States of Matter and Physical Properties

States of Matter

• All matter exists in three states: gas, liquid, and solid.
  • Gas:
  • Consists of molecules separated widely in empty space.
  • Molecules are free to move about throughout the container.
  • Liquid:
  • Molecules are in contact with each other.
  • Intermolecular spaces permit the movement of molecules throughout the liquid.
  • Solid:
  • Molecules, atoms, or ions are arranged in a specific order in fixed positions of a crystal lattice.
  • Particles are not free to move but vibrate in their fixed positions.
• Of the three states of matter, the gaseous state is the most studied and best understood.

Gaseous State

General Characteristics of Gases

1. Expansibility:
   • Gases have limitless expansibility.
   • They expand to fill the entire vessel they are placed in.
2. Compressibility:
   • Gases are easily compressed by the application of pressure to a movable piston fitted in the container.
3. Diffusibility:
   • Gases can diffuse rapidly through each other to form a homogeneous mixture.
4. Pressure:
   • Gases exert pressure on the walls of the container in all directions.
5. Effect of Heat:
   • When a gas confined in a vessel is heated, its pressure increases.
   • Upon heating in a vessel fitted with a piston, the volume of the gas increases.

Parameters of a Gas

• A gas sample can be described in terms of four parameters (measurable properties): a) Volume, V:
  • The volume of the container is the volume of the gas sample.
  • Units: litres (L), millilitres (ml), cubic metres (m³).
  • Relation: 1 litre (L) = 1000.028 cc.
    b) Pressure, P:
  • Defined as the force exerted by the impacts of its molecules per unit surface area in contact.
  • 1 atm = 760 mm Hg = 760 torr = 1.013 × 10⁵ Pa.
    c) Temperature, T:
  • Measured in degrees Celsius (°C) or Kelvin (K).
  • K = °C + 273 (no degree sign is used with K).
    d) Number of Moles, n:
  • Can be found using: n = \frac{m}{M}
    • Where m = mass of the sample, M = molar mass of the gas.

Ideal/Universal Gas Law

• States that the volume of a given amount of gas is directly proportional to the number of moles of gas and temperature, and inversely proportional to pressure.
• Mathematical expression: PV = nRT
  • Where P = pressure, V = volume, n = number of moles, R = gas constant, T = temperature.
• Gas Constants Values:
  • R = 0.0821 \, \text{litre-atm K}^{-1} \text{mol}^{-1}
  • R = 8.314 imes 10^7 \, \text{erg K}^{-1} \text{mol}^{-1}
  • R = 8.314 \, \text{Joule K}^{-1} \text{mol}^{-1}
  • R = 82.1 \, \text{ml-atm K}^{-1} \text{mol}^{-1}
  • R = 62.3 \, \text{litre-mm Hg K}^{-1} \text{mol}^{-1}
  • R = 1.987 \, \text{cal K}^{-1} \text{mol}^{-1}

Kinetic Molecular Theory of Gases

• Developed by Maxwell and Boltzmann (1859) to explain the behavior of gases and gas laws.
• Based on the concept that gases consist of a large number of molecules in perpetual motion.

Assumptions of the Kinetic Molecular Theory

1. A gas consists of extremely small discrete particles called molecules dispersed throughout the container, with negligible actual volume compared to the total volume of the gas.
2. Gas molecules are in constant random motion with high velocities, moving in straight lines and changing direction when colliding with other molecules or container walls.
3. The distance between molecules is large enough that van der Waals attractive forces are assumed not to exist, allowing free movement independent of one another.
4. All collisions are perfectly elastic, resulting in no kinetic energy loss during a collision.
5. The pressure exerted by a gas is caused by collisions of molecules with the walls of the container.
6. The average kinetic energy of gas molecules is directly proportional to absolute temperature (T).

