Distribution coefficient experimental

If 0 = 1 and distribution coefficient experimentally obtained is for equilibrium state, experimental distribution coefficient correlates positively with solubility product ratio with 1 1 slope. However, the experimental values deviate significantly from theoretical line derived here (Fig. 1.35). 

The ternary diagrams shown in Figure 22 and the selectivi-ties and distribution coefficients shown in Figure 23 indicate very good correlation of the ternary data with the UNIQUAC equation. More important, however, Table 5 shows calculated and experimental quarternary tie-line compositions for five of Henty s twenty measurements. The root-mean-squared deviations for all twenty measurements show excellent agreement between calculated and predicted quarternary equilibria. 

Figure 4-23. Calculated and experimental selectivities and distribution coefficients for the type-I ternaries in the 2,2,4-trimethyl pentane-cyclohexane-furfural-benzene system.

By comparing the ratio of the distribution coefficients for a pair of ions, a separation factor (or relative retention) is obtained for a specific experimental condition. 

Thermal expansion mismatch between the reinforcement and the matrix is an important consideration. Thermal mismatch is something that is difficult to avoid ia any composite, however, the overall thermal expansion characteristics of a composite can be controlled by controlling the proportion of reinforcement and matrix and the distribution of the reinforcement ia the matrix. Many models have been proposed to predict the coefficients of thermal expansion of composites, determine these coefficients experimentally, and analy2e the general thermal expansion characteristics of metal-matrix composites (29-33). 

Nonideal Separations. In numerous iastances, the ideal equations 2 and 4 have been verified experimentally. However, ia other experiments different results were obtained, reflecting failure of one ore more of the assumptions made ia deriving equations 2 and 4. Likewise, much theoretical work is concerned with modified assumptions, iucluding varyiag distribution coefficient k (19), eutectic-forming phase behavior (4,20—21), varyiag mass of 2one (22), and soHd-state diffusion (23). 

The process requires the interchange of atoms on the atomic lattice from a state where all sites of one type, e.g. the face centres, are occupied by one species, and the cube corner sites by the other species in a face-centred lattice. Since atomic re-aiTangement cannot occur by dhect place-exchange, vacant sites must play a role in the re-distribution, and die rate of the process is controlled by the self-diffusion coefficients. Experimental measurements of the... 

Summarizing, the greater the forces between the molecules, the greater the energy (enthalpy) contribution, the larger the distribution coefficient, and the greater the retention. Conversely, any reduction in the random nature of the molecules or any increase in the amount of order in the system reduces the distribution coefficient and attenuates the retention. In chromatography, the standard enthalpy and standard entropy oppose one another in their effects on solute retention. Experimentally it has... 

Testing the applicability of equation (10) to liquids where the solvent components associate with themselves is experimentally difficult. Katz et al. attempted to do this by measuring the distribution coefficients of some solutes between hydrocarbon and... 

The results obtained by Katz et al. [15] are shown as experimental points on the curves relating the distribution coefficient of the solute against volume fraction of methanol added to the original mixture in Figure 31. Due to the difficulty of measuring the distribution coefficient of each solute between pure water and hexadecane (because of their extremely high retention), the values were obtained from a polynomial curve fit to the data which gave a value for (K) at a = 0. 

The dimensionless K. is regarded as a function of system T and P only and not of phase compositions. It must be exfjerimentally determined. Reference 64 provides charts of R (T,P) for a number of paraffinic hydrocarbons. K. is found to increase with an increase in system T and decrease with an increase in P. Away from the critical point, it is invariably assumed that the K, values of component i are independent of the other components present in the system. In the absence of experimental data, caution must be exercised in the use of K-factor charts for a given application. The term distribution coefficient is also used in the context of a solute (solid or liquid) distributed between two immiscible liquid phases yj and x. are then the equilibrium mole fractions of solute i in each liquid phase. 

Fig. 2a-c. Kinetic zone diagram for the catalysis at redox modified electrodes a. The kinetic zones are characterized by capital letters R control by rate of mediation reaction, S control by rate of subtrate diffusion, E control by electron diffusion rate, combinations are mixed and borderline cases b. The kinetic parameters on the axes are given in the form of characteristic currents i, current due to exchange reaction, ig current due to electron diffusion, iji current due to substrate diffusion c. The signpost on the left indicates how a position in the diagram will move on changing experimental parameters c% bulk concentration of substrate c, Cq catalyst concentration in the film Dj, Dg diffusion coefficients of substrate and electrons k, rate constant of exchange reaction k distribution coefficient of substrate between film and solution d> film thickness (from ref. 

Figure 4.51. Distribution of experimental data. Six experimental formulations (strengths 1, 2, resp. 3 for formulations A, respectively B) were tested for cumulative release at five sampling times (10, 20, 30, 45, respectively 60 min.). Twelve tablets of each formulation were tested, for a total of 347 measurements (13 data points were lost to equipment malfunction and handling errors). The group means were normalized to 100% and the distribution of all points was calculated (bin width 0.5%, her depicted as a trace). The central portion is well represented by a combination of two Gaussian distributions centered on = 100, one that represents the majority of points, see Fig. 4.52, and another that is essentially due to the 10-minute data for formulation B. The data point marked with an arrow and the asymmetry must be ignored if a reasonable model is to be fit. There is room for some variation of the coefficients, as is demonstrated by the two representative curves (gray coefficients in parentheses, h = peak height, s = SD), that all yield very similar GOF-figures. (See Table 3.4.)...

