Nernst method

The mediated OTTLE/Nernst method, with 2,6-dichlorophenolindophenol as mediator, was employed by Heineman et al. in the measurement of E for cytochrome c [83], For enzymes, the mediated OTTLE/Nernst method is probably the method of choice, since the heterogeneous charge-transfer processes often are very slow the electroactive metal center is insulated by the surrounding protein structure and cannot get close to the electrode surface. 

In potentiometry the potential of an electrochemical cell is measured under static conditions. Because no current, or only a negligible current, flows while measuring a solution s potential, its composition remains unchanged. For this reason, potentiometry is a useful quantitative method. The first quantitative potentiometric applications appeared soon after the formulation, in 1889, of the Nernst equation relating an electrochemical cell s potential to the concentration of electroactive species in the cell. ... 

Since the junction potential is usually of unknown value, it is normally impossible to directly calculate the analyte s concentration using the Nernst equation. Quantitative analytical work is possible, however, using the standardization methods discussed in Chapter 5. 

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

The free energy changes of the outer shell upon reduction, AG° , are important, because the Nernst equation relates the redox potential to AG. Eree energy simulation methods are discussed in Chapter 9. Here, the free energy change of interest is for the reaction... 

As an alternative to plotting a calibration curve, the method of standard addition may be used. The appropriate ion-selective electrode is first set up, together with a suitable reference electrode in a known volume (Ft) of the test solution, and then the resultant e.m.f. ( t) is measured. Applying the usual Nernst equation, we can say... 

The method just described leads to the mean specific heats over a fairly large range. Nernst, Koref, and Lindemann (1910) have recently described a method of measuring the true specific heat at a given low temperature. The substance is contained in a block of copper cooled to the requisite temperature in liquid carbon dioxide, liquid air, etc., and energy is supplied by a heating spiral of platinum wire carrying an electric current, the measurement of the resistance of which serves at the same time to determine the temperature. 

Further particulars of these methods will be found in W. Nernst, Applications of Thermodynamics to Chemistry, 1906 F. Haber, Thermodynamics of Technical Gas Reactions, 2nd edit., trans. Lamb, 1909. 

With the entropy, however, the case is quite otherwise, and we shall now go on to show that as soon as we are in possession of a method of determining the absolute value of the entropy of a system, all the lacunae of the classical thermodynamics can be completed. The required information is furnished by a hypothesis put forward in 1906 by W. Nernst, and usually called by German writers das Nernstsche Wdrmetheorem. We can refer to it without ambiguity as Nernsfs Theorem. ... 

The chemical constants may therefore be determined directly by the measurement of vapour pressures, especially at low temperatures. Equation (9), which is more general, shows that the chemical constant is determined for a. homogeneous gas as soon as we know A, and C, as functions of temperature, and the vapour pressure at one temperature. These data, especially vapour pressures at very low temperatures, are not very well known at present, and some other method must therefore be used in the determination of the chemical constant. Several such methods have been proposed by Nernst (loc. cit. cf. also Haber, Thermodynamics of Technical Gas Reactions, pp. 88—96 Weinstein, Thermodynamik and Kinetik III., 2, pp. 1064—1074). 

Page 14, line 2 The method of Nernst, Koref, and Lindemann, by the use of the copper-calorimeter, determines the mean specific heat over a range of temperature. The mode of procedure is the same as in ordinary calorimetry, except that a hollow block of copper, the temperature of which is determined by means of inserted thermoelements, is used instead of a calorimetric liquid, and the method therefore made applicable to very low temperatures. 

Most measurements include the determination of ions in aqueous solution, but electrodes that employ selective membranes also allow the determination of molecules. The sensitivity is high for certain ions. When specificity causes a problem, more precise complexometric or titri-metric measurements must replace direct potentiometry. According to the Nernst equation, the measured potential difference is a measure of the activity (rather than concentration) of certain ions. Since the concentration is related to the activity through an appropriate activity coefficient, calibration of the electrode with known solution(s) should be carried out under conditions of reasonable agreement of ionic strengths. For quantitation, the standard addition method is used. 

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values and then apply the Nernst equation. If the Ecell turns out to be negative, it indicates that the reaction is not a spontaneous one (an electrolytic cell) or that the reaction is written backwards if it is supposed to be a galvanic cell. If it is supposed to be a galvanic cell, then all you need to... 

Chan (Chapter 6) presents a simple graphical method for estimating the free energy of EDL formation at the oxide-water interface with an amphoteric model for the acidity of surface groups. Subject to the assumptions of the EDL model, the graphical method allows a comparison of the magnitudes of the chemical and coulombic components of surface reactions. The analysis also illustrates the relationship between model parameter values and the deviation of surface potential from the Nernst equation. 

