Thermodynamic Properties of Gases

4 Properties of Gases 4 4.1 Thermodynamic Properties of Gases 4.4.1.1 Gas Density 

This relation is easily transformed to express the ideal gas density  

For real gases, density is expressed by the following relationship  

138 Chapter 4. Methods for the Calculation of Hydrocarbon Physical Properves 

There have been several equations of state proposed to express the compressibility factor. Remarkable accuracy has been obtained when specific equations for certain components are used however, the multitude of their coefficients makes their extension to mixtures complicated. 

Practical expressions for the thermodynamic properties of real gases may obtained by decomposition of the properties into perfect-gas and residual eontributions, followed by evaluation of the latter in terms of the virial equation of state. This separation is motivated by the availability of widely-applieable theory for the prediction, estimation and correlation of perfeet-gas properties, enabling those terms to be written down and evaluated essentially exaetly. Residual properties may then be evaluated in terms of any applieable form of the equation of state. 

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The most satisfactory calciilational procedure for thermodynamic properties of gases and vapors requires PVT data and ideal gas heat capacities. The primary equations are based on the concept of the ideal gas state and the definitions of residual enthalpy anci residual entropy ... 

In Chapter 10. we will calculate the thermodynamic properties of gases from the molecular parameters, and these calculations, which provide the standard state values, are most easily done for the ideal gas. 

The thermodynamic properties of gases are given through equations of state (EoS) which in general may be given as... 

In these charts compressibility and thermodynamic properties of gases and liquids are plotted as functions of the reduced pressure pr = p/pc, for different values of the reduced temperature Tr = T/Tc (Ref 4, pp 239-43)... 

Anthony, J. L., Maginn, E. J., and Brennecke, J. F, Solubilities and thermodynamic properties of gases in the ionic liquid l-n-butyl-3-methyl imidazolium hexafluorophosphate, /. Phys. Chem. B, 106, 7315, 2002. 

The three-dimensional particle in a box corresponds to the real life problem of gas molecules in a container, and is also sometimes used as a first approximation for the free conduction electrons in a metal. As we found for one dimension (Section 2.3), the allowed energy levels are extremely closely spaced in macroscopically sized boxes. For many purposes they can be regarded as a continuum, with no discernible energy gaps. Nevertheless, there are problems, for example in the theory of metals and in the calculation of thermodynamic properties of gases, where it is essential to take note of the existence of discrete quantized levels, rather than a true continuum. 

Braker, W. Mossman, A.L. "The Matheson Unabridged Gas Databook A Compilation of Physical and Thermodynamic Properties of Gases" Matheson Gas Products East Rutherford, NJ, 1974, Vol. I, p. 11. 

Mel nik, Yu.P., 1978. Thermodynamic Properties of Gases under the Conditions of Deep Petrogenesis. Izd. Naukova Dumka, Kiev, 152 pp. (in Russian). 

From equations (11)-(15) and from the definitions in the preceding section, all previously defined thermodynamic functions can be related to T, V, and Ni provided that Qi is a known function of T and V. The problem of calculating thermodynamic properties of gases therefore reduces to the problem of evaluating in terms of Tand K... 

The most satisfactory calculation procedure for the thermodynamic properties of gases and vapors is based on ideal gas state heat capacities and residual properties. Of primary interest are the enthalpy and entropy these are given by rearrangement of the residual property definitions ... 

The thermodynamic properties of gases, liquids, solids and aqueous solutes of interest for desulfurization processes are tabulated for temperatures from 298 K to temperatures as high as 1000 K when possible. Major emphasis has been placed on aqueous lime or limestone scrubbing, but the data can also be used for high temperature gas processes and for N0 processes. 

The thermodynamic properties of gases may readily be calculated from a knowledge of the virial coefficients and their dependence on temperature. For calculations at pressures not much greater than 1 bar, a knowledge of the second virial coefficient is usually sufficient. At higher pressures, the contribution of the third virial coefficient becomes more significant. 

Tiepel, E.W. K.E. Gubbins, "Thermodynamic properties of gases dissolved in electrolyte solutions". Ind. Eng. Chem. Fundam.. vl2, 1. ppl8-25 (1973)... 

Quantum chemistiy methods apply quantum mechanics to solve problems in chemistiy. For physical chemists, quantum chemistiy is employed to calculate the thermodynamic properties of gases, to interpret molecular spectra, to calculate properties of transition states in chemical reactions, to understand intermolecular forces, and to deal with bonding in solids. Organic chemists use quantum chemistiy to evaluate the relative stabilities of molecules, to investigate the mechanisms of chemical reactions, and to analyze NMR speetra while inorganic chemists use quantum chemistiy together with ligand field theory to predict and explain the properties of transition-metal eomplexes. 

A major success of statistical mechanics is the ability to predict the thermodynamic properties of gases and simple solids from quantum mechanical energy levels. Monatomic gases have translational freedom, which we have treated by using the particle-in-a-box model. Diatomic gases also have vibrational freedom, which we have treated by using the harmonic oscillator model, and rotational freedom, for which we used the rigid-rotor model. The atoms in simple solids can be treated by the Einstein model. More complex systems can require more sophisticated treatments of coupled vibrations or internal rotations or electronic excitations. But these simple models provide a microscopic interpretation of temperature and heat capacity in Chapter 12, and they predict chemical reaction equilibria in Chapter 13, and kinetics in Chapter 19. 

Many thermodynamic quantities, such as total internal energy, entropy, chemical potential, etc., for an ideal gas have been derived in the preceeding chapters as examples. In this section we will bring all these results together and list the thermodynamic properties of gases in the ideal gas approximation. In the following section we will see how these quantities can be calculated for real gases, for which we take into account molecular size and molecular forces. 

Solubilities and Thermodynamic Properties of Gases in the Ionic Liquid l- -butyl-3-methylimidazolium Hexafluorophosphate. 

The experience accumulated in working out tables of data on the thermodynamic properties of gases and liquids is of great interest from this point of view. This work has been particularly developed in the USSR. The work of Soviet investigators in thermophysics, which has established the basis for Soviet and international tables of thermophysical properties, has been acclaimed worldwide. Currently, this work is carried out by over 40 research organizations in the USSR under the auspices of the scientific program of the... 

Sinanoglu, O. Pitzer, K. S. (1959). Equation of state and thermodynamic properties of gases at high temperatures I. Diatomic molecules. J. Chem. Phys., 31,960-967. 

The Center on Thermodynamic Properties of Gases and Liquids, which coordinated the thermophysical investigations in higher schools of the USSR, was established at the Moscow Power Institute in 1977. The computerized information system of this center provides users with data on properties of gases and liquids (Sychev Spiridonov 1984 Sychev eta/. 1985a,b). 

As for interactions between hke molecules, our infonnation comes mainly from the thermodynamic properties of gases at low densities and from the transport properties in dilute gases. No experimental study of intermolecular forces on the basis of thermodynamic properties of mixed crystals near 0 K has been performed imtil now. 

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