Transfer activity coefficient estimation

Without some additional relationship it is impossible to resolve y into and "y. By introducing an extrathermodynamic assumption as this additional relationship, it becomes possible to estimate single ion transfer activity coefficients. A widely used assumption is that the transfer activity coefficients of the cation and anion of tetraphenylarsonium tetraphenylboride, Ph4As BPh4, are equal, i.e.,... 

The estimation of transfer activity coefficients was reviewed by Popovych. One method for measurement of transfer activity coefficients for electrolytes or neutral molecules is by measurement of solubility. When the solubility is low, the effects of contamination by traces of water can be profound. Furthermore, reliable solubility values even in water are difficult to obtain. Nevertheless, if saturated solutions of a substance in water and another solvent are considered, and if each solution can be shown to be in equilibrium with the same solid, the value of y, is given by the ratio of the solubility products ( sp)water/( sp)soivent electrolyte producing n ions. For... 

Transfer activity coefficient The electrostatic, or nonspecific, contribution to the transfer activity coefficient can be obtained by estimating the free-energy change involved in transferring a sphere of radius r and charge Zfi from one solvent to another of different dielectric constant. According to the Bom equation, " when 1 mole... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

Usually SmGo is a small difference between two large numbers, so it is more accurate to measure 8mG directly by the techniques discussed above than to estimate it indirectly. Solvation is then usually considered in terms of transfer free energies or activity coefficients. 

A new mathematical model based on moment techniques to describe micro- and macropore diffusion is used to study the mass-transfer resistances of Ci to C4 saturated hydrocarbons in H and Na mordenites between 127° C and 272° C. The intracrystalline diffusion coefficient decreases as the number of carbon atoms increases while the energy of activation increases with the number of carbons. The contribution from individual mass-transfer resistances to the overall mass-transfer processes is estimated. 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

Example 10.5 Diffusion cell and transference numbers The diffusion cell shown in Figure 10.2 has NaCl mixtures in the two chambers with concentrations c1A = lOOmmol/L and c1B = lOmmol/L. The mobilities of Na+ and Cl- ions are different and their ratio yields their transference numbers b+lb = t+/t = 0.39/0.61 (NaCl). The transference number t for an ion is the fraction of the total electric current carried by the ion when the mixture is subjected to an electric potential gradient. For monovalent ions, we have t+lt = 1. Estimate the diffusion potential of the cell at steady-state conditions at 298 K. Assume that activity coefficients are equal in the two reservoirs (Garby and Larsen, 1995). 

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