Selectivity coefficients difference

Ion-exchange isotherms assume different shapes depending on the selectivity factor and the variations in with the level of exchange The rational selectivity coefficient includes the ionic charge and is given by... 

Water Transport. Two methods of measuring water-vapor transmission rates (WVTR) ate commonly used. The newer method uses a Permatran-W (Modem Controls, Inc.). In this method a film sample is clamped over a saturated salt solution, which generates the desired humidity. Dry air sweeps past the other side of the film and past an infrared detector, which measures the water concentration in the gas. For a caUbrated flow rate of air, the rate of water addition can be calculated from the observed concentration in the sweep gas. From the steady-state rate, the WVTR can be calculated. In principle, the diffusion coefficient could be deterrnined by the method outlined in the previous section. However, only the steady-state region of the response is serviceable. Many different salt solutions can be used to make measurements at selected humidity differences however, in practice,... 

According to the nine assumptions and approach a) for the diffusion potential inside the membrane the selectivity coefficient Kg , can be expressed by other parameters. Table 3 shows the results for the different kinds of membranes 66). In some cases the expressions for K J i contain ion-mobilities inside the membrane... 

The advantage of this approach is that it can be used when the response of the electrode is not Nernstian or even linear. However, the drawback is that the selectivity coefficient may change under different experimental conditions, particularly the concentrations at which the measurements were made. In most situations, the selectivity obtained from matched potential method cannot be directly compared to the values obtained from other methods. 

Both approaches lead to identical standard thermodynamic values of exchange (9-10). Such a difference in the choice of the surface concentration scale is of course only important for heterovalent exchange equilibria. For the heterovalent case the numerical value for both selectivity coefficients, Kg (Gaines Thomas) and (Vanselov) differ and, consequently, their variation with surface composition also differs. 

In Section 4.8.2, we will describe a method called Lasso regression. Depending on a tuning parameter, this regression technique forces some of the regression coefficients to be exactly zero. Thus the method can be viewed as a variable selection method where all variables with coefficients different from zero are in the final regression model. 

Results of such single-molecule permeation experiments, using the MV +/ Ru(bpy)3 pair (Fig. 16), and membranes with four different nanotubule i.d.s, are shown in Fig. 17. The slopes of these permeation curves define the fluxes of and Ru(bpy)3 across the membrane. A permeation selectivity coefficient (ai)t can be obtained by dividing the flux by the Ru(bpy)3 flux. 

Minimal Selectivity Coefficients for Three Different Small Molecule/Large Molecule Parrs... 

A similar equation for anions will have a minus sign before the factor of RT/F - the difference arises from the way in which these Nemst-based equations are formulated.) The factor by which we multiply each In a term is called the selectivity coefficient or selectivity ratio. The selectivity coefficient for K" " in the presence of Na+ is said to be 100 because one hundred sodium ions are as noticeable as one potassium ion. 

Fig. 7.1. Dependence of difference between standard Gibbs transfer energies on the logarithm of the selectivity coefficient for an ISE based on 2-nitro-p-cymene. (After Scholler and Simon [185].)...

The most economical procedure for a liquid-liquid extraction would be a single step extraction, since extraction procedures including several steps with the same or with different solvents are laborious and economically disadvantageous. Optimisation of extraction of more than one solute, which give different selective interactions (different response surfaces in the same mixture space), may require several extraction steps with different optimal extraction solvents or separate analysis of each analyte. However, procedures can be used, which select a composition of the extraction liquid that provides satisfactory partition coefficients or extraction yields for all solutes to be extracted. 

However, if the valences of the exchanging cations are equal, the selectivity coefficient or pseudo-equilibrium constant is not affected by concentration. As already mentioned, one isotherm corresponds to a specific temperature in the case of adsorption or ion exchange of equal valence ions, whereas additionally, the same normality is required for the existence of only one isotherm in the case of ion exchange of different valence ions, due to the concentration-valence effect (Helfferich, 1962). The determination of the true equilibrium constant should be based on the thermodynamic activities (activity coefficients) of the species rather than concentrations. It is clear that the difficulties in the determination of activity coefficients also complicate the determination of the true equilibrium constant (Culfaz and Yagiz, 2004). 

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