# Gas constants and their relationships

## Gas Constants & their values

• The Avogadro constant (NA) = 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 (kb) = 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 (NA)
=> N = n NA
• number of moles (n) =number of molecules (N) /Avogadro constant (NA)
n=N/NA
• Boltzmann constant(kb) = molar gas constant(R) / Avogadro constant (NA)
kb = R / NA
• R = NA kb
molar gas constant or Universal Gas Constant(R) = Avogadro constant (NA) x Boltzmann constant (kb)

## 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.