Thermodynamics concentration cells

The concentration overpotential i/c is the component of the overpotential due to concentration gradients in the electrolyte solution near the electrode, not including the electric double layer. The concentration overpotential is usually identified with the Nernst potential of the working electrode with respect to the reference electrode that is, the thermodynamic electromotive force (emf) of a concentration cell formed between the working electrode (immersed in electrolyte depleted of reacting species) and the reference electrode (of the same kind but immersed in bulk electrolyte solution) ... 

If results are required at very high temperatures, as in experiments related to steel making, even short-term survival makes severe demands on the construction of the cell (Komarek and Ipser 1984). However, oxygen concentration cells have been employed with molten ionic slags to determine the thermodynamics of oxide formation in iron between 1500-1600°C (Kay 1979). Other applications include the use of YSZ for studies of semiconducting systems (Sears and Anderson 1989, Lee et al. 1992). 

Warburg on the other hand used the theory of the concentration cell to relate the thermodynamic potential fx, of the mercurous salt, measured in ergs per grm. equivalent with V, the excess of the electric potential of the mercury over that of the dilute acid con-. taining the salt, expressed in volts thus ... 

Concentration cells have been used extensively to determine thermodynamic properties of metallic solutions. The following cell is built to measure the thermodynamic properties of Mg in Mg-M alloys ... 

Measurements of the potentials of galvanic cells at open circuit give information about the thermodynamics of cells and cell reactions. For example, the potential of the cell in Figure 1, when the solution concentrations are 1 molar (1 M) at 25°C, is 1.10 V. This is called the standard potential of the cell and is represented by E°. The available energy (the Gibb s free energy AG°) of the cell reaction given in equation (3) is related to E° by... 

The silver-silver Ion electrode. Of the reversible metal electrodes, silver has been most often employed. There is only one stable oxidation state of silver above 300°C there is no danger of oxide formation because Ag20 is unstable.57 The metal has no observable tendency to dissolve in molten silver salts and is highly reversible in mixed chloride and nitrate eutectics. The Ag(I) ion can be introduced into the melt by either adding silver nitrate to a nitrate melt (AgCl to a chloride melt) or by anodizing a silver electrode. The potentials of silver nitrate concentration cells show ideal thermodynamic behavior up to 0.5 mol % in (Na,K)N03 eutectic and in NaN03.58... 

In a recent study (4) kinetic measurements in a CSTR were combined with simultaneous in situ measurement of the thermodynamic activity of oxygen adsorbed on the catalyst by using the technique of solid electrolyte potentiometry (SEP). The technique originally proposed by C. Wagner (1) utilizes a solid electrolyte oxygen concentration cell with one electrode also serving as the catalyst for the reaction under study. It has already been used to study the oxidation of ethylene on Ag (5) and on Pt (6). 

Isothermal chemistry in fuel cells. Barclay (2002) wrote a paper which is seminal to this book, and may be downloaded from the author s listed web site. The text and calculations of this paper are reiterated, and paraphrased, extensively in this introduction. Its equations are used in Appendix A. The paper, via an equilibrium diagram, draws attention to isothermal oxidation. The single equilibrium diagram brings out the fact that a fuel cell and an electrolyser which are the thermodynamic inverse of each other need, relative to existing devices, additional components (concentration cells and semi-permeable membranes), so as to operate at reversible equilibrium, and avoid irreversible diffusion as a gas transport mechanism. The equilibrium fuel cell then turns out to be much more efficient than a normal fuel cell. It has a greatly increased Nernst potential difference. In addition the basis of calculation of efficiency obviously cannot be the calorific value of the... 

The galvanic cells discussed hitherto (of the first kind) owe their power of yielding electrical energy to the forces of chemical affinity. A second type of cell makes use of the dilution tendency of dissolved substances (osmotic pressure). Galvanic cells of this type are called concentration cells. The thermodynamical theory of these cells was initiated by Helmholtz, and completed later on by Nernst. 

C is a constant which is characteristic of the metal of which the electrode is composed, and is sometimes called the electrolytic solution pressure. Its numerical value is equal to the ionic concentration of a solution against which the metal would have no difference of potential. This quantity is of the greatest importance for the electrochemical behaviour of the metal. It cannot be determined, however, by measurement with concentration cells, for the solution pressure C disappears from the sum of the various potential differences in equation (5). The calculation of C from the total e.m.f. would be possible if we could choose the ionic concentration of one solution, say Cg, so that the potential difference 3 would be zero. Numerous experiments have actually been carried out with the object of constructing an electrode which would have the absolute potential zero against the solution. These experiments, although in themselves interesting and important, are based on special electrochemical hypotheses and not on purely thermodynamical principles. They are therefore beyond the scope of this book. ... 

