Dilute Gas Mixtures

2-Propanol(l) and water vapor(2) are condensing on the cooled surface of a vertical tube. Nitrogen (3) is also present in the vapor mixture fed to the condenser. At the temperature and pressure in the condenser the diffusion coefficients of the three binary gas pairs are 

Near the exit from the condenser the composition in the vapor mixture is Xj = 0.005, 2 = 0.003, X3 = 0.992. Calculate the matrix of multicomponent diffusion coefficients at this composition. 

SOLUTION The matrix [ ] is calculated directly from Eqs. 4.2.7 as demonstrated in Example 4.2.1. The result here is 

As in our last illustration, this matrix is dominated by the diagonal elements. Since the mixture is almost pure nitrogen with only traces of the condensable vapors remaining we may let the mole fraction of nitrogen approach unity, 1, and the mole fractions of 

The vapor-phase catalytic dehydrogenation of ethanol to acetaldehyde involves the diffusion of ethanol to the catalyst surface where it reacts to produce acetaldehyde and hydrogen. Under typical reactor conditions (temperature = 548 K, pressure = 101.3 kPa) the binary diffusivities of the three binary pairs encountered are 

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The olfactometer was calibrated using C02, as the odorous gas, diluted in air to 10000 ppm by volume, and contained in a 30 1 Tedlar bag (Fig. 5) (7). C02-free oxygen was used as the diluting gas. The C02 concentration was was sufficiently low to avoid significantly altering the density of the odorous air. The bag was connected by silicon rubber tubing to the rotameter inlets and the diluted gas mixture was sampled via a tube placed inside the nose-piece and analysed by an infra-red gas analyser, with an accuracy of greater than 1% (Fig. 5). 

It is often possible to predict with accuracy many properties of ideal solutions, such as dilute gas mixtures, as well as liquid mixtures of closely related substances such as pentane and hexane. On the other hand, liquid mixtures of substances with different... 

Can the van der Waals forces lead to the formation of chemical compounds The two Cl atoms in a molecule Cl2 will certainly be attracted to one another by a van der Waals-London force but it can be very simply shown that these forces alone can never lead to the formation of a chemical compound. The peculiar property of these forces is that they always strive to bring like atoms together. Suppose we have a dilute gas mixture containing N atoms of A and N atoms of B further let us imagine that the van der Waals-London forces lead to the formation of molecules AB from these atoms the energy of the system is then... 

A discussion of the theory of the relationship between he and kg may be found in the psychrometry part of this section. Because both theoretical and experimental values of hjk pply only to dilute gas mixtures, the wet-bulb lines at high concentrations nave been omitted. For a discussion of the precautions to be taken in making psychrometric determinations of solvent vapors at low solvent wet-bulb temperatures in the presence of water vapor, see the paper by Sherwood and Comings [TYans. Am. Inst. Chem. Eng., 28,88 (1932)]. 

A more general approach to the diffusion problem is needed. The essential concepts behind the development of general relationships regarding diffusion were given more than a century ago, by Maxwell [39] and Stefan [40]. The Maxwell-Stefan approach is an approximation of Boltzmann s equation that was developed for dilute gas mixtures. Thermal diffusion, pressure diffusion, and forced diffusion are all easily included in this theory. Krishna et al. [38] discussed the Maxwell-Stefan diffusion formulation and illustrated its superiority over the Pick s formulation with the aid of several examples. The MaxweU-Stefan formulation, which provides a useful tool for solving practical problems in intraparticle diffusion, is described in several textbooks and in numerous publications [7,41-44]. 

For dilute gas mixtures we may employ the linearity postulate in irreversible thermodynamics to obtain the transport fluxes for heat and mass. The fundamental theory is examined in chap 2 and we simply refer to the expressions (2.456) and (2.457). Moreover, a particular form of the generalized Maxwell-Stefan equations, i.e., deduced from (2.298) in chap 2, is given by ... 

Curtiss and Bird [18] [19] and Slattery [89] (sect. 8.4.4) state that from kinetic theory of dilute gas mixtures it appears that the coefficients Cgk are determined in such a way that the following relations are satisfied... 

