Measurement of the Standard Electrode Potential

Let us consider the Harned cell, which is a cell without transfer ( jff = 0), to show how a standard electrode potential can be obtained by measuring the concentration dependence of the cell potential and, then, making an extrapolation to the infinitely dilute solution. The electrochemical diagram and the corresponding Nernst equation (4.22) for the Harned cell were considered in Chapter 4. Equation 4.22, which can, first, be simplified if the activity of H2(g) equals 1 (pni = 1 bar and fugacity coefficient is very close to 1) and, second, is rearranged as follows  

FIGURE 5.3 Determination of the standard electrode potential of Ag/AgCl using extrapolation to infinite dilute solution oiE = E + (IRT/F) In to Hcicaq) = 0- 

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Figure 18-9 illustrates measurement of the standard electrode potential for the Ag/AgCl electrode. 

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. 

Measurement of the standard electrode potentials of reactive metals... 

Determination of the Standard Electrode Potential ( from Electrochemical Measurements... 

The cell implicit in the measurement of a standard electrode potential should be arranged so that the standard hydrogen electrode is on the left... 

The measured potential difference across such a cell furnishes the magnitude of the standard electrode potential. 

Taking the polarographic half-wave potential (Ex 2 - - 1.45 volts, versus standard caloriel electrode hence ECil 2 - - 1.18 volts) in l.OAf CN as the measure of the reversible electrode potential (64). 

The first factor determines the tendency for dissolution to occur while the second and third, which are closely related, determine the rate of dissolution. The use of the standard electrode potentials as a measure of nobility is well known. The recognition that the exchange current density is a measure of the reversibility of a process and therefore a quantity characteristic of the reactivity of the system is more recent (13,32). As indicated by the Tafel relations, the exchange current density is a direct measure of the rate of the electrode reaction for any given value of the activation overvoltage (33). The values of iG may then be taken as a criterion for the electrochemical activity of a system. 

Redox equilibria between the various oxidation states of selenium have been little studied. This is apparently a consequence of slow reaction rates. For instance, it has been repeatedly demonstrated that the redox potential measured by a platinum electrode is not affected by the ratio of Se(VI) / Se(lV) present in solution, [87RUN/LIN]. The values of the standard electrode potentials of the important redox couples Se(VI) / Se(IV) and Se(lV) / Se(0) are essentially based on only one experimental investigation each. A more detailed discussion than would normally be required will therefore be made of the two investigations. 

The value of E measured under, or interpolated to, standard conditions, that is °, corresponds to the standard electrode potential for the right-hand electrode. (1.36) can be used to find the standard Gibbs energy change for the reaction occurring at this electrode, and measurements of how E varies with temperature yield values of A,iT and A,A°. The value of for any other cell can be calculated from the difference of the standard electrode potentials for the two electrodes. 

In order to establish a scale of oxidative jx>wer, it is necessary to have a standard, and since these reactions involve electrons, measurement of the reduction electrode potential is a convenient way to do this. The details are given more fully in Topic C3. 

We start our continuation by asking how we might measure standard electrode potentials. Suppose, for example, we wanted to obtain the value of the standard electrode potential of the cell ... 

There are a number of applications of potentiometry. In this book, the reader will learn only two of them (1) estimation of the standard electrode potential and (2) pH measurements. 

The standard electrode potential is a quantitative measure of the readiness of the element to lose electrons. It is therefore a measure of the strength of the element as a reducing agent in aqueous solution the more negative the potential of the element, the more powerful is its action as a reductant. 

In the introductory chapter we stated that the formation of chemical compounds with the metal ion in a variety of formal oxidation states is a characteristic of transition metals. We also saw in Chapter 8 how we may quantify the thermodynamic stability of a coordination compound in terms of the stability constant K. It is convenient to be able to assess the relative ease by which a metal is transformed from one oxidation state to another, and you will recall that the standard electrode potential, E , is a convenient measure of this. Remember that the standard free energy change for a reaction, AG , is related both to the equilibrium constant (Eq. 9.1)... 

