Gas Laws

• How is the motion of gas molecules described?

  Gas molecules move with Brownian motion
• What causes Brownian motion in gas molecules?

  Collisions with larger particles
• How does a gas exert a force on its container?

  Molecules collide with the walls of the container
• What happens during collisions of gas molecules with the container walls?

  Collisions cause a change in momentum
• What does a change in momentum produce?

  A force equal to the rate of change of momentum
• What does Boyle’s Law state?

  Pressure and volume are inversely proportional
• Under what condition does Boyle's Law apply?

  When a gas is at a constant temperature
• What does Charles’ Law state?

  Volume is directly proportional to absolute temperature
• Under what condition does Charles' Law apply?

  When a gas is at a constant pressure
• What happens when the volume of a gas increases according to Boyle's Law?

  The rate of collisions decreases
• What is the effect of decreased collision rate on pressure?

  It causes a decrease in pressure
• What does the Pressure Law state?

  Pressure is directly proportional to absolute temperature
• What happens as temperature increases according to the Pressure Law?

  The average kinetic energy of molecules increases
• How does increased kinetic energy affect the speed of gas molecules?

  It increases the speed of the molecules
• What compensates for the faster speed of molecules at constant pressure?

  The volume of the gas increases
• What are the assumptions made in kinetic theory about gases?

  • Gas contains a large number of molecules
  • Molecules are identical to each other
  • Collisions are perfectly elastic
  • Time for collisions is negligible
  • No intermolecular forces exist
  • Molecules are in constant random motion
  • Gas particles obey Newton’s Laws of motion
• What happens as temperature increases according to the Pressure Law?

  It increases the rate of collisions
• What does a greater rate of collisions lead to according to the Pressure Law?

  A greater force exerted and increase in pressure
• What are ideal gases in kinetic theory?

  • Follow all assumptions made in kinetic theory
  • Exhibit predictable behavior under various conditions
• What type of motion do gas particles exhibit?

  Constant, random Brownian motion
• What causes gas particles to exert pressure on their containers?

  Collisions with each other and container walls
• What is the formula for pressure in terms of force and area?

  P = F/A
• What does impulse equal in a force-time graph?

  Area under the force-time graph
• Why do gas particles take a random path?

  Due to constant collisions changing direction
• What is the relationship between displacement and the number of steps taken?

  Displacement ∝ $d/\sqrt{\text{number of steps}}$
• What does Boyle's Law state about pressure and volume at constant temperature?

  • Pressure (p) and volume (V) are inversely proportional
  • pV = constant
  • As volume decreases, pressure increases

  
• What does Charles' Law state about volume and temperature at constant pressure?

  • Volume (V) is directly proportional to absolute temperature (T)
  • V/T = constant
• What does the Pressure Law state about pressure and temperature at constant volume?

  • Pressure (p) is directly proportional to absolute temperature (T)
  • p/T = constant
• What are the assumptions of ideal gases in Kinetic Theory?

  • Large number of identical molecules
  • Perfectly elastic collisions
  • Negligible collision time
  • No intermolecular forces
  • Constant random motion
  • Obey Newton's Laws of motion
• What is the ideal gas equation?

  pV = nRT
• What does each variable in the ideal gas equation represent?

  p = pressure, V = volume, n = moles, R = gas constant, T = temperature
• What is the value of the gas constant R?

  1. 8.31 J/(mol·K)
• What is the Boltzmann constant k?

  1. 1.38 x $10^{-23}$ J/K
• How is the ideal gas law derived from the three gas laws?

  • Combine Boyle's, Charles', and Pressure Laws
  • pV = nRT or pV = NkT
• How is pressure related to the motion of gas particles in a cubic box?

  Pressure is ⅓ of total pressure in one dimension
• What happens to momentum during a collision with the wall of a container?

  Momentum changes by $2mc$
• How is force calculated in terms of momentum and time?

  Force = change in momentum/time
• What is the relationship between pressure and volume in the ideal gas equation?

  Pressure is equal to $\frac{mc^2}{3V}$
• What is the internal energy of an ideal gas?

  • Sum of kinetic and potential energies
  • For ideal gases, potential energy is negligible
  • Internal energy = kinetic energy
• How is kinetic energy related to temperature in an ideal gas?

  Kinetic energy is approximated to $\frac{3}{2}kT$