Ideal gases

• Absolute Zero


  • The pressure exerted by a gas on its container depends on the temperature of the gas
  • Particles move with more energy as temperature increases, so as the temperature of the gas decreases, the pressure on the container also decreases
  • Absolute zero is the temperature at which gas particles exert no pressure, as they are no longer moving and colliding with their container
  • Absolute zero is equal to -273 °C and is defined as the temperature at which the molecules in a substance have zero kinetic energy, making it impossible to have a lower temperature
• Kinetic Theory of Gases

  • Molecules in a gas are in constant random motion at high speeds
  • Random motion means that the molecules are travelling in no specific path and undergo sudden changes in their motion if they collide with the walls of its container or with other molecules
  • The random motion of tiny particles in a fluid is known as Brownian motion
  • Brownian motion provides evidence that air is made of small particles because larger particles move with random motion when observed floating in the air
• Pressure

  • A feature of gases is that they fill their container
  • The pressure is defined as the force per unit area
  • Gas particles collide with the walls of their containers producing a net force at right angles to the wall, so a gas at high pressure has more frequent collisions with the container walls and a greater force
  • Higher pressure results in a higher force exerted per unit area
• The Kelvin Scale

  • Begins at absolute zero
  • 0 K is equal to -273 °C
  • An increase of 1 K is the same change as an increase of 1 °C
  • It is not possible to have a temperature lower than 0
• Gas molecules bouncing off the walls of a container can be felt by closing the mouth and forcing air into the cheeks, causing strain due to the force of the gas particles pushing at right angles to the cheeks
• Contents of Ideal Gases

  • Kinetic Theory
  • Absolute Zero
  • Temperature
  • The Gas Laws
  • The Pressure Law
  • Boyle's Law
• An increase of 1 K is the same change as an increase of 1 °C
• When a liquid evaporates, molecules escape from the surface of the liquid. The average kinetic energy per molecule decreases
• Temperature conversion between Celsius and Kelvin

  1. θ / C = T / K − 273

  2. T / K = θ / C + 273
• It is not possible to have a temperature lower than 0 K
• The Kelvin temperature scale begins at absolute zero
• The temperature (in Kelvin) is proportional to the average kinetic energy of the molecules


  T ∝ KE
• Conversion chart relating the temperature on the Kelvin and Celsius scales

  • The divisions on both scales are equal
• 0 K is equal to -273 °C
• This means a temperature in Kelvin will never be a negative value
• A change in temperature of 1 K is equal to a change in temperature of 1 °C
• Temperature is proportional to the average kinetic energy per molecule


  The temperature also decreases
• Pressure & Temperature

  1. As the temperature of a gas increases, the average speed of the molecules also increases

  2. Since the average kinetic energy depends on their speed, the kinetic energy of the molecules also increases if its volume remains constant

  3. The hotter the gas, the higher the average kinetic energy

  4. The cooler the gas, the lower the average kinetic energy

  5. If the gas is heated up, the molecules will travel at a higher speed, colliding with the walls more often, creating an increase in pressure

  6. At a constant volume, an increase in temperature increases the pressure of a gas and vice versa
• At constant volume, an increase in the temperature of the gas increases the pressure due to more collisions on the container walls
• Pressure increases when a gas is compressed
• Pressure & Volume

  1. If the temperature of a gas remains constant, the pressure of the gas changes when it is compressed - decreases the volume which increases the pressure

  2. If the temperature of a gas remains constant, the pressure of the gas changes when it is expanded - increases the volume which decreases the pressure
• Since the more energetic molecules have left

  The average kinetic energy per molecule must decrease
• If the gas is compressed, the molecules will hit the walls of the container more frequently, creating a larger overall net force on the walls which increases the pressure
• Diagram B shows that since the temperature is proportional to the pressure, the graph against each is a straight line
• The relationship between the pressure and (Kelvin) temperature for a fixed mass of gas at constant volume can also be written as
• When evaporation takes place

  The more energetic molecules are leaving the surface of the liquid
• Gas laws provide explanations for the relationships between:
• A vacuum pump can be used to remove the air from a sealed container
• If the volume V of an ideal gas is constant, the pressure law is given by: P ∝ T
• Diagram A shows molecules in the same volume collide with the walls of the container more with an increase in temperature
• Boyle's Law equation for comparing pressure and volume before and after a change in a gas

  P1V1 = P2V2
• When the volume decreases (compression)

  The pressure increases
• Pressure law relationship

  P ∝ T
• Boyle's Law equation

  PV = PV
• Pressure and temperature relationship

  P = initial pressure (Pa), P = final pressure (Pa), T = initial temperature (K), T = final temperature (K)
• Increasing the volume of a gas

  Decreases its pressure
• Boyle's Law

  For a fixed mass of a gas held at a constant temperature: pV = constant. This means that the pressure and volume are inversely proportional to each other
• When using gas law, the temperature T must always be in kelvin (K)
• When the volume increases (expansion)

  The pressure decreases
• Pressure law graph represents temperature (in °C) directly proportional to the volume