Ideal Gases

The Ideal Gas Model

    Assumptions of Ideal Gases:

  • The intermolecular forces between gas particles are negligible
  • Collisions between gas particles and with their container are perfectly elastic (no energy is lost)
  • Gas particles have negligible volume, as the distance between particles is immensely greater than their size
  • The particles in a gas are in constant, random, straight-line motion
  • The average kinetic energy of the particles in a gas is proportional to the absolute temperature (in Kelvin)

    Real Gases:

  • Non-ideal gases, which do not adhere to the ideal gas model
  • This is primarily due to two factors:
    • High pressure: the particles are very close at high pressure, and can be influenced by forces of attraction
    • Low temperature: the particles move less rapidly (have lower average kinetic energy), hence there is a greater opportunity for intermolecular forces between the particles to have an effect

    Application of Ideal Gases

  • A lot of gases in real life can be approximated by this model, which allows us to relate and calculate important properties such as volume, pressure, and temperature (discussed further down)
  • However, in reality gases do not always act in an ideal way, and the assumptions of the ideal gas model will not hold when gases start behaving like real gases (occurs at high pressures and low temperatures)

Laws and Properties of Ideal Gases

    Ideal Gases at STP

  • STP (standard temperature and pressure): when the temperature is 273K, and the pressure is 100 kPa
  • When at STP, the volume of 1 mole of any gas will always occupy 22.7 cubic decimeters or liters
    • Thus, to calculate the number of moles of a gas at STP, just divide its volume by 22.7

    Boyle’s Law:

  • At constant temperature, the pressure and volume of a fixed mass of an ideal gas are inversely proportional
  • P ∝ 1/V where T = const

    Charles’ Law:

  • At constant pressure, the volume of a fixed mass of an ideal gas is directly proportional to its absolute temperature
  • V ∝ T where P = const

    Gay-Lussac’s Law:

  • At constant volume, the pressure of a fixed mass of an ideal gas is directly proportional to its absolute temperature
  • P ∝ T where V = const

    Combining Gas Laws

  • The Combined Gas Law: (P1 * V1) / T1 = (P2 * V2) / T2
  • The Ideal Gas Law: PV = nRT
    • T is the absolute temperature in Kelvin
    • R is the universal gas constant (8.31 JK–1mol–1)
    • To calculate the number of moles (n), this can be rearranged to get: n = (PV)/(RT)
    • To calculate the molar mass (M), using M = m/n, we get: M = (mRT)/(PV)