Accurate assessment of the Boyle temperature of nonpolar molecular gases using second virial coefficient with Lennard-Jones (12-6) potential

Abstract

We derived an efficient analytical formula to calculate the second virial coefficient in the Lennard-Jones (12-6) potential. The analytical formula is used to accurately evaluate the Boyle temperature. The Boyle temperature is determined for nonpolar molecules from the second virial coefficient, and the calculated results are compared with other studies. The accuracies of the second virial coefficient and the Boyle temperature are tested by their application to molecules $${\text{Kr}},$$ $${\text{Xe}},$$ $${\text{Ne}},$$ $${\text{Ar}},$$ $${\text{He}},$$ $${\text{H}}_{2} ,$$ $${\text{O}}_{2} ,$$ $${\text{F}}_{2} ,$$ $${\text{Cl}}_{2} ,$$ $${\text{I}}_{2} ,$$ $${\text{Br}}_{2} ,$$ $${\text{SF}}_{6} ,$$ $${\text{SO}}_{3} ,$$ $${\text{CH}}_{4} ,$$ $${\text{C}}_{2} {\text{H}}_{6} ,$$ $${\text{C}}_{3} {\text{H}}_{6} ,$$ $${\text{C}}_{5} {\text{H}}_{10} ,$$ $${\text{C}}_{4} {\text{H}}_{6} ,$$ $${\text{CO}}_{2} ,$$ $${\text{ClFO}}_{3} ,$$ $${\text{CCl}}_{4} ,$$ $${\text{SiH}}_{4} ,$$ $${\text{Ga}}\left( {{\text{CH}}_{3} } \right),$$ $${\text{Ga}}\left( {{\text{CH}}_{3} } \right)_{2}$$ and $${\text{Ga}}\left( {{\text{CH}}_{3} } \right)_{3}$$ . The obtained results for the second virial coefficient at a wide temperature range and the Boyle temperature are in good agreement with the known data available in the literature.