Activity coefficients measurement

The activity coefficient measures the deviation from ideality. Substituting Equation 33 into Equation 30 yields... 

The issue of activity coefficient measurement for binary droplets was addressed by Allen et al. (1990). For low-vapor-pressure species, their diffusional fluxes in the gas phase are independent because of their low gas phase concentrations, and for a quasi-steady process each flux may be written... 

In both of the above examples, we used an anionic buffer (MOPS or cacodylate). The buffer anions have only repulsive interactions with RNA and can be grouped with chloride ions when calculating mean ion activities. Thus, we apply mean ionic activity coefficients measured with KC1 solutions to solutions in which K+ ions are contributed both by KC1 and K-buffer salts. We strongly advise against the use of cationic buffers such as Tris, because of its idiosyncratic interactions with nucleic acids as compared to group I ions, and particularly against mixing KC1 with Tris buffer, which creates a cationic mixture of unknown activity. 

C vapor-liquid equilibrium-activity coefficient, measured range 20-50°C, Cooling et al. 1992)... 

Note that if there is some mutual solubility of the two solvents, activity coefficients measured by this method are actually for solvents which are the dilute solutions of one of the solvents in the other. 

Figure 3. Composition-activity coefficient measurements and calculations...

For a more soluble (or completely miscible) pollutant (i.e., ethanol), a Henry s law constant can be similarly estimated by using its tabulated infinite dilution activity coefficient measured at Tx, by extrapolation using P2sat, from to T2 ... 

The required standard molar Gibbs energies of transfer can be obtained from activity coefficient measurements, using Eq. (4-3a),... 

The term log (1 + 0.002 m M ) arises from the conversion of the rational activity coefficient, measured on the mole-fraction scale, to the molal activity coefficient y according to the relationship... 

With the accumulation of activity coefficient measurements and the search for a theoretical expression ensued, it was discovered that in dilute solutions the logarithm of the activity coefficient was an approximate function of the square root of the molality ... 

Table A6.2 includes historical information on the comparison of ion activity coefficients at the effective ionic strength of seawater. Activity coefficients measured in single salt solutions are compared with those measured in seawater and those calculated from an association model. We have to distinguish between total activity coefficients (cf. equations 3 and 4)...

Direct measurement of riboflavin, FMN, and FAD in plasma or erythrocytes may be made by HPLC, usually with fluorescence detection after protein precipitation or by capillary zone electrophoresis with laser-induced fluorescence detection (CZE-LIF). In a study of riboflavin status and FMN and FAD concentrations in plasma and erythrocytes from elderly subjects at baseline and after low-dose riboflavin supplementation, using both activation coefficient measurements and CE-LIF, it was concluded that concentrations of aU Ba vitamers except plasma FAD are potential... 

Pividal, K. A., Sterner, C., Sandler, S. 1., and Orbey, H., 1992. Vapor-liquid equilibrium from infinite dilution activity coefficients Measurement and prediction of oxygenated fuel additives with alkanes. Fluid Phase Eq., 72 227-249. 

Electrodes of the second kind are available for many anions. In the case of cations, one may use the pure metal or the metal amalgam. The latter choice is convenient for reactive metals such as the alkali and alkaline earth metals. Of course, amalgams containing very reactive metals such as sodium also react with water. However, special techniques have been worked out so that activity coefficient measurements can also be carried out with amalgams involving these metals [5]. 

All models perform clearly less satisfactorily for the activities of heavy alkanes in short-chain ones, especially as the size asymmetry increases. Models without FV corrections such as UNIFAC, ASOG, and FH are particularly poor in these cases. Unfortunately, such activity coefficient measurements, which are used for testing the performance of the models for the activities of polymers, are scarce. Direct measurements for polymer... 

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... 

Eqs. 9.5-9 and 9.6-10 are identical. The important advantage of regular solution theory, however, is that we can calculate its parameters without resorting to activity coefficient measurements. Unfortunately, the parameters derived in this way are not as accurate as those fitted to experimental data. 

Next, one frequently would like to be able to make some assessment of the accuracy of a set of experimental vapor-liquid or activity coefficient measurements. Basic thermodynamic theory (as opposed to the solution modeling of Chapter 9) provides no means of predicting the values of liquid-phase activity coefficients to which the experimental results could be compared. Also, since the liquid solution models discussed in Chapter 9 only approximate real solution behavior, any discrepancy between these models and experiment is undoubtedly more a reflection of the inadequacy of the model than a test of the experimental results. 