One distingnishes practical and standard reference electrodes. A standard RE is an electrode system of particnlar confignration, the potential of which, nnder specified conditions, is conventionally taken as zero in tfie corresponding scale of potentials (i.e., as the point of reference nsed in finding tfie potentials of otfier electrodes). Practical REs are electrode systems having a snfficiently stable and reproducible value of potential which are nsed in the laboratory to measure the potentials of other electrodes. The potential of a practical reference electrode may difier from the conventional zero potential of the standard electrode, in which case the potential of the test electrode is converted to this scale by calculation. 

Girault and Schiffrin [6] and Samec et al. [39] used the pendant drop video-image method to measure the surface tension of the ideally polarized water-1,2-dichloroethane interface in the presence of KCl [6] or LiCl [39] in water and tetrabutylammonium tetraphenylborate in 1,2-dichloroethane. Electrocapillary curves of a shape resembling that for the water-nitrobenzene interface were obtained, but a detailed analysis of the surface tension data was not undertaken. An independent measurement of the zero-charge potential difference by the streaming-jet electrode technique [40] in the same system provided the value identical with the potential of the electrocapillary maximum. On the basis of the standard potential difference of —0.225 V for the tetrabutylammonium ion transfer, the zero-charge potential difference was estimated as equal to 8 10 mV [41]. 

If the sign of the standard reduction potential, E°, of a half-reaction is positive, the half-reaction is the cathodic (reduction) reaction when connected to the standard hydrogen electrode (SHE). Half-reactions with more positive E° values have greater tendencies to occur in the forward direction. Hence, the magnitude of a halfcell potential measures the spontaneity of the forward reaction. 

The standard electrode potential [1] of an electrochemical reaction is commonly measured with respect to the standard hydrogen electrode (SHE) [2], and the corresponding values have been compiled in tables. The choice of this reference is completely arbitrary, and it is natural to look for an absolute standard such as the vacuum level, which is commonly used in other branches of physics and chemistry. To see how this can be done, let us first consider two metals, I and II, of different chemical composition and different work functions 4>i and 4>ii-When the two metals are brought into contact, their Fermi levels must become equal. Hence electrons flow from the metal with the lower work function to that with the higher one, so that a small dipole layer is established at the contact, which gives rise to a difference in the outer potentials of the two phases (see Fig. 2.2). No work is required to transfer an electron from metal I to metal II, since the two systems are in equilibrium. This enables us calculate the outer potential difference between the two metals in the following way. We first take an electron from the Fermi level Ep of metal I to a point in the vacuum just outside metal I. The work required for this is the work function i of metal I. 

In general, the study of the variation of the formal electrode potential of a redox process with temperature has thermodynamic implications. Hence, one is interested in the measurement of AG°, AS° and AH° for the electron transfer process. It is recalled from thermodynamics that, under standard conditions, AE° is directly proportional to the free energy of the redox reaction according to the equation ... 

E is the standard electrode potential, and represents a value of E measured (or calculated) when all activities are 1, when the applied pressure p is 1 atmosphere and with all redox materials participating in their standard states. As for E, E should be cited with subscripts to describe the precise composition of the redox couple indicated. Note that is often written as thus explaining why standard electrode potentials are commonly called nought . The symbol 0 implies standard conditions i.e. 298 K, p and unit activities throughout. 

The amount of zinc in the soil was determined by immersing a rod of clean, pure zinc in the solution of zinc sulfate plus sulfuric acicf and measuring Ez 2+ z,i as —0.864 V. What is the concentration of the zinc solution formed by digesting in acid and what is the activity of the zinc salt In order to answer there questions, we will need to know the standard electrode potential, n —0.760 V. 

Next, we need to decide on what we think is occurring in terms of the system actually before us. Let s suppose that we have a CV which looks as though it describes a simple single reversible electron-transfer reaction. From the experimental trace of current against potential, it should be easy to obtain the standard electrode potential E . In addition, before we start, we measure the area of the electrode. A, and the thermodynamic temperature, T. Next, knowing A, T and E , we estimate a value for the exchange current lo, run a simulation, and note how similar (or not) are... 

Pavlishchuk and Addison [11] have discussed the foregoing discrepancies and made careful measurements of the reference electrodes commonly utilized by investigators in measuring potentials in acetonitrile. The correction to be applied for converting a potential measured against a reference electrode, ref to the ferrocene standard. Eye, can be expressed as ... 

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