Galvanic Cells with Liquid Junctions

Two types of methods are used to measure activity coefficients. Potentiometric methods that measure the mean activity coefficient of the dissolved electrolyte directly will be described in Section 3.3.3. However, in galvanic cells with liquid junctions the electrodes respond to individual ion activities (Section 3.2). This is particularly true for pH measurement (Sections 3.3.2 and 6.3). In these cases, extrathermodynamical procedures defining individual ion activities must be employed. 

Galvanic Cells with Liquid Junction Potentials... 

Equation (13-78) is the fundamental equation for the study of the thermodynamic properties of galvanic cells with liquid junctions. 

Since the cell of Eq. (13-92) is a special case of a galvanic cell with liquid junction, Eq. (13-78) is applicable, and we may write... 

It is clear from Eq. (13-105) that a knowledge of e and ci- permits evaluation of the activity coefficient v . Comparison of results obtained by this method with those from other techniques yields excellent agreement. Thus, the applicability of thermodynamic theory to the case of partial equilibrium in a galvanic cell with liquid junction is demonstrated. 

The Variation of the Standard Potentials of Some Electrodes with the Temperature. In a number of cases the standard potentials of galvanic cells without liquid junctions have been determined over a range of temperatures. From these determinations it has been possible to prepare Table V, which gives the standard potentials of a number of electrodes at intervals of 12.5° from 0° to 50°. Some slight adjustments, of the order of 0.2 millivolt, of the original data have been necessary to bring the figures into accord with the Ho values at 25° adopted in this book. A more complete table of standard potentials of the elements at 25° will be found at the end of Chapter 14. 

Because of the necessity, with galvanic cells without liquid junctions, of finding two reversible electrodes, one for a positive and one for a negative ion constituent, most of the recent work in this field has been carried out with cells of the type ... 

The theory developed here has its most important application in the study oi reversible galvanic cells. Galvanic cells may be separated into two classes those with and those without liquid junction. In Sec. 13-2, we consider a galvanic cell without liquid junction using the necessary criterion for equilibrium [Eq. (13-23)]. In Sec. 13-3, we discuss a cell with liquid junction in terms of the complete conditions for heterogeneous equilibrium. 

In Eqs. (122) and (123), M(Hg) is an alkali metal amalgam electrode, MX the solvated halide of the alkali metal M at concentration c in a solvent S, and AgX(s)/Ag(s) a silver halide-silver electrode. Equation (124) is the general expression for the electromotive force " of a galvanic cell without liquid junction in which an arbitrary cell reaction 0)1 Yi + 0)2Y2 + coiYi + , takes place between k components in v phases. In Eq. (124) n is the number of moles of electrons transported during this process from the anode to the cathode through the outer circuit, F the Faraday number, and the chemical potential of component Yi in phase p. Cells with liquid junctions require the electromotive force E in Eq. (124) to be replaced by the quantity E — Ej), where Ey> is the diffusion potential due to the liquid junction. The standard potential E° for the cell investigated by Eq. (122) is given by the relationship... 

E ceii, eq Can be measured with great precision. If a reaction can be carried out in a galvanic cell without liquid junction, Eq. 14.3.13 provides a way to evaluate ArG under given conditions. If the reaction can only be carried out in a cell with a liquid junction, Eq. 14.3.14 can be used for this purpose provided that the liquid junction potential Ej can be assumed to be negligible or can be estimated from theory. 

So far, a cell containing a single electrolyte solution has been considered (a galvanic cell without transport). When the two electrodes of the cell are immersed into different electrolyte solutions in the same solvent, separated by a liquid junction (see Section 2.5.3), this system is termed a galvanic cell with transport. The relationship for the EMF of this type of a cell is based on a balance of the Galvani potential differences. This approach yields a result similar to that obtained in the calculation of the EMF of a cell without transport, plus the liquid junction potential value A0L. Thus Eq. (3.1.66) assumes the form... 

Parker and Alexander " treated the galvanic cell (B) with liquid junction... 

Even in a galvanic cell with a salt bridge, there is some leakage of ions across the liquid junction, which causes the battery to lose its chemical potential over time. Commercial cells use an insoluble salt to prevent this from happening. 

