Activity coefficient effect

The thickness of the equivalent layer of pure water t on the surface of a 3Af sodium chloride solution is about 1 A. Calculate the surface tension of this solution assuming that the surface tension of salt solutions varies linearly with concentration. Neglect activity coefficient effects. 

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. 

Strangely, Reaction 25.2 proceeds backward in the early part of the calculation (Fig. 25.1), producing a small amount of potassium feldspar at the expense of muscovite and quartz. This result, quite difficult to explain from the perspective of mass transfer, is an activity coefficient effect. As seen in Figure 25.2, the activity coefficient for K+ increases rapidly as the fluid is diluted over the initial segment of the reaction path, whereas that for H+ remains nearly constant. (The activity coefficients differ because the a parameter in the Debyc-IIuckcl model is 3 A for K+ and 9 A for H+.) As a result, aK+ increases more quickly than aH+, temporarily driving Reaction 25.2 from right to left. 

The preferential interaction measured by thermodynamic techniques is, therefore, strictly an activity coefficient effect, which may be expressed in terms of a preferential binding parameter, (dgs/dg2)T,ni,n3 since... 

Since an equilibrium is assumed between the transition state and the reactant(s), and because the corresponding equilibrium constant can be expressed in terms of activity coefficients and concentrations to account for the non-ideality of the medium, it follows that there should be an activity coefficient effect upon reaction rates. This is observed as a dependence of the rate constant upon ionic strength - the kinetic electrolyte effect [2]. Thus, for a bimolecular reaction,... 

Yi = activity coefficient = (effective mole fraction)/(true mole fraction)... 

It is important to realize, however, that the determination of the substrate-micelle binding constant from solubility data relies entirely on data for saturated solutions and that, in the case of ionic surfactants, differences in the counterion interactions with the micelle and the micelle-substrate complex and activity coefficient effects may seriously complicate the results. In these respects, distribution studies with varying substrate and surfactant concentrations are certainly preferable. In view of the assumptions involved in the derivation and application of equations (10) and (11), the agreement between the K values obtained from kinetic data (equation 10) and those obtained from solubility measurements (equation 11) for several substrate-micelle interactions is certainly both remarkable and significant. 

Solution of a base B and its salt BHA When an appreciable concentration of salt is present, activity-coefficient effects may not be negligible. To the extent that = y = y the activity coefiicients largely cancel out in expressions for the calculation of hydrogen ion concentration. The overall reactions considered are ... 

Broadly considered, solubilities depend in part on nonspecific electrolyte effects and in part on specific effects. The nonspecific effects can be considered in terms of activity coefficients (Chapter 2). But activity-coefficient effects often are negligible compared with the uncertainties arising from disregarded or unknown side reactions and also with uncertainties arising from the crystalline state, the state of hydration, the extent of aging of the precipitate, and intrinsic solubility, all of which may contribute to the solubility of the precipitate. To the extent that each can be identified and measured, each can be accounted for. Nevertheless, the magnitude of unsuspected effects makes it expedient to assume activity coefficients of unity unless otherwise specifically indicated for relatively soluble salts or solutions containing moderate amounts of electrolytes. 

Equation (7-4) indicates that the solubility product includes an activity-coefficient term, a term which has been assumed to be unity up to this time. The introduction to this chapter pointed out that errors arising from neglect of the effects of the activity coefficient are usually small when compared with several uncertainties or side reactions. The activity coefficient in Equation (7-4) depends on the kind and concentration of all electrolytes in solution, not merely those involved directly with the precipitate. The correction to solubility calculations that must be made to account for the activity-coefficient effect is known as the diverse ion effect. The appropriate background is discussed in Chapter 2, and Problems 2-1,2-2, and 2-3 are examples of the calculations. For 1 1 electrolytes in solution, activity coefficients can usually be assumed to be unity when concentrations are much less than 0.1 M. Common ion and diverse ion effects can be significant at the same time, for example, when a large excess of common ion is added in a precipitation. The diverse ion effect is one of the reasons that the haphazard addition of a large excess of precipitant should be avoided. 

