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1. Liquid State

Matter commonly exists in three physical states: solid, liquid and gas. A liquid has a definite volume but does not have a definite shape. It takes the shape of the container in which it is placed.

The particles of a liquid are much closer together than the particles of a gas, but they are not fixed in definite positions as in a solid. They can move past one another. Because of this, liquids can flow.

Important characteristics of liquids

• Liquids have a definite volume.
• They do not have a definite shape.
• They are almost incompressible.
• Particles are relatively close together.
• There are intermolecular attractive forces.
• Liquids can flow.
• They possess surface tension and viscosity.
• They show evaporation and boiling.

The behaviour of a liquid is strongly influenced by intermolecular forces. Stronger intermolecular attraction generally means greater surface tension, greater viscosity and lower vapour pressure.

2. Intermolecular Forces

Intermolecular forces are attractive forces acting between molecules. They are weaker than the chemical bonds inside molecules but strongly influence the physical properties of liquids and solids.

1. London dispersion forces

These forces arise because electrons are continuously moving. At a particular instant, electrons may be distributed unevenly, producing a temporary dipole. This can induce a dipole in a neighbouring molecule.

London forces are present in all molecules, including non-polar molecules.

2. Dipole-dipole forces

These occur between polar molecules. The positive end of one polar molecule attracts the negative end of another.

3. Hydrogen bonding

Hydrogen bonding occurs when hydrogen is bonded to a highly electronegative atom such as fluorine, oxygen or nitrogen and is attracted to an electronegative atom of another molecule.

Examples include water, alcohols and ammonia.

Effect on physical properties

Stronger intermolecular attraction usually causes:

• higher boiling point,
• higher viscosity,
• higher surface tension,
• lower vapour pressure.

3. Vapour Pressure

When a liquid is kept in a closed container, some molecules escape from the liquid surface into the vapour phase. At the same time, vapour molecules return to the liquid.

At equilibrium, the rate of evaporation becomes equal to the rate of condensation.

The pressure exerted by the vapour in equilibrium with its liquid at a particular temperature is called vapour pressure.

Factors affecting vapour pressure

Temperature

Vapour pressure increases as temperature increases. At higher temperature, more molecules possess enough kinetic energy to escape from the liquid surface.

Nature of liquid

Liquids with weak intermolecular forces generally have higher vapour pressure.

Intermolecular attraction

Strong intermolecular forces make it difficult for molecules to escape, so vapour pressure decreases.

4. Surface Tension

Molecules inside a liquid are attracted by neighbouring molecules in all directions. Therefore, the net force on an interior molecule is approximately zero.

A molecule at the surface does not have neighbouring liquid molecules above it in the same way. It therefore experiences a net inward attractive force.

As a result, the liquid surface behaves as if it is under tension.

Surface tension is the force acting per unit length perpendicular to a line drawn on the surface of a liquid.

Therefore:

SI unit

The SI unit of surface tension is N m⁻¹.

Examples

• Small water droplets tend to become spherical.
• Some insects can move on the water surface.
• A needle can sometimes float on a water surface if placed carefully.
• Soap reduces the surface tension of water.

Why droplets are approximately spherical

For a given volume, a sphere has the minimum surface area. Since surface tension tends to reduce the surface area, small liquid droplets tend to become spherical.

5. Surface Energy

Molecules at the surface of a liquid possess higher potential energy than molecules inside the liquid. Work is therefore required to increase the surface area.

Surface energy is the work required to increase the surface area of a liquid by one unit.

If the surface area changes by ΔA:

For a single liquid surface this relation is directly useful. For a soap film having two surfaces, the total force and work have to account for both surfaces.

6. Viscosity

Viscosity is the resistance offered by a liquid to the relative motion of its different layers.

A liquid with high viscosity flows slowly, whereas a liquid with low viscosity flows easily.

For example, glycerol is much more viscous than water.

Newton's law of viscosity

For a Newtonian liquid, the shear stress is proportional to the velocity gradient.

Therefore:

Here η is the coefficient of viscosity.

SI unit

The SI unit of viscosity is Pa s.

