KINETICSTUDIES OF PERMANGANATE OXIDATIQN REACTIONS
1107
Kinetic Studies of Permanganate Oxidation Reactions.
111. Reaction
with Tris( 1,lO-phenanthroline)iron(II) by Kenneth W. Hicks1 and John
R. Sutter*
Department of Chemistry, Howard University, Washington, D . C. 20011
(Received March I , 1970)
Publication costs borne completely by T h e Journal of Physical Chemistry
The kinetics of the reaction between tris(1,lO-phenunthroline)iron(II) and permanganate
+
+
+
+
5Fe(phen)a2+ hfn0.i- 8H+ -+ 5Fe(phen)s3f Mn(I1) 4Hz0 has been studied in acidic medium. The progress of the reaction was followed spectrophotometrically at 510 and 590 nm with a Beckman DU spectrophotometer using both a rapid mixing device and a stopped flow device. The empirical rate law - (l/dd [Fe(phen)s2+I - kobsdkII1 [hfn04-l [Fe(phen)32+12 dt ~ I[Fe I (phen)2 + 1 ~ I I[Fe I (phen)a2 +I
+
where kobsd = 9.28 x lo4 M-1 sec-l and ~ I I I / ~ I=I 0.55 at 25.0’ describes the results to greater than 87% completion at a hydrogen ion concentration of 0.115 M . The results obtained at various hydrogen ion concentrations indicate that the protonated forms of both permanganate ion and the intermediate manganate ion play a role in the kinetics. The enthalpy and entropy of activation were evaluated for kobsd using the transition state equation. The value for AH is 15.5 f. 0.7 kcal/mol, while the value for AS is 16.3 2.3 eu.
*
Introduction Tris (1,lO-phenanthro1ine)iron(11), hereafter Fehen)^^+, and the permanganate ion are inert complexesz in that neither complex readily exchanges its ligands with the ~ o l v e n t . ~ , ~ The oxidation of F e ( ~ h e n ) 3 ~has + been examined using a variety of oxidizing agents: Cr(VI),5 P2084--,6 S20a2-,’ Hz02,8chlorine oxidant^,^ and Xtn(II1).lo I n the cases where there was no dissociation of the tris complex prior to oxidation, the general rate expression rate =
lCobsd
+ 8H+ + 5Fe(~hen)+ ~ ~Mn(I1) + + 4Hz0
5 F e ( ~ h e n ) ~ ~Mn04+
This reaction is also of interest since it represents a reaction in the overall Fe(II)-Mn04- oxidation system in which the 1-equiv reduction of permanganate ion to
+ e-
Fe(phen)2+ -+ Fe(phen)a3+ Mn042- -+ Mn04-
The present reaction system is amenable to theoretical calculations using the theory of Marcus, since both reactants are inert complexes. Reactions of labile complexes are more difficult to predict from theory because of the formation and breaking of bonds during the electron transfer process and also because of difficulties in calculating the “electron conductivities” of the bridging groups. Experimental Section Baker Analyzed reagent grade potassium perman-
[Fe(phen)?+][ox]
was found to be valid. Because of these observations it was felt that Fe(phen)32+might be useful in the attempt to elucidate the mechanism of permanganate oxidations. The overall equation for the reaction involved in this study is
+
*
+ e-
-1.06 V” -0.56 V12
Et’’ =
Go =
M n 0 2 - is thermodynamically unfavorable, so that these ions may react via a path other than the secondorder scheme generally encountered. 1 3 , 1 4
(1) This paper is based on a dissertation submitted by K. W. Hicks to the faculty of Howard University in partial fulfillment of the requirements for the Ph.D. degree. (2) H. Taube, Advan. Inorg. Chem. Radiochem., 1, 1 (1959). (3) M. C. R. Symons, J . Chem. Soc., 3676 (1954). (4) E. Eichler and A. C. Wahl, J . Amer. Chem. Soc., 80,4145 (1958). (5) J. H. Espenson and E. L. King, ibid., 85, 3328 (1963). (6) A. A. Green, J. 0. Edwards, and P. Jones, Inorg. Chem., 5 , 1858 (1968). (7) J. Burgess and R. H. Prince, J . Chem. SOC.,1772 (1966). ( 8 ) J. Burgess and R. H. Prince, ibid., 6061 (1965). (9) B. Z. Shakhashiri, Doctoral Thesis, University of iwaryland, College Park, Md, 1967. (10) H. Diebler and N. Sutin, J . Phys. Chem., 68, 174 (1964). (11) G. F. Smith and F. P. Richter, I n d . Eng. Chem., A n a l . Ed., 16, 580 (1944). (12) W. Latimer, “Oxidation Potentials,” 2nd ed, Prentice-Hall, Englewood Cliffs, N. J., 1952, p 241. (13) M. A. Rawoof and J. R. gutter, J . Phys. Chem., 71, 2767 (1967). (14) B. M. Gordon and N. Sutin, J.A m e r . Chem. Soc., 83, 70 (1961). (15) N. Sutin, Annu. Rev. Phys. Chem., 17, 119 (1963).
