Novel correlations between the critical constants of the noble gases

For any particular fluid, the set of three critical constants (CC) – pressure P_c, temperature T_c and molar volume V_c – has a central importance in defining the physical behaviour of the fluid in the gas and liquid states. However, little attention seems to have been paid in the past to the relations between the CC of different substances. In the present paper, some simple and apparently novel relations have been found between the three CC for the set of four noble gases: Ne, Ar, Kr, Xe. Defining the critical quotient Q_c ≡ RT_c/P_c (where R is the Gas Constant) the correlations may be summarised by the dual equation: (V_c/cm³ mol⁻¹) = 27 + 0.31 (T_c/K) = 3.3 + 0.280 (Q_c/cm³ mol⁻¹), which describes the CC data for the quartet Ne–Xe with an average uncertainty of 0.5%. Regarding the other two noble gases, the two isotopes of the lightest member, ³He and ⁴He, show the deviations from these relations that are expected from quantal effects and their low molar masses; while for the heaviest member, Rn, the correlations enable a value of 145(5) cm³ mol⁻¹ to be estimated for V_c that is not otherwise well defined in the literature. By contrast, and contrary to the general assumption, the second lightest member, Ne, apparently does not show appreciable quantal effects in the area, so that Ne–Xe may be considered together as a group. These correlations are compared with the behaviour of a selection of polyatomic fluids; in these comparisons, the NG dual correlation equation provides a reference line defining the presumed simplest behaviour. This and related areas show a “Residual Volume Effect”, in that extrapolating the equivalent temperature and energy parameters to zero for the state of zero-mass point particles, referred to here as the hypothetical element zeronium (Ze), the system in each case still has a finite intercept; this intercept amounts to essentially 34% of the average volume for the present quartet Ne–Xe, rather than the zero volume expected for this condition.