Heat capacity of ideal gas

As summarized e.g. by Štejfa et al. [1] , knowledge of ideal-gas thermodynamic properties is indispensable for the calculation of thermodynamic properties of real fluids and for numerous applications including thermochemistry, equations of states, phase and chemical equilibria, studies of solute-solvent interactions through the solvation heat capacities, thermodynamic correlations such as. SimCor. SimCor method require heat capacities of ideal gas with uncertainty better than 1 percent, therefore state of the art approaches are needed.

Data sources

Current practtice for techological applications is to use values stored in handbooks and databases like CRC Handbook of Chemistry and Physics [2], NIST WebBook [3], DIPPR database, handbook by Poling et al. [4], or the compilation by Stull et al. [5]. While these sources typically contain only numerical values, two volume compilation published by TRC in 1994 [6] contains sources of data used for heat capacity evaluation.

Historical background (from experiment to quantum chemistry and statistical thermodynamics calculations)

Direct or indirect experimental techniques leading to deal-gas heat capacitie are nowadays very scarce and technically limited by volatility of the studied compounds:

calorimetric measurements (recycle flow calorimeters, e.g. Waddington et al., J.Am.Chem.Soc 69(1947)22
or indirect measurements (for example speed-of-sound measurements)
of ideal-gas heat capacities as well as ideal-gas entropies derived from calorimetric measurements from near 0 K, vapor pressure measurements, and a description or estimate of state behavior of fluid (often called third-law entropies in the literature),

Computational methods: With the decline of experimental detarminations, nowadays prevailing way to obtain properties of ideal gas is to apply statistical thermodynamics calculations using either experimental or calculated molecular parameters (fundamental vibrational frequencies, principal moments of inertia, etc.). Electronic structure calculations are currently preferably used and combined with various statistical thermodynamics models ranging from the rigid rotor-harmonic oscillator (RRHO) approximation, variety of approximations accounting for anharmonicity [7-11] to computationally expensive path integral methods [12] affordable only for small molecules [13-15]. A brief overview of the statistical thermodynamics models formerly employed to calculate ideal-gas thermodynamic properties of n-alkanes is given in Section 2.4. in our recent paper [1].

Contribution of our laboratory

For the calculations for flexible molecules, RRHO approximation is inadequate and the application of more advanced models, such as 1-DHR [16], 1-DHR/M [17], or R1SM [18] schemes for the treatment of internal rotations is necessary. An overview on the calculation of ideal-gas thermodynamic properties including the analysis of uncertainties of these calculations can be found in our recent works [1, 16, 19].

Scaling factors

[under construction]

REFERENCES:

[1] Štejfa V.; Fulem M.; Růžička K., Ideal-gas thermodynamic properties of proteinogenic aliphatic amino acids calculated by R1SM approach J. Chem. Phys. 151, 144504 (2019)

[2] J.R. Rumble, D.R. Lide, T.J. Bruno, CRC handbook of chemistry and physics : a ready-reference book of chemical and physical data, CRC Press, Boca Raton, FL, 2018. (updated yearly)

[3] P.J. Linstrom, W.G. Mallard, NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg MD, 20899, https://webbook.nist.gov, May 2017.

[4] B.E. Poling, J.M. Prausnitz, J.P. O'Connell, The properties of gases and liquids, McGraw-Hill, New York, NY, 2001.

[5] D.R. Stull, E.F. Westrum, G.C. Sinke, The chemical thermodynamics of organic compounds, J. Wiley, New York, NY, 1969.

[6] M.L. Frenkel, G.J. Kabo, K.N. Marsh, G.N. Roganov, R.C. Wilhoit, Thermodynamics of Organic Compounds in the Gas State, Thermodynamics Research Center, College Station, TX, 1994.

[7] Pitzer, K. S.; Gwinn, W. D., Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation I. Rigid Frame with Attached Tops. J. Chem. Phys. 1942, 10, 428-440.

[8] Pfaendtner, J.; Yu, X.; Broadbelt, L. J., The 1-D hindered rotor approximation. Theor. Chem. Acc. 2007, 118, 881-898.

[9] Katzer, G.; Sax, A. F., A novel partition function for partially asymmetrical internal rotation. Chem. Phys. Lett. 2002, 368, 473-479.

[10] Zheng, J.; Yu, T.; Papajak, E.; Alecu, I. M.; Mielke, S. L.; Truhlar, D. G., Practical methods for including torsional anharmonicity in thermochemical calculations on complex molecules: The internal-coordinate multi-structural approximation. Phys. Chem. Chem. Phys. 2011, 13, 10885-10907.

[11]. Li, Y.-P.; Bell, A. T.; Head-Gordon, M., Thermodynamics of Anharmonic Systems: Uncoupled Mode Approximations for Molecules. J. Chem. Theory Comput. 2016, 12, 2861-2870.

[12] Feynman, R. P.; Hibbs, A. R.; Styer, D. F., Quantum Mechanics and Path Integrals. Dover Publications: Mineola, NY, 2010.

[13] Lynch, V. A.; Mielke, S. L.; Truhlar, D. G., Accurate vibrational-rotational partition functions and standard-state free energy values for H2O2 from Monte Carlo path-integral calculations. J. Chem. Phys. 2004, 121, 5148-5162.

[14] Lynch, V. A.; Mielke, S. L.; Truhlar, D. G., High-Precision Quantum Thermochemistry on Nonquasiharmonic Potentials: Converged Path-Integral Free Energies and a Systematically Convergent Family of Generalized Pitzer−Gwinn Approximations. J. Phys. Chem. A 2005, 109, 10092-10099.

[15] Chempath, S.; Predescu, C.; Bell, A. T., Quantum mechanical single molecule partition function from path integral Monte Carlo simulations. J. Chem. Phys. 2006, 124, 234101.

[16] C. Červinka, M. Fulem, K. Růžička, J. Chem. Eng. Data 58 (2013) 1382.

[17] M. Fulem, K. Růžička, C. Červinka, et al., Fluid Phase Equilib. 371 (2014) 93.

[18] V. Štejfa, M. Fulem, K. Růžička, et al., Fluid Phase Equilib. 402 (2015) 18.

[19] C. Červinka, M. Fulem, K. Růžička, J. Chem. Eng. Data 57 (2012) 227.