Xhe Journal of Physical Chemistry, Vol. 76,No. 8, 1071
KENNETHW. HICKSAND JOHN R. SUTTER
1108 ganate was used, and the solutions were handled as previously described.la$16 Optical density-concentration plots for permanganate showed that Beer's law is obeyed at 510, 520, and 590 nm, and the extinction coefficients were determined to be 1768 f 15, 2248 f 32, and 273 I 5 M-l cm-l, respectively. The stock solution was diluted before each run to reaction concentration, and the concentration was checked spectrophotometrically. A stock solution of 0.020 M F e ( ~ h e n ) ~was ~ + prepared by weighing a known amount of ferrous ammonium sulfate, Fe(NH&(SO4)2 * 6Hz0,Primary Standard, Thorn Smith, Royal Oak, Mich., and dissolving it in distilled water. A weighed amount of 1,lO-phenanthroline, G. F. Smith Co., Columbus, Ohio, in slight excess (3%) to that needed for complete complexation, based on a 1 : 3 M ratio of iron to ligand, was added. The concentrations of total iron(I1) and complexed iron(I1) under reaction conditions of hydrogen ion concentration and ionic strength were checked potentiometrically using the millivolt scale of a Metrohm E-200 p H meter equipped with a saturated calomelplatinum electrode system. The phenanthroline complex was titrated with standard permanganate. The results showed that all of the iron(I1) was present as Fe(phen)8z+over extended periods of time at most H + concentrations. The extinction coefficient of Fe(phen)s2+was found to be 1.100 0.011 X lo4 and 316 8 M-l cm-l at 510 and 590 nm, respectively. The values for Fe(phen)8a+were 318 f 5 and 818 ll M-' cm-l at the given wavelengths. These values were determined by oxidizing known concentrations of F e ( ~ h e n ) ~to ~+ Fe(phen)2+ with a slight excess of either Ce(1V) or permanganate solutions in 0.5 M sulfuric acid. The sulfate complexes of Ce(1V) or Ce(II1) do not absorb at 590 nm, and the contribution to the total optical density due to the residual permanganate was negligible at the concentrations used. Sodium sulfate, Na2S04, was used to control the ionic strength of the solutions. A solution was prepared by weighing a given amount of anhydrous sodium sulfate (Baker Analyzed reagent), used without further purification, together with a stock sulfuric acid solution (Baker Analyzed reagent) , the mixture being diluted to final volume. The hydrogen ion concentrations for these solutions and the overall ionic strength were calculated by an iterative procedure using Kerker's values for KZ', the dissociation constant for HS04-. l7 For example, a solution consisting of the stoichiometric concentration of HzS04 and Na2S04 of 0.1784 and 0.0742 M,respectively, will have a hydrogen ion concentration of 0.204 &I, a sulfate ion concentration of 0.102 M , and a bisulfate ion concentration of 0.151 M . The ionic strength is 0.456. I n this calculation the value of Kz', the ionization constant for HS04- at 25" from Kerker's table, used is 0.142. Three iterations
*
*
*
The Journal of Physical Chemistry, Vol. 76, No. 8, 1871
were made; the value used for Kz' was changed each time the ionic strength was calculated, until successive values of the concentration agreed. Thus, when HzS04concentration was changed to a new value, the sodium sulfate concentration was also changed in order to fix the ionic strength. The hydrogen ion concentration then was calculated as before. In these calculations the concentrations of permanganate ion and Fe(phen)2+,being low, were neglected. The progress of all the rapid mixing kinetic experiments was measured using the Beckman DU as a monochromator. The phototube compartment was altered in such a manner that a second nine-stage RCA IP28 