CASE STUDIES IN CONTROLLED POTENTIAL
6.2. CASE I. EVALUATING THE FORMAL POTENTIAL AND RELATED PARAMETERS
One of the most important parameters for investigating redox reactions is the formal reduction potential,Eo′, for the reagent under study. The most commonly used method for evaluatingEo′is CV. Consider, for example, the reduction of the ethylenediaminete- traacetic acid (EDTA) complex of ruthenium(III) in aqueous solution (shown here).
O
O O
O O O N N Ru
OO O–
H H III
[Ru (EDTA)(HIII 2O)]–
[Ru (EDTA)(HIII 2O)]–
+ e– [Ru (EDTA)(HII 2O)]2–
CVs for three different concentrations of [Ru(EDTA)(H2O)]−are shown in Figure 6.1A [2]. The dashed vertical line in Figure 6.1A appears at the average of the peak potentials and its position provides an estimate of the formal potential,Eo′(about−0.01 V). It is useful
0.75 40 20 0 –20 –40 –60 –80
60 90 120 30 0 –30 –60 –90 3 × 10–3 mol/dm3
2 × 10–3 mol/dm3 1 × 10–3 mol/dm3
(DMSO) = 1.94 mol/dm3 (DMSO) = 0.39 mol/dm3 (DMSO) = 0.029 mol/dm3 Oxidized form
is stable on this side
Reduced form is stable on this side.
a
a
b
b
c d Eºʹ
0.50 0.25
Potential (V) versus SHE
(A) (B)
Potential (V) versus SHE
Current (μA) Current (μA)
0.00 –0.25 –0.50 0.75 0.50 0.25 0.00 –0.25 –0.50
V = 50 mV/s
V = 200 mV/s
FIGURE 6.1 Cyclic voltammograms of [Ru(EDTA)(H2O)]−and [Ru(EDTA)(DMSO)]−. (A) Cyclic voltam- mograms of [Ru(EDTA)(H2O)]− at different concentrations at a glassy carbon electrode. (B) Cyclic voltammograms of the same solution as in part (A) with the addition of DMSO to yield the indicated concentrations. Dashed vertical line indicates the formal potential of the corresponding complexes.
Source: Adapted with permission from Toma et al. [2]. Copyright 2000, American Chemical Society.
k k to think of the formal potential in a manner similar to the pKa for weak acids. Just as the
pKarepresents a boundary between low pH conditions where the acid form is more stable and high pH conditions where the deprotonated form is more stable, theEo′represents a boundary between conditions where the oxidized and reduced species predominate. At potentials more negative thanEo′, the reduced form of the complex is stable; at potentials more positive thanEo′, the oxidized form is more stable. For this ruthenium complex, the oxidized and reduced forms occupy ranges of stability of similar size. The size of these zones of stability depends on the nature of binding of the metal to the ligands. It is inter- esting to note that the EDTA binds the ruthenium metal in five places rather than six sites as is common for most transition metals. This arrangement leaves the sixth coordination site available to bind with water. This water molecule can be replaced by other ligands.
A very interesting ligand is nitric oxide, NO. The [RuIII(EDTA)(NO)]− complex (shown below) has
O
O S dimethyl sulfoxide O
O O
O– O O–
O O
O O
O O
O O O OO
S
N N
N N N
Ru Ru
[Ru (EDTA)(NO)]–III [Rul (EDTA)(DMSO)]–II
been investigated as a possible pharmaceutical. Nitric oxide is a neurotransmitter, vasodilator (trigger for relaxing arterial blood vessels), as well as an antibacterial and antitumor agent [3]. The relative binding strength of these small ligands can have a big effect on the formal potential of the complex. This effect is demonstrated in Figure 6.1B, where the water in the ruthenium EDTA complex has been exchanged for dimethyl sulfoxide (DMSO) [2]. Additions of DMSO were added to the same solution that was used in Figure 6.1A in stages so that the partial displacement of water by the DMSO was also evident. After the first addition of DMSO, the reduction peak for the water-containing complex was still observed (peak (a) in the figure). The fact that peak (a) is unperturbed indicates that the [RuIII(EDTA)(H2O)]−complex remains intact. It is more stable than the corresponding [RuIII(EDTA)(DMSO)]− complex under these conditions. However, the return peak (b) is almost entirely gone and a new return peak (c) appears near+0.6 V.
