Standard cell potential experimental determination

Eigure 21.10 summarizes the interconnections among the standard free energy change, the equilibrium constant, and the standard cell potential. In Chapter 20, we determined K from AG°, which we found either from A//° and A5° values or from AGf values. Now, for redox reactions, we have a direct experimental method for determining K and AG° measure E eii-... 

The relationships of the type (3.1.54) and (3.1.57) imply that the standard electrode potentials can be derived directly from the thermodynamic data (and vice versa). The values of the standard chemical potentials are identified with the values of the standard Gibbs energies of formation, tabulated, for example, by the US National Bureau of Standards. On the other hand, the experimental approach to the determination of standard electrode potentials is based on the cells of the type (3.1.41) whose EMFs are extrapolated to zero ionic strength. 

When the pH is specified, each biochemical half reaction makes an independent contribution to the apparent equilibrium constant K for the reaction written in terms of reactants rather than species. The studies of electochemical cells have played an important role in the development of biochemical thermodynamics, as indicated by the outstanding studies by W. Mansfield Clarke (1). The main source of tables of ° values for biochemical half reactions has been those of Segel (2). Although standard apparent reduction potentials ° can be measured for some half reactions of biochemical interest, their direct determination is usually not feasible because of the lack of reversibility of the electrode reactions. However, standard apparent reduction potentials can be calculated from for oxidoreductase reactions. Goldberg and coworkers (3) have compiled and evaluated the experimental determinations of apparent equilibrium constants and standard transformed enthalpies of oxidoreductase reactions, and their tables have made it possible to calculate ° values for about 60 half reactions as functions of pH and ionic strength at 298.15 K (4-8). 

In practice there are several limitations to such measurement. Obviously it implies that both members of the half-reaction are sufficiently stable for a cell to be realized. This is a serious difficulty in organic chemistry owing to usual great reactivities of the species formed upon electron transfers. For the most frequent cases it is then impossible to rely on reversible thermodynamic transformations to determine experimental values of standard reduction potentials. However, these important figures, or at least very precisely approximated values, can be obtained from current intensity potential curves or transient electrochemical methods as is discussed in a later section. 

The potential in standard conditions ( °) of other electrochemical pairs can be obtained with respect to Eq. 3.4, permitting the compilation of a list of semireaction potentials (electrochemical series ). In this list, all the semi-reactions are written in such a way to evaluate the tendency of the oxidized forms to accept electrons and become reduced forms (positive potentials correspond to spontaneous reductions) [2]. These potentials can be correlated to thermodynamic quantities if the electrochemical system behaves in a reversible way from a thermodynamic point of view, i.e., when the electrochemical system is connected against an external cell with the same potential, no chemical reaction occurs, while any inhnitesimal variation of the external potential either to produce or to absorb current is exactly inverted when the opposite variation is applied (reversible or equilibrium potentials, Eeq)- When the equilibrium of the semi-reaction considered is established rapidly, its potential against the reference can be experimentally determined. 

The standard Gibbs energy of formation of NiO has been experimentally determined over the temperature range from 900 to 1400 K using a galvanic cell with the solid electrolyte made of 15% calcia-stabilised zirconia. The measured value of AfG (NiO) at 1300 K was - 123.555 kJmol with a precision of+0.057 kJ-mof and an estimated accuracy not worse than 0.200 kJ-mol. This precision is equivalent to an error of only 0.2 - 0.3 mV in the cell potential (emf). In comparison, most previous studies have reported a precision of 1 - 2 mV. Using the third law analysis, the authors obtained for the enthalpy of formation of NiO, Af//° (NiO, 298.15 K) = - 240.110 kJ-mol. ... 

Compare this equation with Eqs. (15.7) and (15.15). By convention, the reference electrode is connected to the negative terminal of the potentiometer (the readout device). The common reference electrodes used in potentiometry are the SCE and the silver/silver chloride electrode, which have been described. Their potentials are fixed and known over a wide temperature range. Some values for these electrode potentials are given in Table 15.3. The total cell potential is measured experimentally, the reference potential is known, and therefore the variable indicator electrode potential can be calculated and related to the concentration of the analyte through the Nemst equation. In practice, the concentration of the unknown analyte is determined after calibration of the potentiometer with suitable standard solutions. The choice of reference electrode depends on the application. For example, the Ag/AgCl electrode cannot be used in solutions containing species such as halides or sulfides that will precipitate or otherwise react with silver. 

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. 

