2.3.4. Active Metal Indicator Electrodes
2.3.4.4. The Standard Hydrogen Electrode. The ultimate reference electrode is based on the half reaction for the reduction of hydrogen ions to molecular hydrogen
2H++2e− ⇄ H2 (2.37)
The corresponding Nernst equation for this half-cell is ENHE=EoH+∕H2− RT
2F ln { PH2
(aH+)2 }
(2.38) In Eq. (2.38), the logarithm term is zero for a hydrogen atmosphere of 1.0 atm and a hydrogen ion activity of 1.00 M. By convention,EoH+∕H
2 =0.This is only a reference point for the purpose of establishing a relative potential energy scale; the absolute value for any single electrode potential is not known. One cannot know the absolute electrode potential because any experiment designed to measure electrode potentials requires two electrodes.
The question of what is the potential of a single electrode is similar to asking “what is the distance to Chicago?” [10]. The obvious concern is from where? The answer only makes sense, if one specifies the starting point for measuring the distance to Chicago. Likewise, there must be a point of reference for measuring the potential at an electrode. An electrode potential can only be measured in an electrochemical cell with a second electrode as a ref- erence. The ultimate reference has been arbitrarily chosen (by the International Union of Pure and Applied Chemists) to be the half-cell for the reduction of hydrogen ions to hydro- gen gas at standard conditions. The apparatus in Figure 2.11 consists of a piece of platinum
k k H2 inlet
H2 outlet
Platinized Pt flag
Glass frit
HCl
FIGURE 2.11 The standard hydrogen electrode (SHE). The half-cell is based on the reduction of hydrogen ions to hydrogen gas. The standard conditions of unit activity hydrogen ions and 1.0 atm pressure of hydrogen gas are an ideal. It is not practical for direct measurements.
metal dipping into a solution of HCl (1.0 M H+activity for standard state) and exposed to a stream of hydrogen gas at 1 atm [12]. In order to enhance the adsorption of hydrogen and the kinetics of electron transfer, the electrode surface is “platinized” by reducing chloro- platinate from solution to form a film of finely divided platinum particles on the Pt plate.
The electrochemical potential of this half-cell is taken to be 0.000 V and standard electrode potentials are reported in comparison to this reference in the literature by convention. This electrode is generally known as the SHE or sometimes, the NHE (for Normal Hydrogen Electrode). However, NHE is technically a misnomer [13]. The term was originally intro- duced when “normal” referred to aconcentrationof 1 M. Because the high ionic strength of a 1 M solution of HCl lowers the activity coefficient, unit molarity is significantly different from unit activity. That being said, NHE and SHE are used synonymously now to mean the hydrogen electrode at unit hydrogen ion activity.
Data forE∘-values for other half reactions are reported in the literature as though they had been measured with this electrode as the reference. The standard reduction poten- tials listed in the literature correspond to the cell potential for the half-cell of interest (at standard state) together with the SHE as a reference electrode and, since the SHE has a half-cell potential of 0.000 V, the measured cell potential is numerically equal to the half-cell potential for the second electrode. However, the direct application of a hydrogen electrode using a hydrogen activity of 1.0 M is not really practical [11]. The aforementioned moder- ate hydrogen ion concentrations (>0.01 M) in the salt bridges develop junction potentials that are difficult to compensate for. Instead, the hydrogen half-cell, as shown in Figure 2.12, is mainly used to calibrate a calomel electrode that, subsequently, is used as a secondary standard reference electrode for work with other half-cells. The cell potentials are plotted versus the log of H+activity and extrapolated toaH+ =1.0 (where the hydrogen reference electrode has a potential of 0.000 V by definition) to find the cell potential that is equivalent
k k 0
0.1 0.2 0.3 0.4 0.5 0.6
–6 –4 –2 0 2
Cell potential Ecell versus NHE
log(αH+) HCl +
sat’d KCl Voltmeter
H2 inlet
FIGURE 2.12 In calibrating a calomel electrode, the electrode is introduced directly into the outer beaker of the hydrogen half-cell (Figure 2.11). In that case, there is only one salt bridge separating the calomel electrode solution and the hydrogen half-cell. That salt bridge contains saturated KCl (or about 4.17 M KCl at 25∘C). KCl salt is added to saturate the solution in the hydrogen half-cell as well.
The high concentration of KCl accounts for most of the ion traffic across the salt bridge and with an equal concentration on both sides, no junction potential develops. Above a level of 0.01 M HCl on the hydrogen electrode side, a hydrogen ion gradient is created through the salt bridge that introduces a voltage error. In order to avoid this error, cell measurements are made for a variety of hydrogen activities below 0.01 M. Then the data is graphed and extrapolated to a hydrogen activity level of 1.0 M. Because the potential of the SHE is defined as 0.000 at those conditions, this extrapolated cell potential is taken as the true reference potential of that calomel electrode on the SHE scale [12].
to the half-cell potential of the secondary reference electrode on the NHE scale. This cali- bration is done mainly for thermodynamic studies or cases where potential measurements of high precision and accuracy are needed.
