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 = 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)

• 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 relates the properties of microscopic particles (e.g. kinetic energy of gas molecules) to their macroscopic properties (e.g. temperature)
  • This is why the units are J K^-1

• Its value is very small because the increase in kinetic energy of a molecule is very small for every incremental increase in temperature