photomultiplier, operating from its own power supply (Calibration Standard 120-B), which replaced the red sensitive phototube of the Beckman DU, could be positioned in the light path with the existing sliding rod. This modification allowed the DU to be used as a monochromator when making kinetic runs, and as a spectrophotometer when making optical density measurements. The separate power supplies increased the signal to noise ratio and improved stability enormously. A rapid mixing syringe, designed by Thompson and Gordon,'* was used to bring the two reactants together rapidly . A constant temperature bath (Forma-Temp Jr., 2095) was used to thermostat the reactant stock solutions in volumetric flasks and the water-jacketed observation compartment of the kinetic equipment at the desired temperature. The equilibration was done for at least 1 hr prior to further dilution of the stock solutions for experiments. The present investigators designed a constant temperature observation compsrtment to fit into the normal Beckman long-path sliding observation cell for use with the rapid mixing device. The water within this compartment completely surrounded both reaction and reference cells. It was found possible to use the same reaction stock solutions for several kinetic runs when working a t moderate acid concentrations. However, at high acid concentrations (approximately 0.5 M), fresh solutions of F e ( ~ h e n ) ~were ~ + prepared from the thermostated stock prior to each run to prevent decomposition. A Durrum-Gibson stopped-flow apparatus (Durrum Instrument Corp., Palo Alto, Calif.) was used to investigate the reaction under conditions where the 50msec mixing time of the Thompson and Gordon rapid mixer could not be tolerated. The monochromator used in conjunction with the mixing chamber was a Beckman Model DU, and the associated power supplies were the same as those used in the rapid mixing experiments. For experiments using the Durrum (16) L. (1966).
J. Kirschenbaum and J. R. Sutter, J . Phys. Chem., 70, 3863
(17) M. Kerker, J. Amer. Chem. Soc., 79, 3664 (1957). (18) R. C. Thompson and G. Gordon, J. Sci. Instrum., 41, 480 (1964).
KINETIC STUDIES OF PERMANGANATE OXIDATION REACTIONS when large hydrogen ion concentrations were used, the acid was added to the permanganate solution while the +. sodium sulfate was added to the F e ( ~ h e n ) ~ ~This procedure gave identical results as when acid was contained in both solutions, but was used to prevent decomposition of the complex, so that the stock solution of the complex could be used over a longer period of time. I n both types of experiment, the output from the photomultiplier (filtered) was fed into a Tektronix storage oscilloscope, and the resultant kinetic trace was then photographed. The analysis of the curve was handled using computer techniques. Edwardsa reported that two discrete peaks were observed at 345 and 360 nm in the reaction of Fe(phen)2+ with peroxydiphosphate, P2084-,while Shakhashi~i~ reported a shoulder a t 355 nm in the reaction of Fehen)^^+ with chlorine gas. In the former case, no blue F e ( ~ h e n ) ~ 3is+formed, while in the latter both the blue complex and another species appear to be formed. A brown solution is known to form when the Fe( ~ h e n ) ~ gcomplex + is allowed to stand in dilute acid, the spectrum being similar to that obtained from solutions which contain Fe(II1) and 1,lO-phenanthroline in a 1:3 molar ratio. This brown color is reported to be that of the dimer19q20and has a n absorbance maximum a t 360 nm. Both Edwards and Shakhashiri attributed this shoulder to the presence of the iron(II1) dimer [(phen)zFe (OH)2Fe(phen)zI4+ or [ (~hen)~Fe-O-Fe (phen)2] +.