In Chapter 10 standard potentials were obtained from measurements on galvanic cells involving only one electrolyte. These cells without transference thus do not involve surfaces between solutions of electrolytes, more commonly called liquid junctions. Although the measurements on cells without liquid junctions can be much more readily interpreted than the results from cells containing such boundaries most of the earlier work was carried out with the latter type of cell. Thus for instance instead of measuring the potential of the cell ... 

A rapid experimental method to determine transfer activity coefficients uses galvanic cells with transference but negligible liquid-junction potentials e.g. the cell... 

When studying nonaqueous systems by means of galvanic cells with aqueous or mixed reference electrodes, we cannot avoid liquid/liquid junctions and estimate the corresponding potential drop from any realistic model. In protic nonaqueous media (alcohols, dioxane, acetone, etc.), a hydrogen electrode can be used it is also suitable for some aqueous/aprotic mixtures. However, the io values for the hydrogen reaction are much lower as compared with purely aqueous solutions. When studies are carried out in nonaqueous media, in order to avoid liquid/liquid junction preference should be given to the reference electrodes in the same solvent as the electrode of interest. 

For the study of the solvent effect, comparable equilibrium constants have to be determined in water and in solution made with non-aqueous solvents or solvent mixtures. Potentiometric (usually pH-metric) equilibrium measurements are used for this purpose in polyfunctional systems. The solvent effect makes the application of potentiometry somewhat difficult. The substitution of water by organic solvents results in changes of the autoprotolysis constant of the solvent changing the pH scale. The lower relative permittivity of the system favours association processes which have to be considered, e.g., in the determination of the ionic strength of the solution. Diffusion potentials at the liquid junctions connecting the galvanic cell with the reference electrode may falsify the measured data. 

Now imagine a reaction vessel that has the same temperature and pressure as the galvanic cell, and contains the same reactants and products at the same activities as in the cell. This reacrion vessel, unlike the cell, is not part of an electrical circuit. In it, the reactants and products are in direct contact with one another, so there is no constraint preventing a spontaneous reaction process. This reaction will be called the direct reaction. For example, the reacrion vessel corresponding to the zinc-copper cell of Fig. 14.2 would have zinc and copper strips in contact with a solution of both ZnS04 and CUSO4. Another example is the slow direct reaction in a cell without liquid junction described on page 453. 

Practically all liquid cells with reversible interfacial equilibria examined can be considered as liquid galvanic cells of the Nernst, Haber, or intermediate type [3]. Usually, a dashed vertical bar ( ) is used to represent the junction between liquids. A double dashed vertical bar ( ) represents a liquid junction in which the diffusion potential has been assumed to be eliminated. 

It is important to note that this equation is not rigorously thermodynamic since neither the single potential of a liquid junction nor the ion activities, % can be measured. However, as will be seen in what follows, correct thermodynamic equations are obtained if equation (3) is combined with equations for electrode processes in such a manner as to include the process for a complete galvanic cell. In such cases it will always be possible to combine the single ion activities into physically measurable mean ion activities. Some examples will be discussed in detail. 

During his Leipzig period, Nernst performed a series of electrochemical studies from which, at the age of twenty-five, he arrived at his well-known equations. These equations described the concentration dependence of the potential difference of galvanic cells, such as batteries, and were of both great theoretical and practical importance. Nernst started with the investigation of the diffusion of electrolytes in one solution. Then he turned to the diffusion at the boundary between two solutions with different electrolyte concentrations he determined that the osmotic pressure difference would result in an electric potential difference or electromotive force (emf). Next he divided both solutions into two concentration half-cells, connected to each other by a liquid junction, and measured the emf via electrodes dipped into both solutions. The data supported his first equation where the... 

However, there remained the question of whether the emf of a galvanic cell arose at the two electrode/electrolyte interfaces, at the contact between the two dissimilar metal electrodes or, in a cell with a liquid junction, at the boundary between the two electrolytes. It was to this problem, and to the quantification of the emf in terms of the solution composition, that Nernst turned his attention. 

Some galvanic cells contain two electrolyte solutions with different compositions. These solutions must be separated by a porous barrier or some other kind of junction in order to prevent rapid mixing. At this liquid junction in the zero-current cell, there is in general a liquid junction potential caused by diffusion of ions between the two bulk eleetrolyte phases. 

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