Chemical Education Today
Letters Interpretation of Second Virial Coefficient Wisniak has presented a clear and concise analysis of the equations of state (EOS) used to describe the behavior of real gases (1). However, a statement in the first of the two concluding observations needs to be reexamined a little. 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 z = PV = 1 + BP + CP 2 + DP 3 + … (1) RT At the Boyle temperature (TB), the condition specified by the author, B = 0 and therefore the EOS gets simplified: z = PV = 1 + CP 2 + DP 3 + … (2) RT 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 P 2 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. Vivek Utgikar National Research Council, NRMRL, U.S. EPA 26 W. Martin Luther King, Jr., Drive Cincinnati, OH 45268
The author replies: I agree with Utgikar that the equation of state PV = nRT represents the definition of an ideal gas, according to the macroscopic viewpoint (no assumptions regarding the structure of matter). Nevertheless, there are several situations where some properties of a real gas are identical to those of the ideal gas. As stated in the paper, at Boyle’s temperature and sufficiently low pressures, the virial equation of state becomes PV = RT, although some of the properties of the gas are different from those of the ideal gas. Similarly, at temperature TH the enthalpy becomes independent of the pressure, although the gas is not ideal. Perhaps the message would be clearer if we write PV ≈ RT, to keep the strict definition of an ideal gas. Jaime Wisniak Department of Chemical Engineering Ben-Gurion University of the Negev Beer-Sheva, Israel
JChemEd.chem.wisc.edu • Vol. 77 No. 11 November 2000 • Journal of Chemical Education
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