1218
J. Phys. Chem. 1995, 99, 1218-1227
Equilibria and Rates of Redox Reactions Involving the 2-tert-Butyl-1,4-benzosemiquinone Radical in Aqueous Solution: An Investigation by Potentiometry, ESR, and Pulse Radiolysis Jurgen K. Dohrmann" and Barbara Bergmann Institut f i r Physikalische und Theoretische Chemie, Freie Universitat Berlin, Takustrasse 3, 0-14195 Berlin, Germany Received: July 27, 1994; In Final Form: November 3, 1994@
Midpoint potentials, E,, for two-electron reduction of 2-tert-butyl- 1,4-benzoquinone (TBQ) were measured in aqueous solution as a function of pH at 22 "C and given ionic strength 1. From E,(pH), the practical pK values, pR(I), of the corresponding hydroquinone (TBQH2) were obtained at given values of 1. By use of an empirical Debye-Hiickel (D-H) type approximation, the values of pK' were extrapolated to I = 0 for estimating the thermodynamical pKa values for acid dissociation of TBQH2 (pKa,l = 10.7 f 0.1; pKa,2 ca. 13.6 f 0.2). Optical absorption spectra and molar extinction coefficients of the transient semiquinone radical (TBQH' and TBQ-) were obtained by pulse-radiolytic one-electron reduction of TBQ in aqueous solution. The pKa of TBQH' is 4.3 f 0.1 at 22 "C in the presence of 2-propanol(2 M) and acetone (0.1 M). Oxidation of TBQH2 by OH' to eventually give T B Q - has been studied (k15 = 8 x lo9 M-' s-l for formation of the intermediate [(HO)TBQHz]' in aqueous solution at 22 "C). The equilibrium for formation of T B Q - from TBQ and TBQH2 was investigated by ESR (aqueous solution, pH 6.8-9.4, I = 0.12 M). Hyperfine couplings and the g value of T B Q - are given. The apparent semiquinone formation constant at pH i, K'f,i(Z), was determined as a function of pH (log K'f.7 = -8.8 f 0.1, pH 7) at I = 0.12 M. The pH-independent thermodynamical formation constants, at I = 0, of TBQH' from TBQ and TBQH2 (log K17 = -14.4 f 0.3) and of T B Q - from TBQ and TBQ2- (log K18 = 1.3 f 0.4) were determined by use of the above pKa values and D-H type approximations. Various other one-electron-transfer reactions involving TBQH' or T B Q have been investigated in detail. The standard potentials, E" (at I = 0), for one-electron reduction of TBQ and of TBQH' (or TBQ-) have been obtained by combining the two-electron reduction potentials of TBQ and the semiquinone formation constants. Pulse-radiolytic equilibration studies of TBQ with 02'- and of TBQ2- with DMAP' (DMAP' = 4-(dimethy1amino)phenoxyl) afforded the redetermination of the thermodynamical standard potential for one-electron reduction of 0 2 (Eo = -0.140 f 0.012 V vs NHE for 1 M 0 2 in aqueous solution at 22 "C and I = 0) and of the midpoint potential of the couple DMAPDMAP-, respectively, at pH 13.5 (Em,13,5= 0.10 f 0.02 V vs NHE at 22 "C and I = 0.5 M). The respective rate and equilibrium constants are given. All these results are discussed in terms of substituent and solvent effects as well as in view of the Marcus theory of electron transfer. Another objective of the present study is to contribute to a better understanding of the properties of the synthetic antioxidant 2- or 3-tert-butyl-4-hydroxyanisole (BHA).
Introduction The 2-tert-butyl-1 ,4-benzosemiquinone radical (TBQH') is the one-electron reduced form of 2-tert-butyl- 1,4-benzoquinone (TBQ). Both the quinone and the corresponding hydroquinone (TBQH2) are metabolites of the synthetic antioxidant 2- or 3-tertbutyl-4-hydroxyanisole (BHA).' BHA protects animals from hazardous effects of radiation and toxic compounds; however, it also promotes tumor growth in various tissues.2 Recently, formation of the semiquinone anion, TBQ-, from TBQH2 as well as from TBQ and production of the superoxide anion, 0 2 * - , have been demonstrated in aerated aqueous solution in the presence of rat liver microsomes and NADPH, and it has been suggested that semiquinone-dependent superoxide radical formation may contribute to the toxicity of BHA.3 Any further attempt of elucidating these processes would require knowledge of thermodynamical and kinetic data of redox and other reactions involving the semiquinone radical. Data for one-electron redox reactions of many other semiquinones are a ~ a i l a b l ebut ~ ~are ,~ lacking for the title radical.
* To whom correspondence @
should be addressed. Abstract published in Advance ACS Abstracts, January 1, 1995.
In the present paper we report reduction potentials of oneelectron couples involving the 2-tert-butyl- 1,Cbenzosemiquinone (TBQH' or TBQ-), pK values for acid dissociation of TBQH2 and TBQH', and rate constants for formation and disappearance of the semiquinone by electron-transfer reactions. Two different approaches were pursued: (1) From measurements of the two-electron reduction potential of the quinone by potentiometry and of the semiquinone formation constant by ESR,both under steady-state conditions as a function of pH in aqueous solution, the one-electron reduction potentials of the quinone and of the semiquinone were determined. (2) From pulse-radiolytic studies of the equilibration between the quinone and the superoxide anion radical in neutral aqueous solution and between the hydroquinone and the 4-(dimethylamino)phenoxy1 radical (DMAP) in strongly alkaline solution, the oneelectron reduction potentials of 0 2 and DMAP', respectively, have been redetermined for testing the internal consistency of the data.4axb More importantly, pulse radiolysis afforded rate and equilibrium constants of various one-electron-transfer reactions being of interest for the redox metabolism of TBQ and TBQH2.