20
F ~ ~ - 3
1C
1109
It was therefore of interest to determine if any dimer was being formed in the oxidation of Fe(~hen)~Z+ by permanganate. Several scans of the spectral region between 330 and 650 nm were made for a given experiment using a 2-cm path reaction cell in the Cary 14 spectrophotometer. All reactions were performed at room temperature with a hydrogen ion concentration of 0.52 M . As a spectral reference, solutions of F e ( ~ h e n ) ~were ~+ oxidized with either Ce(1V) or chlorine water using similar reaction conditions. The spectra of the resulting reaction solutions showed evidence of a shoulder only with the reaction involving the saturated chlorine water. The spectrum of the reaction products of the complex with permanganate was identical with that obtained from the products of the F e ( ~ h e n ) ~ ~ + - C e ( I V ) reaction. Keither spectrum showed any detectable shoulder and the stoichiometric amount of the complex could be accounted for in each case. No detectable amount of dimer was formed in the reaction between permanganate and Fe(phen)2+. The overall stoichiometry of the reaction between permanganate and F e ( ~ h e n ) ~in~acid + was verified to be a ratio of 1 : 5 and can be represented by the equation
+
5 F e ( ~ h e n ) ~ ~lLInOl+
+ 8H+
+
5 F e ( ~ h e n ) ~ ~Afn(I1) +
+ 4H20
Varying amounts of permanganate and the complex were allowed to react. The optical densities of these solutions were measured at 590 nm, the absorbance maximum of F e ( ~ h e n ) ~ ~to+ ,obtain the amount of F e ( ~ h e n ) %produced. ~+ The permanganate concentrations ranged from 0.415 X to 6.805 X M, while the Fe(phen)a2+ was varied from 0.244 X to 4.505 X ill. The hydrogen ion concentration was 0.52 M , the temperature was 25.0", and the ratio Fe(phen)3a+/Mn04-was 4.94 i 0.09. The dependence of the rate of reaction on the concentration of permanganate, Fe(phen)a2+, and the reaction products was determined using rapid mixing and stopped-flow techniques, using the method of initial rates. The concentration of F e ( ~ h e n ) ~was ~ + plotted against time, and the rate of the reaction at t = 0 was determined using a glass prism. The results indicated that the rate law was of the form
k'~~,~[MnO~-l~[~e(p~e~)~~+ n (ca1c)
-
L
.
.
.
.L
.2
.3
l
#
.4 .5 time, seconds
*
"
.6
.7
'
,9
Figure 1. Reaction plot: [MnOc-]o = 16.17 X M; iFe(II)lo = 83.03 X M ; [H+] = 0.043 M ; t = 25.0'; I = 0.45; 1cobsd = 3.263 X 104 M-l sec-1; k' = 0.586.
This relation, when integrated, however does not represent the reaction progress for more than 45% (19) G. Anderegg, Helo. Chem. Acta, 45, 1643 (1962). (20) A. E. Harvey, Jr., and D. L. Manning, J. Amer. Chem. SOC., 74,4744 (1952).
The Journal of Physical Chemistry, Vol. 76, No. 8,1 N l
KENNETHW. HICKS AND JOHNR. SUTTER
1110 ~~~
Table I: Dependence of Rate Constants on the Concentration of Permanganate Ion and Fe(phen)2*; t = 25.0°, I = 0.45 M
[MnOa- 1, M x 108
[Fe(phen)s*+I, M X 106
0,043 0.043 0,043 0,043
16.17 8.355 7.272 5.033
83.14 44.29 37.39 26.67
IH+l*
a
IFe(phen)a*+I, M X 106
kobsd
x
M-1 sec-1
k’
3.21 3.41 2.75 2.94
0.58 0.58 0.58 0.58
Av 3 . 0 8 3 ~0.25 3.98 f 0 . 5 9.11 8.76 8.26 9.68
0.58” 0.59 0.59 0.57 0.57 0.55
0.043 0.104 0.104 0.104 0.104
3.072 2.115 2.115 2.115 1.269
0.104
Av 8.953Z0.44 0.57b 2.115 3,750 8.42 0. 56b M MnSOaadded. k&,sd value obtained only when Mn(I1) concentration omitted from the cdcula-
X 590 nm.
X 510 nm.
17.90 5.00 3.75 2.50 2.00
14.0 f 1
-
tion.
