Cell electromotive force

E Electromotive force, cell voltage, electrode potential V... 

A special example of electrical work occurs when work is done on an electrochemical cell or by such a cell on the surroundings -w in the convention of this article). Themiodynamics applies to such a cell when it is at equilibrium with its surroundings, i.e. when the electrical potential (electromotive force emi) of the cell is... 

In electrochemical cells (to be discussed later), if a particular gas participates in a chemical reaction at an electrode, the observed electromotive force is a fiinction of the partial pressure of the reactive gas and not of the partial pressures of any other gases present. 

A second source of standard free energies comes from the measurement of the electromotive force of a galvanic cell. Electrochemistry is the subject of other articles (A2.4 and B1.28). so only the basics of a reversible chemical cell will be presented here. For example, consider the cell conventionally written as... 

Fig. 5. Energy requirements of the HaH-Hfiroult cell (23—25). E, decomposition of alumina Eg, depolarization by carbon E, anode overvoltage E, counter electromotive force E, bath voltage drop E, bath bubble voltage F/, anode voltage drop Eg, cathode voltage drop E, external voltage drop ...

As a result, the electromotive force (EMF) of the cell is zero In the presence of fluoride ions, cerium(IV) forms a complex with fluoride ions that lowers the cerium(IV)-cerium(IIl) redox potential The inner half-cell is smaller, and so only 5 mL of cerium(IV)-cenum (III) solution is added To the external half-cell, 50 mL of the solution is added, but the EMF of the cell is still zero When 10 mL of the unknown fluonde solution is added to the inner half-cell, 100 mL of distilled water IS added to the external half-cell The solution in the external half-cell is mixed thoroughly by turning on the stirrer, and 0 5 M sodium fluonde solution is added from the microburet until the null point is reached The quantity of known fluonde m the titrant will be 10 times the quantity of the unknown fluoride sample, and so the microburet readings must be corrected prior to actual calculations... 

If electron flow between the electrodes is toward the sample half-cell, reduction occurs spontaneously in the sample half-cell, and the reduction potential is said to be positive. If electron flow between the electrodes is away from the sample half-cell and toward the reference cell, the reduction potential is said to be negative because electron loss (oxidation) is occurring in the sample halfcell. Strictly speaking, the standard reduction potential, is the electromotive force generated at 25°C and pH 7.0 by a sample half-cell (containing 1 M concentrations of the oxidized and reduced species) with respect to a reference half-cell. (Note that the reduction potential of the hydrogen half-cell is pH-dependent. The standard reduction potential, 0.0 V, assumes 1 MH. The hydrogen half-cell measured at pH 7.0 has an of —0.421 V.)... 

This effect appears to be of importance in the case of normal galvanic cells, the electromotive forces of which depend on the concentration of solutions in equilibrium with depolarising solids such as calomel or mercurous sulphate. The exact relationships are, unfortunately, not yet wholly elucidated. 

Electrochemical Method.—In this the value of the equilibrium constant K is calculated from the maximum work measured by means of the electromotive force of a voltaic cell (cf. Chap. XVI.). 

The electromotive force of a voltaic cell is the total amount of work done when unit quantity of electricity passes through the cell. 

A voltaic cell is said to be reversible when an opposing electromotive force greater by an infinitesimal amount than that of the cell reverses the direction of the current, and the material changes occurring in the cell. 

There is a very important equation relating to the electromotive forces of reversible cells which was deduced independently by J. Willard Gibbs (1875) and H. von Helmholtz (1882), and is usually called the Gibbs-Helmholtz Equation. 

If a reversible cell is connected with an external balancing electromotive force capable of slight variation, we can allow a quantity of electricity F = 96540 cmb. to flow through the cell in the current-producing direction whilst the whole is maintained at a constant temperature T. 

The material changes in the cell are completely defined when we know the quantity of electricity passing through, for Faraday s law teaches us that for a quantity F there will always be a gram-equivalent of chemical change, independent of the electromotive force. 

Thus, if we find how the electromotive force changes when the temperature of the cell is altered on open circuit, i.e., when no current is passing, we can at once calculate A, the latent heat, just as we can calculate the latent heat of evaporation of a liquid when we know the variation of its vapour pressure with temperature. Since E changes only slightly with T, we can evaluate dE... 

The heat of formation of a substance iji a voltaic cell may therefore be calculated from the measured Peltier effects and the electromotive force. 

If there exists a temperature T0 at which the electromotive force of the cell vanishes ... 

The theory of concentration cells was first developed with great generality by Helmholtz (1878), who showed how the electromotive force could be calculated from the vapour pressures of the solutions, and his calculations were confirmed by the experiments of Moser (1878). 

The sign of the electrode potential is arbitrarily defined as follows. A kation electrode (e.g., Zn in ZnS04 aq.) is said to be positive when it is positive to a unimolar (f — 1) solution of its ions an anion electrode e.g., CI2 in KC1) is said to be positive when it is positive to a unimolar solution of its ions. If a cell is made up of electrodes reversible with respect to any kinds of ions, its electromotive force is the algebraic difference of its electrode potentials, provided the electromotive force at the contact of the two solutions, due to diffusion (cf. Jahn, Elcktro-chcmie) is neglected. 

The electromotive force of a cell with solutions of given concentrations may be calculated by subtracting the electrode potentials so obtained. 

If E is the electromotive force of the cell, and if r faradays are transported through the cell during the change for which the maximum work is calculated, we have ... 

Equation (6) therefore gives us a means of calculating chemical equilibria from measurements of electromotive force, and vice versa. It must be remembered that E has a sense only when it refers to a reversible cell if the cell is not reversible this simply means that no equilibrium can be set up at its electrodes between the reacting materials. 

Similar considerations apply of course to the opposing electromotive forces of polarisation during electrolysis, when the process is executed reversibly, since an electrolytic cell is, as we early remarked, to be considered as a voltaic cell working in the reverse direction. In this way Helmholtz (ibid.) was able to explain the fluctuations of potential in the electrolysis of water as due to the variations of concentration due to diffusion of the dissolved gases. It must not be forgotten, however, that peculiar phenomena—so-called supertension effects—depending on the nature of the electrodes, make their appearance here, and com-... 

Finally, we may observe that measurements of electromotive force can often serve to distinguish which kind of ions are really present in a solution. A concentration cell containing a solution of a known ion with an electrode reversible to the latter on one side, and the given solution with a similar electrode on the other side is taken. From its electromotive force, the concentration of the particular ion is calculable. In this way, for example, it was found... 

The rule for the calculation of the electromotive force of such a cell is, therefore, according to Nernst (cf. Bed. Ber., 1909,. p. 247) extrapolate the thermochemical data to the lowest possible temperature and put ... 

The electromotive force of a cell can be related to the Gibbs free energy change for the cell reaction by combining equations (9.5), (9.90), and (3.96). We recall that... 

G. Scatchard and R. F. Tefft, "Electromotive Force Measurements on Cells Containing Zinc Chloride. The Activity Coefficients of the Chlorides of the Bivalent Metals", J. Am. Chem. 

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