0022-365419512099-1218$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No.4, 1995 1219
Redox Reactions Involving the TBQ Radical
Experimental Section Materials. 2-tert-Butylhydroquinone (TBQH2) was used as purchased from Fluka (mp 127- 129 "C). 2-tert-Butylquinone (TBQ) was prepared by oxidizing TBQH:! with activated MnO2 (Fluka) in di~hloromethane,~ and it was purified by sublimation in vacuo (mp 58 "C). 4-(N,N-Dimethylamino)phenol(DMAP) was prepared from 4-aminophenol (Fluka) according to the literature.6 Colorless samples of DMAP freshly distilled in vacuo and stored in an atmosphere of argon were used (mp 72 "C). All the other chemicals were of analytical grade. They were used as supplied by Fluka or Merck except where noted. Potentiometry and ESR. Oxygen-free test solutions were prepared in the following manner. TBQ and TBQH2 were dissolved separately in deaerated acetone. By means of airtight syringes, the solutions were rapidly added to aqueous buffer solutions (ca. 5 cm3) freed of dissolved oxygen by purging with argon for 30 min. Mixing was speeded by magnetic stimng. The concentration of TBQ and TBQHz was varied between ca. 0.2 and 1 mM. The pH was adjusted by employing KH2POJ Na2HP04, Na2B407/NaOH, or NaOH. In the pH range 5- 12.5 the ionic strength was kept constant at 0.12 M by adding NaC1. All the solutions contained 1% (v/v) of acetone. The pH was measured with a glass electrode (Schott, H 61, alkali resistant) calibrated with standard buffers. Potentiometry was performed in stirred test solutions at 22 f 2 "C. A 1-cm2bright Pt-foil indicator electrode and an Ag/ AgCU0.1 M KC1 reference electrode (0.279 V vs NHE) separated from the test solution by a ceramic frit were employed for measuring the redox potential of the TBQ/TBQH2 couple by means of a Keithley 195 A digital voltmeter. The potential of the reference electrode was checked vs a calibrated calomel electrode prior to and after each measurement. Establishment of redox equilibrium was examined by recording the potential of the indicator electrode as a function of time. The concentration of the TBQ- radical anion being in redox equilibrium with TBQ and TBQH2 was determined by electron spin resonance at 22 f 2 "C. Spectra were recorded on a Varian E-1 12 X-band spectrometer employing a dual cavity (E-232) and 100-kHz field modulation. The test solution was transferred, under the exclusion of oxygen, to a 0.5-mm flat silica cell located in one of the compartments of the dual cavity. A ruby crystal placed in the other compartment served as an intensity standard. The concentration of TBQ- was obtained from the ESR absorption intensity measured relative to the magnitude of the ruby signal which, in turn, was calibrated by measuring the ESR absorption intensity of 1-4 mM aqueous MnS04 solutions replacing the test solution in the flat cell. The absorption intensity was determined by double integration of the ESR spectrum. Details of the method have been given elsewhere.' The spectrum of TBQ- was recorded ca. 2 min after preparing the test solution in order to avoid any changes in radical concentration by undesired side reactions. The estimated error of concentration was ca. &lo%. Pulse Radiolysis. All pulse-radiolysis experiments were carried out at the Hahn-Meitner-Institut Berlin. Details of the method have been given by Aqueous sample solutions were irradiated in a 1-cm optical path cell using ca. 0.5-1-,us pulses of 1.55-MeV electrons from a Van de Graaff accelerator and were analyzed by kinetic spectrophotometry. Dosimetry was based on the thiocyanate dosimeter (NzO-saturated 1 mM aqueous KSCN containing HC104 at pH 4) adopting a radiation chemical yield (G value) of 0.57 pmol J-' and an extinction coefficient of 720 m2 mol-' at 500 nm for (SCN)**-? Absorbed doses of up to 2 Gy (1 Gy = 1 J kg-') were used and afforded concentrations of at most 2 pM of the radicals to be studied.
The estimated error of concentration was ca. &lo%. All experiments were performed at 22 f 2 "C. Sample solutions containing TBQ, TBQH2, or DMAP as substrates were prepared using Millipore Milli-Q filtered water. Analytical grade 2-propanol and acetone, sodium formate, ethylene glycol, or tert-butyl alcohol (redistilled prior to use) supplied by Fluka or Merck were employed for selecting a specific route of radical formation.8s10.11The pH was adjusted with HC104, phosphate buffer, or KOH. The solutions were flushed with N2, N2/02 mixtures, or N20 as required for the radical reaction to be studied.*2l0 N20 was freed of traces of oxygen by flowing it through a column packed with a copper catalyst and through an oxysorb cartridge (Messer, Griesheim). In the studies involving the 0 2 / 0 2 * - couple the concentration of oxygen was adjusted by flushing the solution with N2 and 0 2 at a rate controlled by calibrated flowmeters. The resulting concentration of oxygen was measured by means of a Clark electrode (Radiometer, Copenhagen). For the reaction between TBQ2- and DMAP the substrates TBQH2 and DMAP were first dissolved in oxygen-free N2O-saturated water containing 0.9 M ethylene glycol. KOH was then added to give a pH of 13.5. Oxidation of TBQ2- and DMAP by air in strongly alkaline solution could thus be prevented."
Results and Discussion
1. Two-Electron Reduction of TBQ and pK Values of TBQHz (Potentiometry). The redox equilibrium was established rapidly at the platinum indicator electrode after mixing TBQ and TBQH2 with the buffer solution. Below pH ca. 12, the emf of the cell became constant after a few seconds and was independent of stirring the solution. Changes in strongly alkaline solution where TBQ decomposed slowly were corrected for by extrapolating the emf to the instant of mixing. From the emf, E, measured at various total concentrations, CO,Q and CO,QH*, of TBQ and TBQHp ( C O ca. 0.2-1 mM), respectively, the midpoint potential,12Em, was calculated by use of eq 1, Em
= E - (RT/2F) ln(~o,d~o,QHJ - A~,jig
(1)
The total concentration, CO,QH*, represents the sum of the acid and base forms of TBQH2 at a given pH. Corrections for the diffusion potential, A Q ) ~were , made by applying the Henderson re1ati0n.l~ For the half-cell reaction TBQ
+ 2e- + 2H+ - TBQH,
(2)
the dependence on the H+ ion activity of the midpoint potential can be expressed by12
+
E,,, = Eo(TBQ,2H+/TBQH2)i(RT/2F') lnfQ(aH?/fQH2
+ Ka,lKa,2/fQ2-) (3)
aH+ Ka,l/fQH-
EO(TBQ,2H+/TBQH2)is the thermodynamical standard potential of the reaction (eq 2) at pH = 0. Ka,1and Ka,2are the ionization constants (at infinite dilution) of TBQH2: TBQH,
3
TBQH-
*
TBQ~-
+H+
(4)
The activity coefficients, fi, depend primarily on the ionic strength, I , of the solution. Figure 1 shows the potential E, as a function of pH. As expected, the values of E, fall on three linear sections, (a), (b), and (c), with slopes of -58.5, -58.5/ 2, and 0 mV/pH at 22 "C, respectively, indicating that the halfcell reaction involves (a) TBQH2, (b) TBQ-, and (c) TBQ2- as
1220 J. Phys. Chem., Vol. 99, No. 4, 1995
Dohrmann and Bergmann TABLE 2: Practical pK Values for TBQHz and TBQH' at 22 f 2 "Cand Ionic Strength I
1
TBQITBQH2
acidbase pair' TBQHmQHTBQH-mB QzTBQH'EBQ-
IIM
0.12 0.7
(2-4) x 10-3
PK' 10.6 f O . l b 13.0 f 0.2b 4.3 f 0.1'
TBQHz = 2-tert-butyl-1,4-dihydroxybenzene, TBQH' = semiquinone radical. Aqueous solution, 1% acetone v/v. Aqueous solution, 1 M 2-propanol, 0.1 M acetone. W
(C) I
6
I
\
I
I
a
12
10
14
PH Figure 1. Midpoint potential, E,,,, for two-electron reduction of 2-tertbutyl-1,4-benzoquinone(TBQ) as a function of pH in aqueous solution (1% acetone v/v) at 22 f 2 "C: (a) phosphate (or borate/NaOH) NaC1, I = 0.12 M; (b) NaOH NaC1, I = 0.12 M; (c) NaOH, I = 0.5-1 M.