A plot of a j, (or uho sCIo s. and called a ,Hci hr the electrolyte literature) versus muci is shown in Figure 17.4 (data in Table 17.2). Appropriately, the activity coefficients measurable as the ratio a /m on this diagram are called 7 ,hci- The reason for using the notation a ,HCi for flHo.sCio.s can be seen by continuing the molecularly-based reasoning we were pursuing before we stopped to consider the similarity to the olivine case. Going back to the relation ... 

Gas chromatography is primarily an analytical separation technique. However, since the basic process is an equilibration of a solute between two immiscible phases, the chromatographic technique may be used to measure such physical properties as activity coefficients, second virial coefficients of gas mixtures, partition coefficients, adsorption and partition isotherms, and complex formation constants. Other properties which can be measured with less accuracy, from secondary measurements or from temperature variation studies, include surface areas, heats of adsorption, and excess enthalpies and excess entropies of solution. A number of reviews and discussions on these measurements have appeared in the literature. The present work is restricted to a review of activity-coefficient measurements. 

The most reliable and comprehensive g.l.c. activity coefficient measurements for n-alkane systems have been done by the Bristol group > " using medium-high-pressure g.l.c. and taking all carrier-gas and solute imperfections into account. They have looked at the Q to Cg n-alkane solutes in Cig to Cga n-alkane solvents. Generally, the results indicate that the smaller the disparity in carbon number between solute and solvent, the closer is the activity coefficient to unity. The measured activity coefficients range from 0.930 for heptane + hexadecane at 303 K to 0.695 for heptane + dotriacontane at 348 K. Activity coefficients for many alk-l-ene + alkane systems have also been measured by this group. ... 

Medium activity coefficient Measure for the change in Gibbs energy when an electrolyte is transferred from one solvent to another solvent at infinite dilution. 

The correlation between entropy and hydration number is illustrated by the ratio of AShyd between La and Lu. Bertha and Choppin estimated this ratio to be 1.2. From activity coefficient measurements, Glueckauf (46) reported outer sphere hydration numbers of 7.5 and 8.7 for La and Lu, respectively, and also a La/Lu ratio of 1.2. Choppin and Graffeo (47) calculated hydration numbers from conductance data and reported a La/Lu hydration ratio of 1.1, while Padova measured molar volumes to obtain a La/Lu hydration ratio of 1.2. The consistency in this ratio calculated by four different methods supports the correlation between the total hydration numbers, the S hyd values, and the atomic number. 

Hydration studies for higher oxidation state actinides are reported for some AnOj salts (UO2 or NpO ) but not for any AnOj systems. The Raman spectra of aqueous uranyl solutions were interpreted to show the presence of six water molecules coordinated in the primary plane perpendicular to the O-U-O axis (Sutton 1952). However, similar hydration numbers have been obtained by methods in which the secondary hydration shell may also contribute to the value. For example, the activity coefficient measurements suggest a hydration number of 7.4 [relative to an assumed hydration number of zero for Cs(I) (Hinton and Amis 1971)]. Similarly, a hydration number of seven has been derived from Gusev s conductivity method (Gusev 1971, 1972,1973). 

From Equation 6.6 it is apparent that SG can be evaluated from calculated values of the transfer free energies of stable solute species, SG, in conjunction with the measured kinetic activation parameters, SAG. The required transfer free energies SG can readily be obtained from activity coefficient measurements using Equation 6.7 in which / refers to solute activity coefficients in the different solvents (y and are referred to the same standard state in solvents... 

Our laboratory in cooperation with several national and international academic and industrial partners is contributing to these efforts by the establishment of various dedicated characterization techniques (like activity coefficient measurements using GC technology) as well as determination of thermodynamic and physicochemical properties from a continuously growing portfolio of (functionalized) ionic liquids. Based on the received property data we published several papers related to the adjacent prediction of properties (like molar enthalpy of vaporization, parachor, interstice volume, interstice fractions, thermal expansion coefficient, standard entropy etc.). Additionally our laboratory created and launched a new most comprehensive Ionic Liquid property data base—delph-IL.(www.delphil.net). This fast growing collections of IL data will supvport researchers in the field to find and evaluate potential materials for their applications and hence decrease the time for new developments. 

Activity coefficient measurements using GC technique 2.1 Introduction... 

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