This indicates that the reduced form of the water complex converts to the DMSO complex very rapidly. The DMSO form of the reduced complex is thermodynamically favored over the water form. At higher concentrations of DMSO, a new reduction peak (d) appears paired with the new oxidation peak (c). This pair of peaks represents the oxidation and reduction of the DMSO complex. A dashed line has been placed at the average of the peak potentials for peaks (c) and (d) representing theEo′for this couple. TheEo′for the DMSO complex has shifted by over half a volt to more positive values (+0.53 V). The positive position of theEo′indicates that the reduced form of the complex is much more stable than the oxidized form in the DMSO complex. The DMSO stabilizes the Ru(II) form by binding more strongly to it than the ligand does the Ru(III). The oxidation state of the metal center is crucial to the binding because the bond between the metal center and
k k DMSO is primarily the result of electron density from a d-orbital on the metal donating
to a𝜋*-orbital (anti-bonding orbital) on the ligand. The Ru(III) metal ion has one fewer electron to share [2, 4]. (The acceptor orbital on the DMSO happens to be an anti-bonding orbital. That may seem contradictory. Putting electrons into an anti-bonding orbital does lower the bond order for the S—O bond in the DMSO, but it provides an effective mode for sharing electrons between the metal and ligand.) Water does not have a𝜋-orbital to provide that type of interaction. Water donates an electron pair to an empty d-orbital on the ruthenium. The important conclusion is that DMSO stabilizes the reduced form of the complex much more than the oxidized form and that causes a large shift in the formal potential of the complex. Just how much of a difference in the metal–ligand binding strength there is between the two redox forms of the DMSO-containing complex can actually be calculated from the data provided in the cyclic voltammograms in Figure 6.1B [2].
The equilibrium constant for the ligand exchange is a measure of the binding strength of the DMSO with the metal center. Consider ligand exchange for the Ru(III) complexes.
[RuIII(EDTA)(H2O)]−+DMSO⇄[RuIII(EDTA)(DMSO)]−+H2O (6.1) The corresponding equilibrium constant for Reaction (6.1) can be written as follows:
KIII= [RuIII(EDTA)(DMSO)−][H2O]
[RuIII(EDTA)(H2O)−][DMSO] = [RuIII(EDTA)(DMSO)−]
[RuIII(EDTA)(H2O)−][DMSO] (6.2) where the activity of H2O is assumed to be unity because it is the solvent. With the use of Eq. (6.2) and current measurements from Figure 6.1B, it is possible to calculate an esti- mate ofKIII. As DMSO is added to the system, more of the water complex converts to the DMSO complex. Assume that the Ru(III) is present in only as [RuIII(EDTA)(H2O)]− and [RuIII(EDTA)(DMSO)]−. Then the following is true:
[RuIII(EDTA)(H2O)−] + [RuIII(EDTA)(DMSO)−] = [RuIII]total (6.3) In Section 5.3.5.2, it was noted that the peak current is proportional to the concentra- tion of the electroactive species. The key relationship is the Randles–Sevcik equation (6.4).
Because the background current is easiest to estimate for the peak closest to the start of the scan, we will work with the peak marked (d) for the reduction of the DMSO-containing complex.
ip(d) = (2.69×105)n32AD12𝜈12[RuIII(EDTA)(DMSO)−] (6.4) Assuming that the voltammogram for the highest concentration of DMSO represents the conditions where virtually all of the water in the complex has been displaced by DMSO, then:
ip(d)max= (2.69×105)n32AD12𝜈12[RuIII(EDTA)(DMSO)−]max
= (2.69×105)n32AD12𝜈12[RuIII]total (6.5)
k k These three equations can be used to express the fraction of oxidized ruthenium in the
DMSO complex:
RuIIIfraction in DMSO form= [RuIII(EDTA)(DMSO)−]
[RuIII]total = ip(d)
ip(d)max (6.6) Because the fraction of the RuIIIin the DMSO form and the fraction in the H2O form must sum to unity, the fraction for the H2O form is given by
RuIIIfraction in H2O form= [RuIII(EDTA)(H2O)−]
[RuIII]total =1−RuIIIfraction in DMSO form
=1− ip(d)
ip(d)max (6.7)
Dividing Eq. (6.6) by Eq. (6.7) gives a useful ratio:
[RuIII(EDTA)(DMSO)−]∕[RuIII]total
[RuIII(EDTA)(H2O)−]∕[RuIII]total = ip(d)∕ip(d)max 1−i ip(d)
p(d)max
= [RuIII(EDTA)(DMSO)−] [RuIII(EDTA)(H2O)−]
= ip(d)
ip(d)max−ip(d) (6.8)
Substituting into Eq. (6.2) yields an expression that can be used to calculate the equi- librium constant,KIII. Using estimates of the current at (d) for the middle concentration and the current at the maximum concentration (forip(d)max) gives:
KIII= [RuIII(EDTA)(DMSO)−]
[RuIII(EDTA)(H2O)−][DMSO] = ip(d)
{ip(d)max−ip(d)}[DMSO]
= 48μA
{72μA−48μA}[0.39 M]=5.1 (6.9)
A binding constant of 5 is not particularly strong. This number is a measure of the RuIII–DMSO bond. It is interesting to compare that number with the binding constant for the reduced DMSO-containing complex. Fortunately, the voltammograms in Figure 6.1 provide the data for calculating that value, too.