+
+
(7)
TABLE 1: Midpoint Potentials E,,,$ for Two-Electron Reduction of TBQa at pH i E&mV vs NHE PH conditionsb 640 =t5 0 extrapolated from E,,i at pH 5.5-9, I = 0.12 M 232 f 3 7 I = 0.12 M -49 f 5 14 NaOH, I ca. 1 M
and
2-tert-Butyl-l,4-benzoquinone.Aqueous solution (1% acetone v/v) at 22 f 2 "C and ionic strength I .
the leading two-electron reduced form of TBQ in the respective pH range. The values of Emon line (a) are in good agreement with the polarographic half-wave potentials reported for twoelectron oxidation of TBQH214in aqueous/50% ethanolic acetate buffer at pH 5-6.5. Table 1 lists Emat pH 0, 7, and 14. Em,0has been obtained by extrapolating straight line (a) in Figure 1 to pH = 0 under the reasonable assumption that fQ equals ~ Q at H I~ = 0.12 M. Under this assumption, Em,0= 640 f 5 mV at 22 f 2 "C should closely approximate the standard potential, E0(TBQ,2H+/ TBQH2), in eq 3. The value is close to that for 2-methyl-1,4benzoquinone12(644 mV in aqueous solution at 25 "C). Both values are ca. 60 mV more negative than the standard potential of the couple l,4-benzoquinone/hydroquinone12 (699 mV at 25 "C), suggesting that the tert-butyl and the methyl group exert the same +I effect on the two-electron reduction potential of the quinone. The standard potential of the couple TBQfTBQ2- is defined by12
+
Eo(TBQ/TBQ2-) = Eo(TBQ,2H+/TBQH2)
(RTf2F) ln(Ka,IKa,J (5) Combining eq 5 with eq 3 written for pH 14 and allowing for incomplete dissociation of TBQH- (pKr2 = 13, see below), one obtains
RTln(l 2F
+ lO-I4/K',)
coefficient,fQ2-, of TBQ2- cannot be calculated precisely at the high ionic strength of the solution at pH 14. Debye-Huckel type expressions used in the literature4a(see below) suggest that E"(TBQ/TBQ2-) may be ca. 25 mV more negative than the midpoint potential, Em.14 = -49 f 5 mV, determined in the present work. The practical pK values,12 pK'1 and pK'2, of TBQH2 correspond to the pH of the intersection points of straight line (b) with straight lines (a) and (c), respectively, in Figure 1. pK'1 and pK'2 refer to the first and second ionization constants, respectively, expressed a ~ ~ ~ , ~ ~
(6)
The last term (-1.2 mV) is negligibly small. The activity
The pK' values thus obtained (Table 2) are valid only for the composition and ionic strength of the solutions used for determining the midpoint potentials. The following relations connect the values of pK'(T) at ionic strength Z with the thermodynamical pKa values for acid dissociation at infinite d i l u t i ~ n : ~ ~ ? . ' ~ PKa,, = pK'I(I) - logCfQH-!fQH2)I
(9)
pKa,2 = pK',(I) - logCfQ2-!fQH-)I
(10)
In an attempt to estimate the pKa values by means of eqs 9 and 10, we use the empirical Debye-Huckel type relation logf, = -AIz+z-lZ1'2(1 + I 1/2)-1
+ BZ
(11)
for the mean activity coefficientf+ of a (z+,z-)-valent electrolyte (A % 0.5 M-ll2, B x 0.1 M-' in aqueous solution at room temperature for ionic strengths of up to ca. 1 in conjunction with the relation for the activity coefficient5 of an individual ion (charge number z,) M)4a315
l o g 4 = VZ,2(v+z+2
+
+
+ V-zL2)-' logf,
(12)
where Y = v+ v- and V+Z+ v-z- = 0 for the electroneutral ele~trolyte.'~Corrections for the activity coefficients in eqs 9 and 10 by use of eqs 11 and 12 and the assumption fQHZ = 1 for the nonelectrolyte TBQH2 place pKa,l at 10.7 f 0.1 and pKa,z at ca. 13.6 f 0.2. The difference between pKa,l and pK'1 at I = 0.12 M is of the order of the experimental error of pK'1. The value of pKa,2 can be no more than a reasonable estimate. In any case, pK'2 at I = 0.5-1.0 M underestimates the value of pKa.2. The first and second ionization constants reported by Baxendale and Hardy for hydroquinone (1,4-dihydroxybenzene;pK1 = 9.9, pK2 = 11.4) and some of its methyl derivatives in aqueous solution ( I = 0.65 M) demonstrate that methyl substituents lower the acid strength of hydroquinone.16 It is seen from Table 2 that the terr-butyl group acts similarly.
