← Chemistry — Std 11
🧪

States of Matter

Ch. 11Std 11

Easy Overview

Why does water expand when it freezes? Why do gases exert pressure? Why is diamond so hard but iodine so soft? The state of matter — solid, liquid, or gas — depends on the balance between intermolecular forces and thermal energy. Raise the temperature, and solids melt, liquids boil; lower it, and gases condense, liquids freeze. Gases obey simple laws (Boyle, Charles, Avogadro) which combine into the ideal gas equation PV = nRT. But real gases deviate at high pressure and low temperature — that's where van der Waals equation comes in. The kinetic molecular theory explains pressure as molecular collisions, temperature as average kinetic energy, and diffusion as random molecular motion. Liquids have surface tension, viscosity, and vapor pressure. Solids can be crystalline (regular repeating patterns) or amorphous (disordered). The type of crystal — ionic, covalent, molecular, or metallic — determines its properties: melting point, hardness, and conductivity.

Intermolecular Forces — The Glue Between Molecules

Dispersion (London) forces: temporary dipoles from electron fluctuations — present in all molecules, strength ↑ with molecular size and surface area. Dipole-dipole: between polar molecules, stronger than dispersion for small polar molecules. Hydrogen bonding: H bonded to N/O/F attracted to lone pair on another N/O/F (5-30 kJ/mol). Ion-dipole: between ion and polar molecule (solvation of salts in water). Ion-induced dipole: ion polarizes neutral molecule. Strength order: ion-dipole > H-bond > dipole-dipole > dipole-induced dipole > London dispersion. Intermolecular forces determine boiling points: H₂O (100°C, H-bonding) vs H₂S (-60°C, dipole-dipole).

The Gas Laws — Boyle, Charles, and Avogadro

Boyle's law (1662): P ∝ 1/V at constant n,T — PV = constant. Charles's law (1787): V ∝ T at constant n,P — V/T = constant. Gay-Lussac's law: P ∝ T at constant n,V — P/T = constant. Avogadro's law (1811): V ∝ n at constant P,T — equal volumes of gases at same T,P contain equal molecules. Combined gas law: P₁V₁/T₁ = P₂V₂/T₂. Molar volume: 22.4 L at STP (0°C, 1 atm), 24.5 L at RTP (25°C, 1 atm). All are limiting laws — accurate for ideal behavior at low P and high T.

Ideal Gas Equation — PV = nRT

Combines all gas laws: PV = nRT. R = ideal gas constant = 0.0821 L·atm·mol⁻¹·K⁻¹ = 8.314 J·mol⁻¹·K⁻¹ = 62.36 L·mmHg·K⁻¹·mol⁻¹. STPD conditions: 0°C (273.15 K), 1 atm (760 mmHg). Standard molar volume: 22.414 L. Applications: find molar mass (M = mRT/PV), density (d = PM/RT), number of moles. Dalton's law of partial pressures: P_total = ΣP_i. Partial pressure = mole fraction × total pressure. Gas collected over water: P_dry = P_total - P_vapor(H₂O). Mole fraction X_i = n_i/n_total.

Kinetic Molecular Theory of Gases

Five postulates: (1) Gases consist of tiny particles in constant random motion. (2) Volume of molecules negligible compared to container. (3) No intermolecular forces between molecules. (4) Collisions are perfectly elastic (no energy loss). (5) Average KE ∝ T (KE = ³/₂RT for one mole, = ³/₂kT per molecule). Derived from postulates: PV = ⅓mnu² (where u = root mean square speed). Explains Boyle (more molecules hit walls at higher P), Charles (faster molecules at higher T → more force), Avogadro (more molecules → more collisions).

