Potential difference, metal-solution

One can have more complicated cells (Fig. 6.30), and in all of them it can be seen that the attempted measurement of a metal-solution potential difference will conclude with the measurement of the sum of at least two interfacial potential differences, i.e., the desired PDM /s and as many extra potential differences as there are new phase boundaries created in the measurement. In symbolic form, therefore, the potential difference V indicated by the measuring instrument can be expressed as... 

Fig. 6.29. If electrode M, and the connecting wires M2 are dissimilar metals, a contact potential difference PC /M, at the metal Mumetal M2 interface is generated in the measurement process in addition to the extra metal-solution potential difference PDm2/S-...

The analysis of the process of measuring potential differences across phase boundaries demonstrates the impossibility of using standard potential measuring devices to determine the value of a single metal-solution potential difference. The electrochemist proceeds, therefore, somewhat humbled but not defeated. He or she must ask how much information about the potential difference across an elec-trode/electrolyte interface can be obtained. 

Can One Measure Changes in the Metal-Solution Potential Difference ... 

Of course, if this constant is taken as zero for all the metals with which the potentials of the other systems are compared, there will be no effect of this constant, but one may never forget that the relative electrode potential, to which reference is so often made, is in fact not a metal-solution potential difference. 

Can the potential difference across an interface be structured, or separated into contributions This potential difference depends on the arrangement of charges, oriented dipoles, etc. Can one speak of separate contributions to the total potential difference from the excess charges on the metal and solution phases, on the one hand, and from the oriented dipoles, on the other Perhaps these individual contributions can be measured or calculated. Thereafter, one may be able to add them together to calculate the elusive metal-solution potential difference. 

Total metal-solution potential difference with respect to an uncharged infinite... 

This kinetically deduced equation relates A e, the metal-solution potential difference [a Galvani potential difference (Section 6.3.10)], to the concentration (and in a more complete treatment, the activity) of those ions in the solution that undergo electron transfer at the interface. It will he seen later that (7.40) is quite near the famous equation that bears Nernst s name. 

The electrode potential is defined as the potential difference between the terminals of a cell constructed of the half-cell in question and a standard hydrogen electrode (or its equivalent) and assuming that the terminal of the latter is at zero volts. Note therefore that the electrode potential is an observable physical quantity and is unaffected by the conventions used for writing cells. The statement. . . the electrode potential of zinc is —0.76 volts. . . implies only that a voltmeter placed across the terminals of a cell consisting of standard hydrogen electrode and the zinc electrode would show this value of potential difference, with the zinc terminal negative with respect to that of the hydrogen electrode. An electrode potential is never a metal/solution potential difference , not even on some arbitrary scale. 

The first exponential shows the potential dependence of the rate constant upon the measured applied metal—solution potential difference (0m — 0s)- The second exponential is the double layer correction to the rate constant and accounts for the effects of both concentration and potential at the pre-reaction plane. 

The Metal-Solution Potential Difference at Redox Electrodes... 

We summarize the findings in this section as follows In any redox reaction, the metal-solution potential difference is a function of the metal used, whereas the total cell potential is independent of it. 

To resolve the apparent inconsistency of the summary statement of Section 5.2, let us consider yet another example. Assume that a gold electrode and a platinum electrode are dipped into the same solution of Fe VFe VH SO and both electrodes behave reversibly with respect to this redox couple. We have already established that the metal-solution potential difference at the two interphases is different, since each includes the term (J., as seen in Eq. 3IB. Yet the measured potential of this cell must be zero, since both electrodes are assumed to behave reversibly in the same solution. We could tentatively state that since electrons are neither produced nor consumed in the overall cell reaction, their chemical potential in the different phases cannot affect the measured potentials. 

Looking at this example in more detail, we note that the difference between the two metal-solution potential differences is ... 

A better method of measuring changes in the metal-solution potential difference at the working electrode (which we shall refer to from now on as "changes in the potential of the working electrode ) is to use a three-electrode system, like the one in Fig. 1C. 

The surface tension of an electrode in contact with solution depends on the metal-solution potential difference. The equation describing this dependence is called the electrocapillary equation. It follows from the Gibbs adsorption isotherm, as we shall show in a moment. Before we do that, however, let us write this equation and discuss some of its consequences. 

As such, it cannot depend on the connecting wires, yet it would appear from Eq. 21B that the potential differences at the Ag/Cu and Cu"/Zn interphases do contribute to the measured potential. In this context we might ask ourselves how Eq. 21B would be modified if we used another metal wire, say nickel, to connect the electrodes to the terminals of the voltmeter. The two metal-solution potential differences would not be affected, but instead of... 

Now, the metal used as the electrode does not appear explicitly in any of the last three equations, but it is implicit in the half-cell reactions, since the electrons are either taken from or returned to the metal, and we might expect the metal-solution potential difference to include a term for the chemical potential of electrons in platinum. To show this, consider Eq. 27B at equilibrium. We can write... 

We have seen that there is no ambiguity in the thermodynamic definition of the NHE scale. A detailed analysis, in terms of the various A(t) values at different interphases in the cell, is less straightforward. At first we might be tempted to assign a zero value to the metal-solution potential difference at the normal hydrogen electrode... 

This is clearly not an acceptable choice, since we have seen that the metal-solution potential difference at a redox electrode depends on the metal employed. Thus, if the condition given by Eq. 41B would define the zero for the NHE scale, we could set up a different normal hydrogen electrode employing, say, iridium instead of platinum. Since... 

Now, we can write a Nemst-type equation for the absolute metal-solution potential difference at the reversible potential, namely... 

Fig. 5E Model showing how p can be independent of potential. The metal-solution potential difference A( ) is the sum of its value at equilibrium Ad), and the value 5(A(b) added when an over-...

Equation 28J is not quite correct, since it implies that the absolute metal-solution potential difference at the PZC is zero. In other words, it implies that we can measure the absolute metal-solution potential difference, which is not the case, as we showed in detail at the outset of this book. The error is, however, only a constant, which can be lumped into the equilibrium constant and has no effect on the potential dependence of 0. 

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