J. Phys. Chem., Vol. 99, No. 4, 1995 1221
Redox Reactions Involving the TBQ Radical
I
R
6000 -
I
A
I
I
1
4
2
X I nm Figure 2. Transient absorption spectra observed immediately after electron pulse radiolysis of an Nz-saturated aqueous solution containing 70 pM TBQ, 1 M 2-propanol, and 0.1 M acetone at (a) pH 7 (phosphate buffer) and (b) pH 2.1 (HC104). Dose ca. 1.5 Gy. However, for hydroquinone and 2-methyl- and 2,3,5,6-tetramethylhydroquinone the difference pK2 - pK1 is 1.5- 1.6,16 while for TBQH2 (Table 2) pK'z - pK'1 is 2.4. The monoanion TBQH- may exist in two tautomeric forms, a and p, resulting from deprotonation of either of the two nonequivalent OH groups of TBQH2. For such a case it can be shown that, in eq 3, Ka,1 has to be replaced by &(a) Ka,l@) and Ka,lKa,~by Ka,i(a)Ka,2(a) or Ka,l@)Ka,Z(p). (The two product terms are equal on thermodynamical grounds). If Ka,l(a) is at least 5 times larger than Ka,l@), tautomer a may be considered the leading monoanion form in the dissociation equilibria (eq 4), and the relation for the dependence of the midpoint potential, Em,on the H+ ion activity virtually coincides with eq 3, where Ka,l x Kql(a) and Ka,2 Ka,2(a). From a plot of Em vs pH the practical pK (pK'1 and pK'2) values for the leading dissociation equilibria would be obtained in this case. If, on the other hand, Ka,l(a) and Ka,l@)are approximately equal, the plot of E, vs pH would give apparent pK' values made up of contributions from both tautomers. Moreover, for &'(a) = &I@), the difference between the apparent pK' values for the second and first deprotonation reaction is 0.6 pK units larger than the difference, P K ' ~ ( ~-)pKtl(a), of the true practical pK values of tautomer a (or p). It cannot be excluded that this special case applies to the deprotonation equilibria of TBQH2. For symmetrical hydroquinones, eq 3 is valid strictly, since there are no tautomers. A plot of Em vs pH would then give the true pK values. It should be emphasized that the various cases cannot be distinguished by potentiometric measurements. 2. Absorption Spectra of TBQH and TBQ- and pK Value of TBQH (Pulse Radiolysis). Pulse radiolysis has been applied previously for determining the pK values for deprotonation of several short-lived semiquinone radicals from the dependence on pH of the optical absorption of the conjugate forms of the radi~a1.l~ On pulse radiolysis of an Nz-saturated solution of TBQ (70 pM) containing excess 2-propanol (1 M), acetone (0.1 M), and phosphate buffer (pH 5-8) or HC104 (pH 2-4) transient absorption spectra with maxima at 432 nm in alkaline solution and 411 nm in acid solution (pH < 3) were observed (Figure 2). By analogy with previous pulse-radiolytic investigations of one-electron-reducedp-benzoq~inones'~~'~ spectra (a) and (b) in Figure 2 are attributed to the conjugate forms of the 2-tertbutyl- 1,4-benzosemiquinone, TBQ'- and TBQH', respectively. On the assumption that all primary species of water radiolysis
+
1
I
6
8
PH
Figure 3. Variation of optical density at 430 nm (normalized to dose) with pH after electron pulse irradiation of Nz-saturated aqueous solutions of TBQ (70 pM) containing 2-propanol (1 M) and acetone (0.1 M) at 22 "C. pH 2-4, HC104; pH 4.6-8, phosphate buffer (2 mM total concentration). (eaq-, OH', and H)'O produce the (CH&COH radical, which in tum converts the quinone to the semiquinone,'* the molar extinction coefficients are c(TBQ-, 432 nm) = 6500 M-' cm-l f 10% and c(TBQH', 41 1 nm) = 3750 M-' cm-I f 10%.The shape of the spectra, the absorption maxima, and the extinction coefficients are close to those reported for the respective conjugate forms of the semiquinones from p-benzoquinone18 and 2-methyl-p-benzoquinone.l9 Figure 3 shows the dependence on pH of the optical density at 430 nm measured ca. 5 ps after electron pulse irradiation of N~saturatedsolutions of TBQ containing excess 2-propanol and acetone. The values have been normalized to the total concentration of the semiquinone (TBQH' TBQ-) produced. The sigmoid shape of the pH dependence demonstrates establishment of the dissociation equilibrium18
+
TBQH'
-
TBQ'-
+ H+
(13)
on the time scale of the experiment. The curve shown in Figure 3 has been calculated according to
From the best fit we obtain ~K'QH.= 4.3 f 0.1 for TBQH' at ionic strengths of 2-4 mM (Table 2). This value is virtually identical with the pKa for the equilibrium eq 13 at infinite dilution and is very close to PKa = 4.45 f 0.1 reported for 2-methyl-p-benzo~emiquinone~~ in aqueous solution (1 M each of 2-propanol and acetone). Again, this points to the (+) inductive effect of the substituent on the pKa (4.1 f 0.l1*J9)of the p-benzosemiquinone radical. Further, our value corroborates an earlier estimate, pKa I4.25, from a continuous-flow ESR study of TBQH2 oxidation where the acidic proton has been assigned to the oxygen at C-4, meta to the substituent in TBQH'.20 On pulse radiolysis of TBQ in an N2-saturated aqueous solution containing tert-butyl alcohol (0.8 M) and of TBQ in NzO-saturated aqueous solution containing either 2-propanol (1 M) or sodium formate (0.1 M), transient spectra virtually identical with those shown in Figure 2 were obtained. Molar extinction coefficients of TBQ- (phosphate, pH 7) determined on the basis of known G values for one-electron reduction of
1222 J. Phys. Chem., Vol. 99, No. 4, 1995
Dohrmann and Bergmann
p-benzoquinone by the solvated electron in the presence of tertbutyl alcohol18 and by the (CH&COH or the 02.- radical in the presence of 2-propanol or formate, respectively, in N20saturated solutions18 were in reasonable agreement with the value given above. On pulse radiolysis (ca. 1 Gy) of an NzO-saturated aqueous solution containing TBQH2 (0.1 mM) and phosphate buffer (equimolar mixture, 4 mM total concentration, pH 6.8), formation of TBQ- was observed by kinetic spectrophotometry at 430 nm. N20 converts hydrated electrons into OH' radicals N20 OH' N2 OH-, k = 9.1 x lo9 M-' s-1).21 (eqAs with 1,Cdihydroxybenzene (QH2) studied previously under the same conditions,22formation of TBQ- is likely to proceed by phosphate-catalyzed H20 and H+ ion elimination from the first-formed OH' radical adduct to TBQH2,
+
-
+ +
-
TBQ'-
+ H 2 0 + H+
(15)