Factors affecting viscosity

• Nature of the liquid
• Intermolecular forces
• Temperature
• Molecular size and shape

In most liquids, viscosity decreases as temperature increases because molecules can move more easily and intermolecular resistance becomes less important.

7. Stokes' Law

When a small spherical particle moves slowly through a viscous liquid, it experiences a resisting force.

According to Stokes' law:

where:

• F = viscous resistance
• η = coefficient of viscosity
• r = radius of spherical particle
• v = velocity of particle

Terminal velocity

When a spherical particle falls through a liquid, its velocity eventually becomes constant. This is called terminal velocity.

For a small spherical particle:

Here ρs is the density of the particle and ρl is the density of the liquid.

This relation is useful in viscosity measurements and sedimentation-type calculations.

8. Effect of Temperature on Liquid Properties

Surface tension

Surface tension generally decreases with increase in temperature because intermolecular cohesive forces become less effective as molecular kinetic energy increases.

Viscosity

Viscosity of liquids generally decreases with increase in temperature.

Vapour pressure

Vapour pressure increases with increase in temperature.

9. Capillary Action

The rise or fall of a liquid in a narrow tube is called capillary action.

Water rises in a glass capillary because adhesive attraction between water and glass is strong and the water surface forms a concave meniscus.

Mercury behaves differently and forms a convex meniscus in glass.

Capillary rise equation

where:

• h = height of rise or depression
• γ = surface tension
• θ = angle of contact
• r = radius of capillary tube
• ρ = density of liquid
• g = acceleration due to gravity

From the equation, smaller capillary radius produces greater capillary rise when other factors remain constant.

Applications

• Movement of water through plants.
• Absorption of liquids by paper.
• Ink movement in paper.
• Liquid movement through narrow pores.
• Laboratory capillary tubes.

10. Cohesion and Adhesion

Cohesive force

Cohesive force is the attraction between molecules of the same substance.

Example: attraction between water molecules.

Adhesive force

Adhesive force is the attraction between molecules of different substances.

Example: attraction between water and glass.

Relation to meniscus

If adhesion between liquid and container is stronger than cohesion within the liquid, the liquid tends to climb the walls.

If cohesion is stronger, the liquid tends to pull away from the walls.

11. Evaporation

Evaporation is the conversion of liquid into vapour from the surface of a liquid at temperatures below its boiling point.

Only molecules having sufficient kinetic energy can escape from the liquid surface.

Factors affecting evaporation

• Temperature
• Surface area
• Nature of liquid
• Wind speed
• Humidity of surrounding air

Increasing surface area generally increases the rate of evaporation because more molecules are exposed at the surface.

Cooling during evaporation

The molecules with higher kinetic energy escape first. The average kinetic energy of the remaining molecules decreases, producing cooling.

12. Boiling

Boiling is the rapid conversion of liquid into vapour throughout the liquid when the vapour pressure of the liquid becomes equal to the external pressure.

Boiling point

The temperature at which vapour pressure of a liquid becomes equal to the external pressure is called its boiling point.

Effect of external pressure

If external pressure decreases, the boiling point decreases.

If external pressure increases, the boiling point increases.

This is why water boils at a temperature lower than 100°C at high altitude.

13. Solid State

A solid has a definite shape and a definite volume. Its particles are closely packed and have restricted movement around their mean positions.

Main characteristics of solids

• Definite shape
• Definite volume
• Very low compressibility
• High density compared with gases
• Strong intermolecular or interparticle forces
• Particles mainly vibrate about fixed positions

The arrangement of particles determines many physical properties of solids.

14. Classification of Solids

Solids can be classified according to the type of particles present and the forces holding them together.

1. Molecular solids

Their constituent particles are molecules. The forces may be London forces, dipole-dipole forces or hydrogen bonds.

Examples: iodine, solid CO₂, ice.

2. Ionic solids

They contain positive and negative ions held by strong electrostatic forces.

Examples: NaCl, KCl, MgO.

3. Covalent or network solids

Atoms are connected by strong covalent bonds forming a large network.

Examples: diamond, silicon carbide.

