Limiting activity coefficient measurement

Dohnal, V., Hovorka, S. (1999) Exponential saturator A novel gas-liquid partitioning technique for measurement of large limiting activity coefficients. Ind. Eng. Chem. Res. 38, 2036-2043. 

Smiley191 has measured gas-liquid retention volumes to obtain values for the activity coefficients at infinite dilution for eight different five-carbon hydrocarbons in NMA. The activity coefficients were determined at 40, 70, and 100 °C and, from the temperature dependence, values for the partial molar heats of solution were calculated. Frost and Bittrich192) have reported limiting activity coefficients of benzene and cyclohexane in NMA at 25 and 50 °C. 

Li, J., Carr, P.W. (1993) Measurement of water-hexadecane partition coefficients by headspace gas chromatography and calculation of limiting activity coefficients in water. Anal Chem. 65, 1443-1450. 

Direct measurement of y would confirm whether or not the solution is infinitely dilute at saturation. Lobien and Prausnitz (23) have attempted to measure this effect in a few systems by comparing the solubility limit with measurements of y from differential ebulliometry. The systems they studied all had solubilities of a few percent, and for these systems they found significant deviations from yi = 1/xi. It would be useful to have measurements for more dilute solubilities, but in this case the limiting activity coefficient becomes very large, and ebulliometry is inapplicable for high relative volatilities. Perhaps such data could be taken by ebulliometry for systems where the solute is much less volatile than water, or by chromatographic methods. 

Limiting activity coefficient data fcr a few water solvent systems measured by various researches using the techniques discussed are shown in Table II. The y ... 

Here, both the excess chemical potential, and the activity coefficient measure the deviations from similarity of the two quantities. This is fundamentally different from the deviations from the ideal-gas behavior (i.e., total lack of interactions), discussed in section 6.1. Here the limiting behavior of the activity coefficient is... 

C. A. Eckert and S. R. Sherman, "Measurement and Prediction of Limiting Activity Coefficients," Fluid Phase Equil., 116, 333 (1996). 

Equation-of-state approaches are preferred concepts for a quantitative representation of polymer solution properties. They are able to correlate experimental VLE data over wide ranges of pressure and temperature and allow for physically meaningful extrapolation of experimental data into unmeasured regions of interest for application. Based on the experience of the author about the application of the COR equation-of-state model to many polymer-solvent systems, it is possible, for example, to measure some vapor pressures at temperatures between 50 and 100 C and concentrations between 50 and 80 wt% polymer by isopiestic sorption together with some infinite dilution data (limiting activity coefficients, Henry s constants) at temperatures between 100 and 200 C by IGC and then to calculate the complete vapor-liquid equilibrium region between room temperature and about 350 C, pressures between 0.1 mbar and 10 bar, and solvent concentration between the common polymer solution of about 75-95 wt% solvent and the ppm-region where the final solvent and/or monomer devolatilization process takes place. Equivalent results can be obtained with any other comparable equation of state model like PHC, SAFT, PHSC, etc. 

Standard potentials Ee are evaluated with full regard to activity effects and with all ions present in simple form they are really limiting or ideal values and are rarely observed in a potentiometric measurement. In practice, the solutions may be quite concentrated and frequently contain other electrolytes under these conditions the activities of the pertinent species are much smaller than the concentrations, and consequently the use of the latter may lead to unreliable conclusions. Also, the actual active species present (see example below) may differ from those to which the ideal standard potentials apply. For these reasons formal potentials have been proposed to supplement standard potentials. The formal potential is the potential observed experimentally in a solution containing one mole each of the oxidised and reduced substances together with other specified substances at specified concentrations. It is found that formal potentials vary appreciably, for example, with the nature and concentration of the acid that is present. The formal potential incorporates in one value the effects resulting from variation of activity coefficients with ionic strength, acid-base dissociation, complexation, liquid-junction potentials, etc., and thus has a real practical value. Formal potentials do not have the theoretical significance of standard potentials, but they are observed values in actual potentiometric measurements. In dilute solutions they usually obey the Nernst equation fairly closely in the form ... 

The stability constants are defined here in terms of concentrations and hence have dimensions. True thermodynamic stability constants K° and (3° would be expressed in terms of activities (Section 2.2), and these constants can be obtained experimentally by extrapolation of the (real) measurements to (hypothetical) infinite dilution. Such data are of limited value, however, as we cannot restrict our work to extremely dilute solutions. At practical concentrations, the activities and concentrations of ions in solution differ significantly, that is, the activity coefficients are not close to unity worse still, there is no thermodynamically rigorous means of separating anion and cation properties for solutions of electrolytes. Thus, single-ion activity coefficients are not experimentally accessible, and hence, strictly speaking, one cannot convert equations such as 13.6 or 13.8 to thermodynamically exact versions. 

The standard emf E° of the cell was determined by means of an extrapolation technique involving a function of the measured emf E (which was measured experimentally), taken to the limit of zero ionic strength /. A linear function of I was observed when the Debye-Hiickel equation (in its extended form) (12) was introduced for the activity coefficient of hydrobromic acid over the experimental range of molalities m. With this type of mathematical treatment, the adjustable parameter became a0, the ion-size parameter, and a slope factor / . This procedure is essentially the same as that used in our earlier determinations (7,10) although no corrections of E° for ion association were taken into account (e = 49.5 at 298.15°K). 