Molecular Speeds — RMS, Average, and Most Probable

Root mean square speed: u_rms = √(3RT/M). Average speed: u_avg = √(8RT/πM). Most probable speed: u_mp = √(2RT/M). Ratio u_rms : u_avg : u_mp = 1.000 : 0.921 : 0.816. At 25°C: N₂ (u_rms = 515 m/s) < He (1360 m/s) — lighter molecules move faster. Maxwell-Boltzmann distribution: shows spread of speeds at a given T. As T ↑, the curve broadens and shifts right (more molecules at higher speeds). Lighter molecules have broader distributions. Effusion (Graham's law): rate ∝ 1/√M — H₂ effuses 4× faster than O₂.

Real Gases and Deviations from Ideality

Real gases deviate at high P (molecules closer → volume significant) and low T (intermolecular forces become important). Compression factor Z = PV/nRT. Ideal: Z=1. Z<1: attractive forces dominate (easier to compress than ideal — occurs at moderate P). Z>1: repulsive forces/volume dominate (harder to compress — at very high P). At Boyle temperature (T_B), gas behaves ideally over a range of P. For each gas: T_B ≈ 2.5×T_c (critical temperature). N₂: T_B = 327 K, He: T_B = 23 K (near ideal at most conditions).

Van der Waals Equation — Correcting for Reality

(P + a/V²)(V - nb) = nRT. 'a' corrects for intermolecular attractions (units: atm·L²/mol²). Larger a = stronger attractions (H₂O: 5.46, He: 0.034). Larger molecules with more electrons have higher 'a'. 'b' corrects for finite molecular volume (units: L/mol). b = 4 × actual volume of molecules. Larger molecules = larger b. Van der Waals equation better predicts behavior at high P and near condensation. Cubic in V — solving gives three real roots below T_c (one liquid, one gas, one meaningless). T_c: temperature above which gas cannot be liquefied by pressure alone.

Liquefaction of Gases and Critical Phenomena

A gas can be liquefied by cooling below its critical temperature (T_c) and applying sufficient pressure. T_c: highest T at which gas can be liquefied. P_c: pressure needed at T_c. V_c: molar volume at critical point. For CO₂: T_c = 304.2 K (31°C), P_c = 73 atm — above 31°C, CO₂ cannot be liquefied (hence 'critical'). Liquefaction methods: Linde's method (Joule-Thomson expansion cooling), Claude's method (adiabatic expansion doing work). Critical constants relate to van der Waals constants: a = 27R²T_c²/64P_c, b = RT_c/8P_c. Practical applications: liquid air separation, cryogenics, liquefied natural gas (LNG) transport.

Liquid State — Properties and Behavior

Between solid and gas — molecules have enough energy to move past each other (fluidity) but not enough to escape (cohesion). Vapor pressure: pressure of vapor in equilibrium with liquid at given T. Increases with T (Clausius-Clapeyron equation: ln(P₂/P₁) = -ΔH_vap/R(1/T₂ - 1/T₁)). Boiling point: when vapor pressure = external pressure (normal BP = 1 atm). Surface tension: molecules at surface experience net inward pull → minimizes surface area (raindrops spherical). Capillary action: adhesion to walls > cohesion → liquid rises in narrow tube. Viscosity: resistance to flow — decreases with T, increases with molecular size and intermolecular forces.

Solid State — Crystalline and Amorphous

Crystalline: regular 3D arrangement (lattice + basis = crystal). Long-range order, sharp melting point, anisotropic properties (different in different directions). Examples: NaCl, diamond, quartz. Amorphous (glass-like): disordered arrangement, short-range order only. No sharp melting point (softens over range), isotropic. Examples: glass, rubber, plastics, gels. Polymorphism: same substance can form different crystal structures (carbon: diamond, graphite; CaCO₃: calcite, aragonite). Unit cell: smallest repeating unit. Lattice points: positions of atoms/ions in crystal. Seven crystal systems and 14 Bravais lattices describe all possible arrangements.