For unknown activities the measurement of the standard electrode potential is more complicated. The standard electrode potential is defined at /ra = 1 mol kg with the hypothetical activity coefficient of y = 1 (ideal diluted solution). First principal experimental determinations of standard potentials may only be made by extrapolation to this hypothetical value. For measurements, selected cell arrangements are used with complete elimination of the diffusion potential and with diluted electrolytes. For the correction of the activity the Debye-Hiickel approximation (Eq. (1.15)) may be used, for example, for the Hamed cell Ag/AgCl, HCl (m+)/Pt(H2). A concentration corrected potential value is plotted versus the square root of the molaUty. The extrapolation to 7ra+ = 0 gives the standard potential of the Ag/AgCl electrode (Figure 3.5). Using this electrode as reference electrode other standard potentials can be determined. 

Application of assumptions (1) and (2) and of cells of type XII allows construction of a common potential scale for various interfaces of immiscible electrolyte solutions. To achieve this goal in practice it is necessary to determine experimentally the standard distribution potential of TEAPi, or the formal potential of TBA" or any other reference standard in the water-given solvent system (w/s), versus the zero TEAPi water-nitrobenzene system. For this purpose, the cells schematically shown below can be used [64-67, 124-125] ... 

Since the measured cell potential difference is actually the potential difference between two electrodes, it immediately comes to mind to assimilate each of the bracketed terms into the potential of each of the electrodes. They are called electrode potentials. E° and °2, which are in the two subgroups, exhibit characteristic values of both couples Oxi/Redi and Oxa/Reda. These constants are called standard potentials of both couples and are symbolized (Oxi/Redi) and °(Ox2/Red2). Assigning numerical values to and E°2 has been a problem since the experimental determination of absolute electrode potentials hence, assigning those to standard electrode potentials is impossible (see the electrochemistry part). It was solved by assigning relative values to them. The strategy was based on the fact that if absolute electrode potentials are not measurable, the difference between them can be. Thus, an electrode standard potential has been chosen conventionally for the couple H+w/H2(g) (hydrogen electrode). Its standard electrode has been set definitively to the value 0.0000 V at every temperature ... 

It is not obligatory to be under standard conditions in order to determine the standard electrode potentials with the help of the preceding general cell (Fig. 2.5). Successive measurements in experimental conditions such as the activity coefficients of the couple members approaching unity permit their determination. 

In order to overcome the difficulty due to the discrepancy of the values of activities and concentrations, which may be important, the concept of formal potentials E° has been devised. (The symbol E° of formal potentials is, unfortunately, the same as that used for standard biological potentials.) The formal potential is that which is experimentally observed with solutions containing both Ox and Red forms of the couple at the unit concentration and that also may contain other species whose concentrations are specified. They take into account the variations in activity coefficients with the ionic strength, the acid-base equilibria involving the Ox and/or Red form(s), and their possible complexations with the other solution species. They are experimentally determined using electrochemical cells of the classes described above, after measurements of their zero-current cell potentials. The formal potentials can be used only when the experimental conditions of the redox reaction under study are the same as those under which they have been determined. 

The membrane perm-selectivity (y.m) is defined as the ratio between the actual and theoretical transfer of counterions through any IEM. It can be simply determined as the percentage ratio between the experimental and theoretical Donnan potential differences as measured using a test system consisting of two cells provided with calomel electrodes and filled with well-mixed standardized aqueous solutions of KC1 (at 0.1 and 0.5 kmol/m3), kept at 25 °C, and separated by the IEM sample under testing. 

Table III contains the experimental quantities (except the potential, E) and the constants used to determine the standard potentials of the cell (Equation 3). The ion-size parameter a for water and terf-butanol-water solvents is 5.50 A, and for ethanol and ethanol-water it is 5.00 A.

In this case the formal potential includes correction factors for activity coefficients, acid-base phenomena (hydrolysis of Fe " to FeOH " ), complex formation (sulfate complexes), and the liquid junction potential used between the reference electrode and the half-cell in question. Although the correction is strictly valid only at the single concentration at which the potential has been determined, formal potentials may often lead to better predictions than standard potentials because they represent quantities subject to direct experimental measurement. 

Acidity scales are used commonly to assess the chemical and biological state of seawater. The international operational scale of pH fulfills the primary, requirement of repro ducibility and leads to useful equilbrium data. Nevertheless, these pH numbers do not have a well defined meaning in respect to all marine processes. Seawater of 35%o salinity behaves as a constant ionic medium, effectively stabilizing both the activity coefficients and the liquid junction potential. It may be possible, therefore, to determine hydrogen ion concentrations in seawater experimentally. One method is based on cells without a liquid junction and is used to establish standard values of hydrogen ion concentration (expressed as moles of H /kg of seawater) for reference buffer solutions. 

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