Such an addition-elimination sequence is common to many substituted benzenes eventually being oxidized by the OH' radical.23 On addition of tert-butyl alcohol (t-BuOH up to 1.6 mM) to the test solution the maximal concentration of TBQformed ca. 100 p s after the electron pulse decreased with increasing concentration of t-BuOH in a manner consistent with competitive scavenging of OH' by TBQH2 and t-BuOH. During this time interval dismutation of TBQ- could be neglected due to the low dose applied, and dehydration of [(HO)TBQH2]' should be completed since k-HzO for [(HO)QH2]' is 1.2 x lo5 s-l under otherwise identical conditions.22a The reciprocal maximal concentration of TBQ- increased linearly with increasing concentration of t-BuOH. From this dependence and by use of k(OH'+t-BuOH) = 7.6 x lo8 M-' s-l as a reference,24we estimate kl5 as 8 x lo9 M-' s-l at 22 "C. This value is of the same order as those reported for OH' radical ) ~ ~ addition to 1,4-dihydroxybenzene (1.2 x 1OloM-' s - ~ and 4-tert-butyl-1,2-dihydroxybenzene (7.6 x lo9 M-' s-1).25 No attempt has been made to study the elimination step of the reaction sequence, eq 15, directly. 3. Semiquinone Formation Constants (ESR). Equilibria between a number of substituted p-benzosemiquinones and the corresponding quinones and hydroquinones have been investigated previously by spectrophotometry in strongly alkaline solution.26albExcept for tetramethyl-p-benzoquinone,most other benzoquinones are susceptible to attack by OH- ions.26a In order to avoid this difficulty, we decided to study the formation equilibrium of TBQ- by ESR in neutral and weakly alkaline solutions. After mixing TBQ and TBQH2 with oxygen-free buffer solutions, the well-known eight-line ESR spectrum of TBQ- 2o was seen. The signal strength remained constant while recording the spectrum, even at the highest pH of 9.4. This indicates that reaction of TBQ with OH- and formation of TBQ- from TBQH2 by traces of oxygen were negligible. The hyperfine couplings (in units of millitesla) of the three nonequivalent ring protons were 0.162, 0.218, and 0.276. The g value was 2.0046. These parameters are in close agreement with those reported previously for TBQ- in aqueous LiOH at room t e m p e r a t ~ r e . ~ ~ The concentration of TBQ- was determined by doubleintegration of the two outermost hyperfine lines. The apparent semiquinone formation constant at pH i , K'f,i, is defined by4a
K'ei depends on the ionic strength. In the presence of only one of the conjugate forms of the semiquinone and the hydroquinone, K'f,i refers to a single equilibrium, independent of pH; otherwise it does not. Figure 4 shows the dependence on pH of log K'f,, as determined from the concentration of TBQ- equilibrated with various initial concentrations of TBQH2 (0.9-2 mM) at constant concentration of TBQ (0.5 mM, limited by solubility) and constant ionic strength (0.12 M). At pH 7 we obtain log K'f,7 = -8.8 f 0.1. In the pH range investigated, TBQH' and the anion forms of TBQH2 can be disregarded (see pK' in Table 2). Hence, the slope of log K'f,i vs pH expected from eq 16 for pH ca. 6-9 is two, in agreement with observation (Figure 4). Combination of K'f,i with the pK' values of TBQH' and TBQH2 results in the pH-independent equilibrium constants K' (in units of concentration at a given ionic strength, r ) of the following reproportionation reactions, TBQ
+ TBQH, = 2TBQH'
(17)
TBQ
+ TBQ2- = 2TBQ'-
(18)
and
Taking activity coefficients of the ions into account (eqs 11 and 12) and assuming& = 1 for the neutral species, we estimate log Kf,7 = -9.0 f 0.1, log K17 = -14.4 f 0.3, and log Kl8 = 1.3f0.4atI=OandlogK'18= l.Of0.4atZ=O.l2M(22 f 2 "C). The error in log K'18 derives mainly from those in the pK' values of TBQH2. The calculated mean value of K'l8 is 10 at I = 0.12 M. The equilibrium constants K'lg and K18 for nonzero and zero ionic strength, respectively, are connected by
~
K',, = Kl&f~*-!f&
2
(19)
It is seen from eqs 11, 12, and 19 that K'1g decreases with increasing ionic strength. Equilibrium constants corresponding to K'1g have been reported for the p-benzosemiquinone anion and a number of its methyl derivatives26a-b in aqueous solution. Inspection of these values does not reveal a correlation between the equilibrium constants and the number of methyl Even considering the difference in ionic strength, K'18 determined in the present work is somewhat larger than the highest value reported for the methyl-substituted analogues?6aK' = 6 for the 2,5-dimethylp-benzosemiquinone anion ( I = 0.375 M, 25 "C). It should, however, be noted that the extinction coefficients used for the p-benzosemiquinone anion26aand the durosemiquinone anion26b are ca. 1.3 times larger than those determined by pulse radioly~is.'~It can, therefore, not be excluded that the equilibrium constants for these semiquinones are, in fact, by a factor of at least 1.7 larger than reported in refs 26a and 26b. 4. One-Electron-Transfer Reactions Involving the Semiquinone. ( a ) Reduction Potentials from Potentiometric and Semiquinone Formation Data. The midpoint potentials, E&O/ S ) and E,,i(S/R), for the one-electron couples O/S and S/R, respectively, where 0 = TBQ, S = TBQH' TBQ-, and R = TBQH:: TBQHTBQ2- at pH i and a given ionic strength were calculated from the potentiometric data for twoelectron reduction of TBQ (section 1) in conjunction with the semiquinone formation constants (section 3). The principles
+
+
+
J. Phys. Chem., Vol. 99, No. 4, 1995 1223
Redox Reactions Involving the TBQ Radical
TABLE 4: Standard Potentials E" for One-Electron Couples Involving 2-tert-Butyl-l,4-benzosemiquinone"~ redox coupleC E"lmV vs NHE 219 f 15 TBQ, H'ITBQH' -32 k 6 TBQITBQTBQH', H+/TBQH* 1061 f 15 1315 f 6 TBQ-, 2H+/TBQHz -112 f 15 TBQ-/TBQ2Aqueous solution (1% acetone vlv), 22 f 2 "C. From E,(OlS), &(SIR) and pK' after extrapolation to I = 0 by means of eqs 11 and 12. For abbreviations, see Tables 1 and 2.
-10
I
I
,
1
7
8
9
W
'.
1
0.8
TBQ, I = 0.5 M
I
PH
Figure 4. Dependence on pH of log K'f,i for formation of TBQ- from TBQ (0.5 mM) and TBQHl (0.9-2 mM) in aqueous solution (1% acetone vlv) at 22 "C and I = 0.12 M (phosphate, NaCl). TABLE 3: Midpoint Potentials E,,,, for One-Electron Reduction of TBQ (0)and the Corresponding Semiquinone (S) at pH ia Em.i(OISb)lmV E&3RVmV uH 219 f 14 1061 f 14 0 -25 f 6 489 f 6 7 -23 f 6d -75 f 15d 14 In aqueous solution (1% acetone vlv) vs NHE at 22 ic 2 "C. I = 0.12 M unless otherwise indicated. S = TBQH' + TBQ-. R = TBQH2 + base forms. d l= 1 M. of such calculations have been outlined by W a ~ - d m a n .The ~~ values obtained at pH 0, 7, and 14 are collected in Table 3. From thermodynamics$~12~28
where Eo(TBQ,H+/TBQH') is the standard potential for oneelectron reduction of TBQ to give TBQH',
TBQ
+ H+ + e- -TBQH'
+
From eq 20 for
UH+
0 I
,
2
0
I
4
.
l
,
6
l
I
8 1 0 1 2 1 4 PH
Figure 5. Dependence on pH of the midpoint potentials (a) E,,,(OlS) and (b) E,,,(SIR) for one-electron reduction of 0 = TBQ and S = TBQH' TBQ-, respectively, from data extrapolated to I = 0.5 M. (c) Midpoint potential for two-electron reduction of TBQ ( I = 0.5 M). Aqueous solution (1% acetone vlv), 22 "C.
