Gas constants and their relationships

Gas Constants & their values

• The Avogadro constant (N_A) = 6.02 × 10²³ particles per mole
• The molar gas constant or universal gas constant (R) = 8.31 J mol⁻¹ K⁻¹
• The Boltzmann constant (k_b) = 1.38 × 10⁻²³ J K⁻¹

Gas constants and their relationships

• For an ideal gas of n moles and N molecules:
  number of molecules (N) = number of moles (n) x Avogadro constant (N_A)
  => N = n N_A
• number of moles (n) =number of molecules (N) /Avogadro constant (N_A)
  n=N/N_A
• Boltzmann constant(k_b) = molar gas constant(R) / Avogadro constant (N_A)
  k_b = R / N_A
• R = N_A k_b
  molar gas constant or Universal Gas Constant(R) = Avogadro constant (N_A) x Boltzmann constant (k_b)

Some examples & facts

• In 1 mole of hydrogen (2 g) there are 6.02 × 10²³ molecules (hydrogen exists as H₂).
• In 1 mole of oxygen (32 g) there are 6.02 × 10²³ molecules (oxygen exists as O₂).
• In 1 mole of copper (63 g) there are 6.02 × 10²³ atoms.
• In 1 mole of uranium-235 (235 g) there are 6.02 × 10²³ atoms.
• For example, if we have 2 kg of uranium in a fuel rod we have 2000 / 235 = 8.51 moles, and this contains 8.51 × 6.02 × 10²³ = 5.12 × 10²⁴ atoms and so 5.12 × 10²⁴ uranium nuclei.