In fundamental SEC studies retention is often described in terms of a distribution coefficient. The theoretical distribution coefficient Kg is defined as the ratio of solute concentration inside and outside of the packing pores under size exclusion conditions. The experimental distribution coefficient as defined in Equation 1, is a measurable quantity that can be used to check the theory. 

The transfer energies and distribution coefficients refer to two mutually saturated, i.e., in a sense, mixed solvents. It should be noted that this is a case where, under conditions of distribution equilibrium, the quantities in question can be experimentally measured this would not be possible with mutually miscible solvents [34],... 

The un-ionized form is assumed to be sufficiently lipophilic to traverse membranes in the pH-partition hypothesis. If it were not, no transfer could be predicted, irrespective of pH. The lipophilicity of compounds is experimentally determined as the partition coefficient (log P) or distribution coefficient (log D) [16]. The partition coefficient is the ratio of concentrations of the neutral species between aqueous and nonpolar phases, while the distribution coefficient is the ratio of all species between aqueous and nonpolar phases [17,18],... 

The values of P and selectivity factors are calculated from the experimentally derived solute polarity distribution coefficient for the test solutes ethanol, dioxane, and nitromethane. The solute distribution... 

Usually, however, the distribution coefficients determined experimentally are not equal to the ratios of the solubility product because the ratio of the activity coefficients of the constituents in the solid phase cannot be assumed to be equal to 1. Actually observed D values show that activity coefficients in the solid phase may differ markedly from 1. Let us consider, for example, the coprecipitation of MnC03 in calcite. Assuming that the ratio of the activity coefficients in the aqueous solution is close to unity, the equilibrium distribution may be formulated as (cf. Eq. A.6.11)... 

The numerical values of the distribution coefficients X and D have been derived from experimental data for a large number of systems (e.g. (10, 11, 13). From the constancy of either X or D values it can be determined whether or not the system yielded homogeneous precipitates. In either case, the numerical value of X or D should be equal to ... 

In this way and by numerical evaluation, Driessens (2) proved that the experimental activities could be explained on the basis of substitutional disorder, according to Equation (27), within the limits of experimental error. It seems, therefore, that measurements of distribution coefficients and the resulting activities calculated by the method of Kirgintsev and Trushnikova (16) do not distinguish between the regular character of solid solutions and the possibility of substitional disorder. However, the latter can be discerned by X-ray or neutron diffraction or by NMR or magnetic measurements. It can be shown that substitutional disorder always results in negative values of the interaction parameter W due to the fact that... 

This straightforward application is obvious for type I systems only, for which coprecipitation diagrams like Figure 3 can be calculated and experimentally verified. As can be seen from Figures 4 and 5, the apparent distribution coefficient, X, for systems of... 

Thermodynamic calculations based on the compositional dependence of the equilibrium constant are applied to solubility data in the KCl-KBr-H20 system at 25°C. The experimental distribution coefficient and activity ratio of Br /Cl in solution is within a factor of two of the calculated equilibrium values for compositions containing 19 to 73 mole percent KBr, but based on an assessment of uncertainties in the data, the solid solution system is clearly not at equilibrium after 3-4 weeks of recrystallization. Solid solutions containing less than 19 and more than 73 mole percent KBr are significantly farther from equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. 

The present study examines the approach to equilibrium in the very soluble salt system KCl-KBr-H20. Soluble salt reactions are known to be relatively rapid and there is greater likelihood for equilibrium to be established. Solubility in the KCl-KBr-H20 system has been well studied at 25°C (6-8) and has been assumed previously to attain equilibrium (3,8). By examining the compositional dependence of the experimental distribution coefficient, Stoessell and Carpenter (9) concluded equilibrium was not established during coprecipitation of trace Br in KC1. 

Although equilibrium was not established, it was more closely approached in the KCl-KBr-H20 system than in carbonate systems. For example, in a similar analysis of the strontianite-aragonite solid solution system (4 ), it was found that the experimental distribution coefficient for Sr substitution from seawater into aragonite is 12 times larger than the expected equilibrium value. Most of the distribution coefficients for the KCl-KBr-H20 system are within a factor of two of the equilibrium value, but clearly not at equilibrium. Considerable caution should be exercised before reaching the conclusion that equilibrium is established at relatively low temperatures in other solid solution-aqueous solution systems. 

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

The review of Martynova (18) covers solubilities of a variety of salts and oxides up to 10 kbar and 700 C and also available steam-water distribution coefficients. That of Lietzke (19) reviews measurements of standard electrode potentials and ionic activity coefficients using Harned cells up to 175-200 C. The review of Mesmer, Sweeton, Hitch and Baes (20) covers a range of protolytic dissociation reactions up to 300°C at SVP. Apart from the work on Fe304 solubility by Sweeton and Baes (23), the only references to hydrolysis and complexing reactions by transition metals above 100 C were to aluminium hydrolysis (20) and nickel hydrolysis (24) both to 150 C. Nikolaeva (24) was one of several at the conference who discussed the problems arising when hydrolysis and complexing occur simultaneously. There appear to be no experimental studies of solution phase redox equilibria above 100°C. 

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