Activity ionic medium

Ruthenium- and cobalt-catalyzed hydroformylation of internal and terminal alkenes in molten [PBuJBr was reported by Knifton as early as in 1987 [2]. The author described a stabilization of the active ruthenium-carbonyl complex by the ionic medium. An increased catalyst lifetime at low synthesis gas pressures and higher temperatures was observed. 

In the author s group, much lower-melting benzenesulfonate, tosylate, or octyl-sulfate ionic liquids have recently been obtained in combination with imidazolium ions. These systems have been successfully applied as catalyst media for the biphasic, Rh-catalyzed hydroformylation of 1-octene [14]. The catalyst activities obtained with these systems were in all cases equal to or even higher than those found with the commonly used [BMIM][PF6]. Taking into account the much lower costs of the ionic medium, the better hydrolysis stability, and the wider disposal options relating to, for example, an octylsulfate ionic liquid in comparison to [BMIM][PF6], there is no real reason to center future hydroformylation research around hexafluorophosphate ionic liquids. 

All equilibrium constants in the present discussion are based on the concentration (not activity) scale. This is a perfectly acceptable thermodynamic scale, provided the ionic strength of the solvent medium is kept fked at a reference level (therefore, sufficiently higher than the concentration of the species assayed). This is known as the constant ionic medium thermodynamic state. Most modern results are determined at 25 °C in a 0.15 M KCl solution. If the ionic strength is changed, the ionization constant may be affected. For example, at 25 °C and 0.0 M ionic strength, the pXj of acetic acid is 4.76, but at ionic strength 0.15 M, the value is 4.55 [24]. 

In this work the concepts of ionic medium, effective ionic strength and free versus total activity coefficients are examined. Then they are applied to the study of permissible and incorrect translations of equilibrium constants from one medium to another. 

The activity of water is obtained by inserting Eq. (6.12) into Eq. (6.11). It should be mentioned that in mixed electrolytes with several components at high concentrations, it is necessary to use Pitzer s equation to calculate the activity of water. On the other hand, uhjO is near constant (and = 1) in most experimental studies of equilibria in dilute aqueous solutions, where an ionic medium is used in large excess with respect to the reactants. The ionic medium electrolyte thus determines the osmotic coefficient of the solvent. 

It can be shown that the virial type of activity coefficient equations and the ionic pairing model are equivalent, provided that the ionic pairing is weak. In these cases, it is in general difficult to distinguish between complex formation and activity coefficient variations unless independent experimental evidence for complex formation is available, e.g., from spectroscopic data, as is the case for the weak uranium(VI) chloride complexes. It should be noted that the ion interaction coefficients evaluated and tabulated by Cia-vatta [10] were obtained from experimental mean activity coefficient data without taking into account complex formation. However, it is known that many of the metal ions listed by Ciavatta form weak complexes with chloride and nitrate ions. This fact is reflected by ion interaction coefficients that are smaller than those for the noncomplexing perchlorate ion (see Table 6.3). This review takes chloride and nitrate complex formation into account when these ions are part of the ionic medium and uses the value of the ion interaction coefficient (m +,cio4) for (M +,ci ) (m +,noj)- Io... 

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

The infinite dilution activity scale is useful for ionic equilibria in fresh waters, but for equilibria in sea water one gains precision by applying an ionic medium activity scale. Measuring pH in sea water gives less information than total alkalinity and total carbonate. Calculations on redox equilibria are simplified by introducing the master variable pE -----log e. ... 

The "ionic medium activity scale, on the other hand, is so defined that the activity coefficient, yA = A / [A] approaches unity as the solution approaches the pure solvent (in this case the ionic medium)—Le., when the concentrations go toward zero for all other species than water and the medium ions. 

Experience shows that the activity coefficients on this scale stay near unity (usually within experimental error) as long as the concentrations of the reactants are kept low, say less than 10% of the concentrations of the medium ions. The activity ( concentration) of several ions, notably H+, can be determined conveniently and accurately by means of e.m.f. methods, either with or without a liquid junction. In the latter case the liquid junction potential is small (mainly a function of [H+] ) and easily corrected for (3). The equilibrium constant for any reaction, on the ionic medium scale, may then be defined as the limiting value for the concentration quotient ... 

We cannot distinguish between such species simply because we do not vary the water activity < H20 >. Working with an ionic medium, we also keep the activities of the medium ions practically constant, and so we cannot distinguish between species containing various amounts of the medium ions. Hence, one must understand that the formulas for various species include an unknown number of water molecules and medium ions. For instance, if our ionic medium is the model sea water referred to above, we would mark true concentrations by asterisks. 

Determining solubility constants in aqueous solutions generally involves analytical work to determine concentrations [ ] or potentiometric measurements to obtain activities. The ratio of activity and concentration—i.e., the activity coefficient and its change with concentration— depends on the choice of the standard state. If pure water is chosen as a standard state, the activity coefficients approach unity only in dilute solutions. It is therefore necessary to express the so-called thermodynamic constants TK (48) in terms of activities. If, on the other hand, one chooses as reference an aqueous solution of comparatively high and constant ionic strength, the activity coefficients remain close to unity even at rather high concentrations of the reacting species. In this case, we may use stoichiometric constants K (48), expressed in molarities, M, and related to a particular ionic medium. 

