Electromotive force of concentration cells

It has already been mentioned that the electromotive force of concentration cells with transference is the sum of the both electrode potentials and the liquid junction potential which arises, when two solutions of the same substance but of different concentrations are brought into contact the value of the mentioned potential is finally given by the equations (VI-28) and (VI-29). 

Electromotive Force of Concentration Cells —In the preceding chapter (Chap VII) it has been shown that the simple osmotic theory of the production of emf of a cell reversible with respect to the cation leads to the expression—... 

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... 

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

In this cell, the following independent phases must be considered platinum, silver, gaseous hydrogen, solid silver chloride electrolyte, and an aqueous solution of hydrogen chloride. In order to be able to determine the EMF of the cell, the leads must be made of the same material and thus, to simplify matters, a platinum lead must be connected to the silver electrode. It will be seen in the conclusion to this section that the electromotive force of a cell does not depend on the material from which the leads are made, so that the whole derivation could be carried out with different, e.g. copper, leads. In addition to Cl- and H30+ ions (further written as H+), the solution also contains Ag+ ions in a small concentration corresponding to a saturated solution of silver chloride in hydrochloric acid. Thus, the following scheme of the phases can be written (the parentheses enclose the species present in the given phase) ... 

What is wrong with the following argument If the terminals of an electrochemical cell are constructed from the same metal, the chemical potential of electrons [species i in Eq. (36)] at the terminals, which depends only on T, P and concentrations, are the same. From Eq. (36), the electromotive force of the cell is therefore zero ... 

In a concentration cell with transference two solutions of different concentration are brought into direct contact, either in a suitably designed junction, or by means of a porous diaphragm. At the interface of both solutions an electric double layer is formed the potential difference across which must be included into the total electromotive force of the cell. Before deriving, however, the relations for determining the EMF of such cells, the origin and magnitude... 

The addition of organic solvents to water should modify acid-base phenomena, but assessment of such effects poses many problems, as only the measured pH of aqueous solutions can be interpreted in terms of hydrogen ion concentrations. The quantitative comparison of the acidities of partially aqueous solutions is therefore a problem of far greater complexity than the measurements of pH values in aqueous media. As mentioned earlier, a proton activity (paH) is defined in such a way that — log paH is equal to pH when the medium is water, and its value can be measured both by the electromotive force of a cell with liquid junction and by the spectrophotometry of colored indicators. 

The oxidation-reduction potentials for half reactions such as Fe" —> Fe + e are measured by putting a piece of platinum or other inert metal into a solution containing ferrous and ferric ions in standard concentrations, and combining this half cell with the standard hydrogen half cell. Again, the platinum serves to conduct electrons and to catalyze the equilibrium between ferrous and ferric ions. The electromotive force of the cell... 

Before we discuss standard electrode potential, we will talk about electromotive force (emf). The electromotive force of a cell is the potential difference between the two electrodes. This can be measured using a voltmeter. The maximum voltage of a cell can be calculated using experimentally determined values called standard electrode potentials. By convention, the standard electrode potentials are usually represented in terms of reduction half-reactions for 1 molar solute concentration. The standard electrode potential values are set under ideal and standard-state conditions (latm pressure and 25°C temperature). From the MCAT point of view, you can assume that the conditions are standard, unless stated otherwise. Table 12-1 shows a list of standard electrode potentials (in aqueous solution) at 25°C. 

This formula is correct when the cell voltage on open circuit is equal to the electromotive force of the cell, which is achieved when the cell has reached steady state and there are no more concentration or temperature gradients of the H2SO4 solution. The electroljrte in fully charged traction and SLI batteries has most often a relative density of 1.28. According to the data in Fig. 3.4, this H2SO4 relative density corresponds to an electromotive force of 2.125 V. 

For the electrochemical reactions of charge to proceed at the two electrodes, the external voltage applied to the cell, Uch, should be higher than the electromotive force of the cell, AE, at the given H2SO4 concentration. The difference between the two voltages is called polarization of the cell (battery), A(7p. 

The decrease in free energy of the system in a spontaneous redox reaction is equal to the electrical work done by the system on the surroundings, or AG = nFE. The equilibrium constant for a redox reaction can be found from the standard electromotive force of a cell. 10. The Nernst equation gives the relationship between the cell emf and the concentrations of the reactants and products under non-standard-state conditions. Batteries, which consist of one or more galvanic cells, are used widely as self-contained power sources. Some of the better-known batteries are the dry cell, such as the Leclanche cell, the mercury battery, and the lead storage battery used in automobiles. Fuel cells produce electrical energy from a continuous supply of reactants. 

