Equilibrium Constants from emfs

Some of the most important results of electrochemistry are the relationships among cell emf, free-energy change, and equUibiium constant. Recall that the free-energy change AG for a reaction equals the maximum useful work of the reaction (Section 19.5). 

For a voltaic cell, this work is the electrical work, nFEcen (whoe n is the number of moles of electrons transferred in a reaction), so when the reactants and products are in their standard states, you have 

With this equation, emf measurements become an important source of thermodynamic information. Alternatively, thermodynamic data can be used to calculate cell emfs. These calculations are shown in the following examples. 

Calculating the Free-Energy Change from Electrode Potentials 

Using standard electrode potentials, calculate the standard free-energy change at 25°C for the reaction 

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Calculation of equilibrium constant from emf of a cell The equilibrium constant of a chemical reaction can be calculated from the standard free-energy change by the equation... 

This expression can be rearranged to allow us to calculate the equilibrium constant from the cell emf ... 

First, calculate the standard emf of the cell from the standard reduction potentials in Table 19.1 of the text. Then, calculate the equilibrium constant from the standard emf using Equation (19.5) of the text. 

Calculating the equilibrium constant from cell emf Given standard potentials (or standard emf), calculate the equilibrium constant for an oxidation-reduction reaction. (EXAMPLE20.il)... 

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

Calculate the equilibrium constant for a reaction from the standard cell emf (Toolbox 12.3 and Example 12.8). 

The calorimetric method gives equilibrium constants that agree reasonably well with values obtained from other methods, such as conductance measurements or cell EMF measurements. The reliability is increased when a combination of calorimetric measurements with conductivity or cell EMF measurements is used in establishing the equilibrium conditions, especially when more than one reaction is significant. 

On the basis of emf data, obtained for the system MgCl2-KCl at 800°C, the equilibrium constant of reaction (109) was calculated to be 1.8 10 3. Such a low value of the dissociation constant is an indication of the high stability of the MgCl42 ion. The conclusion which results from these thermodynamic studies is that there are complex species present in melts of alkali chlorides containing magnesium chloride. 

Equation (4.12.1) shows how the value of AGd appropriate to the chemical equation under study can be computed from emf measurements Eq. (4.12.2) accomplishes the same for the equilibrium constant. 

Equation 3 was obtained by combining the Nemst equation for the emf of Cell I with the equilibrium constant of the acidic dissociation of glycine. In Equations 2 and 3, E° is the standard emf of the cell in the respective solvent composition and these values were obtained from an earlier work (20). In Equation 4, /3 is the linear slope parameter for the plot of pK/ vs. I, a0 is the ion-size parameter, A and B are the Debye-Huckel constants on the molal scale (20) for the respective mixed solvent systems, and I is the ionic strength given by mi. 

It should be emphasized that many of the potentials listed in tables of standard electrode potentials are values calculated from thermodynamic data rather than obtained directly from cell emf data. As such they are valuable for calculating equilibrium constants of reactions, but caution should be exercised in using them to predict the behavior of electrodes. A steady value for an electrode potential does not necessarily represent the thermodynamic or equilibrium value. 

We have from our study on pyrovanadate equilibria in the pH range 10.8 - 12 at 25 °C found that the medium dependence in Na(Cl), TBA(Cl), and Na,TBA(Cl) media can be explained with medium cation complexation to the vanadate species. Although vast medium concentration ranges have been covered, no Debye-Huckel parameters have to be used. Moreover, since Na, TBA and medium independent equilibrium constants have been determined, the pyrovanadate system can be modeled at any Vtot, [Na ], and [TBA ]. An analogous study on the H - HV04 system in the pH range 7 - 12 is in progress and it seems that medium cation complexes can explain all EMF/NMR data. 

This equation is used to calculate a numerical value of a,- from emf measurements vs. the SHE hence, as for the value of E (V V5. the SHE), the numerical value of depends on the SHE convention. Equilibrium constants may be written for these half cell reactions in the following way ... 

The author has used liquid-liquid extraction with thenoyltrifluoroacetone (TTA) and potentiometry using a fluoride selective electrode to determine the stoichiometiy and equihbrium constants of the fluoride complexes of Th(lV) and U(1V) only the Th(IV) data will be discussed here as the U(1V) data have been reviewed previously in [1992GRE/FUG]. The experiments have been made in a 4 M HCIO4 ionic medium at 20°C. The experimental data are described in detail and this study provides very useful information on the quality of the two experimental approaches used. The same author has previously studied the Zr(lV) and Hf(lV) systems using the same experimental approach. The slope of the ion selective electrode was determined experimentally and equilibrium was assumed to be attained when the emf changed by less than 0.1 mV/h. The experiments were made at three different total concentrations of Th(lV), 0.90, 1.79 and 4.48 mM and with the total concentration of HF varying from 0.406 to 225 mM. This corresponds to a concentration of free fluoride, 8 x 10 < [F ] < 5 x 10 M. The analysis of the experimental emf data is straightforward and the conditional equilibrium constants for the two reactions ... 

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. 

Thus, if we can determine the standard emf, we can calculate the equilibrium constant. We can determine the fE u of a hypothetical galvanic cell made up of two couples (Sn ISn and Cu ICu ) from the standard reduction potentials in Table 13.1. 

As was the case for the equilibrium constant (see Section 10.4), the temperature dependence of the emf can also be determined from the thermodynamic properties of the cell. We start with the van t Hoff equation (Equation 10.16) for the temperature dependence of the equilibrium constant... 

Although the formation of a series of complexes was obvious to chemists, at the beginning only the determination of the composition of the predominating species and their overall equilibrium constants appeared accessible. Bodlander (5) developed a general potentiometric method for the determination of these characteristics. The essence of this method is that the free metal ion concentration is calculated from the EMF of an appropriately constructed concentration cell. If the mass action law is applied to the dissociation of M L... 

Thus, the equilibrium constant for a redox reaction can be obtained from the value of the standard emf for the reaction. 

The measurement of cell emfs gives you yet another way to obtain equilibrium constants. Combining the previous equation, AG° = —nFEceih with the equation AG° = -i rin K from Section 19.6, you get... 

The equilibrium constant for this last reaction, obtained from emf measurements, is Ki2- For reactants and products of the same size and charge type the simplest form of the Marcus cross-relationship is... 

The equilibrium constant of any reaction can be determined if we can resolve the reaction into two partial reactions for which the potentials are given in a table. From the resultant emf, we calculate K as shown above,... 

The relationship between the equilibrium constant of a redox reaction and the EMF of the corresponding galvanic cell (potential cell) is the subject of Nemst s law. It is of tremendous interest in analytical chemistry from both theoretical and practical points of view. 

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