Ideal Gas Equation (DP IB Physics)

Ideal Gas Equation

• The two ideal gas equations, derived from the empirical gas laws, are:

• The variables will be outlined below

• The empirical gas laws can be combined to give a single constant, known as the ideal gas constant, R

• An ideal gas is defined as:

  A gas which obeys the ideal gas equation at all pressures, volumes and temperatures

• Combining the gas laws leads to the ideal gas equation:

• Where:

  • P = pressure (Pa)

  • V = volume (m³)

  • n = number of moles (mol)

  • R = 8.31 J K^–1 mol^–1 (ideal gas constant)

  • T = temperature (K)

Constants

• The ideal gas constant R is the macroscopic equivalent of the Boltzmann constant

  • The ideal gas constant is associated with macroscopic quantities such as volume and temperature

  • The Boltzmann constant is associated with the thermal energy of microscopic particles

• The Boltzmann constant is defined as the ratio of the ideal gas constant R and Avogadro's constant N_A:

• Recall from the Amount of Substance revision note that

• This gives another form of the ideal gas equation:

• Where:

  • N = number of molecules

  • k_B = 1.38 × 10⁻²³ J K⁻¹ (Boltzmann constant)