The results of moving boundary determinations of transference numbers in which the modern developments of the method have been employed are given in Table IV, and are mainly due to the investigations of Longsworth. The figures in this table will be referred to a number of times in following chapters. The transference numbers are of use in interpreting the results of determinations of the potentials of concentration cells as activity coefficients which, in turn, may be used to test the validity of the thermodynamic aspects of the interionic attraction theory of electrolytes. In addition the transference numbers, alone, and with conductance measurements, are of utility in connection with tests of the interionic attraction theory of electrolytic conductance. 

As already stated the limiting value of K is the thermodynamic ionization constant, K, which in this case is 1.753 X 10 c. Another method for obtaining thermodynamic ionization constants is given in Chapter 11, depending on measurements of the electromotive force of concentration cells without liquid junction. Using that method Harned and Ehlers found 1.754 X 10"R for the ionization constant of acetic acid at 25°. However, that constant is based on molalities, m, rather than concentrations, C. The relation between the ionization constants may be readily shown to be... 

Basic equations for almost every subfield of electrochemistry from first principles, referring at all times to the soundest and most recent theories and results unusually useful as text or as reference. Covers coulometers and Faraday s Law, electrolytic conductance, the Debye-Hueckel method for the theoretical calculation of activity coefficients, concentration cells, standard electrode potentials, thermodynamic ionization constants, pH, potentiometric titrations, irreversible phenomena. Planck s equation, and much more, a indices. Appendix. 585-item bibliography. 197 figures. 94 tables, ii 4. 478pp. 5-% x 8. ... 

Tsurumi et al. have assembled a hydrogen concentration cell using an NH4 /H30 P"/p-gallate ceramic to measure e.m.f. values the results agree well with a thermodynamically estimated value . The group have also assembled a steam concentration cell and claim that the e.m.f. values cannot be explained by means of a simple equation . Both studies found that the large resistance of the electrolyte, which is much greater than expected for the bulk resistance makes the measurement of e.m.f. difficult. 

For an assessment ofthemicrostmctural stability of 9Cr-lMo steel, precise data on the thermodynamic activities ofCr and C as a function of service temperature are needed. The adaptation of high temperature fiourine concentration cells with CaF as the electrofyte for studies on this alloy has paved the way for the direct measurement ofCr activity as a function of temperature. Thus the chromium activity could be reproducibly determine in 9Cr- IMo steel for the first time and is found to lie between 0.054 and 0.076 in the temperature range of900 to 1100 K. 

The cell voltage is always lower than the OCV because when the electrochemical reaction occurs, the voltage decays by a term A Ere due to thermodynamic concentration polarization ... 

The degrees of dissociation and hydration numbers calculated from vapor pressures correlate quantitatively with the properties of dilute as well as concentrated solutions of strong electrolytes. Simple mathematical relations have been provided for the concentration dependences of vapor pressure, e.m.f. of concentration cells, solution density, equivalent conductivity and diffusion coefficient. Non-ideality has thus been shown to be mainly due to solvation and incomplete dissociation. The activity coefficient corrections are, therefore, no longer necessary in physico-chemical thermodynamics and analytical chemistry. 

The operation of potentiometric sensors is based on the measurements of concentration cell emf (see Chaps. 1 and 8), which makes it possible to extract the activity, concentration, or partial pressure of potential-determining species at the working electrode vs. RE. The WE potential may be established by a thermodynamic equilibrium or by a nonequdihrium steady state, whereas key requirements to the reference electrodes are related to their reversibility, stability, and, often, fast equilihratirMi on changing external conditions. The solid-state potentiometric sensors are used for a wide variety of technological applicatirms and probed species [2,3,5,15,18,86-91] their application for oxidic glass melts is addressed in Chap. 8. 

From thermodynamic conadeiarions, the liquid junction jiotential Fg of a concentration cell with transference as shown in III can be written as follows ... 

Potentiometric sensors (Fig. 19.2, left) are able to measure free oxygen and oxygen in an established thermodynamically equilibrium, e.g. the ratio of partial pressures of burnt and non-bumt components. They are oxygen concentration cells which can be symbolised by... 

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