Since the study of diffusion-limited reactions in solution seeks to discover more about the nature of the reaction path, the nature of the encounter pair, the energetics of the reaction and possibly the rate of reaction of the encounter pair, ftact, it is to be recommended that experimentalists actively seek to measure the diffusion coefficients of the reactants (or similar species), as well as any other parameters which may have an important bearing on the rate coefficient. By so doing, some of the uncertainty in estimating encounter distance may be removed and inconsistencies between diffusion coefficients measured independently and those obtained from an analyses of rate coefficient time dependence may provide valuable insight into the nature of the diffusion process at short distances. 

Experimental data on only 26 quaternary systems were found by Sorensen and Arlt (1979), and none of more complex systems, although a few scattered measurements do appear in the literature. Graphical representation of quaternary systems is possible but awkward, so that their behavior usually is analyzed with equations. To a limited degree of accuracy, the phase behavior of complex mixtures can be predicted from measurements on binary mixtures, and considerably better when some ternary measurements also are available. The data are correlated as activity coefficients by means of the UNIQUAC or NRTL equations. The basic principle of application is that at equilibrium the activity of each component is the same in both phases. In terms of activity coefficients this... 

A general formulation of the problem of solid-liquid phase equilibrium in quaternary systems was presented and required the evaluation of two thermodynamic quantities, By and Ty. Four methods for calculating Gy from experimental data were suggested. With these methods, reliable values of Gy for most compound semiconductors could be determined. The term Ty involves the deviation of the liquid solution from ideal behavior relative to that in the solid. This term is less important than the individual activity coefficients because of a partial cancellation of the composition and temperature dependence of the individual activity coefficients. The thermodynamic data base available for liquid mixtures is far more extensive than that for solid solutions. Future work aimed at measurement of solid-mixture properties would be helpful in identifying miscibility limits and their relation to LPE as a problem of constrained equilibrium. 

A fundamental concept in all theories for determining activity coefficients is that ionic interactions are involved. These interactions cause a deviation in the free energy associated with the ions from what it would be if they did not occur. Consequently, at the limit of an infinitely dilute solution, activity coefficients go to 1 because there are no ionic interactions. This basic consideration also leads to the idea that as the concentration of ions increases, their extent of interaction must also increase. Ionic strength is a measure of the overall concentration of ions in a solution and the fact that more highly charged ions exert a greater influence on ionic interactions. It is calculated as ... 

Figure 2 Comparison of measured mean ionic activity coefficients with those predicted by the Debye-Huckel limiting law. (Data from Handbook of Chemistry and Physics, 77th ed. A James, M Lord. VNR Index of Chemical Physical Data. New York Van Nostrand Reinhold, 1992.

Even with the definition of the Reference State, chemical thermodynamics alone cannot provide a unique methodology for the measurement of single-ion activity coefficients. An infinitude of possibilities exists, each of that calls upon its own extra thermodynamic set of conventions according to criteria of experimental convenience and intended application. However, chemical thermodynamics does provide general constraints that limit any set of arbitrary conventions defining single-ion activities. 

The consensus of experts is that pH cannot be measured more accurately than 0.05 in natural waters. Two important limitations on accuracy arc activity coefficient corrections and liquid junction potentials. 

The values of the electrode standard potentials were obtained by measuring the EMF s of suitably arranged cells at varying concentrations and by extrapolating the found values into a state of infinitely diluted solutions in which the activity coefficients of electromotively active substances equal unity. To determine standard potentials is very laborious and requires considerable care. A detailed description of the working method and the method of results evaluation is beyond the limits of this book it is, therefore, necessary to refer to the pertinent technical literature" ... 

Measurements of emf (electromotive force) are to be made with this cell under reversible conditions at a number of concentrations c of HCl. From these measurements relative values of activity coefficients at different concentrations can be derived. To obtain the activity coefficients on such a scale that the activity coefficient is unity for the reference state of zero concentration, an extrapolation procedure based on the Debye-Huckel limiting law is used. By this means, the standard electrode emf of the silver-silver chloride electrode is determined, and activity coefficients are determined for all concentrations studied. 

Thus arose the Debye-HUckel expression for the experimentally inaccessible individual ionic-activity coefficient. This expression could be transformed into the Debye-Htickel limiting law for the experimentally measurable mean ionic-activity... 

The experimentally determined activity coefficients, based on vapor pressure, freezing-point and electromotive force measurements, for a number of typical electrolytes of different valence types in aqueous solution at 25 , are represented in Fig. 49, in which the values of log / are plotted against the square-root of the ionic strength in these cases the solutions contained no other electrolyte than the one under consideration. Since the Debye-Htickel constant A for water at 25 is seen from Table XXXV to be 0.509, the limiting slopes of the plots in Fig. 49 should be equal to —0.509 the results to be expected theoretically, calculated in this manner, are shown by the dotted lines. It is evident that the experimental results approach the values required by the Debye-Hiickel limiting law as infinite dilution is attained. The influence of valence on the dependence of the activity coefficient on concentration is evidently in agreement with theoretical expectation. Another verification of the valence factor in the Debye-Hiickel equation will be given later (p. 177). 

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