This strategy takes advantage of Hess’ Law. The ligand exchange process and the for- mal potentials for the two different complexes are related by the equations in Figure 6.2 [2].
There are conceptually two different paths that might be followed in order to go from [RuIII(EDTA)(DMSO)]−as a reactant to the reduced product [RuII(EDTA)(DMSO)]−. First of all, one can merely add an electron (step 4 in Figure 6.2). Alternatively, one can first exchange the DMSO ligand for H2O, reduce that complex and then swap the water ligand with DMSO. Because the products and reactants are in equilibrium states, the energy spent to get from one to the other is independent of the path. Consequently, the energy spent going from [RuIII(EDTA)(DMSO)]− to [RuII(EDTA)(DMSO)]− by steps 1, 2, and 3 is the
k k
III
III
III
II
II
II
[Ru
[Ru
(EDTA)(H2O)]– [Ru (EDTA)(H2O)]2−
(EDTA)(DMSO)]– [Ru (EDTA)(DMSO)]2−
2
4 + e–
+ e– + DMSO
K
+ DMSO K 1 3
FIGURE 6.2 Equilibria relating the different forms of some ruthenium–EDTA complexes. The energy required to go from [RuIII(EDTA)(DMSO)]− to [RuII(EDTA)(DMSO)]− is the same following the path 1+2+3 as amount of energy associated with the direct reduction of [RuIII(EDTA)(DMSO)]−in a single, one-electron process (step 4). Source: Adapted from with permission from Toma et al. [2]. Copyright 2000, American Chemical Society.
same as the energy spent in the direct electron transfer, step 4. Expressed in terms of the Gibbs’ free energy change:
ΔG1+ ΔG2+ ΔG3= ΔG4=RTln(KIII) −nFEo′2 −RTln(KII) = −nFEo′4 (6.10) In Eq. (6.10), the free energy change associated with the formal potential for an electron transfer reaction is−nFEo′in joules. The free energy change associated with an equilibrium constant is−RTln(Keq) in joules. The sign was changed forKIIIbecause the direction for step 1 represents the inverse of the formation of the RuIII–DMSO complex (opposite to the direction for whichKIIIwas defined). All of the terms are defined or can be evaluated from the voltammograms in Figure 6.1 except forKII, the formation constant for the RuII–DMSO complex. From Figure 6.1, it appears thatEo′2 = −0.01 V andEo′4 = +0.53 V versus standard hydrogen electrode (SHE). The ideal gas constant,R, has a value of 8.314 J/K. The temper- ature was 298 K and Faraday’s constant is 96 485 C/mol. Solving Eq. (6.10) forKIIgives:
RT ln(KII) =RT ln(KIII) −nFEo′2 +nFEo′4 = (8.314)(298)ln(5.1) + (1)(96 485){0.53− (−0.01)}
=5.25×104 (6.11)
ln(KII) = 5.25×104
(8.314)(298) =21.2 and KII=e21.2=1.6×109 (6.12) The binding constant for the DMSO and Ru(II) is about 300 million times stronger than it is for the Ru(III) complex. Consequently, the DMSO ligand stabilizes the reduced form of the complex and that results in a much more positiveEo′. Another way of thinking about the outcome is that the [RuIII(EDTA)(DMSO)−] complex is easier to reduce than the [RuIII(EDTA)(H2O)−]. The DMSO complex is a stronger oxidizing agent than the water complex.