Diffusion Coefficients in Liquids at Infinite Dilution

The gas-phase diffusion coefficients are calculated using the equation given in Ref. [40]. The liquid-phase diffusion coefficients of components at infinite dilution in... 

This equation is simply Pick s first law of diffusion. Note that Ui — 0, but Ui is nonzero. Furthermore, for this binary system of solute i in a liquid s, the ideal solution binary diffusion coefficient D (valid at infinite dilution) is... 

In liquids, predictive methods for diffusivity are typically semiempirical, relating the diffusivity of a solute at infinite dilution to the solvent viscosity, the molar volumes of the components, and sometimes other quantities [15]. For finite concentrations, the manner in which the diffusion coefficients pass from one infinite-dilution limit to the other is sometimes complex, and the models that exist [15] typically have a parameter that must be fitted to data. 

Diffusion coefficients in liquids are of die order of 10"a frVs (10 m2/s) unless (he solution is highly viscous or the solute has a very high molecular weight. Table 2.3-3 presents a few exparimenial diffusion coefficients for liquids at room temperature in dilute solution. Ertl and Dulllen. Johnson and Babb.2 and Himmdblau21 provide extensive tabulations of diffusion coefficients in liquids. It is probably safe to say (hat most of the reported exparimenial diffusivities were computed based on Fick s Second Law without consideration of whether or not (he system was thermodynamically ideal. Since the binary diffusion coefficient in liquids may vary strongly with composition, tabulations and predictive equations usually deal with the diffiisivity of A at infinite dilution in B, Z> , and the diffusiviiy of B at infinite dilution in A, D a. Separate consideration is then given to the variation of tha diffusiviiy with composition. 

A wastewater stream of 0.038 m3/s, containing 10 ppm (by weight) of benzene, is to be stripped with air in a packed column operating at 298 K and 2 atm to reduce the benzene concentration to 0.005 ppm. The packing specified is 50-mm plastic Pall rings. The airflow rate to be used is five times the minimum. Henry s law constant for benzene in water at this temperature is 0.6 kPa-m3/mol (Davis and Cornwell, 1998). Calculate the tower diameter if the gas-pressure drop is not to exceed 500 Pa/m of packed height. Estimate the corresponding mass-transfer coefficients. The diffusivity of benzene vapor in air at 298 K and 1 atm is 0.096 cm2/s the diffusivity of liquid benzene in water at infinite dilution at 298 K is 1.02 x 10 5 cm2/s (Cussler, 1997). 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

Table A16 Experimental diffusion coefficient of water in organic liquids at 20-25 °C at infinite dilution...

This theory also gives good quantitative agreement with available experimental data for these properties. For example, for the non-LC backbone polymer polyisoprene [see Figure 3(a)] at infinite dilution in hexane [CHj-(Cl -CHj] in the I liquid phase at T - 293 K, the infinite dilution diffusion coefficient D g (in units of... 

This table lists diffusion coefficients at infinite dilution for some binary liquid mixtures. Although values are given to two decimal places, measurements in the literature are often in poor agreement. Therefore most values in the table cannot be relied upon to better than 10%. 

In (5.51), r stands for the intrinsic reaction rate at liquid bulk conditions. For worst-case-estimations, one should use a highest rate value possible in the considered RD column. In this respect it should be kept in mind that the reaction rates under RD conditions strongly depends on the operating pressure that influences the boiling temperatures, that is the reaction temperature. D g/ represents the effective diffusion coefficient of a selected reaction component inside the catalyst particles. One should use the component with the lowest mole fraction Xj in the liquid bulk mixture as key component [35]. Its effective diffusion coefficient can be estimated from the diffusion coefficient at infinite dilution Dg((/ = (sfr)D with the total porosity e and the tortuosity r of the applied catalyst. Based on (5.51) one can say that intraparticle diffusion resistances will be negligible, if 1. 

The diffusion coefficient Dj of solute 1 in solvent 2 at infinitely dilute solution is a fundamental property. This is different from the self-diffusion coefficient Dq in pure liquid. Both Di and Dq are important properties. The classical approach to Di can be done based on Stokes and Einstein relation to give the following equation... 

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