Ideal Gas Equation (CIE A Level Physics)

• The equation of state for an ideal gas (or the ideal gas equation) can be expressed as:

• Where:
  • p = pressure (Pa)
  • V = volume (m³)
  • n = amount of substance / number of moles (mol)
  • R = molar gas constant (8.31 J K^-1 mol^-1)
  • T = temperature (K)

• The ideal gas equation can also be written in the form:

• Where:
  • N = number of molecules
  • k = Boltzmann constant (1.38 × 10^-23 J K^–1)
• Remember that the number of moles and the number of molecules are related by Avogadro's constant

• An ideal gas is therefore defined as:

A gas which obeys the equation of state pV = nRT at all pressures, volumes and temperatures

• The Boltzmann constant, k, is used in the ideal gas equation and is defined by the equation:

• Where:
  • R = molar gas constant
  • N_A = Avogadro’s constant

• Boltzmann’s constant therefore has a value of:

• The Boltzmann constant has the units J K^-1 because
  • it relates the properties of microscopic particles, e.g. kinetic energy of gas molecules
  • to their macroscopic properties, e.g. temperature

• The Boltzmann constant is very small because the increase in kinetic energy of a molecule is very small for every incremental increase in temperature