Kinetic Molecular Theory

Kinetic-Molecular Theory of Matter

Objectives

• State the kinetic-molecular theory of matter and explain how it describes properties of matter.

• List the five assumptions of the kinetic-molecular theory of gases.

• Define ideal gas and real gas.

• Describe gas properties: expansion, density, fluidity, compressibility, diffusion, and effusion.

• Describe conditions where real gases deviate from ideal behavior.

The Kinetic-Molecular Theory

• Based on the idea that particles are always in motion.

• Explains properties of solids, liquids, and gases using particle energy and forces between them.

The Kinetic-Molecular Theory of Gases

• Ideal Gas: A hypothetical gas that perfectly fits all KMT assumptions.

• KMT Assumptions:

  1. Gases consist of many tiny particles far apart relative to their size.

     • Most of the volume is empty space.

  2. Collisions between gas particles and container walls are elastic collisions.

     • Elastic Collision: No net loss of total kinetic energy.

  3. Gas particles are in continuous, rapid, random motion, possessing kinetic energy (KE).

  4. There are no forces of attraction between gas particles.

  5. The temperature of a gas measures the average kinetic energy of the particles.

     • Gas particles have kinetic energy KE = \frac{1}{2}mv^2

• All gases at the same temperature have the same average kinetic energy.

• Lighter gas particles have higher average speeds than heavier ones at the same temperature.

• Hydrogen molecules have higher speeds than oxygen molecules at the same temperature.

KMT and the Nature of Gases

• KMT applies only to ideal gases.

• Many gases behave nearly ideally at low pressure and high temperature.

Expansion

• Gases lack definite shape or volume.

• They fill any container completely.

• Gas particles move rapidly in all directions with insignificant attraction between them.

Fluidity

• Attractive forces between gas particles are insignificant, allowing them to glide past one another easily.

• Liquids and gases are both fluids because they flow.

Low Density

• Gaseous substance density at atmospheric pressure is about 1/1000 the density of the same substance in liquid or solid state.

• This is because particles are much farther apart in the gaseous state.

Compressibility

• During compression, gas particles, initially far apart, are crowded closer together.

Diffusion and Effusion

• Random and continuous motion carries gas molecules throughout available space and mix with one another, even without being stirred.

• Diffusion: Spontaneous mixing of particles of two substances caused by their random motion.

• Effusion: Process by which gas particles pass through a tiny opening.

• Effusion rates of different gases are directly proportional to their particle velocities.

• Lower mass molecules effuse faster than higher mass molecules.

Deviations of Real Gases from Ideal Behavior

• All real gases deviate from ideal gas behavior.

• Real Gas: A gas that does not behave completely according to KMT assumptions.

• Gases are most likely to behave non-ideally at very high pressures and low temperatures.

• The more polar a gas's molecules are, the more it deviates from ideal behavior.

Liquids

Objectives

• Describe particle motion and liquid properties according to KMT

• Discuss liquid-to-gas change (vaporization). Define vaporization.

• Discuss liquid-to-solid change (freezing). Define freezing.

Properties of Liquids and KMT

• Liquid: Form of matter with definite volume that takes the shape of its container.

• Attractive forces between liquid particles are more effective than in gases.

• Attraction caused by intermolecular forces:

  • London dispersion forces

  • Dipole-dipole forces

  • Hydrogen bonding

Review of Intermolecular Forces (IMF)

• London Dispersion Forces

  • Present between non-polar molecules.

  • Weak forces from temporary shifts in electron density.

• Dipole-Dipole Forces

  • Attractions between oppositely charged regions of polar molecules.

• Hydrogen Bonds

  • Occur between molecules with hydrogen bonded to a small, highly electronegative atom (N, O, F) with at least one lone electron pair.

Properties of Liquids and KMT

• Particles in a liquid are not bound in fixed positions; they move constantly.

• Liquids are fluids: Substances that can flow and take the shape of their container.

• Relatively High Density

  • At normal atmospheric pressure, substances are hundreds of times denser in the liquid state than in the gaseous state.

• Relative Incompressibility

  • Liquids are much less compressible than gases because liquid particles are more closely packed.

• Ability to Diffuse

  • Liquids gradually diffuse throughout other liquids in which they can dissolve.

  • Constant, random motion of particles causes diffusion in liquids.

Properties of Liquids and KMT

• Diffusion is slower in liquids than in gases.

  • Liquid particles are closer together.

  • Attractive forces slow movement.

