Nernst expression

The first three equations above lend themselves to treatment by equilibria expressions and the last two by the Nernst expression. In all five cases it is the pH that is being solved for. The estimated values taken from the E-pH diagram are presented in brackets for comparison. 

Step (7). Writing E and pH equations. For each of the above three equations, the Nernst expression is written out, then the equation is solved for E as a function of pH. For each of the last two equations, the equilibrium constant is written out, the equation is put into logarithmic form, and is then solved for the pH. 

The potential of oxygen over platinum responded nicely to changes in oxygen pressure according to the Nernst expression (5). The reference electrode was silver immersed in 0 1M silver nitrate in the fused alkali nitrates, the mixture being contained in a thin glass envelope. To test the effect of changes in oxide ion concentration on the potential, a source of pure alkali oxide was needed. It is also ulti-... 

M Ag, in order to calculate the self-dissociation constants. Since alkali oxides are extremely difficult to prepare in the pure state and to handle, it was decided to produce the oxide ion coulometrically. Consequently, a known current of approximately 8 microamp. was run through the cell, the oxygen electrode acting as the cathode. The current was drawn from an electronically controlled constant current device and timed so that the number of equivalents of charge passing could be calculated. This was assumed to be the number of oxide ions produced. The variation in potential with oxide ion followed the Nernst expression very precisely. 

Values of E° by definition refer to conditions under which all species are in their standard states at 298 K. For non-standard conditions the electrode potential, E, of a redox reaction is given by the familiar Nernst expression (equation 24), where... 

One of the most important and extensively used indicator electrode systems is the glass-membrane electrode that is used to monitor hydronium ion activity. Although developed in 1909, it did not become popular until reliable electrometer amplifiers were developed in the 1930s. When the outside surface of the glass membrane is exposed to an ionic solution, a response for the hydronium ion activity meets with the Nicholsky equation, which is similar to the Nernst expression. In view of the importance and widespread use of the hydronium or pH electrode, this system is discussed in a separate chapter. 

The electrochemical potential of electrons in a redox electrolyte is given by the Nernst expression ... 

When Tip,redox is moved down , i.e., more positive, the band-bending increases, Fsc increases and therefore s0 decreases. A similar alteration in Cox affects redox through the Nernst expression. In both instances, we are influencing the Fermi level at the interface at equilibrium. Thus, in a sense, io is a quantitative measure of the extent of rectification of a given interface, i.e., a smaller k value translates to better rectification. 

Returning to the reaction shown in Equation 19-4, substitute Nernst expressions for the two electrode potentials in Equation 19-6 to give... 

If we substitute the Nernst expression for each couple into this equation, we find that at equilibrium... 

Both metallic and membrane electrodes have been used to detect end points in potentiometric titrations involving complex formation. Mercury electrodes are useful for EDTA titrations of cations that form complexes that are less stable than HgY- . See Section 21D-1 for the half-reactions involved and Equation 21-5 for the Nernst expression describing the behavior of the electrode. Hanging mercury drop and thin mercury film electrodes appropriate for EDTA titrations are available from a number of manufacturers. As always, whenever mercury is used in experiments like these, we must take every precaution to avoid spilling it, and it must be stored in a well-ventilated hood or a special cabinet to remove the toxic vapors of the liquid metal. Before working with mercury, be sure to read its Materials Safety Data Sheet (MSDS), and follow all appropriate safety procedures. 

In view of 6., the Nernst expression for a half-cell is given by... 

This relation, first obtained by Nernst, expresses the diffusion coefficient in terms of the ion conductivities. Some values of the diffusion coefficients for several electrolytes are given in Table 31.7. 

The Nernst expression can also be used for the half-cells. Thus for the Cu half-cell,... 

The potential of the standard hydrogen half-cell can be set at zero since only differences are measured, and the hydrogen value always cancels in these differences. In the cell above, the activities of H2, Haq, and Ag° are 1, as defined for the standard hydrogen half-cell and a pure solid. Putting these into the Nernst expression above shows why we can call this the half-cell potential for the silver couple ... 

The half-reactions in (c), (e), and (f) are obtained by combining the solubility constant expressions in (d) and (g) with the basic Nernst expressions (a) and (b), equations (12-6) and (12-7). One example should make the method clear. Let us derive the e line. 

The previous equation in terms of (OH ) is more correctly the Nernst expression for (e). It is convenient to express all of our equations for the diagram in terms of pH. But, note that the E° of0.305 V applies to unit activity (H" ) or pH zero. At pH 14, or pOH zero, either form... 

Here, Ei (/ = A, B) is the equilibrium potential of the metal-component i in the alloy A Bi- defined by modified Nernst expression ... 

In the case of an electrochemical reaction, substitution of the relationships AG = -nFE and AG = - f into the expression of a reaction free energy and division of both sides by -nF gives the Nernst expression for an electrode reaction described in Eq. (4.11) ... 

And again these equations are equivalent and only reflect the pH condition of the environment. The corresponding Nernst expression... 

A corrosion reaction can be considered as composed of two half cell reactions. One of the half cell reactions corresponds to oxidation reaction taking place on the anode, and the other half cell reaction corresponds to reduction reaction taking place on the cathode of the cell. The contribution of each half cell reaction to the Nernst expression can be derived as follows ... 

Note that O2 is the oxidized state and OH is the reduced state, for the above reaction (from lUPAC-Nernst expression). 

When Eqs. (29) and (30) are combined, the resulting Nernst expression relates the half-cell potential to the effective concentrations (activities) of the redox couple,... 

This activated platinum electrode system is the equivalent of an NHE and, therefore, conforms to the Nernst expression of Eq. (116). Rearrangement gives... 

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