Solvent activity coefficients measurement

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. 

The competition model and solvent interaction model were at one time heatedly debated but current thinking maintains that under defined r iitions the two theories are equivalent, however, it is impossible to distinguish between then on the basis of experimental retention data alone [231,249]. Based on the measurement of solute and solvent activity coefficients it was concluded that both models operate alternately. At higher solvent B concentrations, the competition effect diminishes, since under these conditions the solute molecule can enter the Interfacial layer without displacing solvent molecules. The competition model, in its expanded form, is more general, and can be used to derive the principal results of the solvent interaction model as a special case. In essence, it seems that the end result is the same, only the tenet that surface adsorption or solvent association are the dominant retention interactions remain at variance. 

The above separation of charge and geometric progression of the transition state has at least one disturbing consequence. Reaction transition states are commonly characterized by various parameters. These include kinetic isotope effects, the Bransted parameter, and solvent activity coefficients. The question immediately arises do these measures of transition state structure measure charge or geometric progression On the basis of the previous discussion, they can, at best, measure one but not both of these parameters. Let us first consider the Bransted parameter a. 

The most satisfactory way of estimating solvent activity coefficients is by electrochemical measurements of the EMF of appropriate cells, or by polarographic methods (Kolthoff, 1964). Some measurements have been made (Kolthoff and Thomas, 1965 Nelson and Iwamoto, 1961 Koepp, Wendt and Strehlow, 1960 Coetzee et al., 1963 Alexander and Parker, 1966). The electrochemical methods are aimed at measuring liquid junction potentials between two half-cells in different solvents (Kolthoff and Thomas, 1965) and rely heavily on assumptions such as (i) and (ii). 

A simple, but rough, way of applying assumptions (i), (ii) and (iii) is to measure the solubilities of the appropriate salts in the reference solvent and in other solvents of comparable dielectric constant. Provided that saturated solutions are not too concentrated, that there is no ion association, that the solutes do not react with the solvent and that the solid phase, which is in equilibrium with the saturated solution, is the same in each solvent, then solubilities lead directly to solvent activity coefficients. Since all saturated solutions of a salt, AB, have the same activity, we can write (19), in which is the concentration in saturated reference solvent and c is the concentration in the saturated solvent, S. 

This question is not easy to answer. One approach is to utilize individual solvent activity coefficients for anions, e.g. y - (cf. Table 5), which have been calculated by making certain assumptions, as already outlined. These can be combined with rates and measured values of °ycHsi equation (9) to give solvent activity coefficients for transition states. The results of such assumptions and calculations are shown in Table 9. Positive values of log yf mean that the solute i is more solvated by DMF than by the solvent S. 

Since pressure measurements are relatively simple, Eq. 11.5-4 can be the basis for determining solvent activity coefficients in a solvent-solute system, provided a suitable leakproof membrane can be found. Osmotic pressure measurements are, however, more commonly used to determine the molecular weights of proteins and other macromolecules (for which impermeable membranes are easily found). In such cases an osmometer, such as the one shown in schematic form in Fig. 11.5-1, is used to measure the equilibrium pressure difference between the pure solvent and the solvent containing the macromolecules (which are too large to pass through the membrane) the pressure difference AF, which is the osmotic pressure 77, is equal to pg/t, where p is the solution density and h is the difference in liquid heights. If the solute concentration is small, we have... 

In a similar fashion, solubility measurements (of a gas in a liquid, a liquid in a liquid, or a solid in a liquid) can be used to determine the activity coefficient of a solute in a solvent at saturation. Also, measurements of the solubility of a solid solute in two liquid phases can be used to relate the activity coefficient of the solute in one liquid to a known activity coefficient in another liquid, and freezing-point depression or boiling-point elevation measurements are frequently used to determine the activity of the solvent in a solute-solvent mixture. We have also showed that osmotic-pressure measurements can be used to determine solvent activity coefficients, or to determine the molecular weight of a large polymer or protein. 

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. 

A measurement of — /ta also gives us the solvent activity coefficient, based on the pure-solvent reference... 

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... 

The activity of any ion, a = 7m, where y is the activity coefficient and m is the molaHty (mol solute/kg solvent). Because it is not possible to measure individual ionic activities, a mean ionic activity coefficient, 7, is used to define the activities of all ions in a solution. The convention used in most of the Hterature to report the mean ionic activity coefficients for sulfuric acid is based on the assumption that the acid dissociates completely into hydrogen and sulfate ions. This assumption leads to the foUowing formula for the activity of sulfuric acid. 

Another method to determine infinite dilution activity coefficients (or the equivalent FFenry s law coefficients) is gas chromatography [FF, F2]. In this method, the chromatographic column is coated with the liquid solvent (e.g., the IL). The solute (the gas) is introduced with a carrier gas and the retention time of the solute is a measure of the strength of interaction (i.e., the infinite dilution activity coefficient, y7) of the solute in the liquid. For the steady-state method, given by [FF, F2] ... 

For ideal solutions, the activity coefficient will be unity, but for real solutions, 7r i will differ from unity, and, in fact, can be used as a measure of the nonideality of the solution. But we have seen earlier that real solutions approach ideal solution behavior in dilute solution. That is, the behavior of the solvent in a solution approaches Raoult s law as. vi — 1, and we can write for the solvent... 

When a solute is added to an acidic solvent it may become protonated by the solvent. If the solvent is water and the concentration of solute is not very great, then the pH of the solution is a good measure of the proton-donating ability of the solvent. Unfortunately, this is no longer true in concentrated solutions because activity coefficients are no longer unity. A measurement of solvent acidity is needed that works in concentrated solutions and applies to mixed solvents as well. The Hammett acidity function is a measurement that is used for acidic solvents of high dielectric constant. For any solvent, including mixtures of solvents (but the proportions of the mixture must be specified), a value Hq is defined as... 

The thermodynamic properties of real electrolyte solutions can be described by various parameters the solvent s activity Oq, the solute s activity the mean ion activities a+, as well as the corresponding activity coefficients. Two approaches exist for determining the activity of an electrolyte in solution (1) by measuring the solvent s activity and subsequently converting it to electrolyte activity via the thermodynamic Gibbs-Duhem equation, which for binary solutions can be written as... 

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... 

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