4. Metallic solids

Metal atoms or positive metal centres are held together by metallic bonding with delocalized electrons.

Examples: copper, iron and aluminium.

15. Crystalline Solids

A crystalline solid has a regular, repeating three-dimensional arrangement of its constituent particles.

Characteristics

• Long-range order
• Definite geometrical shape when properly developed
• Sharp melting point
• Definite heat of fusion
• Often anisotropic
• Cleavage along definite planes

Anisotropy

Anisotropy means that some physical properties vary with direction in the crystal.

Electrical conductivity, refractive index and thermal expansion may show directional differences in crystals.

16. Amorphous Solids

Amorphous solids do not possess long-range periodic arrangement of particles.

Examples include glass, rubber and many plastics.

Characteristics

• No long-range regular arrangement
• They soften over a range of temperature
• They are generally isotropic
• They do not have definite cleavage planes

17. Crystal Lattice

A crystal lattice is a regular three-dimensional arrangement of points representing the positions of particles in a crystal.

Each lattice point has an identical environment.

Unit cell

The smallest repeating portion of a crystal lattice that can reproduce the complete crystal by translation is called the unit cell.

Repetition of the unit cell in three dimensions gives the complete crystal structure.

18. Unit Cell

A unit cell is described using three edge lengths and three angles.

The edge lengths are represented by:

The angles are:

The relation between these parameters determines the crystal system.

Primitive and centered unit cells

A primitive unit cell has lattice points only at the corners.

A centered unit cell contains additional lattice points at the body centre, face centres or certain positions depending on the lattice type.

19. Seven Crystal Systems

Crystals are grouped into seven crystal systems according to their unit-cell geometry.

20. Bravais Lattices

There are fourteen possible three-dimensional Bravais lattices distributed among the seven crystal systems.

21. Cubic Unit Cells

Cubic crystals are particularly important because their geometry makes numerical calculations easier.

The three important cubic unit cells are:

1. Simple cubic (SC)
2. Body-centred cubic (BCC)
3. Face-centred cubic (FCC)

Simple cubic

Particles occupy the eight corners of the cube.

Each corner particle contributes one-eighth to a particular unit cell.

Coordination number = 6.

Packing efficiency ≈ 52.4%.

Body-centred cubic

BCC contains particles at the eight corners and one particle at the body centre.

Coordination number = 8.

Packing efficiency ≈ 68%.

Face-centred cubic

FCC contains particles at the eight corners and at the centre of each of the six faces.

Coordination number = 12.

Packing efficiency ≈ 74%.

22. Number of Atoms per Unit Cell

A particle at a corner is shared among eight neighbouring unit cells.

A particle at a face is shared between two unit cells.

A particle on an edge is shared among four unit cells.

A particle completely inside the unit cell belongs entirely to that cell.

Examples

Simple cubic:

BCC:

FCC:

23. Coordination Number

Coordination number is the number of nearest neighbouring particles surrounding a particular particle.

FCC therefore has a more closely packed arrangement than BCC and simple cubic.

24. Packing Efficiency

Packing efficiency is the percentage of total space in a unit cell actually occupied by particles.

Simple cubic

For simple cubic:

Number of atoms:

Packing efficiency ≈ 52.4%.

BCC

In BCC, atoms touch along the body diagonal.

Therefore:

Packing efficiency ≈ 68%.

FCC

In FCC, atoms touch along the face diagonal.

Therefore:

Packing efficiency ≈ 74%.

25. Radius-Edge Relations

These relations are very important for unit-cell numerical problems.

Simple cubic

Body-centred cubic

Therefore:

Face-centred cubic

Therefore:

26. Density of a Unit Cell

The theoretical density of a crystalline solid can be calculated from its unit-cell parameters.

The general relation is:

where:

• ρ = density
• Z = number of particles per unit cell
• M = molar mass
• a = edge length of cubic unit cell
• NA = Avogadro constant

Avogadro constant:

Important unit conversion

If the edge length is given in pm, convert it to cm before using the density formula if density is required in g cm⁻³.