Crystal Systems and Bravais Lattices

Seven crystal systems based on unit cell parameters (edge lengths a, b, c and angles α, β, γ): cubic (a=b=c, α=β=γ=90°), tetragonal (a=b≠c, all 90°), orthorhombic (a≠b≠c, all 90°), hexagonal (a=b≠c, α=β=90°, γ=120°), rhombohedral (a=b=c, α=β=γ≠90°), monoclinic (a≠b≠c, α=γ=90°, β≠90°), triclinic (a≠b≠c, all angles ≠90°). Bravais lattices: primitive (P, lattice points only at corners), body-centered (I, corner + center), face-centered (F, corners + face centers), base-centered (C, corners + two opposite faces). Total 14 Bravais lattices. Cubic is most symmetric: simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC).

Close Packing in Solids — HCP and CCP

Atoms are spheres in closest possible arrangement. Hexagonal close packing (HCP): ABAB... layers — Mg, Zn, Ti. Cubic close packing (CCP = FCC): ABCABC... layers — Cu, Ag, Au. Both have 74% packing efficiency (26% empty space = voids). Coordination number = 12 (each atom touches 12 neighbors). Voids: tetrahedral (4 atoms around, smaller) and octahedral (6 atoms around, larger). Number of tetrahedral voids = 2N; octahedral = N (where N = close-packed atoms). For CCP: each unit cell has 4 atoms, 8 tetrahedral voids, 4 octahedral voids. Interstitial compounds: small atoms (H, C, N) occupy voids in metal lattices, modifying properties.

Types of Crystalline Solids

Ionic (NaCl, MgO): ions held by electrostatic forces — high MP, brittle, conduct when molten/dissolved, soluble in polar solvents. Coordination number depends on radius ratio. Covalent network (diamond, SiC, SiO₂): atoms held by covalent bonds — extremely high MP (diamond 3550°C), very hard, semiconductors or insulators, insoluble. Molecular (I₂, ice, naphthalene): molecules held by weak forces (London, dipole) — low MP, soft, insulators, soluble in nonpolar solvents (or water via H-bonding). Metallic (Cu, Fe, Na): positive ions in electron sea — high MP for d-block, excellent conductors, malleable and ductile, lustrous.

Imperfections in Solids — Defects

Point defects: vacancy (missing atom, Schottky defect in ionic solids — equal numbers of cation and anion vacancies), interstitial (extra atom in void), Frenkel defect (cation moves to interstitial site, leaving vacancy — common in AgCl, ZnS). Line defects (dislocations): edge and screw — determine plastic deformation. Non-stoichiometric defects: excess metal (F-centers — produce color: NaCl yellow when heated in Na vapor) or metal deficiency. Defects impact properties: F-centers in NaCl give color and semiconductivity. Impurities in semiconductors (doping): n-type (Group 15 in Si — extra e⁻) or p-type (Group 13 in Si — electron holes).

Electrical Properties of Solids

Conductors: metals (conduction band partially filled — e⁻ mobile), resistivity 10⁻⁸ to 10⁻⁶ Ω·m. Insulators: large band gap (5-10 eV) — diamond, quartz, glass. Semiconductors: small band gap (0.5-3 eV) — Si (1.1 eV), Ge (0.7 eV). Conductivity ↑ with T (unlike metals — more electrons jump to conduction band). Intrinsic: pure, equal e⁻ and holes. Extrinsic: doped with impurities. Superconductors: zero resistance below T_c (Meissner effect — expels magnetic field). High T_c superconductors: YBa₂Cu₃O₇ (T_c = 92 K, liquid N₂). Applications: MRI, maglev trains, particle accelerators.

Liquid Crystals — The Fourth State

Molecules with rigid, rod-like shape, one or more polar groups. Nematic: molecules aligned in same direction (long-range orientational order) but no positional order — used in LCDs (twisted nematic display: electric field changes orientation → light transmission controlled). Smectic: molecules aligned + layered (more ordered). Cholesteric (chiral nematic): layers rotated slightly — selective reflection of specific λ (thermometers). Thermotropic liquid crystals: transition temperatures depend on heating. Lyotropic: concentration-dependent in solution (soap micelles). Applications: LCD screens, thermometers (medical, mood rings), optical sensors.