Ideal Gases vs Real Gases

• An ideal gas conforms to all assumptions of the kinetic theory of gases under all conditions of temperature and pressure.
• Real gases differ from ideal gases as follows:
  a) Ideal gases have negligible molecular volume, whereas real gases have appreciable volume.
  b) No attractive forces exist between ideal gas molecules, while real gases do have attractive forces.
  c) Molecular collisions in ideal gases are perfectly elastic, which is not always the case in real gases.
• Real gases obey gas laws under moderate temperature and pressure but deviate significantly at low temperatures and high pressures.

Kinetic Gas Equation

• Developed from the kinetic molecular theory, expressing PV of a gas in terms of molecules, molecular mass, and molecular velocity: PV = \frac{2}{3} nmu
  • Where:
    • m = mass of one molecule.
    • u = root mean square velocity of the gas molecules.

Liquid State

• Molecules are in contact with each other and are held by strong intermolecular forces.
• Molecules move past one another through intermolecular spaces, controlling physical properties.

Physical Properties of Liquid State

A) Vapour Pressure

• The process of molecules transitioning from the liquid to the gaseous state is called vaporization or evaporation; the reverse is called condensation.
• In a closed vessel, high kinetic energy molecules escape into space, leading to dynamic equilibrium between liquid and vapour phases.
  • Vapour pressure definition: the pressure exerted by the vapour in equilibrium with the liquid at a set temperature.

Effect of Temperature on Vapour Pressure

• Increasing liquid temperature raises vapour pressure because higher kinetic energy allows more molecules to escape into the gas phase.
• Boiling point is defined as the temperature at which the vapour pressure equals atmospheric pressure (1 atm or 760 torr).
• Example: Water boils at 100°C at sea level, and pressure variation affects the boiling point (e.g., decreases at higher elevations).

B) Surface Tension (γ)

• Describes the elastic behavior of the surface layer of a liquid due to intermolecular forces.
• Liquid molecules at the surface experience inward pull because there are no balancing forces, causing contraction to minimize surface area.
• Defined as the force per unit length required to counterbalance the net inward pull.
• Units:
  • CGS: dynes cm⁻¹.
  • SI: N m⁻¹.
• Temperature effect: Surface tension decreases with increased temperature due to higher molecular kinetic energy reducing intermolecular force impacts.

C) Viscosity (η)

• Viscosity measures a fluid's resistance to flow, indicating internal friction.
• Higher viscosity means more resistance to flow.
• Defined by the relation between force, area, and velocity difference.
  • F = ηA \frac{dv}{dx}
• Units of viscosity:
  • CGS: g cm⁻¹ s⁻¹ (poise), with smaller units centipoise (10⁻² poise) and millipoise (10⁻³ poise).
  • SI: kg m⁻¹ s⁻¹.
  • 1 poise = 1 g cm⁻¹ s⁻¹ = 0.1 kg m⁻¹ s⁻¹.
• Effect of temperature: Viscosity generally decreases with temperature increase (% decrease per °C increase).
• Measurement: Viscosity can be determined using Poiseuille’s equation:
  • 
    ext{time} \left ( t \right ) = \frac{8lV}{\pi Pr}
    
  • Where
    • t = time of flow,
    • V = volume,
    • P = pressure-head (fluid height),
    • r = radius of the tube,
    • l = length of tube.
• Relative viscosity can be determined with respect to water flow times.
• Example Problem: Calculation of ethanol viscosity using Ostwald viscometer.

D) Refractive Index (n)

• Defined as the ratio of the velocity of light in vacuum to its velocity in the substance.
• Change in light direction when passing from air into a liquid is called refraction.
• Knows relation with Snell’s Law:
  • n = \frac{\sin i}{\sin r}
  • Where i = angle of incidence, r = angle of refraction.

E) Optical Activity

• Describes when plane-polarized light is rotated by certain organic compounds possessing a chiral carbon.
• Types:
  • Levorotatory (l): Rotates light to the left (anticlockwise).
  • Dextrorotatory (d): Rotates light to the right (clockwise).

Solid State

• Atoms, ions, and molecules are held together by strong chemical forces (ionic, covalent).
• Solids are rigid with definite shape and do not translate, only vibrate in fixed positions.

