cathode, metal-salt solution electrolyte (Cu, Ag, Zn, Al); anode mud holds noble metals. Zone refining — for ultra-pure semiconductors (Si, Ge, Ga); based on impurities being more soluble in molten than solid zone; molten band moved along, impurities swept to one end. • Common alloys: Brass = Cu + Zn; Bronze = Cu + Sn; Solder = Pb + Sn; Stainless steel = Fe + Cr + Ni; Steel = Fe + C (~0.1–2%); Duralumin = Al + Cu + Mg + Mn (aircraft); German silver = Cu + Zn + Ni (no silver); Bell metal = Cu + Sn; Amalgam = alloy containing mercury (Hg).