If the edge length is given in Å:

27. Voids in Crystal Structures

When particles are packed together, some empty spaces remain between them. These spaces are called voids.

The two important types are:

1. Tetrahedral void
2. Octahedral void

Tetrahedral void

A tetrahedral void is surrounded by four particles.

In close packing, the number of tetrahedral voids is twice the number of particles.

Octahedral void

An octahedral void is surrounded by six particles.

In close packing:

where N is the number of close-packed particles.

28. Miller Indices

Miller indices are a set of three integers used to specify the orientation of a crystal plane.

They are written as:

Basic procedure

1. Determine the intercepts of the plane along the crystallographic axes.
2. Take the reciprocals of the intercepts.
3. Clear fractions to obtain the smallest whole numbers.
4. Write the result as (h k l).

A plane parallel to an axis has an infinite intercept along that axis. Its reciprocal therefore becomes zero.

29. Crystal Defects

An ideal crystal would have a perfectly regular arrangement of particles. Real crystals contain imperfections called crystal defects.

Defects can affect density, electrical conductivity, diffusion, colour and mechanical properties.

Main types

• Point defects
• Line defects
• Surface defects
• Volume defects

In introductory solid-state chemistry, point defects are particularly important.

Point defect

A point defect is a localized imperfection involving one or a few lattice positions.

30. Stoichiometric Defects

Stoichiometric defects do not disturb the ideal ratio of positive and negative ions in an ionic crystal.

1. Vacancy defect

A vacancy defect occurs when an atom or ion is missing from its normal lattice position.

The number of missing positive and negative ions can maintain electrical neutrality.

2. Interstitial defect

An interstitial defect occurs when an extra particle occupies an interstitial space between normal lattice positions.

Schottky defect

In an ionic crystal, equal numbers of cations and anions are absent from their normal lattice sites.

Electrical neutrality is maintained, but the density decreases because some ions are missing.

Typical example: NaCl.

Frenkel defect

A smaller ion, usually a cation, leaves its normal lattice position and occupies an interstitial site.

No ion is actually lost from the crystal, so density remains approximately unchanged.

Typical examples include AgCl and ZnS.

31. Non-Stoichiometric Defects

Non-stoichiometric defects produce a deviation from the ideal ratio of ions or atoms in the solid.

Metal excess defect

A crystal can show metal excess when there are additional positive charge centres balanced by electrons or other defects.

One common mechanism involves anion vacancies.

An anion vacancy may trap an electron and behave as a colour centre.

Metal deficiency defect

In some solids, the number of metal ions is less than required by the ideal stoichiometric formula.

This can occur when some metal ions have different oxidation states and the overall electrical neutrality is maintained.

32. Electrical Properties of Solids

Solids can be classified according to their ability to conduct electricity.

Conductors

Conductors contain mobile charge carriers and conduct electricity readily.

Metals such as copper and aluminium are good conductors.

Insulators

Insulators have very few freely mobile charge carriers.

Glass and many plastics are examples.

Semiconductors

Semiconductors have electrical conductivity between that of conductors and insulators.

Silicon and germanium are important examples.

Intrinsic semiconductor

A pure semiconductor is called an intrinsic semiconductor.

Extrinsic semiconductor

A semiconductor whose conductivity is modified by adding a small amount of impurity is called an extrinsic semiconductor.

n-type semiconductor

Doping with a suitable higher-valency impurity can provide additional electrons.

Electrons are the major charge carriers.

p-type semiconductor

Doping with a suitable lower-valency impurity produces electron vacancies called holes.

Holes act as the major charge carriers.

33. Magnetic Properties of Solids

Magnetic behaviour depends mainly on the arrangement and spin of electrons.

Diamagnetic substances

Diamagnetic substances contain no unpaired electrons and are weakly repelled by an external magnetic field.

Paramagnetic substances

Paramagnetic substances contain one or more unpaired electrons and are attracted by a magnetic field.

Ferromagnetic substances

Ferromagnetic substances show strong attraction toward a magnetic field and can retain magnetization.

Iron, cobalt and nickel are common examples.

