Activity electrolyte solution

Derive the equation of state, that is, the relationship between t and a, of the adsorbed film for the case of a surface active electrolyte. Assume that the activity coefficient for the electrolyte is unity, that the solution is dilute enough so that surface tension is a linear function of the concentration of the electrolyte, and that the electrolyte itself (and not some hydrolyzed form) is the surface-adsorbed species. Do this for the case of a strong 1 1 electrolyte and a strong 1 3 electrolyte. 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

The Nemst equation above for the dependence of the equilibrium potential of redox electrodes on the activity of solution species is also valid for uncharged species in the gas phase that take part in electron exchange reactions at the electrode-electrolyte interface. For the specific equilibrium process involved in the reduction of chlorine ... 

Passivity—a condition of a metal or alloy in which the material is normally thermodynamically unstable in a given electrolytic solution but remains visibly unchanged for a prolonged period. The electrode potential of a passive metal is always appreciably more noble than its potential in the active state. 

There is a third experimental design often used for studies in electrolyte solutions, particularly aqueous solutions. In this design the reaction rate is studied as a function of ionic strength, and a rate variation is called a salt effect. In Chapter 5 we derived this relationship between the observed rate constant k and the activity coefficients of reactants l YA, yB) and transition state (y ) ... 

An important assumption was that the solution was dilute (in this case natural water of approximately lOOp.p.m. total dissolved solids) since there are difficulties in applying mass transport equations for certain situations in concentrated electrolyte solution, where a knowledge of activities is uncertain and this can lead to large errors. 

Table 6.2 Activity coefficient relationships for electrolyte solutions (single electrolyte)... 

Most of the methods we have described so far give the activity of the solvent. Often the activity of the solute is of equal or greater importance. This is especially true of electrolyte solutions where the activity of the ionic solute is of primary interest, and in Chapter 9, we will describe methods that employ electrochemical cells to obtain ionic activities directly. We will conclude this chapter with a discussion of methods based on the Gibbs-Duhem equation that allow one to calculate activities of one component if the activities of the other are known as a function of composition. 

This expression is often used to determine activity coefficients (7 ) of the solute in electrolyte solutions. 

Equation (7.45) is a limiting law expression for 7 , the activity coefficient of the solute. Debye-Htickel theory can also be used to obtain limiting-law expressions for the activity a of the solvent. This is usually done by expressing a in terms of the practical osmotic coefficient

electrolyte solute, it is defined in a general way as... 

Chapters 7 to 9 apply the thermodynamic relationships to mixtures, to phase equilibria, and to chemical equilibrium. In Chapter 7, both nonelectrolyte and electrolyte solutions are described, including the properties of ideal mixtures. The Debye-Hiickel theory is developed and applied to the electrolyte solutions. Thermal properties and osmotic pressure are also described. In Chapter 8, the principles of phase equilibria of pure substances and of mixtures are presented. The phase rule, Clapeyron equation, and phase diagrams are used extensively in the description of representative systems. Chapter 9 uses thermodynamics to describe chemical equilibrium. The equilibrium constant and its relationship to pressure, temperature, and activity is developed, as are the basic equations that apply to electrochemical cells. Examples are given that demonstrate the use of thermodynamics in predicting equilibrium conditions and cell voltages. 

The most important quality of the pzc is that it contains information about the structural details of the metal/solution interface. In the absence of surface-active electrolytes, the pzc depends only on the nature of the metal and the solvent.3,4,5 Conversely, the pztc is not exclusively relevant to the structure of the interface this is truer the larger the value of in Eq. (8) (or of At where i is the species to which the electrode is reversible e.g., H+ for the Pt group metals in the H adsorption region). 

The C, values for Sb faces are noticeably lower than those for Bi. Just as for Bi, the closest-packed faces show the lowest values of C, [except Bi(lll) and Sb(lll)].28,152,153 This result is in good agreement with the theory428,429 based on the jellium model for the metal and the simple hard sphere model for the electrolyte solution. The adsorption of organic compounds at Sb and Bi single-crystal face electrodes28,152,726 shows that the surface activity of Bi(lll) and Sb(lll) is lower than for the other planes. Thus the anomalous position of Sb(lll) as well as Bi(lll) is probably caused by a more pronounced influence of the capacitance of the metal phase compared with other Sb and Bi faces28... 

The first studies of the electrical double-layer structure at Sn + Pb and Sn + Cd solid drop electrodes in aqueous surface-inactive electrolyte solutions were carried out by Kukk and Piittsepp.808 Alloys with various contents of Pb (from 0.2 to 98%) were investigated by impedance.615,643,667,816 Small amounts of Pb caused dramatic shifts of toward more negative values. For alloys with Pb bulk content 0.2%, was the same as for pc-Pb. The was independent of Crf and frequency. C xt Cjl plots were linear, with/pz very close to unity. Thus the surface of Sn + Pb alloys behaves as if it were geometrically smooth, and Pb appears to be the surface-active component. 

Anodically polished and then cathodically reduced Cd + Pb alloys have been studied by impedance in aqueous electrolyte solutions (NaF, KF, NaC104, NaN02, NaN03).827 For an alloy with 2% Pb at cNap 0.03 M, Emfo = -0.88 V (SCE) and depends on cNaF, which has been explained by weak specific adsorption of F" anions. Surface activity increases in the sequence F" < CIO4 < N02. The Parsons-Zobel plot at E is linear, with /pz = 1.33 and CT° = 0.31 F m"2. Since the electrical double-layer parameters are closer to those for pc-Pb than for pc-Cd, it has been concluded that Pb is the surface-active component in Cd + Pb alloys827 (Pb has a lower interfacial tension in the liquid state). 

Figure 15. Electrocapillary energy for the formation of a breakthrough pore in a thin surface oxide film on metals as a function of pore radius.7 AE E - Epzc, where Epzc is the potential-of-zero charge of the film-free metal. Al is the activation banier for the formation of a breakthrough pore and r is its critical radius. M, metal OX, oxide film EL, electrolyte solution, h a 2 x I O 9 m, am = 0.41 J m-2, a = 0.01 J m-2, ACj= 1 F m"2. a, AE=0.89 V b, AE=0.9 V c,A = 1.0 V. (From N. Sato, J. Electmckem. Soc. 129,255,1982, Fig. 2. Reproduced by permission of The Electrochemical Society, Inc.)...

Solid Bi2S3 does not appear in the expression for K,p, because it is a pure solid and its activity is 1 (Section 9.2). A solubility product is used in the same way as any other equilibrium constant. However, because ion-ion interactions in even dilute electrolyte solutions can complicate its interpretation, a solubility product is generally meaningful only for sparingly soluble salts. Another complication that arises when dealing with nearly insoluble compounds is that dissociation of the ions is rarely complete, and a saturated solution of Pbl2, for instance, contains substantial... 

More precisely, all the solutes should be at unit activity, not unit molarity. Activities differ appreciably from molarities in electrolyte solution because ions interact over long distances. However, we ignore this complication here. 

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