Interfacial activity coefficients

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

The film pressure of a myristic acid film at 20°C is 10 dyn/cm at an area of 23 A per molecule the limiting area at high pressures can be taken as 20 A per molecule. Calculate what the film pressure should be, using Eq. IV-36 with / = 1, and what the activity coefficient of water in the interfacial solution is in terms of that model. 

Information on the coefficients is relatively undeveloped. They are evidently strongly influenced by rate of drop coalescence and breakup, presence of surface-active agents, interfacial turbulence (Marangoni effect), drop-size distribution, and the like, none of which can be effectively evaluated at this time. 

The interfacial free energy y(T, a, o e. Oac. A) depends only on temperature, the activities, and the difference between the electrostatic potentials of electrode and electrolyte, A, which, apart from a, are aU well-defined and experimentally accessible quantities. Therefore, the accurate calculation of y depends on the accuracy of evaluating or the corresponding activity coefficient/.. 

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 triple layer model has been described in detail elsewhere (11, 16, 17) however, the model as reported here has been slightly modified from the original versions (11, 15) in two ways (i) metal ions are allowed to form surface complexes at either the o- or 8-plane insted of at the 8-plane only, and (ii) the thermodynamic basis of the TLM has been modified leading to a different relationship between activity coefficients and interfacial potentials. The implementation and basis for these modifications are described below. 

Another interpretation of the electrocapillary curve is easily obtained from Equation (89). We wish to investigate the effect of changes in the concentration of the aqueous phase on the interfacial tension at constant applied potential. Several assumptions are made at this point to simplify the desired result. More comprehensive treatments of this subject may be consulted for additional details (e.g., Overbeek 1952). We assume that (a) the aqueous phase contains only 1 1 electrolyte, (b) the solution is sufficiently dilute to neglect activity coefficients, (c) the composition of the metallic phase (and therefore jt,Hg) is constant, (d) only the potential drop at the mercury-solution interface is affected by the composition of the solution, and (e) the Gibbs dividing surface can be located in such a way as to make the surface excess equal to zero for all uncharged components (T, = 0). With these assumptions, Equation (89) becomes... 

The interfacial pd selectivity coefficient, the factor multiplying a is determined by the ratio K /K, by the activity coefficient ratio, and by the mobility ratio, when the internal diffusion potential contribution is added. Clearly interferences should correlate with the ratio K /1C, which can be determined from salt extraction coefficients K KX/K K for a series of positive drugs, using common anion salts. This result is well documented in the literature (7,8). A curious correlation for N-based drugs studied by us and by Freiser ( ) is a trend in selectivity... 

The interfacial tension at the flat interface is calculated using eq 5.2, but with the activity coefficients equated to unity. Hence... 

This equation holds strictly only if the activity coefficients f(/ v,max - vrs)/rw and f(/M do not change with varying the interfacial electric field at constant /j. Assuming, for simplicity, that the electric field is constant across the whole compact layer (0 < x < d), the partial derivatives in Eq. (25) can be replaced by ratios of finite increments, yielding 4,6... 

RTfVw) nNw because yw was set equal to 1. For an exact treatment when many interfaces are present (e.g., in the cytosol of a typical cell), we cannot set yw equal to 1 because the activity of water, and hence the osmotic pressure (n), is affected by proteins, other colloids, and other interfaces. In such a case, Equation 2.11 suggests a simple way in which a matric pressure may be related to the reduction of the activity coefficient of water caused by the interactions at interfaces. Equation 2.11 should not be viewed as a relation defining matric pressures for all situations but rather for cases for which it might be useful to represent interfacial interactions by a separate term that can be added to Fly, the effect of the solutes on FI. 

Although FI and aw may be the same throughout some system, both Fly and t in Equation 2.11 may vary. For example, water activity in the bulk of the solution may be predominantly lowered by solutes, whereas at or near the surface of colloids the main factor decreasing ciw from 1 could be the interfacial attraction and binding of water. As already indicated, such interfacial interactions reduce the activity coefficient of water, yw. 

Calculations of the relations between the input and output amounts and compositions and the number of extraction stages are based on material balances and equilibrium relations. Knowledge of efficiencies and capacities of the equipment then is applied to find its actual size and configuration. Since extraction processes usually are performed under adiabatic and isothermal conditions, in this respect the design problem is simpler than for thermal separations where enthalpy balances also are involved. On the other hand, the design is complicated by the fact that extraction is feasible only of nonideal liquid mixtures. Consequently, the activity coefficient behaviors of two liquid phases must be taken into account or direct equilibrium data must be available. In countercurrent extraction, critical physical properties such as interfacial tension and viscosities can change dramatically through the extraction system. The variation in physical properties must be evaluated carefully. 

An alternative method for estimating activity coefficient involves a consideration of interfacial tension between solute and solvent. Amidon, Yalkowsky, and Leung.f reported this method to estimate the solubility of organic solutes in water ... 

X is the concentration of the adsorbate A which is varied in order to study the effect of bulk concentration on the interfacial surface excess y is the concentration of the electrolyte whose activity is kept constant. The corresponding electrolyte concentration is kept reasonably high to provide electrical conductivity to the solution. For low values of x, the electrolyte concentration is constant. However, at higher concentrations of organic solute, the activity coefficient of the electrolyte varies with organic solute concentration. Thus, in general, the concentration of the electrolyte must also be varied in order to keep its activity constant. It is also important that the ions of the electrolyte not adsorb on the electrode to a significant extent. 

This simple relation corresponds to a complicated phenomenon, because the solubility of the salt may be changed in the interfacial region (more than in the bulk solution) and both activity coefficients of the salt and the neutral substance are altered. The modifications of these may be different on the different faces. 

The majority of electrochemical problems can be solved without separating the emf into absolute potentials . However, it should be mentioned that the problem concerning the structure of the interfacial potential drop becomes the topical problem for the modern studies of electrified interfaces on the microscopic level, particularly, in attempts of testing the electrified interfaces by probe techniques [92-94]. The absolute scales are also of interest for electrochemistry of semiconductors in the context of calibrating the energy levels of materials. This problem is related to another general problem of physical chemistry - the determination of activity coefficient of an individual charged species. 

A material that is strongly adsorbed at an interface may be termed a surface active material (a surfactant ), and will normally produce a dramatic reduction in interfacial tension with small changes in bulk phase concentration. In dilute solution, it is assumed that the activity coefficient of a material, 72, can be approximated as unity so that the last term in Equation (9.15) can be substituted for by the molar concentration, C2. The practical applicability of this relationship is that the relative adsorption of a material at an interface, its surface activity, can be determined from measurement of the interfacial tension as a function of solute concentration ... 

In the studies interfacial adsorption should be taken into consideration as in most cases this results in the largest measurements error in partition and activity coefficients, particularly for solutes of different polarity to the stationary phase. 

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