2.3.4. Active Metal Indicator Electrodes
2.3.4.1. An Active Metal Electrode of the First Kind. Consider a piece of silver metal in contact with an aqueous solution of silver nitrate (Figure 2.4)
Whereas, it was assumed that platinum atoms on an electrode surface remain inert, silver atoms on a metallic silver surface are more active. That is, silver oxidizes more easily than platinum or gold. Tiny quantities of silver cations do leave the surface for the OHP and, in the process, each silver ion leaves behind an electron in the surface. The reverse process is also probable. It is possible for returning silver ions to find a place on the metal surface and become part of the metal by taking an electron out of the conduction band of the metal making the metal surface more positively charged. The process reaches an equilibrium that depends on the conditions. A net charge separation builds up between the metal and the OHP, leading to an electrical potential difference between the metal and solution. If one deliberately adds silver ions to the surrounding solution, the equilibrium shifts and that changes the potential on the surface. The electrode potential is controlled by this equilibrium reaction:
Ag++e− ⇄ Ag (2.21)
In writing the Nernst equation, metallic silver is the reduction product, so its activity should appear in the numerator of the logarithm term. Because metallic silver is a solid, its activity is unity by definition. So the net expression for the potential difference driving the reaction is written as follows:
E=EoAg+∕Ag−RT F ln
{ 1 aAg+
}
=EoAg+∕Ag− (0.059 16)log {
1 aAg+
}
(2.22) where 0.059 16 V is the value of 2.303(RT/F) at 298 K. For this electrode,Edepends solely on the silver ion activity. This kind of electrode is, therefore, called an indicator electrode, meaning its potential directly indicates an activity of a species in solution (Figure 2.5).
It might appear that the silver wire could act as a selective sensor for Ag+. That is true in limited situations. The problem is that metallic silver can also exchange electrons with
k k –7.00
0.40 0.50 0.60 0.70 0.80 0.90 1.00
–6.00 –5.00 –4.00 –3.00 –2.00 –1.00 0.00 Silver electrode potential
E (V)
log(αAg+)
FIGURE 2.5 Plot of the half-cell potential at a silver metal electrode as a function of silver ion activity.
other electroactive solution species and behave in a manner similar to the platinum elec- trode described earlier. There is the possibility that more than one half reaction could be contributing to the potential at the silver electrode surface in complicated solutions. Under those circumstances, the relationship given in Eq. (2.22) may not hold. Consequently, a bare silver wire is not often used as a sensor for Ag+ions; there are better electrochemical devices for determining silver ion activity. Several other metal ions develop a redox poten- tial with their corresponding metallic form. As with the Ag+/Ag combination, these metals can be used to monitor the solution activity of the corresponding ion. However, this strat- egy is only for situations where other electroactive species that might exchange electrons with the metal are absent. Some examples are Cu+/Cu/, Bi+/Bi, and Ni2+/Ni [10].
2.3.4.2. An Active Metal Electrode of the Second Kind. In the previous case, sil- ver ions in solution are in equilibrium with the metal, and the potential is controlled by the activity of the free silver ions. An important second case arises if the solution sur- rounding the electrode contains anions that form a sparingly soluble salt with silver ions.
For example, in the presence of chloride ions, silver precipitates to form crystalline silver chloride that has a solubility product of 1.78×10−10(Figure 2.6) [11].
AgCl ⇄ Ag++Cl− (2.23)
In the presence of a solution of chloride ions, the silver ion concentration is controlled by the chloride activity:
Ksp= (aAg+)(aCl−) =1.78×10−10 (2.24) or
(aAg+) = Ksp
(aCl−) (2.25)
k k OHP
= Ag+ ion Metallic Ag
Ag wire
KCl solution
AgCl coating
= K+ ion
= Cl– ion AgCl coating
e–
e–
FIGURE 2.6 AgCl/Ag electrode. A coating of silver chloride provides silver ions close to the silver metal surface. Electron transfer is very favorable permitting the rapid conversion between Ag+and Ag metal. A chloride ion moves between the outer Helmholtz plane (OHP) and the AgCl crystal as necessary to balance the charge. The boundary potential between the solid AgCl and the OHP depends on the chloride ion activity in solution.