When using the Nernst equation on a cell reaction in which the overall reaction is not supplied, only the half-reactions and concentrations, there are two equivalent methods to work the problem. The first way is to write the overall redox reaction based upon E° values,... 

To appreciate that an ISE must be selective if its measurements are to be useful, and how the Nernst equation can be adapted to take account of the ISE selectivity by using the concept of a selectivity coefficient (or ratio ). To leam how the problems of selectivity can be overcome by using a standard-addition method, such as drawing a Gran plot - one of the more useful of such methods. 

It is a good idea, when using such simple Nernst plots as an analytical method of determining an activity, to check that the intercept at jc = 0 is indeed the standard electrode potential. (There are many compendia listed in the Bibliography at the end of this book that cite large numbers of values, as does Appendix 3.)... 

Such a mechanism is not incompatible with a Haven ratio between 0.3 and 0.6 which is usually found for mineral glasses (Haven and Verkerk, 1965 Terai and Hayami, 1975 Lim and Day, 1978). The Haven ratio, that is the ratio of the tracer diffusion coefficient D determined by radioactive tracer methods to D, the diffusion coefficient obtained from conductivity via the Nernst-Einstein relationship (defined in Chapter 3) can be measured with great accuracy. The simultaneous measurement of D and D by analysis of the diffusion profile obtained under an electrical field (Kant, Kaps and Offermann, 1988) allows the Haven ratio to be determined with an accuracy better than 5%. From random walk theory of ion hopping the conductivity diffusion coefficient D = (e /isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by... 

Method 2 is the separate solution method [38,135], The EMF of a cell consisting of an ISE and a reference electrode is measured in a solution of determinand J alone (in the absence of interferent K) and then in a solution of interferent K alone (in the absence of determinand J), the activities of the determinand and the interferent in the two solutions being the same. If the respective values of EMF are Ei and E2 and E ise for both ions are given by the simple Nernst equation, then can be calculated from the relationship,... 

In potentiometry with ISEs, however, the second Gran method [46] has found especially wide use, not only in titrations, but also in multiple addition methods in general. In these methods, the concentration of the test substance is plotted against the volume of the titrant or of the standard solution and thus the curve is linearized. The end-point in the titration or the determinand concentration in a multiple addition method is found as the intercept of the straight line with the volume axis. Linearization is attained by taking the antilogarithm of the Nernst equation ... 

These equations, for the case of solid diffusion-controlled kinetics, are solved by arithmetic methods resulting in some analytical approximate expressions. One common and useful solution is the so-called Nernst-Plank approximation. This equation holds for the case of complete conversion of the solid phase to A-form. The complete conversion of solid phase to A-form, i.e. the complete saturation of the solid phase with the A ion, requires an excess of liquid volume, and thus w 1. Consequently, in practice, the restriction of complete conversion is equivalent to the infinite solution volume condition. The solution of the diffusion equation is... 

Potentiometry is a method of obtaining chemical information by measuring the potential of an indicator electrode under zero current flow. It is based on the Nernst equation, which expresses the electrode potential as a function of the activity (or activities) of the chemical species in solution. The information obtained varies with indicator electrode, from the activity (concentration) of a chemical species to the redox potential in the solution. The potential of the indicator electrode is measured against a reference electrode using a high inptit-impedance mV/pH me-... 

The formation of nitric oxide from its elements was investigated by Nernst at 1,538° and 1,737°C., the decomposition by Jellinekf between 650° and 1,750° C. Both investigations were made by the streaming method. Each of the reactions is stated to be bimolecular. 

TITRATION (Potentiometric). This analytical method is based in principle upon the Nernst equation, which may be written in the form... 

The concentrations are then used instead of the activities in various-thermodynamic expressions (e.g., the equilibrium law, and Nernst s equation for the e.m.f.). Some physical chemists are suspicious of this method. However, it is just as thermodynamic as the traditional one, the only difference being that another activity scale is used. 

Methods. All solutions were prepared to be ImM Cytochrome c, 0.1mM DCIP, 0.10M alkali halide, and 0.10M phosphate buffer at pH 7.0 or pD 7.0. The DCIP served as a mediator-titrant for coupling the Cytochrome c with the electrode potential. E° values were measured using a previously described spectropotentiostatic technique using an optically transparent thin-layer electrode (OTTLE) (7,11,12). This method involved incrementally converting the cytochrome from its fully oxidized to fully reduced state by a series of applied potentials. For each potential a spectrum was recorded after equilibrium was attained. The formal redox potential was obtained from a Nernst plot. The n value... 

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