Assumii that the polypeptides in a salt solution do not appreciably affect the activity coefficient of free surfactant concentration, a decrease in surfactant activity in the presence of the polypeptide as reflected by the measured electromotive force of the cell represents a decrease in free surfactant concentration because of the bindii of the surfactant to the polypeptide. The degree of bindii, x, is simply... 

The electromotive force of the cell with no ion transfer (AE ) is 2.040 V and it is determined on the basis of Gibbs free energies of the products and reagents participating in the reaction. The concentration of H2SO4 and the temperature of the cell will also impact the cell electromotive force. The open cell potential for lead-acid batteries is 2.10 to 2.13 V and the nominal voltage of a single practical lead-acid battery is 2 V. 

Here E q is the equilibrium (open circuit) voltage, or emf (electromotive force) of the cell, i is the current density, iR,- is the ohmic potential drop, and qc and qA are the polarisation of the cathode and the anode, respectively. As shown in Eq. (7) each of the polarisation may be further split in an activation-related contribution (subscript a) and a concentration (i.e., diffusion) related contribution (subscript c). 

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. 

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). 

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 lUPAC Commission for Analytical Nomenclature defines the calibration curve [138] as the dependence of the electromotive force of the given ISE -reference electrode cell on the logarithm of the activity or concentration of the given substance. It is recommended that the potential be plotted on the ordinate (the vertical axis) and the logarithmic function of the activity or concentration on the abscissa (the horizontal axis), with the concentration increasing from the left to the right. 

Dependence of Electromotive Force on Concentrations Calculate the electromotive force (in volts) registered by an electrode immersed in a solution containing the following mixtures of NAD+ and NADH at pH 7.0 and 25 °C, with reference to a half-cell of E ° 0.00 V... 

The cell potential E (also called the cell voltage or electromotive force) is an electrical measure of the driving force of the cell reaction. Cell potentials depend on temperature, ion concentrations, and gas pressures. The standard cell potential E° is the cell potential when reactants and products are in their standard states. Cell potentials are related to free-energy changes by the equations AG = —nFE and AG° = —mFE°, where F = 96,500 C/mol e is the faraday, the charge on 1 mol of electrons. 

G. J. Burch and Y- H. Yeley found that when the metals, copper, silver, bismuth, and mercury are introduced into purified nitric acid of varying degrees of concentration, and a couple made with platinum, the electromotive force of such a cell increases considerably until it reaches a constant and (in most cases) a maximum value. This rise of electromotive force is attributed to the production of nitrous... 

As shown in Figure 18, the potential is almost proportional to the logarithm of H2 concentration diluted in air. When H2 is diluted in N2, the observed potential corresponds to the electromotive force of a H2-02 fuel cell, and in fact the EMF was as large as about 1.0 V with a theoretical slope of 30 mV/decade, as shown in the same figure. It has been shown that in the case of H2 diluted in air, the following electrode reaction, i.e., electrochemical oxidation of hydrogen (2) and electrochemical reduction of oxygen (3), are important. 

The activity a2 of an electrolyte can be derived from the difference in behavior of real solutions and ideal solutions. For this purpose measurements are made of electromotive forces of cells, depression of freezing points, elevation of boiling points, solubility of electrolytes in mixed solutions and other characteristic properties of solutions. From the value of a2 thus determined the mean activity a+ is calculated using the equation (V-38) whereupon by application of the analytical concentration the activity coefficient is finally determined. The activity coefficients for sufficiently diluted solutions can also be calculated directly on the basis of the Debye-Hiickel theory, which will bo explained later on. 

The electromotive force of a given cell apart from temperature and pressure also depends on the concentration of the active substances in the system. This dependence for a common reaction... 

It is immediately evident from these equations why the hydrochloric acid concentration in the first cell increases, and in the second decreases. The process proceeds until the current becomes zero, i. e. until the activity and, therefore, the concentration of the hydrochloric acid in both cells will finally equal (a4 )1 — (a )2j. The electromotive force of the described double cell has its origin in a reversible transference of hydrochloric acid from higher to lower concentration. 

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