Phase Diagrams — Mapping States of Matter

A phase diagram shows state (solid, liquid, gas) as function of T and P. Triple point: three phases coexist (H₂O: 0.01°C, 4.58 mmHg). Critical point: beyond which liquid and gas indistinguishable. Melting/freezing curve: slope for H₂O is negative (unusual — ice less dense than water, melts under pressure → ice skates). For most substances, slope is positive. Sublimation curve: solid↔vapor. Vaporization curve: liquid↔vapor (ends at critical point). Phase rule (Gibbs): F = C - P + 2. For water at triple point: C=1, P=3 → F=0 (invariant). Applications: freeze-drying (below triple point — sublimation), supercritical CO₂ extraction (decaffeination).

Comparison of States — Gases, Liquids, and Solids

Density: gases << liquids ≈ solids (except ice < water). Compressibility: gases high, liquids low, solids negligible. Shape: gases fill container, liquids take container shape, solids retain shape. Diffusion: gases fastest (Graham's law), liquids slow (∝1/√M), solids extremely slow. Intermolecular forces: gases (negligible), liquids (moderate), solids (strong). Molecular motion: gases (translational, rotational, vibrational), liquids (limited translation + rotation), solids (vibrational only). Enthalpy changes: fusion (ΔH_fus, melting), vaporization (ΔH_vap, boiling), sublimation (ΔH_sub, solid→gas directly). ΔH_sub = ΔH_fus + ΔH_vap.

Key Points

  • •Intermolecular forces: dispersion < dipole-dipole < H-bond < ion-dipole
  • •Boyle: PV=const; Charles: V/T=const; Avogadro: V∝n at same T,P
  • •Ideal gas: PV=nRT, R=0.0821 L·atm·mol⁻¹·K⁻¹
  • •Dalton: P_total = ΣP_i; P_i = X_i × P_total
  • •Kinetic theory: KE ∝ T; PV = ⅓mnu²; u_rms = √(3RT/M)
  • •Graham's law: rate of effusion ∝ 1/√M
  • •Real gases deviate: van der Waals (P + a/V²)(V - nb) = nRT
  • •Compression factor Z = PV/nRT; Z=1 ideal, Z<1 attraction, Z>1 repulsion
  • •T_c: critical temp above which gas can't be liquefied
  • •Vapor pressure: Clausius-Clapeyron ln(P₂/P₁) = -ΔH_vap/R(1/T₂ - 1/T₁)
  • •Crystalline: regular lattice, sharp MP, anisotropic. Amorphous: disordered, no sharp MP
  • •7 crystal systems, 14 Bravais lattices; cubic: SC, BCC, FCC
  • •HCP (ABAB) and CCP/FCC (ABCABC): 74% packing efficiency, CN=12
  • •Ionic (high MP), covalent network (very hard), molecular (low MP), metallic (conducting)
  • •Schottky (vacancy), Frenkel (interstitial), F-centers (color centers)
  • •Semiconductors: band gap; n-type (extra e⁻), p-type (hole); conductivity ↑ with T
  • •Liquid crystals: nematic (LCD), smectic, cholesteric — rod-like molecules
  • •Phase diagram: triple point, critical point; water's negative melting slope

Practice Questions

  • Derive ideal gas equation from gas laws. Calculate volume of 2 mol CO₂ at STP.
  • Calculate u_rms of O₂ at 27°C. Compare with H₂ at same temperature.
  • Explain deviations from ideal behavior. What is van der Waals equation?
  • State Graham's law. If O₂ takes 30 s to effuse, how long for H₂ under same conditions?
  • Explain: (i) Surface tension (ii) Viscosity (iii) Vapor pressure
  • Differentiate crystalline and amorphous solids with examples.
  • Explain close packing: HCP vs CCP. Calculate packing efficiency for FCC.
  • What are Schottky and Frenkel defects? Give examples.
  • Explain phase diagram of water. Why does ice float?
  • What are liquid crystals? Explain nematic phase and LCD working.