Chapter Review

Liquids and Solids

Liquid Properties and Hydrogen Bonding · Crystalline Solids and Lattice Energy

Intermolecular Forces

Attractive forces between molecules that determine physical state and properties like boiling point, vapour pressure, and viscosity. They are electrostatic in origin and far weaker than covalent bonds.

Key Points

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    Four types in order of increasing strength: London dispersion < dipole-induced dipole < dipole-dipole < hydrogen bonding
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    London dispersion forces are present in ALL molecules — they arise from instantaneous dipoles in electron clouds
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    Dipole-dipole forces occur only in polar molecules and are roughly 1% as strong as covalent bonds
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    Hydrogen bonding is the strongest intermolecular force — requires H bonded to F, O, or N
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    Polarizability (not polarity) governs London force strength: larger electron clouds distort more easily
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    London forces increase with molecular size and number of atoms — explains why boiling points rise down a group

Evaporation and Vapour Pressure

Evaporation is a surface phenomenon where high-energy molecules escape the liquid at any temperature. In a closed container, evaporation and condensation reach dynamic equilibrium, establishing a constant vapour pressure.

Key Points

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    Evaporation is a surface phenomenon only — bulk molecules are surrounded and cannot escape
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    Evaporation cools the remaining liquid because the highest-energy molecules leave first
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    Vapour pressure depends ONLY on temperature and nature of the liquid — not on amount, surface area, or container volume
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    A larger surface area increases both evaporation and condensation rates equally, so equilibrium vapour pressure is unchanged
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    Weaker intermolecular forces → higher vapour pressure (e.g., isopentane 580 torr vs glycerol 0.00016 torr at 20 °C)
  • •
    Vapour pressure increases nonlinearly with temperature — the increment grows dramatically near the boiling point
  • •
    Manometric measurement: , where is the mercury height difference between the two limbs
Formula

Boiling Point

The temperature at which a liquid's vapour pressure equals the external atmospheric pressure. Bubbles form throughout the bulk liquid and the temperature remains constant during boiling as added heat breaks intermolecular forces.

Key Points

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    Boiling occurs throughout the bulk; evaporation occurs only at the surface at any temperature
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    Temperature stays constant during boiling — added heat converts liquid to vapour, not raising temperature
  • •
    Higher external pressure → higher boiling point; lower pressure → lower boiling point
  • •
    Water boils at 69 °C on Mount Everest (323 torr) vs 100 °C at sea level (760 torr)
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    Stronger intermolecular forces → higher boiling point (water 100 °C vs diethyl ether 34.6 °C)
  • •
    Vacuum distillation lowers boiling points below normal, allowing heat-sensitive substances like glycerin to be distilled without decomposition
Formula

Energetics of Phase Changes

Energy is absorbed or released during phase changes. All three enthalpy changes (fusion, vapourisation, sublimation) are positive (endothermic) because energy is needed to overcome intermolecular forces.

Key Points

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    Enthalpy hierarchy: — sublimation requires the most energy, fusion the least
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    because molecules separate much farther apart during vapourisation than during melting
  • •
    For water: = 40.6 kJ mol⁻¹ at 100 °C
  • •
    values reflect intermolecular force strength — H₂O (40.6) >> CH₄ (8.6) kJ/mol
  • •
    Dynamic equilibrium characterises all reversible phase changes — forward and reverse rates are equal
  • •
    At the melting point, solid and liquid coexist in dynamic equilibrium (e.g., ice and water at 0 °C)
Formula

Hydrogen Bonding

The strongest intermolecular force, occurring when H bonded to F, O, or N is attracted to a lone pair on a neighbouring electronegative atom. H-bonds are about 20× weaker than covalent bonds but far stronger than ordinary dipole-dipole forces.

Key Points

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    Two conditions required: H bonded to F/O/N (donor) and a lone pair on F/O/N of another molecule (acceptor)
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    Water forms up to 4 H-bonds per molecule (2 H donors + 2 lone-pair acceptors) — the most of any common substance
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    First-row hydrides (NH₃, H₂O, HF) have anomalously high boiling points due to H-bonding — the anomaly is absent in Group IVA
  • •
    H₂O has a higher boiling point than HF despite O being less electronegative than F — because water forms 2 H-bonds per molecule vs ~1 for HF
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    H-bonding determines solubility in water: ethanol and small carboxylic acids dissolve; hydrocarbons do not
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    Applications: protein α-helices, DNA double helix, soap cleansing action, textile strength, adhesive properties of glue and honey

Anomalous Properties of Water

Water is densest at 4 °C, not at 0 °C. Ice has an open tetrahedral H-bonded structure with ~9% more volume than liquid water, making it less dense and able to float.