Types of Solids

a) Crystalline Solids (True Solids):

• Exist as small crystals in a repeating three-dimensional pattern (crystal lattice).
• Example: Sugar, salt.
  b) Amorphous Solids:
• Have random arrangements and lack regular crystalline structure.
• Examples: Rubber, plastics, glass, and termed super-cooled liquids.

Anisotropy and Isotropy

• Anisotropic Crystalline solids exhibit directional property differences (physical properties vary with direction).
• Isotropic Amorphous solids display uniform properties in all directions due to random arrangement.

Characteristics of Crystals

• Habit: External shape of the crystal.
• Faces: Plane surfaces of a crystal.
• Interfacial Angles: Angles between faces that are consistent for a given crystalline substance.

Symmetry in Crystals

• Types of symmetry elements:
  1. Plane of Symmetry: Divides crystal into equal mirror-image parts.
  2. Axis of Symmetry: Imaginary line for rotational symmetry (two-fold, three-fold, etc.).
  3. Centre of Symmetry: Point where equal distances from any line drawn through it meet the surface.

Crystal Structure

• Crystal Lattice: Arrangement of particles in patterns extending in all directions.
• Unit Cells: Fundamental repeating units in a crystal lattice.
  • Parameters defined by lengths (a, b, c) and angles (α, β, γ).
• Bravais Lattices: Seven basic unit cell types categorized by relative axial lengths and angles.

Types of Unit Cells

1. Cubic:
   • • Simple cubic: 8 corner atoms (equiv. 1 atom).
   • Body-centered cubic: 8 corner + 1 center (equiv. 2 atoms).
   • Face-centered cubic: 8 corners + 6 faces (equiv. 4 atoms).
2. Coordination Number: Number of adjacent particles in the lattice.
   • Coordination number for simple cubic = 6, body-centered = 8, face-centered = 12.

Classification of Crystals Based on Bonds

1. Ionic Crystals:
   • Formed by positive and negative ions held by ionic bonds.
   • Properties:
     • High melting and boiling points (extensive energy needed).
     • Hard and brittle (strong attractions cause brittleness under pressure).
2. Molecular Crystals:
   • Formed by molecules held by van der Waals forces, resulting in low melting points.
3. Network Covalent Crystals:
   • Atoms bonded by covalent bonds, producing a giant molecule (example: diamond).
4. Metallic Crystals:
   • Lattice composed of atoms with delocalized valence electrons, explaining electrical conductivity.

Crystal Defects

• Real crystals contain defects that affect physical/chemical properties:
  a) Vacancy Defect: Caused by structural unit removal (e.g., Schottky defect).
  b) Interstitial Defect: Ion occupies interstitial spaces in the lattice (e.g., Frenkel defect).
  c) Impurity Defect: Foreign atoms occupy regular or interstitial sites.

Metal Alloys

• Produced by introducing elements into a metallic crystal:
  • Substitutional Alloy: Host metal replaces similar-sized atoms (e.g., brass).
  • Interstitial Alloy: Small atoms occupy interstitial spaces (e.g., steel).

Semiconductors

• Elements like silicon and germanium are nonconductors, but conductivity improves with impurity addition:
  a) n-type Semiconductors: Excess negative charge flow (e.g., arsenic in silicon).
  b) p-type Semiconductors: Positive holes arise (e.g., boron in silicon).
• Applications: Used in modern electronic devices (e.g., rectifiers, transistors).

Liquid Crystals

• Exhibit properties between liquids and crystalline solids.
• Orientation of molecules is crystal-like but flows like a liquid.
• Applications involve technology in displays.

Polymorphism

• Occurrence of multiple crystalline forms for the same substance.
• Allotropes: Specific term used for elements with different forms.

Classification of Allotropy

1. Enantiotropy: Reversible transition between forms at specific temperatures (e.g., sulphur).
2. Monotropy: One stable form changes to another at all temperatures without reversal.
3. Dynamic Allotropy: Coexisting forms in equilibrium across temperature range.