Liquid phases thermodynamic properties

In addition to deciding on the method of normalization of activity coefficients, it is necessary to undertake two additional tasks first, a method is required for estimating partial molar volumes in the liquid phase, and second, a model must be chosen for the liquid mixture in order to relate y to x. Partial molar volumes were discussed in Section IV. This section gives brief attention to two models which give the effect of composition on liquid-phase thermodynamic properties. 

This definition gives values for a> of essentially zero for spherically symmetric molecules (e.g., the noble gases). Values of o) for 176 compounds are tabulated in Appendix I. For the species in Fig. 4.3, values of to are 0.00, 0.2415, 0,4869, and 0.6341, respectively, for methane, toluene, n-decane, and ethyl alcohol. Modification of the R-K equation by the addition of as a third constant greatly improves its ability to predict vapor pressures and other liquid-phase thermodynamic properties. 

An improved agreement is obtained between experimental data and model calculations if the coefficients and become substance dependent. Furthermore, by making Qa and O temperature-dependent, the accuracy of the model is further improved. Walas provided a list of 16 different approaches regarding the adjustment of the a and b parameters in the Redlich-Kwong equation of state. A major hmitation of the Redlich-Kwong equation of state is its inability to correlate liquid-phase thermodynamic properties and, consequently, predict VLE. Subsequent cubic equations of state presented below provide an improvement in this respect. 

M. J. Vlot, S. Claassen, H. E. Huitema, J. P. v. d. Eerden. Monte Carlo simulation of racemic liquid mixtures thermodynamic properties and local structures. Mol Phys 97 19, 1997 M. J. Vlot, J. C. v. Miltenburg, H. A. Oonk, J. P. V. d. Eerden. Phase diagrams of scalemic mixtures. J Chem Phys 707 10102, 1997. 

The prediction of volatilities and melting points of pure ionic liquids was possible by associating first principles calculations and calorimetric measurements, as presented, for example, by Verevkin and co-workers. They showed that the knowledge of gas-phase thermodynamic properties is important for the modelling of vapour-liquid equilibrium on pure ionic fluids [97]. 

Like most solvents, the solvent properties of COj improve as pressure and temperature increase. In cleaning, we rely on the liquid-phase solvent properties. It is important to note that, thermodynamically, liquid carbon dioxide is unstable at room temperature and atmospheric pressure, but this thermodynamic condition only refers to equilibrium states, not non-equilibrium states. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

Denotes excess thermodynamic property Denotes value for an ideal solution Denotes value for an ideal gas Denotes liquid phase... 

Denotes phase transition from liquid to vapor Denotes residual thermodynamic property Denotes a total value of a thermodynamic property V Denotes vapor phase... 

Data on the gas-liquid or vapor-liquid equilibrium for the system at hand. If absorption, stripping, and distillation operations are considered equilibrium-limited processes, which is the usual approach, these data are critical for determining the maximum possible separation. In some cases, the operations are are considerea rate-based (see Sec. 13) but require knowledge of eqmlibrium at the phase interface. Other data required include physical properties such as viscosity and density and thermodynamic properties such as enthalpy. Section 2 deals with sources of such data. 

For liquid mixtures at low pressures, it is not important to specify with care the pressure of the standard state because at low pressures the thermodynamic properties of liquids, pure or mixed, are not sensitive to the pressure. However, at high pressures, liquid-phase properties are strong functions of pressure, and we cannot be careless about the pressure dependence of either the activity coefficient or the standard-state fugacity. 

A condition of phase equilibrium is the equality of the chemical potentials in the two phases. Therefore, at all points along the two-phase line, //(g) = p( ). But, as we have noted above, the approach to the critical point brings the liquid and gas closer and closer together in density until they become indistinguishable, At the critical point, all of the thermodynamic properties of the liquid become equal to those of the gas. That is, Hm(g) = Um(g) - /m(l),... 

A simple example of how molecular electronic structure can influence condensed phase liquid crystalline properties exists for molecules containing strongly dipolar units. These tend to exhibit dipolar associations in condensed phases which influence many thermodynamic properties [29]. Local structural correlations are usually measured using the Kirkwood factor g defined as... 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Phase changes, which convert a substance from one phase to another, have characteristic thermodynamic properties Any change from a more constrained phase to a less constrained phase increases both the enthalpy and the entropy of the substance. Recall from our description of phase changes in Chapter 11 that enthalpy increases because energy must be provided to overcome the intermolecular forces that hold the molecules in the more constrained phase. Entropy increases because the molecules are more dispersed in the less constrained phase. Thus, when a solid melts or sublimes or a liquid vaporizes, both A H and A S are positive. Figure 14-18 summarizes these features. 

The thermodynamic properties of a number of compounds are shown in Appendix D as pressure-enthalpy diagrams with lines of constant temperature, entropy, and specific volume. The vapor, liquid, and two-phase regions are clearly evident on these plots. The conditions under which each compound may exhibit ideal gas properties are identified by the region on the plot where the enthalpy is independent of pressure at a given temperature (i.e., the lower the pressure and the higher the temperature relative to the critical conditions, the more nearly the properties can be described by the ideal gas law). 

For the non-oxidative activation of light alkanes, the direct alkylation of toluene with ethane was chosen as an industrially relevant model reaction. The catalytic performance of ZSM-5 zeolites, which are good catalysts for this model reaction, was compared to the one of zeolite MCM-22, which is used in industry for the alkylation of aromatics with alkenes in the liquid phase. The catalytic experiments were carried out in a fixed-bed reactor and in a batch reactor. The results show that the shape-selective properties of zeolite ZSM-5 are more appropriate to favor the dehydroalkylation reaction, whereas on zeolite MCM-22 with its large cavities in the pore system and half-cavities on the external surface the thermodynamically favored side reaction with its large transition state, the disproportionation of toluene, prevails. 

The term parametric pumping was coined by Wilhelm et al. [Wilhelm, Rice, and Bendelius, Ind. Eng. Chem. Fundam., 5,141-144 (1966)] to describe a liquid-phase adsorption process in which separation is achieved by periodically reversing not only flow but also an intensive thermodynamic property such as temperature, which influences adsorptivity. Moreover, they considered the concurrent cycling of pressure, pH, and electrical and magnetic fields. A lot of research and development has been conducted on thermal, pressure, and pH driven cycles, but to date only gas-phase pressure-swing parametric pumping has found much commercial acceptance. 

Keenan, J. H., F. G. Keyes, P. G. Hill and J. G. Moore, 1969, Steam Tables, Thermodynamic Properties of Water Including Vapor, Liquid, and Solid Phases. Wiley, New York. 

The thermodynamic properties of single-component condensed phases are traditionally given in tabulated form in large data monographs. Separate tables are given for each solid phase as well as for the liquid and for the gas. In recent years analytical representations have been increasingly used to ease the implementation of the data in computations. These polynomial representations typically describe the thermodynamic properties above room temperature (or 200 K) only. 

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