Estimation of diffusivity in a gas mixture

Assume that the critical value (l A X obtained at P 1 atm pressure can be used. 

The predictions may not be satisfactory as the critical value is estimated at a low pressure of 1 atm. The critical value may also obtained from Eq. (2.74) 

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Example 2.13 Estimation of diffusivity in a gas mixture at low pressure Estimate the diffusivity of carbon dioxide in benzene at 318 K and 1 atm. 

Example 2.16 Estimation of diffusivity of a component through a gas mixture Estimate the diffusivity of carbon dioxide (C02) through a gas mixture of benzene and methane with the known mole fractions given in the following table. The mixture is at 300 K and 2 atm. Welty et al. (1984)... 

Consider the problem of steady-state one-dimensional diffusion in a mixture of ideal gases. At constant T and P, the total molar density, c = P/RT is constant. Also, the Maxwell-Stefan diffusion coefficients D m reduce to binary molecular diffusion Dim, which can be estimated from the kinetic theory of gases. Since Dim is composition independent for ideal gas systems, Eq. (6.61) becomes... 

We should also keep in mind that the process conditions may directly influence the composition of the furnace gas mixture, so in this sense the diffusivity ratio a will vary with pressure and temperature due to variations inx., whether or not the ratios D, /D, are constant. In this case, the present analysis may be combined with a simple zero or one-dimensional auxiliary model of reactant injection and transport within the furnace. Using the specified injection rate and assumed trial values for the optimum pressure and temperature, the results presented here can be used with such an auxiliary model to compute the composition of the furnace gas mixture. From this estimate of the composition, a value for a and new candidate values for the optimum pressure and temperature can then be calculated. This computational procedure may then be repeated, each time using the final estimates of the optimum conditions as initial guesses for the next iteration. This method should converge quickly because the value of a is a fairly weak function of the composition. 

Ammonia is being absorbed from a stagnant mixture of nitrogen and hydrogen by contact with a 2 N sulfuric acid solution. At one place in the apparatus where the pressure is 1 bar and the temperature 300 K, the analysis of the gas is 40% NH3 (1), 20% N2 (2), and 40% H2 (3) by volume. Estimate the effective diffusivity of ammonia in the gaseous mixture. 

Estimate the effective diffusivity of hydrogen in ethane in a porous solid with an average pore size of 4000 A, 40% porosity, and tortuosity of 2.5. The gas mixture is at a pressure of 10 atm and a temperature of 373 K. For this system, the ordinary diffusion... 

A mixture of ethanol and water vapor is being rectified in an adiabatic distillation column. The alcohol is vaporized and transferred from the liquid to the vapor phase. Water vapor condenses—enough to supply the latent heat of vaporization needed by the alcohol being evaporated—and is transferred from the vapor to the liquid phase. Both components diffuse through a gas film 0.1 mm thick. The temperature is 368 K and the pressure is 1 atm. The mole fraction of ethanol is 0.8 on one side of the film and 0.2 on the other side of the film. Calculate the rate of diffusion of ethanol and of water, in kg/m2-s. The latent heat of vaporization of the alcohol and water at 368 K can be estimated by the Pitzer acentric factor correlation (Reid et al., 1987)... 

In the "diffusion flame" method developed by von Hartel and Polanji (Z. physikal. Chem. B 1930,11, 97) sodium vapour is introduced throu a nozzle into an excess of organic halide and the extent of penetration before it is completely consumed by reaction is measured. In an experiment made by Cvetanovic and Le Roy (J. Chem. Phys. 1952, 20, 1016) at 532.7 K, a stream of sodium vapour at a partial pressure = 8.3 x 10" mm Hg in nitrogen carrier gas was passed through a nozzle of radius r = 0.125 cm into a stream of nitrogen and ethyl chloride vapour at a partial pressure p = 2.5 x 10" mm Hg. The radius R of the spherical zone of reaction made visible by illumination with sodium D-line resonance radiation was 1.55 cm. The partial pressure P of sodium at the visibility limit was estimated to be 7 X 10" mm Hg. The diffusion coef5cient D of sodium in the reaction mixture is 130 cm s. ... 

The selection of a proper sorbent for a given separation is a complex problem. The predominant scientific basis for sorbent selection is the equilibrium isotherm. Diffusion rate is generally secondary in importance. The equilibrium isotherms of all constituents in the gas mixture, in the pressure and temperature range of operation, must be considered. As a first and oversimplified approximation, the pure-gas isotherms may be considered additive to yield the adsorption from a mixture. Models and theories for calculating mixed gas adsorption (Yang, 1987) should be used to provide better estimates for equilibrium adsorption. Based on the isotherms, the following factors that are important to the design of the separation process can be estimated ... 

The reaction under consideration may involve a solvent and/or one or more liquid-phase products, thus making it a multi-component diffusion system. In such cases, Z>b represents the solute diffusivity in the liquid mixture including the products. To simplify the effort to make a reasonable estimate of Z>b, the relatively insignificant components may be neglected. For example, the following expression can then be used to calculate the diffusivity of a solute, gas or liquid, in 2-solvent liquid system (39) ... 

This identification means that it is possible to use experimental values of diffusion coefficients or the viscosities of binary mixtures and pure components to estimate the internal energy diffusion coefficients through equation (4.125). What evidence there is for both pure gases (Section 4.2) and gas mixtures (Vesovic etal. 1995) suggests that the mass and internal energy diffusion coefficients seldom differ substantially, so that this is a reasonable approximation. In any event, owing to the fact that the approximate theory is used in an interpolatory manner in this formulation, it has usually been possible to predict the thermal conductivity of binary and multicomponent gas mixtures with errors of a few percent. 

SO2 uptake was measured at total system pressures in the range of 20 to 50 Torr, consisting of 17.5 Torr H2O vapor with the balance either helium or argon. The observed mass accommodation coefficients, 74, are plotted in Figure 2 as a function of the inverse of the calculated diffusion coefficient of SO2 in each H20-He and l O-Ar mixture. The diffusion coefficients are calculated as a sum of the diffusion coefficients of SO in each component. The diffusion coefficients for SO in He and in Ar are estimated from the diffusion coefficient of SO2 in H 0 (Dg p = 0.124 (101) by multiplying this value by the quantity (mH-/mH Q)V2, anti (mAr/m 2o) 2> respectively. The curves in Figure 2 are plots ofEquation 7 with three assumed values for 7 0.08,0.11 and 0.14. The best fit to the experimental values of is provided by 7 = 0.11. Since gas uptake could be further limited by liquid phase phenomena as discussed in the following section, 7502 = 0.11 is a lower limit to the true mass accommodation coefficient for SO2 on water. 

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