+
12 for estimating the activity coefficient, fq-,of TBQ- at I = 0.12 M. All the values of Em,r and E" listed in Tables 3 and 4, respectively, have been calculated by similar procedures starting either from eq 20 or from the expression for the midpoint potential for one-electron reduction of the semiquinone,
aH?/fQH2
F
In
+
+ aH+Ka,l/fQH- + Ka,lKa32/fQ2aHJfQp
(25)
KQHJfQ-
where Eo(TBQH',H+/TBQH2) is the standard potential of the reaction
TBQH'
+ RT 7In K Q p +
+ e- -TBQ'-
0.2
+ H+ + e- -TBQH,
(26)
(22)
where the sum of the first two terms equals the standard potential, Eo(TBQ/TBQ'-), for the half-cell reaction TBQ
w
E,(SIR) = E"(TBQH*,H+/TBQH~)
/
(24)
we calculate E"(TBQ,H+/TBQW) and E"(TBQ/TBQ'-) (see Table 4) by using the pK of TBQH' (section 2) and eqs 11 and
Figure 5 shows the variation of the midpoint potentials with pH (eqs 3, 20, and 25) as calculated from the experimental data adjusted to I = 0.5 M. It should be recalled that midpoint potentials depend on pH and the ionic strength, while standard potentials refer to pH 0 and infinite dilution. The latter requirement is only partly fulfilled for the values given in Table 4 which have been obtained by taking interionic interactions into account in an approximative manner (eqs 11 and 12) while (reasonably) assuming unity activity coefficients for all uncharged redox components. The errors given in Tables 3 and 4 have been estimated by considering the propagation of errors in the experimental data. Thermodynamical data for one-electron reduction of various other quinones and semiquinones are k n ~ w n . Em,7(o/s) ~ ~ , ~ for
1224 J. Phys. Chem., Vol. 99, No. 4, 1995
Dohrmann and Bergmann
0.1 W
I
,.
z
methyl o
o
>
-. -0.1 >
$ 2
/'/
I
tert-butyl
2.5-dimethyl
2,6-dimethyl
'
I
-0.2
u1
-0.3
.
-0.9
-0.8 E112
-0.7 (O/S) I V
-0.6 VS.
-0.5
0
200
600
1000
800
t I /As
SCE
Figure 6. Correlation between midpoint (or standard) potentials Em.7 in aqueous solution at pH 7 and polarographic half-wave potentials Eln in acetonitrile for one-electronreduction of various alkyl-substituted 1,4-benzoquinones(20-25 "C). Data from refs 4a,b, 29, and 30a-c. Solid point from present work.
400
Figure 7. Transient absorption of TBQ- at 430 nm (solid points) after electron pulse radiolysis of an aqueous solution containing 60 p M TBQ, 1.25 mM 0 2 , and 0.1 M sodium formate at pH 6.9 (4 mM phosphate). Calculated curve for kobs = 8.8 x lo3 s-l. 7
2.0 I
I
0 = TBQ (Table 3) is ca. 100 mV more negative than the corresponding recommended value (78 mV) for 1,4-benzoh quinone (l)4aand even ca. 50 mV more negative than that 1.0 (a) I reported for 2-methyl-1,4-benzoq~inone~~ (2). This indicates a stronger +I effect of the tert-butyl group on the one-electron than on the two-electron reduction potential of 1 (section 1) and parallels the sequence of the polarographic half-wave potentials, E1/2,of these quinones in acetonitrile (1,-0.5 1 V;30a 2,-0.58 V;30aTBQ, -0.61 V30bvs SCE). As shown in Figure 2.5 I I 6, there is an excellent linear correlation between reported values of Em,7(O/S)in aqueous s o l ~ t i o n ~ and ~ , ~ , in ~ ~a c e t o n i t ~ i l e ~ ~ ~ - ~ for one-electron reduction of various alkyl-substituted 1,4benzoquinones, including TBQ from the present work. The slope of unity indicates that the difference, AG"H,o - AG'CH~CN, in the free energy of formation of the semiquinone anion from the corresponding benzoquinone in the two solvents is constant 0 20 40 60 80 and independent of alkyl substituents. Similarly, the one[O,$iTBQl electron reduction potentials of methyl-substituted 1,4-benzoFigure 8. Dependence on TBQ and 0 2 concentration of the observed quinones in water at pH 7 and in dimethylformamide correlate rate constant for equilibrating TBQ with 02'- (a) and of the ratio with unit slope.42 Em,14(S/R)for S = TBQ- (Table 3) is again between initial 02'-and equilibrium TBQ- concentration (b)from pulse considerably more negative than the corresponding values of radiolysis of aqueous solutions containing TBQ (a, 33 pM; b, 19 p M ) , 2331or 74 mV32calculated for the 1,4-benzosemiquinoneanion. 0 2 (0.25-1.25 mM), sodium formate (0.1 M), and phosphate (4 mM, (b) Redox Potentials and Rate Constants from Pulse RadipH 6.8) at 22 f 2 "C. olysis. With the objective of checking the internal consistency containing TBQ (10-80 pM), sodium formate (0.1 M), and of the one-electron potentials given in Tables 3 and 4 we applied phosphate buffer (pH 6.8) was (2.2 f 0.4) x lo9M-' s-' at 22 pulse radiolysis for studying redox equilibration of 0 2 / 0 2 * - 29,33 "C. Considering k27, k(Oz+COz'-) = 4 x lo9 M-' s-1,34and with TBQ/TBQ- and of 4-(dimethylamino)phenoxyl/phenoxide the 20-fold excess of 0 2 over TBQ, the transient absorbance (DMAP'DMAP-)" with TBQ'-/TBQ2-. shown in Figure 7 can be attributed to redox equilibration Figure 7 shows the 430-nm absorbance of TBQ- observed between TBQ and 0 2 ' after pulse-irradiating TBQ in aqueous solution containing 0 2 (1.25 mM), TBQ (60 pM), and excess sodium formate (0.1 M) k28 at pH 6.9 (phosphate buffer). Under these conditions the TBQ 0,'- === TBQ'0, (28) k-zs primary species of water radiolysis (H, OH, and eaq-) react almost exclusively with HC02- (H, OH) and 0 2 (H, eaq-) to as previously demonstrated for various other quinones. 