Solute activities

Fig. V-11. Electrocapillary curves (a) adsorption of anions (from Ref. 113) (b) absorption of cations (from Ref. 6) (c) electrocapillary curves for -pentanoic acid in QAN HCIO4. Solute activities from top to bottom are 0, 0.04761, 0.09096, 0.1666, and 0.500 (from Ref. 112).

Still another situation is that of a supersaturated or supercooled solution, and straightforward modifications can be made in the preceding equations. Thus in Eq. IX-2, x now denotes the ratio of the actual solute activity to that of the saturated solution. In the case of a nonelectrolyte, x - S/Sq, where S denotes the concentration. Equation IX-13 now contains AH, the molar heat of solution. 

For gases, pure solids, pure liquids, and nonionic solutes, activity coefficients are approximately unity under most reasonable experimental conditions. For reactions involving only these species, differences between activity and concentration are negligible. Activity coefficients for ionic solutes, however, depend on the ionic composition of the solution. It is possible, using the extended Debye-Htickel theory, to calculate activity coefficients using equation 6.50... 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

In an attempt to explain the nature of polar interactions, Martire et al. [15] developed a theory assuming that such interactions could be explained by the formation of a complex between the solute and the stationary phase with its own equilibrium constant. Martire and Riedl adopted a procedure used by Danger et al. [16], and divided the solute activity coefficient into two components. 

It is not appropriate here to consider the kinetics of the various electrode reactions, which in the case of the oxygenated NaCl solution will depend upon the potentials of the electrodes, the pH of the solution, activity of chloride ions, etc. The significant points to note are that (a) an anode or cathode can support more than one electrode process and b) the sum of the rates of the partial cathodic reactions must equal the sum of the rates of the partial anodic reactions. Since there are four exchange processes (equations 1.39-1.42) there will be eight partial reactions, but if the reverse reactions are regarded as occurring at an insignificant rate then... 

Direct measurements of solute activity are based on studies of the equilibria in which a given substance is involved. The parameters of these equilibria (the distribution coefficients, equilibrium constants, and EMF of galvanic cells) are determined at different concentrations. Then these data are extrapolated to very low concentrations, where the activity coincides with concentration and the activity coefficient becomes unity. 

The net retention volume and the specific retention volume, defined in Table 1.1, are important parameters for determining physicochemical constants from gas chromatographic data [9,10,32]. The free energy, enthalpy, and. entropy of nixing or solution, and the infinite dilution solute activity coefficients can be determined from retention measurements. Measurements are usually made at infinite dilution (Henry s law region) in which the value of the activity coefficient (also the gas-liquid partition coefficient) can be assumed to have a constant value. At infinite dilution the solute molecules are not sufficiently close to exert any mutual attractions, and the environment of each may be considered to consist entirely of solvent molecules. The activity... 

For dilute solutions, activities can be replaced by concentrations in Eqs. (6.1.9), yielding... 

Solution Activation 50 mg of supported Pt20 DEN was mixed with a solvent/acid mixture (see Table 1) in a 50 ml round bottom flask and refluxed for 2 - 6 hrs. Solid samples were separated from solution by vacuum filtration and dried in vacuum oven at 50°C overnight. To prepare sample 6 (see Table 1), supported Pt20 DENs were mixed with HN03/H20 (volume pore volume of Si02) in a sample vial, heated to 70°C for 2hrs, and dried in a vacuum oven at 50°C overnight. 

Since mild activation conditions appear to be important, a number of solution activation conditions were tested. PAMAM dendrimers are comprised of amide bonds, so the favorable conditions for refro-Michael addition reactions, (low pH, high temperature and the presence of water) may be able to cleave these bonds. Table 1 shows a series of reaction tests using various acid/solvent combinations to activate the dendrimer amide bonds. Characterization of the solution-activated catalysts with Atomic Absorption spectroscopy, FTIR spectroscopy and FTIR spectroscopy of adsorbed CO indicated that the solution activation generally resulted in Pt loss. Appropriate choice of solvent and acid, particularly EtOH/HOAc, minimized the leaching. FTIR spectra of these samples indicate that a substantial portion of the dendrimer amide bonds was removed by solution activation (note the small y-axis value in Figure 4 relative... 

In Chapter 17 (Section 17-11), we stated that for heterogeneous equilibria, terms for pure liquids and pure solids do not appear in K expressions because their activity values are essentially 1. In the discussion in Section 18-4, these terms are temporarily included. In dilute solutions, activities are equal to concentrations. 

This choice of a standard state seems like impossible mental gymnastics, but it allows activity to follow a molal scale, so that in dilute solutions activity and molality - despite the fact that activity is unitless - are equivalent numerically. A species molality m , the number of moles of the species per kilogram of solvent, is related to its activity by... 

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

Invented by H. E. Benson in 1952 and then developed with J. H. Field at the U.S. Bureau of Mines. First licensed by the Benfield Corporation of Pittsburgh, subsequently acquired by the Union Carbide Corporation, and now licensed by UOP. The current UOP version includes new solution activators and incorporates zeolites or membrane processes for complete separation of acid gases and minimal loss of product gases. More than 650 plants were operating in 1996. Variations include the Benfield HiPure process and the Benfield LoHeat process. See also Carsol, CATACARB, Giammarco-Vetrocoke, HiPure. 

At oxide surfaces, the surface activities of H+ and OH are not fixed in a similar way. Then the variation in surface potential with solution activity of H+ depends on the chemical and electrostatic properties of the interface. For the many oxides that are insulators, it is much more difficult to obtain a measurement of the surface-solution potential differences than it is for conductors such as Agl. Thus there is uncertainty whether the dependence of surface potential on pH is approximately Nernstian or significantly sub-Nernstian. 

This change has two attractive features (1) It eliminates the separation of activity coefficients into short- and long-range interactions, which cannot be evaluated separately in practice, and (2) implicitly incorporates an expected effect of surface potential on solution activity through the activity coefficient relationship of Equation 22. Table II summarizes the relevant reaction and activity coefficient terms based on the above modifications of the TLM. 

Although nearly identical solid-aqueous solution compositions are observed in recrystallization from two directions under conditions of total constant composition, this alone is insufficient proof of the establishment of equilibrium. In order to test for equilibrium, the solid solution activity coefficients must be determined and used to compare observed solid and aqueous solution compositions with the appropriate values expected at equilibrium. 

Table VI summarizes values of the activity coefficient ratio Ygr-/YC].- in the saturated solution for each average solid composition (as calculated from the model of Table II), the calculated provisional equilibrium distribution coefficient (Equation 12) and the provisional equilibrium aqueous solution activity ratio of Br to Cl- (Equation 13) based on the data of Table V.

Using the experimental solution compositions (Table IV) and the calculated aqueous solution activity coefficient ratio Ygr-/Y( - (Table VI), Figure 4 shows the slopes of log K... 

Values for the parameters are determined by a least squares fit of experimental data using eq (5) for experiments such as galvanic cells measurements that measure solute activity and thus y/Yref values, and eq (6) for experiments such as vapor pressure measurements that measure solvent activity and thus (f) values. All the original data are used in a single fitting program to determine the best values for the parameters. A detailed description of the evaluation procedure has been illustrated for the system calcium chloride-water (Staples and Nuttall, 1977), and calculations deriving activity data from a variety of experimental technique measurements have also been described. 

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