Substituting for the silver ion activity in the Nernst equation for silver ion reduction to silver metal gives:
E=EoAg+∕Ag− RT F ln
{ 1 aAg+
}
=EoAg+∕Ag−RT F ln
{(aCl−) Ksp
}
(2.26)
Once again, the potential relies on the activity of only one ion, namely chloride in this case. Consequently, it is an indicator of the chloride activity. This type of indicator electrode is called an electrode of the second kind in older literature. With an active metal electrode of the first kind, the potential-controlling ion is the same element as the metal making up the electrode. With an active metal electrode of the second kind, the potential-controlling ion reacts with the ion made from the metal controlling the metal ion activity and, therefore, the potential indirectly. A convenient device can be made by depositing a coating of AgCl(s) directly onto the surface of the silver metal. The silver ions from the salt can be reduced directly to metallic silver:
AgCl+e−Ag ⇄ Ag+Cl− (2.27)
From this reaction equation, the Nernst equation becomes:
E=EoAg∕AgCl−RT
F ln{aCl−} (2.28)
The half reaction for the reduction of AgCl is related to the half reaction of Ag+as can be seen in Figure 2.7. There are two paths for the reduction AgCl. First of all, the salt can be reduced in a single step as indicated by path 1. Alternatively, the salt can dissolve to form
k k AgCl + e– Ag + Cl–
Ag+ + Cl– Ksp
+ e– 1
2
3
FIGURE 2.7 The reduction of AgCl to metallic Ag by two paths.
silver ions and chloride ions as indicated by step 2 followed by the reduction of the silver ions in solution by step 3. In both cases, the end result is metallic silver and chloride ions.
Hess’ law applies here. That is, the free energy change going from AgCl to the products by way of path 1 is equal to the free energy change for the path following step 2 and step 3. Considering this equivalence at standard state:
ΔGo1= ΔGo2+ ΔGo3 (2.29)
−nFEoAg∕AgCl = −RT ln(Ksp) −nFEoAg+∕Ag (2.30) Rearranging Eq. (2.30), one can solve forEoAg∕AgCl.
EoAg∕AgCl=EoAg+∕Ag+ RT
nFln(Ksp) (2.31)
Consequently, the standard potential for the reduction of AgCl in Eq. (2.28) is a com- bination of two terms, the standard reduction potential for silver ions and the solubility product for silver chloride. Equation (2.31) provides a means of evaluating any one of these terms given data for the other two. Therefore, the standard electrode potential for the reduction of AgCl(s)is given by
EoAg∕AgCl=EoAg+∕Ag+RT
F ln{Ksp} =0.779+ (0.059 16)log(1.78×10−10) = +0.222 V (2.32) An interesting outcome of this arrangement is a device that responds to the logarithm of the chloride ion activity in solution.
A reliable way of measuringEoAg∕AgClwould be to plot the potential at a silver/silver chloride electrode versus the logarithm of the chloride ion activity as in Figure 2.8. As Eq. (2.28) indicates, this plot will form a line that goes throughE =EoAg∕AgCl at a chlo- ride activity of 1 M. This approach is recommended, because multiple measurements are required and the uncertainty in the resulting value is smaller than it would be using a single solution of 1 M chloride activity to measureEoAg∕AgCldirectly.
k k 0
0.1 0.2 0.3 0.4 0.5 0.6
–6 –5 –4 –3 –2 –1 0
log(aCl–)
Potential of Ag/AgCl (V) Eo = +0.222 V
FIGURE 2.8 Plot of the potential of a silver/silver chloride electrode versus log(aCl−). The value of the standard potential,EoAg∕AgCl, for this half reaction is equal to the voltage at they-intercept.