Key Points

  • •
    Ice has a regular tetrahedral lattice with large empty spaces — each H₂O is H-bonded to 4 neighbours (analogous to diamond's carbon lattice)
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    Liquid water is denser because H-bonds constantly break and reform, allowing closer packing
  • •
    Above 4 °C: normal thermal contraction dominates → density increases as temperature drops
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    Below 4 °C: ordered H-bond cluster formation dominates → volume expands and density decreases
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    Ice floats and acts as an insulating blanket, allowing aquatic life to survive under frozen lakes
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    Without H-bonding, ponds would freeze from the bottom up, killing all aquatic life
Formula

Crystalline vs Amorphous Solids

Crystalline solids have a definite, repeating 3D arrangement of particles throughout the entire material, while amorphous solids (glass, plastics, rubber) lack long-range order and soften over a temperature range.

Key Points

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    Crystalline: definite geometric shape, sharp melting point, cleavage planes, may show anisotropy
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    Amorphous: no definite shape, soften gradually, no cleavage planes, isotropic
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    Anisotropy: physical properties (refractive index, conductivity, thermal expansion) vary with crystal direction — e.g., graphite conducts far better parallel to its layers
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    Crystallites are small ordered regions within amorphous solids — they lack long-range periodicity
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    Amorphous solids can be made by melting a crystal and rapidly cooling it, preventing particle rearrangement
  • •
    Allotropy: elements existing in multiple crystalline forms (e.g., carbon as diamond cubic and graphite hexagonal)

Crystal Lattice and Unit Cell

The crystal lattice is a 3D array of points representing particle positions. The unit cell is the smallest repeating block that contains all structural features of the crystal, defined by six crystallographic elements: three edge lengths and three inter-axial angles.

Key Points

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    Every lattice point has an identical environment — the entire crystal is built by repeating the unit cell in 3D
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    Sharing rules: corner particle → 1/8 per cell, edge → 1/4, face → 1/2, body centre → 1 (fully owned)
  • •
    Seven crystal systems: cubic (most symmetric), tetragonal, orthorhombic, monoclinic, hexagonal, rhombohedral, triclinic (least symmetric)
  • •
    Hexagonal is the only system with a 120° angle; triclinic has all axes and all angles unequal and non-90°
  • •
    Common crystals: NaCl is cubic; graphite and ice are hexagonal; rhombic sulphur and BaSO₄ are orthorhombic
Formula

Ionic and Molecular Crystals

Ionic crystals are continuous lattices of alternating cations and anions held by strong, non-directional electrostatic forces. Molecular crystals consist of molecules held together by weak intermolecular forces.

Key Points

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    Ionic: hard, high melting point, brittle, conducts when molten/dissolved, high density — e.g., NaCl, MgO
  • •
    Molecular: soft, low melting point, volatile, electrical insulator, low density — e.g., I₂, CO₂, ice, sugar
  • •
    Ionic crystal geometry depends on radius ratio (), not chemical identity — NaCl and CsF share the same geometry
  • •
    Radius ratio 0.414–0.732 → octahedral (CN = 6, e.g., NaCl); 0.732 → cubic (CN = 8, e.g., CsCl)
  • •
    NaCl unit cell: 4 formula units — Cl⁻ at corners + face centres, Na⁺ at edge centres + body centre
  • •
    Brittleness in ionic crystals: sliding layers cause like-charge alignment → electrostatic repulsion → fracture
  • •
    Solubility rule: polar molecular crystals dissolve in polar solvents; non-polar dissolve in non-polar solvents
Formula

Lattice Energy

The energy released when one mole of an ionic crystal forms from its gaseous ions. It is exothermic (negative) during formation and endothermic (positive) during dissociation. Magnitude depends on ionic charges and sizes.

Key Points

  • •
    Lattice energy is expressed in kJ mol⁻¹ — NaCl = −787 kJ mol⁻¹
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    Smaller ions → stronger electrostatic attraction → more negative lattice energy (NaF −895 > NaCl −787 > NaBr −728 > NaI −690)
  • •
    Higher ionic charges → dramatically more negative lattice energy (Mg²⁺/O²⁻ >> Na⁺/Cl⁻)
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    Down a group, lattice energy decreases (less negative) because ionic radii increase and electrostatic attraction weakens
  • •
    Higher lattice energy → higher melting point, greater hardness, lower solubility
  • •
    Quick comparison rule: smaller ions + higher charges → more negative lattice energy
Formula

Formulas

Boiling Point Condition

Boiling occurs when liquid vapour pressure equals external atmospheric pressure

Vapour Pressure (Manometric Method)

Atmospheric pressure plus mercury height difference between the two manometer limbs

Enthalpy Hierarchy of Phase Changes

Sublimation requires the most energy, then vapourisation, then fusion

Unit Cell Ion Counting

Corner ions shared by 8 cells, edge by 4, face by 2, body unshared

Radius Ratio

Determines ionic crystal geometry: 0.414–0.732 → octahedral (CN=6); ≥0.732 → cubic (CN=8)

Lattice Energy Trend

Lattice energy increases (more negative) with higher ionic charges and smaller ionic radii

Lattice Energy (Formation)

Energy released when gaseous ions form one mole of ionic solid; exothermic, negative ΔH

Maximum Density of Water

Water reaches maximum density at 4 °C due to competing thermal contraction and H-bond cluster expansion