The author states, "the behavior according to PV = RT is a necessary but not sufficient condition for a gas to be ideal." When the pressure-independent form of the virial equation is used to describe the behavior of a real gas, we have

(1)

At the Boyle temperature (T_B), the condition specified by the author, B = 0 and therefore the EOS gets simplified:

(2)

Equation 2 is the rigorous form of the EOS that describes completely and accurately the behavior of the gas. The consequence of the additional constraint imposed by the author (low pressure) is that the contributions by terms of the order of P² and higher are negligible, and hence the behavior can be approximated by the EOS:

z 1 or PV RT

(3)

Equation 3 is not exactly the same as PV = RT, which is the ideal gas law. The rigorous equality between PV and RT is indeed a necessary and sufficient condition for describing the behavior of an ideal gas. If the thermodynamic properties of the real gas have dependence different from that dictated by the ideal gas law, then the inference is (and should be) that the ideal gas law is only a close approximation of the actual behavior of the gas. The difference between the actual and idealized P-V-T behaviors of the gas may be insignificant. However, it is important that equality (between PV and RT) be reserved strictly for the ideal gas approximation used in all other cases. It is necessary to do that because, as stated by Baron in an earlier issue of this Journal, while the formal aspects of thermodynamics are simple, the concepts are subtle and require much thinking before they are understood (2). Further, quite often understanding is replaced by mere arithmetic calculations of various thermodynamic quantities. It is desirable that clarity be maintained regarding the use of EOS, particularly the ideal gas law.

Literature Cited

1. Wisniak, J. J. Chem. Educ. 1999, 76, 671.
2. Baron, M. J. Chem. Educ. 1989, 66, 1001.

See also the author's reply