34. Worked Numericals

Numerical 1: Surface tension

A force of 0.072 N acts along a line of length 0.30 m on a liquid surface. Calculate surface tension.

Numerical 2: Capillary rise

A liquid has surface tension 0.072 N m⁻¹, density 1000 kg m⁻³ and contact angle 0°. If the capillary radius is 0.0005 m, calculate the height of rise.

Numerical 3: Atoms in BCC

Calculate the number of atoms present in a BCC unit cell.

Numerical 4: Density of a cubic crystal

A metal crystallizes in a BCC structure. Its molar mass is 56 g mol⁻¹ and the edge length is 288 pm. Calculate its theoretical density.

Numerical 5: Number of tetrahedral voids

If a close-packed arrangement contains 100 particles, calculate the number of tetrahedral and octahedral voids.

Numerical 6: BCC radius

Calculate the atomic radius of a BCC crystal whose edge length is 300 pm.

Numerical 7: FCC radius

An FCC crystal has an edge length of 400 pm. Calculate the atomic radius.

35. Common Mistakes

Liquid state

• Do not confuse surface tension with viscosity.
• Do not say viscosity increases with temperature for ordinary liquids.
• Do not confuse evaporation with boiling.
• Remember that boiling occurs throughout the liquid.
• Do not forget cosθ in the capillary-rise equation.
• Keep units consistent in viscosity and surface-tension calculations.

Solid state

• Do not confuse crystalline and amorphous solids.
• Remember that a corner atom contributes 1/8.
• A face-centred atom contributes 1/2.
• An edge atom contributes 1/4.
• A body-centred atom contributes 1.
• BCC contains 2 atoms per unit cell.
• FCC contains 4 atoms per unit cell.
• Simple cubic contains 1 atom per unit cell.
• BCC atoms touch along the body diagonal.
• FCC atoms touch along the face diagonal.
• Schottky defect decreases density.
• Frenkel defect does not significantly change density.
• Do not forget to convert pm or Å into cm when calculating density in g cm⁻³.

36. TU Examination Preparation

Important 2-mark questions

1. Define surface tension.
2. What is viscosity?
3. Define vapour pressure.
4. What is capillary action?
5. Define crystal lattice.
6. What is a unit cell?
7. Define coordination number.
8. What is packing efficiency?
9. What are tetrahedral voids?
10. What are octahedral voids?
11. Define Schottky defect.
12. Define Frenkel defect.
13. What is an amorphous solid?
14. What is a semiconductor?

Important 5-mark questions

1. Explain surface tension and discuss the factors affecting it.
2. Explain viscosity and derive or state the relation for Newton's law of viscosity.
3. Explain capillary action and derive the expression for capillary rise.
4. Distinguish between crystalline and amorphous solids.
5. Explain simple cubic, BCC and FCC unit cells.
6. Explain Schottky and Frenkel defects.
7. Explain the seven crystal systems.

Important 10-mark questions

1. Explain the liquid state with reference to vapour pressure, surface tension, viscosity, evaporation, boiling and capillary action.
2. Explain crystal lattice, unit cell, crystal systems and Bravais lattices in detail.
3. Explain simple cubic, BCC and FCC structures and derive their coordination numbers and packing efficiencies.
4. Derive the density equation for a cubic unit cell and solve related numerical problems.
5. Explain different types of crystal defects with suitable examples.
6. Discuss the electrical and magnetic properties of solids.

Very important numerical areas

• Surface tension
• Capillary rise
• Viscosity
• Stokes' law
• Atoms per unit cell
• Coordination number
• Packing efficiency
• Radius-edge relationship
• Density of unit cell
• Number of tetrahedral and octahedral voids

37. Quick Revision

Liquid state

Solid state

Defect revision

• Schottky → ions missing → density decreases.
• Frenkel → ion displaced to interstitial site → density essentially unchanged.
• Vacancy → missing particle.
• Interstitial → extra particle in an interstitial site.
• Metal excess → excess metal character due to defects/electrons.
• Metal deficiency → fewer metal ions with charge balance maintained by oxidation states.

38. Quick Check

Select the correct answer. These questions are mainly for quick revision before an exam.