Theory Exercises

Molecular Theory of Matter

The kinetic molecular theory explains the behavior of matter by describing the motion and interactions of particles (atoms and molecules). This theory helps us understand why different states of matter have different properties.

Basic Assumptions of Kinetic Molecular Theory

1. All Matter is Made of Particles

  • Matter consists of tiny particles (atoms, molecules, or ions)
  • These particles are incredibly small and invisible to the naked eye
  • The space between particles is much larger than the particles themselves

2. Particles are in Constant Motion

  • All particles are constantly moving
  • This motion is random and occurs in all directions
  • Even in solids, particles vibrate around fixed positions
  • Motion never stops, even at very low temperatures

3. Kinetic Energy and Temperature

  • The average kinetic energy of particles is directly proportional to temperature
  • Higher temperature = faster particle movement
  • Lower temperature = slower particle movement
  • At absolute zero (-273°C), particle motion theoretically stops

4. Intermolecular Forces

  • Particles experience attractive and repulsive forces
  • These forces determine how particles interact with each other
  • Strength of forces varies between different substances
  • Forces become weaker as distance between particles increases
Example: Explaining diffusion with kinetic theory
Observation: A drop of food coloring spreads throughout a glass of water. Kinetic theory explanation:
  1. Constant motion: Both water molecules and dye molecules are constantly moving
  2. Random direction: Particles move in all directions randomly
  3. Collisions: Particles collide with each other, changing directions
  4. Net spreading: Over time, dye molecules spread from high concentration to low concentration
  5. Equilibrium: Eventually, dye molecules are evenly distributed
Key insight: No external force is needed - diffusion happens due to natural particle motion!

Particle Behavior in Different States

Solids

  • Particle arrangement: Ordered, fixed positions in a lattice structure
  • Particle motion: Vibration around fixed positions
  • Kinetic energy: Low (limited movement)
  • Intermolecular forces: Very strong, hold particles in place
  • Distance between particles: Very small, particles touching

Liquids

  • Particle arrangement: Less ordered, particles can move around each other
  • Particle motion: Translation and rotation, sliding past neighbors
  • Kinetic energy: Medium (moderate movement)
  • Intermolecular forces: Moderate, allow movement while maintaining proximity
  • Distance between particles: Small, particles close but mobile

Gases

  • Particle arrangement: Random, no fixed structure
  • Particle motion: Rapid, straight-line motion in all directions
  • Kinetic energy: High (fast, random movement)
  • Intermolecular forces: Very weak or negligible
  • Distance between particles: Large, mostly empty space

Temperature and Kinetic Energy

Absolute Temperature Scale

The Kelvin scale directly relates to average kinetic energy:
  • 0 K (-273°C): Absolute zero, theoretical minimum kinetic energy
  • Higher K: Greater average kinetic energy
  • Relationship: KE ∝ T (kinetic energy proportional to absolute temperature)

Distribution of Kinetic Energies

  • Not all particles have the same kinetic energy at a given temperature
  • Maxwell-Boltzmann distribution describes energy spread
  • Some particles have higher energy, some lower than average
  • Higher temperature spreads the distribution to higher energies

Pressure and Molecular Motion

Origin of Gas Pressure

  • Pressure results from particle collisions with container walls
  • More frequent collisions = higher pressure
  • Faster-moving particles = greater force per collision
  • Pressure = Force/Area from molecular impacts
Example: Why heating a gas increases pressure
Scenario: A sealed container of gas is heated. Step-by-step explanation:
  1. Heat added: Energy is transferred to gas particles
  2. Increased kinetic energy: Particles move faster on average
  3. Faster collisions: Particles hit container walls more frequently
  4. Greater force: Each collision has more energy/force
  5. Higher pressure: More force per unit area on walls
Mathematical relationship: P ∝ T (Gay-Lussac's Law)

Explaining Physical Properties

Diffusion

  • Definition: Mixing of particles due to random motion
  • Cause: Constant, random particle movement
  • Rate factors: Temperature, particle size, medium density
  • Examples: Perfume spreading, food coloring in water

Thermal Expansion

  • Higher temperature increases particle motion
  • Greater motion requires more space
  • Materials expand when heated, contract when cooled
  • Gases expand most, solids least