2.3.4.5. Comparing Reference Electrodes.Most workers use calomel or sil- ver/silver chloride reference electrodes for their experiments. That raises the question of how one can compare the results between experiments when the reference electrodes are different. The convention is to convert the measured cell potential to the SHE scale. That is, one calculates the potential that would have been observed had the reference electrode been the SHE instead (using Eq. (2.39)):
Ecell vs SHE=Ecell vs Ref1+ERef 1 vs SHE (2.39) For example, Figure 2.13 indicates the half-cell potentials for a few common reference electrodes in a ladder diagram. The values of the various reference electrode potentials are listed with respect to the SHE on the left. Also, included in the diagram is the stan- dard electrode potential for the ferricyanide/ferrocyanide (Fe(CN)63−/Fe(CN)64−) redox couple on the same scale. If a group of workers were to measure the solution potential for
k k SHE
Ag/AgCl, 1 M KCl Saturated calomel, SCE
Fe(CN)6–3/Fe(CN)6–4 0.361
Pb2+/Pb° –0.125
+0.139 V –0.347 V
+0.119 V –0.367 V +0.178 V +0.400 V
New reading
0.242 0.222
0.000
FIGURE 2.13 Diagramming half-cell potentials on an energy ladder using the SHE electrode as the zero point helps in converting measured cell potentials using one reference half-cell to the scale for a different reference electrode. For example, a solution with an equimolar mixture of Fe(CN)63−/Fe(CN)64−
would have a cell potential of+0.139 V using a Ag/AgCl (1 M KCl) reference electrode or a value of +0.119 V for an SCE reference. A half-cell with 1 M Pb2+and a metallic lead electrode would produce a cell potential of −0.347 V with a Ag/AgCl (1 M KCl) reference electrode or a value of −0.367 V combined with an SCE reference electrode. Consider a new mixture that produces a cell potential of +0.178 V versus a Ag/AgCl (1 M KCl) reference electrode. It would have a value of+0.400 V on the SHE scale [14].
a mixture of Fe(CN)63− and Fe(CN)64−, ions at the same activity using a platinum elec- trode and a Ag/AgCl (1.0 M KCl) reference electrode, they would read a cell potential of +0.139 V. The best way for them to report their results would be not only to present the value that they measured with their apparatus but also to calculate the value that one would expect to see had the SHE electrode been used as a reference, namely+0.361 V (=Ecell vs Ref 1+ERef 1 vs SHE=0.139+0.222). Reporting the value on the SHE scale is a conve- nience for other workers who might want to predict what they would see upon repeating the first group’s work, but using their own reference electrode. For example, if the sec- ond team wanted to know what cell potential that they would see for the solution with the same ferricyanide/ferrocyanide composition measured against a calomel reference electrode, they would merely subtract their reference electrode potential from the value reported against the SHE, namely, 0.361−0.242= +0.119 V. Diagramming the relationships for half-cell potentials on the SHE scale, as in Figure 2.13, can be more helpful than trying to remember equations for converting between reference electrodes.
Also shown in Figure 2.13, is the standard potential for the reduction of Pb2+ions to metallic lead. This process has anEothat is more negative than the potential for the SHE.
Consequently, the reduction of Pb2+would appear at even more negative voltages in a cell using either a Ag/AgCl or a calomel reference electrode.
k k TABLE 2.1 Temperature dependence of two common
reference electrodes, calomel (saturated KCl)=SCE and Ag/AgCl (1 M KCl)
Temperature (∘C) ESCE(V) EAgCl/Ag(V)
0 0.236 55
5 0.234 13
10 0.231 42
15 0.250 8 0.228 57
20 0.247 6 0.225 57
25 0.244 4 0.222 34
30 0.241 7 0.219 04
35 0.239 1 0.215 65
Source: Heinemann 1989 [10]. Reprinted with permission of John Wiley & Sons.
Potentials for reference electrodes (and, therefore, cell potentials) are subject to changes in temperature. Some temperature effects are readily apparent, as it is with the coefficient for the logarithm term in the Nernst equation (see Eq. (2.5)). However, other temperature effects are subtler. The fact that the reference potential for the Ag/AgCl electrode depends on the Ksp of AgCl introduces another temperature effect, because equilibrium constants are temperature-dependent. Also, activity coefficients and junction potentials are sensitive to temperature. Consequently, careful work requires consistent temperature control for measuring all sample and standard solutions. Table 2.1 shows the variation in the reference electrode potential with temperature for the SCE and for the silver/silver chloride electrode in 1.0 M KCl [10].