2.3.4.3. Reference Electrodes. An electrode of the second kind provides a very con- venient method for creating a reference electrode. A silver chloride-coated silver wire is an easy-to-prepare and effective example of this type of electrode. This device is often called a silver/silver chloride electrode (or, sometimes, merely a silver chloride electrode). The sur- rounding chloride activity can easily be fixed and the electrode potential is set. The half-cell potential for a silver/silver chloride electrode with 1 M KCl is+0.222 V. A popular alter- native is to use a saturated KCl solution (∼4.17 M at 25∘C) so that there is no variation in the chloride activity, if any evaporation occurs. This saturated KCl, silver/silver chloride reference has a reference potential of+0.199 V. All of the species involved in the electron transfer are a part of the solid coating or the underlying silver. The electron transfer in either direction is very rapid. Chloride ions are a part of the overall reaction, but they are not directly involved in electron transfer with the silver. They mainly act to confine the sil- ver ions to the coating. At high concentrations of chloride (≥0.1 M), this electrode robustly maintains the potential predicted by Eq. (2.28). If a silver chloride electrode is placed into an electrochemical cell along with an inert indicator electrode, such as a platinum wire and an outside voltage is applied to the cell, the silver chloride electrode will not budge from its rest potential as predicted by Eq. (2.28). All of the energy from the outside power source will be transferred to the double layer at the platinum electrode. This behavior is ideal for a reference electrode in an electrochemical measurement system. The key attribute is that the reference remains at its fixed potential regardless of current being forced through the cell in one direction or the other. Such an electrode is said to be “nonpolarizable.” In prac- tice, such ideal behavior is limited to low levels of current (less than a few microamps).
In voltammetric experiments, an auxiliary electrode is usually added to carry the current for the reference electrode as a precaution. (Three-electrode systems are discussed in more detail in Chapters 5 and 7.)
Of course, applying a voltage to an electrochemical cell is a voltammetric experiment.
An auxiliary electrode is not common in potentiometric work. In a potentiometric
k k Internal solution
fill port
KCl solution Porous frit or asbestos fiber salt bridge
Silver wire
AgCl coating
Pt wire indicator electrode
Sample solution
FIGURE 2.9 A complete potentiometric cell with a silver/silver chloride reference electrode and a Pt indicator electrode. This arrangement is commonly used for direct measurement of the redox potential of a sample solution or for a redox titration of an electroactive analyte, such as in the determination of vitamin C.
experiment, the cell current is nominally zero. (In practice it is finite, but very small, typically <1 pA.) Figure 2.9 shows an electrochemical cell for a simple potentiometric experiment, such as for a titration of vitamin C with I3−, a mild oxidizing agent. A platinum wire serves as an indicator electrode. Because a silver chloride electrode is nonpolarizable, changes in potential at the indicator electrode do not move the potential at the reference electrode in a potentiometric experiment either. Consequently, any change observed in the cell potential can be interpreted as a change in the potential of the indicator electrode. Therefore, as described in Chapter 1:
Ecell=Emeasured=Eindicator+Ejunction−Ereference (2.33) or
Eindicator=Emeasured−Ejunction+Ereference (2.34) The indicator potential,Eindicator, from Eq. (2.34) is related to the analyte concentration through the Nernst equation (Eindicator is the same as the Esoln in Eq. (2.5)) for a redox system.
The silver/silver chloride reference electrode is the most commonly used reference in modern practice, but two other reference electrodes deserve special mention. The first of these is based on the reduction of a mercury(I) chloride salt, also known as calomel (see Figure 2.10). The half reaction is
Hg2Cl2+2e− ⇄ 2Hg+2Cl− (2.35)
Ecalomel=EoHg
2Cl2∕Hg−RT
2F ln{aCl−}2 =EoHg
2Cl2∕Hg− RT
F ln{aCl−} (2.36)
k k Saturated
KCl solution
Porous frit or asbestos fiber salt bridge
Platinum wire Mercury
Hg/Hg2Cl2 KCl mixture
Porous frit or glass wool Fill port
FIGURE 2.10 Saturated calomel electrode (SCE).
The standard potential, Eo, for the calomel electrode (with a 1 M KCl solution) is +0.282 V and the saturated calomel electrode or SCE (a calomel electrode containing a saturated KCl solution) has a half-cell potential of+0.242 V [10].