A dilute gas mixture is assumed to behave as a continuum when the mean free path of the molecules is much smaller than the characteristic dimensions of the problem geometry. A relevant dimensionless group of variables, the Knudsen number Kn, is defined as [47, 30, 31] ... 

Although they have not experienced Substantial industrial development, processes have also been developed to produce an ethylene/acetykse mixture of a suitable composition directly, and by the type (c) scheme, to perform the rest of the operations to produce vinyl chloride, without separation or purification of the components of the stream produced. These techniques have been proposed by SBA and especially Kureha. This type of method, which uses a dilute gas mixture, avoids costly fractionation of acetylene and ethylene, replacing them by the easier fractionation of vinyl chloride and ethylene dichloride. 

Early Iheoties for multicomponent diffusion in gases ware obtained from kinetic theory approaches and culminated in the Stefan-Maxwell eqmitions7 for dilute gas mixtures of constant molar density. In one dimension,... 

The D j ate the binary diffusion coefficients (or an / — j mixture thus, no additional information is required for computations of multicomponent diffusion in dilute gas mixtures although one might prefer a form in which the fluxes appeared explicitly. Generalization of the Stefan-Maxweli form to dense gassa and to liquids has been suggested. 1 but in these cases there is no rigorous relationship to the binety diffusivilies. Furthermore, Ihe form of Eq- (2.3-10) in which the fluxes du not appear explicitly has little to recommend it. 

The chemiluminescence arising from dilute gas mixtures of sodium and fluorine has been attributed to NaF2 formation [321]. 

Many absorbers and strippers deal with dilute gas mixtures and liquid solutions, and it is satisfactory in these cases to assume that the operation is isothermal. But actual absorption operations are usually exothermic, and when large quantities of solute gas are absorbed to form concentrated solutions, the thermal effects cannot be ignored. If by absorption the temperature of the liquid is raised to a considerable extent, the equilibrium solubility of the solute will be appreciably reduced and the capacity of the absorber decreased (or else much larger flow rates of liquid will be required). For stripping, an endothermic process, the temperature of the liquid tends to fall. To take into account thermal effects during absorption and stripping, energy balances must be combined with the material balances presented in Chapter 3. 

Thermochemical investigations have shown that temperature levels of about 900°C are required for the deposition of pure metal films at atmospheric pressure unless the carbonyl is fed as an extremely dilute gas mixture. At these high temperatures, however, gas-phase nucleation is a serious problem in obtaining dense and adherent films [184]. 

The formulas required to calculate the number of trays will only be mentioned here without derivation. For dilute gas mixtures Henry s law often applies so that, in terms of mole fractions, y = mx. Also, the total flow of liquid, L (in kmol/hr), and of gas, F (in kmol/hr) is substantially constant. The operating line and the equilibrium line are then both straight and the relation between ingoing and outgoing flow and the number of trays are obtained analytically, for absorption and in terms of mole fractions ... 

Indifferent behavior occurs on the molecular level when the interactions between particles (such as in dilute gas mixtures) are nonexistent or when they are of the same size independently of the type of particles. 

Arsine gas has a very important commercial application in the production of modem microelectronic components. It is used in a dilute gas mixture with an inert gas and its ready thermal decomposition is exploited to enable other growing crystals to be doped with minute traces of arsenic to give n-type semiconductors. 

Finally, just as thermophoresis has as a limit thermal diffusion- in dilute gas mixtures, so one would expect a thermophoretic effect on particles suspended in dense gases and liquids, whose limit would be thermal diffusion of mixtures in these media. The photophoretic effect may have been observed by BARKAS [2.145] in aqueous solutions of colloids. More recently, McNAB and MEISEN [2.146] have reported experimental evidence of thermophoresis in liquids for 1.011 and 0.79 ym spheres in water and n-hexane. They report that their data for the thermophoretic velocity are described by an empirical equation... 

Here, as earlier, we are restricting our attention to systems of pure monatomic gases. The theory as well as the comparison with experiment can be generalized to include dilute gas mixtures and dilute gases of polyatomic molecules (cf. Sections 2.4.4.1 and 2.4.4.2). 

D Simplified Design Methods for Absorption of Dilute Gas Mixtures in Packed Towers... 

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