  • Increased temperature increases diffusion rate.

• Surface Tension

  • Force that pulls adjacent parts of a liquid's surface together, minimizing surface area.

  • Stronger attraction between particles leads to higher surface tension.

• Capillary Action

  • Attraction of liquid surface to solid surface.

  • Pulls liquid molecules upward, against gravity, causing meniscus formation in a test tube or graduated cylinder.

• Evaporation and Boiling

  • Vaporization: Process by which a liquid or solid changes to a gas.

  • Evaporation: Particles escape from the surface of a nonboiling liquid and enter the gas state.

  • Boiling: Change of a liquid to bubbles of vapor throughout the liquid.

  • Evaporation occurs because particles have different kinetic energies.

• Formation of Solids

  • Cooling a liquid decreases the average energy of its particles.

  • Freezing/Solidification: Physical change of liquid to solid by removing energy as heat.

Solids

Objectives

• Describe particle motion and solid properties according to KMT.

• Distinguish between two types of solids.

• Describe different types of crystal symmetry.

• Define crystal structure and unit cell.

Properties of Solids and KMT

• Solid particles are more closely packed than in liquids or gases.

• Stronger intermolecular forces than in corresponding liquids or gases.

• Particles vibrate in relatively fixed positions.

• Solids are more ordered than liquids and gases.

Types of Solids

• Crystalline Solids: Particles arranged in an orderly, geometric, repeating pattern (crystals).

• Amorphous Solids: Particles arranged randomly (sometimes classified as supercooled liquids).

Properties of Solids

• Definite Shape and Volume

  • Maintain definite shape without a container.

  • Have definite volume because particles are closely packed.

• Definite Melting Point (crystalline solid)

  • Melting: Physical change of solid to liquid by adding energy as heat.

  • At the melting point, kinetic energies of particles overcome attractive forces.

• Amorphous solids have no definite melting point due to their random structure.

• High Density and Incompressibility

  • Generally most dense in solid state due to close packing.

  • Considered incompressible for practical purposes.

• Low Rate of Diffusion

  • Diffusion rate is millions of times slower in solids than in liquids.

Crystalline Solids

• Crystal Structure: Total three-dimensional arrangement of particles in a crystal.

• Lattice: Coordinate system representing particle arrangement.

• Unit Cell: Smallest portion of a crystal lattice showing the three-dimensional pattern of the entire lattice.

Types of Crystalline Solids

• Atomic

  • Unit Particles: Atoms

  • Characteristics: Soft to very soft; very low melting points; poor conductivity

  • Examples: Group 18 elements

• Molecular

  • Unit Particles: Molecules

  • Characteristics: Fairly soft; low to moderately high melting points; poor conductivity

  • Examples: I2, H2, O2, NH3, CO2, C{12}H{22}O{11} (table sugar)

• Covalent Network

  • Unit Particles: Atoms connected by covalent bonds

  • Characteristics: Very hard; very high melting points; often poor conductivity

  • Examples: Diamond (C) and quartz (SiO_2)

• Ionic

  • Unit Particles: Ions

  • Characteristics: Hard; brittle; high melting points; poor conductivity

  • Examples: NaCl, KBr, CaCO3

• Metallic

  • Unit Particles: Atoms surrounded by mobile valence electrons

  • Characteristics: Soft to hard; low to very high melting points; malleable and ductile; excellent conductivity

  • Examples: All metallic elements

Binding Forces in Crystals

1. Ionic Crystals

   • Positive and negative ions arranged in a regular pattern.

   • Ex: NaCl, KBr, CaCO3 (generally group 1 or 2 metals and gr 16/17 nonmetals or polyatomic ions)

   • Properties:

     • Hard and brittle

     • High melting points

     • Good insulators

2. Covalent Network Crystals

   • Each atom is covalently bonded to its nearest neighboring atoms.

   • Ex: Diamond (C) and quartz (SiO_2)

   • The covalent bonding extends throughout a network that includes a very large number of atoms.

   • Properties:

     • Very hard and brittle,

     • High melting points

     • Usually nonconductors or semiconductors.

3. Metallic Crystals

   • Metal cations surrounded by a sea of delocalized valence electrons.

   • Ex: All metallic elements (Fe, Au, Ag, etc)

   • The electrons come from the metal atoms and belong to the crystal as a whole.

   • The freedom of these delocalized electrons to move throughout the crystal explains the high electric conductivity of metals.

4. Covalent Molecular Crystals

   • Covalently bonded molecules held together by intermolecular forces.