19,29,33 form C0z'- and 0 2 * - , r e s p e ~ t i v e l y . ' In ~ ~turn, ~ ~ C0z'- produces The flat maximum in TBQ- absorbance represents the closest an equivalent amount of 0 2 ' - by rapid reduction of excess 0 2 . 3 4 approach to the equilibrium, eq 28, which, however, is slightly Since no initial sharp rise of TBQ- absorption was seen, perturbed by competing disproportionation of TBQ- (vide formation of TBQ- by reaction of H, eaq-, or C0z'- with TBQ infra). The overall rate constant for equilibration, k&s = was negligible. The rate constant for kzs[TBQ] + k-28[02], taken from the rising portion of TBQabsorbance in Figure 7 is 8.8 x lo3 s-'. Figure 8 shows the TBQ C0,'- k,,TBQ'C02 plots29,33appropriate for determining (a) the rate constants k28 (27) and k-2s and (b) the equilibrium constant K'28 from kobs and determined by electron pulsing N2O-saturated aqueous solutions the equilibrium absorbance of TBQ-, respectively, as observed c
+
+
+
+
J. Phys. Chem., Vol. 99, No. 4, 1995 1225
Redox Reactions Involving the TBQ Radical
TABLE 5: Rate and Equilibrium Constants for One-Electron-TransferReactions Involving 2-tert-Butyl-1,4-benosemiquinone (TBQH or TBQ-) reaction" krh4-l S-' k,lM-ls-I log K (15) TBQHz + OH' TBQ- HzO H+ (8.0 f 0.5) x lo9 (17) TBQ TBQHz 2 TBQH' ca. 2.5 x (1.3 f 0.2) 109 b.d - 14.4 f 0.3 ca. 4 x 109 (18) TBQ + TBQ2-*2 TBQ(7.5 f 0.5) x lo8 b,eJ 1.0 f 0.4 cf (27) TBQ + C0z'TBQ- + COz (2.2 f 0.4) 109 b (28)TBQ + 02.- * TBQ- + 0 2 (1.1 It 0.2) x lo8g.' (1.6 f 0.5) x lo6 1.85 f 0.1 b,g (30)TBQ2-+ 'CHzCHO + HzO TBQ- + CH3CHO OH(1.7 i 0.6) x lo9b,k (31) TBQz- + DMAP TBQ- DMAP(2.9 f 0.4) x 10' b~',k (2.7 f 1.0) x lo5b~',k 3.05 iz 0.15 (34) TBQH' TBQ- TBQ + TBQH(1.0 f 0.5) x 109 b~
-
+
+
--
+
+
-.+
+
Numbers refer to text. Aqueous solution, 22 f 2 "C. See text for cosolvents and solutes. Pulse radiolysis. ESR. k, = 2k33. e k, = 2k35. f l DMAP = 4-(dimethy1amino)phenoxyl. I = 0.5 M. In 0.8 M t-BuOH. Ir In 0.9 M ethylene glycol.
= 0.12 M. g I = 0.1 M.
at various concentrations of TBQ and 0 2 . We obtain k28 = (1.1 f 0.2) x 108M-' S - ' , k-28 = (1.6 f 0.5) x lo6 M-' S-', and, from both plots, K'28 = 70 f 15 at 22 "C and 0.1 M ionic strength. Table 5 summarizes the equilibrium and rate constants of the various reactions involving TBQH' or TBQ'- as studied in the present work. From published data on electron transfer from 02.- to methyl-substituted 1,4-ben~oquinones>~ the equilibrium corresponding to eq 28 shifts to the left with increasing number of methyl groups. K'28 and k28 for TBQ are ca. 10 times smaller than the respective values for 2-methyl- 1 , 4 - b e n z o q ~ i n o n eand ~~*~~ are close to those r e p ~ r t e d ~for ~ ,2,5~ ~ and , ~ ~2,6-dimethyl1,Cbenzoquinone. Obviously, screening by the bulky tertbutyl group lowers the reactivity of TBQ toward 0 2 ' - more than expected from the +I effect. It has previously been shown that rate and equilibrium constants for electron transfer from 02'to methyl-substituted benzoquinones conform to the Marcus r e l a t i ~ n s h i p . ~The ~ data for TBQ (Table 5) accord with the previous finding and suggest a reorganization energy of ca. 80 kJ/mol for the forward reaction, eq 28. By combining E"(TBQ/TBQ'-) and R 2 8 from Tables 4 and 5, respectively, and by making use of eqs 11 and 12, we determine the standard potential of the 02/02*- couple by means of the relation
as -0.140 f 0.012 V vs NHE for 1 M 0 2 at 22 "C. This value is consistent with the one-electron reduction potential of 0 2 (-0.155 V for 1 M 0 2 , ionic strength not defined) reported by Meisel and C ~ a p s k iwho , ~ ~ utilized the same pulse-radiolytic method and employed data for the duroquinone12,16,26b and indigodi~ulfonate~~ redox systems for calculating the oneelectron reduction potentials of these reference systems. On the basis of the one-electron reduction potential of methyl viologen as a standard, Wardman reestimated the midpoint potential, Em,7,of Oz(1 M)/O2'- as -0.179 0.011 V.43 The estimate employed a revised value of Em,~(DQ/DQ'-)determined pulse-radiolytically (DQ = duroquinone) and the previously reported33 equilibrium constant for reduction of DQ by 0 2 * - . Using -0.179 V43 for the oxygen reduction potential in eq 29, K'28 would be ca. 4 times larger than found in the present study. Although our value of E0(02/02'-)is consistent with the earlier further measurements based on other reference couples are clearly needed to resolve the present uncertainty in the oxygen reduction potential. For further studying the one-electron reduction of TBQ-, the hydroquinone anion, TBQ2-, was reacted with the 4-(dimethy1amino)phenoxyl radical (DMAP) generated by pulse radiolysis in alkaline solution. Figure 9 shows the transient absorption at 490 nm of DMAP' after pulse irradiating (ca. 1.5
*
12 m I
9 -
.6 -
9
0
0
I
I
-
..
-TBQ 2- t DMAP' . TBQ'- t DMAP-*\
TBQ2-
+ 'CH,CHO
k30
TBQ'-
* *
.-.
..