completion, the rate falling off as products accumulate, and a more useful expression of the rate law
- d [Mn04-1 dt
- -
5
(d [Fe(phen)a2+1) dt
k o b s d h 1 1 WnO4-I
[Fe(phenh2+I2 ~ I Z[Fe(phen)3*+] I ~ I[Fe(phen)~~++l I (1)
+
was found to represent the data for more than 8701, of the reaction when a suitable value for the ratio ~ I I I / ~ I termed I, IC’, was chosen. The temperature was 25.0°, the hydrogen ion concentrations were 0.043 and 0.104 M , and the ionic strength was 0.45. Integration of eq 1 gives the expression
[(Bo
+ c”);] + M
(2)
whereA = [MnO4-], B = [Fe(II)], C = [Fe(III)], y = 5Ao - Bo, k’ = k111/k11, and the subscript 0 refers to conditions at time = 0. The concentration of permanganate ion may be calculated from the equation
where D ,= absorbance at any time, D, = absorbance at infinite time, E’ = (eFe(III) - ~ ~ ~ ( 1-1 )1 / b ~ ~ n ~ 4 - ) Z , where E is the extinction coefficient and 1 is the path length. That value of k‘ was selected for each experiment which gave the best linear plot for over three half-lives and whose intercept agreed closest with the constant of integration, M , calculated from the initial concentration of reactants. The value of the rate constant, kobsd, was determined by a linear least-squares program using the values determined by eq 2, and their corresponding time values. The progress of a reaction is The Journal of Physical Chemistry, Val. 76, N o . 8,3971
shown in Figure 1. The ordinate, F , is the right-hand side of eq 2, excluding M . The intercept obtained by extrapolation to a somewhat arbitrary zero time is seen to be 0.66 X lo3, where the value calculated from the best k‘ and initial conditions is 1.02 X lo3. This is excellent agreement, for it represents an error of about 8 msec in the (‘choice” of the start of the reaction (zero time) from the original oscilloscope trace. The inverse dependence of the rate expression on F e ( ~ h e n ) ~was ~ + verified by performing the reaction using the rapid mixing device, with known quantities of F e ( ~ h e n ) $ ~present + initially. Known amounts of Fe(phen)s2+, in excess of that of the permanganate present, were allowed to react. This produced solutions which contained known amounts of F e ( ~ h e n ) ~ ~ + , Fe(~hen)~~ and + , Mn(I1). More permanganate was then added rapidly, and the subsequent reaction was recorded. The results of all concentration studies are given in Table I, and all entries are the average of at least three determinations. Experiments with added MnS04 (Table I) showed that added Mn(I1) had no effect on the rate constant. The dependence of the rate constant on the hydrogen ion concentration was determined using the stoppedflow apparatus with the hydrogen ion concentrations varying over a range of 0.043 to 0.398 M . The temperature was held constant at 25.0”, while the ionic strength was maintained a t 0.45 with sodium sulfate. The rate constants are presented in Table 11. The temperature dependence of the reaction rate constants was measured at a constant hydrogen ion concentration and ionic strength of 0.115 and 0.45, respectively. The results are presented in Table 111. Discussion The hydrogen ion dependence of kobsd in the empirical rate law (eq 1) was investigated and kobsd was found to be linearly related to the hydrogen ion concentration. A least-squares fit of the data in Table I1 to an equation
1111
TONS KINETICSTUDIES OF PERMANGANATE OXIDATIONR E A C ~
~~
namic standard values for the protonation equilibrium constants a t infinite dilution have been corrected to our ionic strength of 0.45, using the Davies equation.23 Making the usual steady-state approximations on Mn(V1) one obtains
~~
Table I1 : Dependence of the Rate Constants on Hydrogen Ion Concentration; 1 = 25.0°, I = 0.45, [Mn04-]0 = M 2.115 x 10-6 M, [Fe(phen)3zt]o= 5.000 X W+I,
x lo-‘, M-1 sea-1
kIII/kII
3.08 6.21 8.95 9.28 15.7
0.58 0.54 0.57 0.55 0.48 0.31
kobsd
M
0.043 0.074 0.104 0.115 0.204 0.398
= k’
30.0
[MnOe-] [Fe(II)J2{ k1k3
[Fe(III) I (k2
Av 0.50&0.08 = (7.4 zk 0.1)
kobsd
x
+ (6.1 zk 2.2) X lo8