The constant-capacitance model (Goldberg, 1992) assigns all adsorbed ions to inner-sphere surface complexes. Since this model also employs the constant ionic medium reference state for activity coefficients, the background electrolyte is not considered and, therefore, no diffuse-ion swarm appears in the model structure. Activity coefficients of surface species are assumed to sub-divide, as in the triplelayer model, but the charge-dependent part is a function of the overall valence of the surface complex (Zk in Table 9.8) and an inner potential at the colloid surface exp(Z F l,s// 7). Physical closure in the model is achieved with the surface charge-potential relation ... 

The composition of these complexes and their stability constants have been determined for a large number of metal ions primarily with the use of emf methods (200, 201). The free hydrogen ion concentration and in some cases the free metal ion concentration are determined as functions of the stoichiometric hydrogen ion and metal ion concentrations. From measurements on series of solutions of different concentrations the number of metal atoms in a complex and its charge can be derived, but no information is obtained on the number of water molecules in the complex. Since emf measurements are influenced by changes in activity factors they have usually been done in an inert ionic medium of high concentration (3 M NaC104) and at low metal ion concentrations. The major complexes formed, however, have been found to be stable also in the concentrated solutions needed for X-ray diffraction measurements, and the stability constants determined seem to be... 

Potentiometric methods have eliminated the problems that beset earlier studies, due to the high electrolyte concentrations required for ideal electrode behavior. Following the so-called constant ionic medium principle [91], a large excess of an indifferent (or inert or swamping) electrolyte is added, so that the activity coefficients of the species can be considered constant when their concentration (very low compared to that of the indifferent electrolyte) are changed over a wide range. 

Because of difficulties in precisely calculating the total ion activity coefficient (y) of calcium and carbonate ions in seawater, and the effects of temperature and pressure on the activity coefficients, a semi-empirical approach has been generally adopted by chemical oceanographers for calculating saturation states. This approach utilizes the apparent (stoichiometric) solubility constant (K ), which is the equilibrium ion molal (m) product. Values of K are directly determined in seawater (as ionic medium) at various temperatures, pressures and salinities. In this approach ... 

The Ionic Medium Scale This convention can be applied to solutions that contain a swamping concentration of inert electrolyte in order to maintiiin a constant ionic medium. The activity coefficient, f = A /[A], beconries unity as the solution approaches the pure ionic medium, that is, when all concentrations other than the medium ions approach zero ... 

Figure 3.2. Activity coefficients depend on the selection of the reference state and standard state, (a) On the infinite dilution scale the reference state is an infinitely dilute aqueous solution the standard state is a hypothetical solution of concentration unity and with properties of an infinitely dilute solution. For example, the activity coeffic ent of in a HCl solution, / hcm varies with [HCl] in accordance with a Debye-Hiickel equation (dashed line, left ordinate) (see Table 3.3) only at very great dilutions does /become unity. On the ionic medium scale, for example, in I M KCl, the reference...

State is the ionic medium (i.e., infinitely diluted with respect to HCl only). In such a medium /hci (solid line, right ordinate) is very nearly constant, that is,/Hci = 1- Both activity coefficients are thermodynamically equally meaningful. (Adapted from P. Schindler.) (b) A comparison of activity coefficients (infinite dilution scale) of electrolytes and nonelectrolytes as a function of concentration (mole fraction of solute) m = moles of solute per kg of solvent (molality) = number of moles of ions formed from 1 mol of electrolyte 1 kg solvent contains 55.5 mol of water. (From Robinson and Stokes, 1959. Reproduced with permission from Butterworths, Inc., London.)... 

As equation 23 illustrates, a change in the activity scale convention merely changes kf. In an ideal constant ionic medium, equation 23 becomes... 

Both activity scales are thermodynamically equally well defined. In constant ionic medium, activity (= concentration) can frequently be determined by means of emf methods. 

Activity coefficients defined within the infinite dilution activity scale cannot be formulated theoretically for the ionic medium of seawater. Since the oceans contain an ionic medium of practically constant composition, the ionic medium activity scale might be used advantageously in studying acid-base and other equilibria in seawater (see also Appendix 6.2 in Chapter 6). 

Equilibrium constants are either or are defined in terms of the constant ionic medium activity scale. 

In dealing with redox equilibria, we are also confronted with the problem of evaluating activity corrections or maintaining the activities under consideration as constants. The Nernst equation rigorously applies only if the activities and actual species taking part in the reaction are inserted in the equation. The activity scales discussed before, the infinite dilution scale and the ionic medium scale, may be used. The standard potential or standard pe on the infinite dilution scale is related to the equilibrium constant for / = 0 of the reduction reaction... 

These authors used activities instead of concentrations, but at constant ionic strength (constant ionic medium scale), the rate law can be written in terms of concentrations. 

Acidity scales are used commonly to assess the chemical and biological state of seawater. The international operational scale of pH fulfills the primary, requirement of repro ducibility and leads to useful equilbrium data. Nevertheless, these pH numbers do not have a well defined meaning in respect to all marine processes. Seawater of 35%o salinity behaves as a constant ionic medium, effectively stabilizing both the activity coefficients and the liquid junction potential. It may be possible, therefore, to determine hydrogen ion concentrations in seawater experimentally. One method is based on cells without a liquid junction and is used to establish standard values of hydrogen ion concentration (expressed as moles of H /kg of seawater) for reference buffer solutions. 

The constant ionic medium reference state determines the activity coefficients of the aqueous species. 

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