   • Ex: C{12}H{22}O_{11} (table sugar)

   • Nonpolar molecules are held together by only weak London dispersion forces.

   • Polar molecules are held together by dispersion forces, by dipole-dipole forces, and sometimes by hydrogen bonding.

   • Properties:

     • Low melting points

     • Easily vaporized

     • Relatively soft, and are good insulators.

Changes of State

Objectives

• Explain the relationship between equilibrium and changes of state.

• Interpret phase diagrams.

• Explain what is meant by equilibrium vapor pressure.

• Describe the processes of boiling, freezing, melting, and sublimation.

Possible Changes of State

• Solid → liquid: Melting (ice → water)

• Solid → gas: Sublimation (dry ice → CO_2 gas)

• Liquid → solid: Freezing (water → ice)

• Liquid → gas: Vaporization (liquid bromine → bromine vapor)

• Gas → liquid: Condensation (water vapor → water)

• Gas → solid: Deposition (water vapor → ice)

Changes of State and Equilibrium

• Phase: Any part of a system that has uniform composition and properties.

• Condensation: Process by which a gas changes to a liquid.

• Vapor: A gas in contact with its liquid or solid phase.

• Equilibrium: A dynamic condition in which two opposing changes occur at equal rates in a closed system.

Liquid-Vapor Equilibrium System

• Rate of condensation = rate of evaporation → equilibrium.

Equilibrium Vapor Pressure of a Liquid

• Equilibrium Vapor Pressure: Pressure exerted by a vapor in equilibrium with its corresponding liquid at a given temperature.

• Equilibrium vapor pressure increases with increasing temperature.

• Increasing temperature increases the average kinetic energy of the liquid's molecules.

• Every liquid has specific equilibrium vapor pressure at a given temperature.

• Volatile Liquids: Liquids that evaporate readily, having relatively weak attractive forces.

  • Example: ether

• Nonvolatile Liquids: Liquids that do not evaporate readily, having relatively strong attractive forces.

  • Example: molten ionic compounds

Boiling

• Boiling: Conversion of a liquid to a vapor within the liquid as well as at its surface.

• Boiling Point: Temperature at which the equilibrium vapor pressure of the liquid equals the atmospheric pressure.

• Lower atmospheric pressure = lower boiling point.

• At the boiling point, temperature remains constant as long as pressure does not change.

• Normal Boiling Point: Boiling point at normal atmospheric pressure (1 atm, 760 torr, or 101.3 kPa).

  • Normal boiling point of water is exactly 100°C (212^\circF).

Molar Enthalpy of Vaporization

The amount of energy as heat that is needed to vaporize one mole of liquid at the liquid’s boiling point at constant pressure is called the liquid’s molar enthalpy of vaporization, \Delta H_v

• Magnitude measures attraction between liquid particles; stronger attraction means higher molar enthalpy of vaporization.

Freezing and Melting

• Freezing: Physical change of liquid to solid.

  • Involves loss of energy as heat: liquid → solid + energy

  • Occurs at constant temperature for pure crystalline substances.

• Melting: Reverse of freezing, also occurs at constant temperature: solid + energy → liquid

• At the freezing/melting point, particles of the liquid and the solid have the same average kinetic energy.

• At equilibrium, melting and freezing proceed at equal rates.

Molar Enthalpy of Fusion

• The amount of energy as heat required to melt one mole of solid at the solid’s melting point is the solid’s molar enthalpy of fusion, \Delta H_f.

• Magnitude depends on the attraction between solid particles.

Sublimation and Deposition

• At sufficiently low temperature and pressure, a liquid cannot exist.

• Under such conditions, a solid substance exists in equilibrium with its vapor instead of its liquid: solid + energy → vapor

• Sublimation: Change of state from solid directly to gas.

• Deposition: Reverse process, change of state from gas directly to solid.

Phase Diagrams

• Phase Diagram: Graph of pressure versus temperature that shows conditions under which phases of a substance exist.

• Triple Point: Temperature and pressure at which solid, liquid, and vapor coexist at equilibrium.

• Critical Point: Indicates the critical temperature and critical pressure.

• Critical Temperature (t_c): Temperature above which the substance cannot exist in the liquid state.

• Critical Pressure (P_c): Lowest pressure at which the substance can exist as a liquid at the critical temperature.

Supercritical Fluids

• Substances that exist above a critical point of pressure and temperature where no separate liquid and gas phases exist.