The gas phase itself cannot be neglected when activity-coefficient effects are under consideration, because of interactions involving molecules of solute-solute, solute-gas, and gas-gas. Activity coefficients calculated according to Equation (2-37) can be corrected by the inclusion of additional terms known as second virial coefficients. Usually this correction to the activity coefficient for solute-solute interactions is made according to... 

Cities of seawater, information on both the nature of the species and the extent of such associations is needed. Many difficulties are involved in evaluation of the degree of association between a cation and a ligand even in electrolyte solutions less complicated than seawater. It is difficult to separate the effects of ionic strength and of ion association. Either the ion association is known from other experiments or the activity coefficient effect is known from other experiments (both involve nonthermodynamic assumptions). 

Czaban JD, Cormier AD, Legg KD. Establishing the direct potentiometric normal range for Na/K residual liquid junction potential and activity coefficient effects. Chn Chem 1982 28 1936-45. 

In high-salinity waters such as seawater, both ion-pairing and activity-coefficient effects (see Chap. 4) increase the concentrations of species limited by the solubility of minerals. For example, in pure water saturated with respect to calcite, the molal solubility product ZmCa x ZmCOf" = 10 whereas in seawater this product equals 10 If the concentration of carbonate is constant, this corresponds to a 250-fold increase in the concentration of dissolved calcium in seawater relative to that in pure water. 

The more saline a water, the more soluble minerals tend to be in it, both because of complex formation and activity-coefficient effects (see Chap. 4). 

Czaban, J. D., Cormier, A. D., and Legg, K. D., The apparent suppression of Na/K data obtained with ion-selective electrodes is due to junction potential and activity coefficient effects, not bicarbonate binding. Clin. Chem. (Winston-SaUm, N.C.) 28, 1703—1705... 

Figure 3.2. Same as Figure 3.1, but with a log molality scale. The pH values of the crossover points are approximately the pK values of carbonic acid ionization, Equations (3.53) and (3.54) (very slightly different due to activity coefficient effects). 

Electrodes that behave in a Nernstian manner will have slopes equal to 59.16 mV per plon unit for monovalent cations, (59.16/2) mV per plon unit for divalent cations, —59.16 mV per plon unit for monovalent anions, and so on, at 25°C. [Where plon is defined exactly as is pH, as the negative logarithm to the base 10 of the ion concentration (activity) in M. So we have pF, pCa, pAg, and so on.] Many plots of concentration vs. voltage for ISEs deviate from hnearity due to activity coefficient effects, so an alternate approach is to use the MSA for calibration, especially for complex matrices. 

The system is thermodynamically ideal activity coefficient effects are not considered. 

This corresponds to solubility of 2.2 x lO g dm at 25 C, neglecting activity coefficient effects. 

In Section II.E, activity coefficients effects on proton adsorption will be discussed. 

The purpose of this section will be to make a semiquantitative estimate of the magnitude of activity coefficient effects in the proton adsorption process at the S-MO interface. In Section II.B, proton adsorption equations were derived with and without activity coefficient effects Eqs (24)-(26) and (27)-(29), respectively. The former... 

Equations (66)-(68) express the activity coefficient effects for the proton adsorption processes represented by mass action Eqs (20)-(22), respectively. Since general explicit equations for activity coefficients cannot be derived solely from thermodynamics [13, 14], Eqs (66)-(68) have been derived by combining electrostatic theory with Gibbs-Lewis thermodynamics. For solute ions, the procedure is commonly referred to as the Debye-Hiickel model (Chapter 4) [8, 9, 15], while for surface site ions the activity coefficient derivations are based on the primitive interfacial model (chapter 4) [16]. 

The ideal surface-site mole fractions for ID proton adsorption were calculated for Fig. 5 with Eqs (27)-(29). The surface-site mole fractions for AC proton adsorption with activity coefficient effects included were caleulated by substituting Eqs (72), (74), and (76) into adsorption equations (24)-(26). 

An equal number of equations and variables allows the elimination of all the unknown variables in all the cation adsorption equations derived so far if activity coefficient effects are ignored, so that Vj does not require evaluation. Evaluation of will be discussed at the end of this section. 

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