106[H+]
Table I11: Dependence of t’heRate Constants on Temperature; [H+] = 0.115 M , I = 0.45, [MnOl-lo = 2.115 x 10-6 M’, [Fe(phen)32+]o = 5.000 X 10-6 M t,
kobsd
“C
M-1
18.00 25.00 28.10 32.75
x k’
sea-1
5.11 9.28 13.82 19.02 AH*,bSd AS*,,,d
= =
0.55 0.55 0.48 0.45
[
+ iLIIn(VI1)
]*
(A)
]*
(B) for the reduction process with path A being the major one. I n view of the quite obvious importance of the proton in overcoming a thermodynamically forbidden reaction between Fe(phen)a2+and permanganate ion, and of the reported permanganic acid species HMn04,21 we shall interpret the experimental results by considering the following reaction sequence. The thermodyFe(I1)
Mn04-
[
1
+ Fe(I1)
Mn0422
+ Fe(II1)
(I)
+ Fe(I1) HMn04- + Fe(II1) + Fe(I1) A + Fe(II1)
(111)
+ Fe(I1) -% HMn02- + Fe(II1)
(IV)
“ l
HMn04 HMn04-
=
K1[H+][Mn04-]
=
Kz[H+][Mn042-]
(VI)
where kobsd = (kl kl’KI[H+]} = 7.42 X 105[H+] 6.1 X lo3 in the empirical rate law. This value of 6 X lo3 M-l sec-l for kl may be compared with that expected on the basis of Marcus theory, 4 X lo3, suggesting that this step proceeds by an outer-sphere mechanism with a minimum of inner-sphere reorganization. A value of 1.2 X 10” M-’ sec-l is calculated for ICzl using the experimental value of kl and the equilibrium constant determined from Eo values, and compares with an experimental value for a diff usion-controlled reaction of this charge type for ion-pair formation.24 While kz does seem fast for a redox reaction, BaxendaleZ5has reported a value for the reaction between permanganate and Cd+ of 2 X 1O’O M-’ sec-l. The value of kl’ calculated from the above equation and K1 is kl’ = 2.4 X los M-’ sec-l. From the reported values of K1 and Kz and the equilibrium constant for step I, a value of 5.45 X lo4 is computed for the equilibrium constant for step 11, and thus k2’ = 4.5 X lo3 M-’ sec-I. Alternatively, this would require the potential for the half-cell HMn04
+ e- -+HMn04-
(11)
2’
HMn04-
+
to be Er0 = 1.3 V, a value consistent with the observed
1‘
HMn04
+
[Mn04-] [Fe(II)I2ka’{k1 ~ ’ K[€€+I} I [Fe(II)]ka’ [Fe(III)]kz’
+
15.5 =!c 0.7 kcal/mol 16.3 zk 2.3 eU
+ Mn(VI1) + H +
+ k~’K2[H+I)
One expects, according to Marcus theory, k3 to be much, much less than k~ since step I11 is even less thermodynamically favorable than step I. At 0.1 M [H+], k2 is less than 10% of kz’Kz[H+]; at lower hydrogen ion concentration one can observe kobsd falling off the linear plot. Values of kobsd were not determined at lower t h m about 0.05 M [H+] because instability of the iron complexes made reproduction of the k’s difficult. If, then, kS = 0, and kz’K2[H+] is >> IC2, an approximation that is true a t all but the lowest hydrogen ion concentration, the rate law becomes rate =
of that form yields kobad = (7.42 0.11) X 105[H+]4(6.1 i 2.2) X lo3 with the errors cited being the probable errors. The empirical rate law, eq 1, and the hydrogen ion dependence of kobsd indicate that two paths are available Fe(I1)
+ kh’K2[H+] +
Kl = 2.99 X
K Z= 4.0 X lo8 2 2
(21) A. Carrington and M. C. R. Symons, Chem. Rev., 63, 443 (1963); N. Baily, A. Carrington, K. A. K. Lott, and M. C. R . Symons, J . C’hem. Soc., 290 (1960). (22) M.W.Lister arid Y . Yoshino, Can. J . Chem., 38, 2342 (1960). (23) C. W.Davies, “Ion Association,” Butterworths, Washington, D. C., 1962,p 39. (24) A. Elder and S. Petrucci, Imrg. Chem., 9, 19 (1970). (25) J. H. Baxendale, Symposium on Relaxation Kinetics, State University of New York a t Buffalo, Summer 1965.
Th.e Journal of Physical Chemistry, Vol. 76, No. 8, 1071
KINNETHW. HICKS AND JOHN R. SUTTIR
1112 value of kl'. The speed of the reaction thus stems from the rather sharp increase in the reduction potential due to protonation, making this path thermodynamically allowed. Further, using an average value of k' = 0.5, ka' is equal to 2.24 X loa M-l sec-' at I = 0.45 and 25". This result is quite large when compared to the expected value for the nonprotonated reactants and products, i.e., ka, step 111. The overall E" value for step 111, -0.775 V,26leads to a calculated value of ka
