• Giora Rytwo Dept. of Environmental Sciences, Tel Hai College
  • Yaniv Olshansky Dept. of Environmental Sciences, Tel Hai College, Environmental Physical Chemistry Laboratory, MIGAL – Galilee Research Institute


Upper Division Undergraduate, Physical Chemistry, Gases, Virial Equation


Chemistry educators teaching chapters on "real gases" usually present to the students the "virial development" of Kamerlingh Onnes for the equation of state, which takes into account interactions of the molecules in aggregates by a successive series of parameters (B, C, etc.), yielding a polynomial equation on the concentration (equivalent to the inverse of the molar volume). A well known transformation of the virial equation to a polynomial equation as a function of pressure is also widely used, with suitable coefficients (B', C', etc.). The literature presents relationships between the second and third virial coefficients for both equations, for example B' = B/RT. Students usually assume that both formulations should deliver to similar calculated results. However, when using the relationships mentioned above to perform calculations for the same gas conditions of pressure and temperature, discrepancies are observed in the molar volume obtained by the two formulations of the virial equation. Chemistry educators are required to present such discrepancies, explain them and interpret them. In addition to that, a possible alternative practical approach is to develop a relationship between the second virial coefficients B and B', that yields suitable results when using both formulations.


Atkins, P., & de Paula, J. (2006). Physical Chemistry (Vol. 8th). New York: W.H.Freemand and Co.

Boschi-Filho, H., & Buthers, C. C. (1997, January). Second Virial Coefficient For Real Gases At High Temperature.

Box, G. E. P. (1976). Science and Statistics. Journal of the American Statistical Association, 71(356), 791–799. http://doi.org/10.2307/2286841

Dymond, J. H., Cholinski, J. A., Sza̧franski, A., & Wyrzykowska-Stankiewicz, D. (1986). Second virial coefficients for N-alkanes; recommendations and predictions. Fluid Phase Equilibria, 27(0), 1–13. http://doi.org/http://dx.doi.org/10.1016/0378-3812(86)87037-6

Estrada-Alexanders, A. F., Guzmán, O., & Pérez-Vidal, B. (2012). High-precision virial coefficients of argon and carbon dioxide from integration of speed of sound data in the pressure-temperature domain. Molecular Physics, 110(11-12), 1349–1358. Retrieved from http://www.scopus.com/inward/record.url?eid=2-s2.0-84862538649&partnerID=40&md5=40a4b4a072a830aaab8314d86f254655

Hayden, J. G., & O’Connel, J. P. (1975). A Generalized Method for Predicting Second Virial Coefficients. - Industrial & Engineering Chemistry Process Design and Development. - American Chemical Society. http://doi.org/- 10.1021/i260055a003

Kehiahian, H. V. (2005). Virial Coefficients of Selected Gases. In D. R. Lide (Ed.), CRC Handbook of Chemistry and Physics, Internet Version 2005 (pp. 6–32). Boca Raton, FL: CRC Press. Retrieved from <http://www.hbcpnetbase.com>

O’Connel, J. P., & Prausnitz, J. M. (1967). Empirical Correlation of Second Virial Coefficients for Vapor-Liquid Equilibrium Calculations. - Industrial & Engineering Chemistry Process Design and Development. - American Chemical Society. http://doi.org/- 10.1021/i260022a016

Pitzer, K. S., & Curl, R. F. J. (1957). The Volumetric and Thermodynamic Properties of Fluids. III. Empirical Equation for the Second Virial Coefficient1. - Journal of the American Chemical Society. - American Chemical Society. http://doi.org/- 10.1021/ja01567a007

Riddell, R. J., & Uhlenbeck, G. E. (1953). On the Theory of the Virial Development of the Equation of State of Monoatomic Gases. The Journal of Chemical Physics, 21(11), 2056–2064. http://doi.org/http://dx.doi.org/10.1063/1.1698742

Salzman, W. R. (2004). The Virial Expansion. Retrieved October 1, 2015, from http://www.chem.arizona.edu/~salzmanr/480a/480ants/VIRIAL/virial.html

Tsonopoulos, C. (1974). An empirical correlation of second virial coefficients. AIChE Journal, 20(2), 263–272. http://doi.org/10.1002/aic.690200209

Wisniak, J. (2003). Heike Kamerlingh—The Virial Equation of State. Indian Journal of Chemical Technology, 10, 564–572.

Additional Files



How to Cite

Giora Rytwo, & Yaniv Olshansky. (2016). ON THE TEACHING OF THE DIFFERENT FORMULATIONS OF THE VIRIAL EQUATION. International Education and Research Journal (IERJ), 2(5). Retrieved from http://ierj.in/journal/index.php/ierj/article/view/269