Multicomponent gaseous systems

The treatment of the extended Langmuir isotherm of a binary system is due to Markham and Benton (1931). Here, we present the general treatment for a multicomponent gaseous system containing N species. The assumptions made by... 

Generally in chemistry it is common to work with gas mixtures. One of the first researchers who studied multicomponent gaseous systems was John Dalton (1766-1884), who went oti to enunciate, in 1881, the law that bears his name At a constant temperature the pressure of a gas mixture in a defined volume is equal to the sum of the partial pressures of each gas (as long as they do not react). Mathematically it can be expressed as... 

In this section we have assumed that the adsorption isotherm of an adsorbate is unaffected by the presence of constituents other than the adsorbate in the fluid mixture. If such ideaiir> is assumed for the Langmuir isotherm developed in the previous example, you could use the derived expression for any gaseous system containing carbon tetrachloride and the same activated carbon. In reality, however, the presence of other solutes that have an affinity for the carbon surface alters the CCI4 equilibrium behavior. An accurate system representation would require data or models for the complete multicomponent mixture. 

The molecular diffusivity of a binary gas mixture is essentially independent of composition. In multicomponent mixtures the diffusivity becomes, in principle, concentration dependent, but such variations are generally relatively small so that the assumption of a concentration-independent diffusivity is usually a good approximation for most gaseous systems. Other important general conclusions which follow from Eq. (5.15) are that the molecular diffusivity is inversely dependent on total pressure and proportional to a low power of temperature. The combined effect of the factor in the numerator and the temperature-dependent function 2 i/kT) in the denominator yields an overall temperature dependence of approximately T . 

In binary gaseous systems the diffusivity is a property of the system determined by the two gases present. However, in multicomponent systems the fluxes of the various components will affect the diffusivity of any given component in the mixture. 

A simple example of the analysis of multicomponent systems will suffice for the present consideration, such as the calculation of the components in a gaseous mixture of oxygen, hydrogen and sulphur. As a first step, the Gibbs energy of formation of each potential compound, e.g. S2, H2S, SO, SO2, H2O etc. can be used to calculate the equilibrium constant for the formation of each compound from the atomic species of the elements. The total number of atoms of each element will therefore be distributed in the equilibrium mixture in proportion to these constants. Thus for hydrogen with a starting number of atoms and the final number of each species... 

These multicomponent calculations are now computerized, and complicated systems, such as tire Si-C-H-Cl quaternaty, may be solved by the use of commercially available software, e. g. the IVTAN database. The solution to this multicomponent system which is obtained by this means is somewhat subjective, since, at the time of writing for example, data are available for 72 gaseous species in the quaternary system Si-C-H-Cl. Choosing 19 of the most probable of tlrese, and using tire IVTAN software to solve this multicomponent equilibrium, yields the following results for tire most probable species (see Table 3.2). 

Compared with the non-electrochemical interface discussed in the previous section, where a sofid was in contact with a surrounding gaseous atmosphere, the electrode/ electrolyte interface is a multicomponent system and, besides temperature and partial pressures/concentrations, it is also influenced by the electrode potential. This results in greater complexity, which requires additional considerations prior to deriving an expression for the interfacial stability. 

Soils are multicomponent systems consisting of solid, liquid, and gaseous phases. These three phases are constantly in a dynamic state, trying to maintain equilibrium. Any type of perturbation in one phase influences the other two phases so that a new equilibrium state is approached. An equilibrium process that has been extensively investigated in soil systems employing the Freundlich equation involves sorption. Consider the reaction... 

CVD normally involves a multi-component and a multi-phase system. There are various ways to calculate thermodynamic equilibrium in multicomponent systems. The following is a brief discussion of the optimization method where the minimization of Gibbs free energy can be achieved. The free energy G of a system consisting of m gaseous species and s solid phases can be described by. 

Aerosol-assisted CVD introduces rapid evaporation of the precursor and short delivery time of vapor precursor to the reaction zone. The small diffusion distance between the reactant and intermediates leads to higher deposition rates at relatively low temperatures. Single precursors are more inclined to be used in AACVD therefore, due to good molecular mixing of precursors, the stoichiometry in the synthesis of multicomponent materials can be well controlled. In addition, AACVD can be preformed in an open atmosphere to produce thin or thick oxide films, hence its cost is low compared to sophisticated vacuum systems. CVD methods have also been modified and developed to deposit solid phase from gaseous precursors on highly porous substrates or inside porous media. The two most used deposition methods are known as electrochemical vapor deposition (EVD) and chemical vapor infiltration (CVI). 

Due to the fragmentation of the investigated molecules during the ionization process in the mass spectrometer (for example, the m/z peak at 28 for CO and CO2 in Figure IB) and possible overlapping of characteristic IR bands, the identification of the gaseous species, especially in multicomponent systems, is sometimes difficult. However, an even more complicated problem is the quantitative interpretation of spectrometric data, which needs the calibration of the system, i.e. the determination of the relationship between the observed intensities of the ion current (MS) or absorbance (IR-spectra) and the amount of the analyzed species. 

To proceed further, we need to know the dependence of the function on density, which can be obtained by resorting to the virial expansion. Now, the molecules having different orientations may be regarded as belonging to different species, so that in effect we have a multicomponent system. The virial expansion of the free energy of a gaseous mixture in ascending powers of the density is well known for our present purpose we use the form... 

The approach of IAS of Myers and Prausnitz presented in Sections 5.3 and 5.4 is widely used to calculate the multicomponent adsorption isotherm for systems not deviated too far from ideality. For binary systems, the treatment of LeVan and Vermeulen presented below provides a useful solution for the adsorbed phase compositions when the pure component isotherms follow either Langmuir equation or Freundlich equation. These expressions are in the form of series, which converges rapidly. These arise as a result of the analytical expression of the spreading pressure in terms of the gaseous partial pressures and the application of the Gibbs isotherm equation. 

In a mixture of gases of comparable concentrations, diffusion of any component due to a concentration gradient causes the counter-diffusion of other components. Physically, redistribution of one component must be compensated for by the diffusion of other components in order to preserve constant pressure in the system. The fluxes of gaseous components in a multicomponent mixture are related by Stefan-Maxwell equations (Bird et al., 1960) ... 

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