+ CH3CH0 + OH-
(30)
was determined as (1.7 f 0.6) x lo9 M-' s-' under the same conditions, however, in the absence of DMAP-. Formation of TBQ'- in the presence of DMAP- (Figure 9) proceeds predominantly by redox equilibration according to
+
TBQ~- DMAP'
k-31
TBQ*-
+ DMAP-
(3 1)
as shown by Steenken and Netal' for a large number of other hydroxyphenols. (From k15, k30, k(DMAP-+'CH2CHO) = 2.2 x lo9 M-l s-l,ll and the concentration of the solutes, any other route of TBQ'- formation would be at least 10 times slower). From Figure 9 it is seen that the concentrationof DMAP merges in an equilibrium value after ca. 100 ps. From the plot of the observed rate constant for equilibration as a function of the total concentration of TBQH2, we obtain k31 = (2.9 f 0.4) x lo8 M-' S-', k-31 = (2.7 f 1.0) x lo5 M-' s-', and K'31 = (1.1 f 0.5) x lo3 at 22 "C and ca. 0.5 M ionic strength. In calculating k31 from kobs, the incomplete dissociation of TBQH2 at pH 13.5 has been taken into account by use of the pK values given in Table 2.
1226 J. Phys. Chem., Vol. 99, No. 4, 1995
Dohrmann and Bergmann
By means of the relation E,,,~,,(DMAP'IDMAP-)
and were analyzed as a function of pH at constant ionic strength ( I = 0.01 M). At pH 2-3, kobs was independent of pH. This indicates that the first of the following three competing reactions,
+
= EO(TBQ'-~BQ~-)
(RT/F) W'3&.-YQ*-)
(32)
TBQH. where E,,,,,,(DMAP'/DMAP-)
= EO(DMAP*/DMAP-)
+
+
+
+
(33)
kuTBQ + TBQH-
(34)
TBQH' f TBQ'-
TBQ'the midpoint potential for one-electron reduction of DMAP at pH 13.5 can be calculated from the standard potential of TBQ'-/ TBQ2- (Table 4) and K'31 if additional use is made of eqs 11 and 12 for estimating the ratio of the activity coefficients of TBQ'- and TBQ2-. We obtain Em,13,5(DMAP/DMAP-) = 0.10 f 0.02 V vs NHE at 22 k 2 "C and Z = 0.5 M. Steenken and Neta reported a more positive value, 0.17 V in 0.5 M KOH, as obtained from the equilibrium constant for the corresponding reaction of DMAP with BQ2- (BQH2 = 1,4-dihydroxybenzene) and the one-electron reduction potential of BQ'- (23 mV at unspecified ionic strength33)taken as a referer~ce."~~'On their potential scale (Table 4 of ref 1l), Em,13.5(DQ'-/DQ2-) for the durosemiquinone anion is again more positive than the value calculated33 from the two-electron reduction potential of DQ'* and the formation constant26bof DQ'-. The discrepancy has been noted previously and was attributed to an uncertainty in the pK values.31 On the other hand, it is seen from the thermodynamical relations, eqs 29 and 32, that knowledge of activity coefficients is required for establishing well-defined half-cell potentials. This requirement can be met in an approximate manner only, e.g., by eqs 11 and 12 used in the present work. Moreover, it cannot be excluded that specific solvation of the various species by the cosolvent necessary for radiochemical radical production (0.9 M ethylene glycol in the present case) affects the activity coefficients of neutral molecules and individual ions differently, in addition to the effects of ionic strength. This view is supported by the strong dependence on solvent composition of the DQ'- formation ~ o n s t a n t .We ~ think that remeasurement of both the two-electron reduction potential of quinones and the formation constant of the corresponding semiquinone anions for a range of pH, cosolvents, and ionic strengths may provide one-electron reduction potentials more appropriate for being used as reference values in analyzing pulse-radiolytic redox equilibration studies. (c) Disproportionation Reactions. Semiquinone radicals (QH' and Q'-) may disproportionate to give the corresponding quinone and hydroquinone via three competing pathways (QH' QH', QH' Q'-, Q'Q'-), the relative rate of which is controlled by the pH and the ionic strength. For studying these reactions the 2-tert-butyl- 1,4-benzosemiquinone was produced by pulse radiolysis at low dose (1- 1.5 Gy) in aqueous solution containing TBQ (40- 100 pM), NaC104, and the following additives: (a) 2-propanol (0.8 M) and acetone (0.08 M) at pH < 4 (HC104), (b) tert-butyl alcohol (0.8 M) at pH 5-7 (phosphate buffer). The decay rate was monitored by spectrophotometry at 41 1 nm (TBQH', pH < 4) or at 432 nm (TBQ'-, pH > 5). Second-order decay was observed in the solutions containing 2-propanol. With tert-butyl alcohol as cosolvent no good second-order kinetics was found. The same observation has been made for the decay of various other s e m i q ~ i n o n e s . ~ ~ This may point to differences in solvation of the semiquinones or to a slow cross-reaction with the tert-butyl alcohol radical. No further investigation has been made into this matter. Values of the rate constants (kobs) were determined from the initial slope of the decay curves assuming a second-order reaction throughout
+ TBQH*k,,TBQ + TBQH, + TBQ*- -TBQ + TBQ,k3 5
(35)
is rate-controlling in this regime. At pH 5-7, kobs varied with the H+ ion concentration as predicted for competition between the other two reactions. Variation of the concentration of TBQ (10-100 pM) at constant pH did not affect kobs. Possible formation of an intermediate complex between the quinone and the semiquinone as reported for the quinone analogues FMN and FMNH' (FMN= flavin mononu~leotide)~~ can, therefore, be ruled out. From the dependence on H+ ion concentration of kobsand by taking the pKa of TBQH' into account (Table 2), the rate constants (in units of M-' s-l) for disproportionation were determined as 2k33 = (1.3 f 0.2) x lo9,k34 = (1.0 k 0.5) x lo9, and 2k35 = (7.5 k 0.5) x lo8 at 22 k 2 "C and Z = 0.01 M. In spite of the bulky tert-butyl group, 2k33 is virtually identical with the corresponding rate constant for the 1,4benzosemiquinone radical and even 6-fold larger than reported for 2-(bromomethy1)-1,4-ben~osemiquinone.~~~~~ Surprisingly, 2k35 for the reaction between the semiquinone anions is not much different from k34 for the reaction between the neutral and the anion form of the semiquinone and is only a factor of ca. 2 smaller than for the two neutral species. We therefore studied the contribution of the reaction, eq 35, to the observed overall rate by varying the ionic strength at constant pH of 6.2. The slope of the plot log kobs vs 1 4- 2Z1I2)according to the modified Bronsted-Bjemm relation40 was ca. 0.9 for ionic strengths, I , of 4.8 mM- 1.46 M (NaC104), close to the expected value for self-reaction of two singly charged anions. This indicates that even at pH 6 disproportionation proceeds primarily by reaction between two semiquinone anions. Further, the effect of ionic strength supports the analysis of the variation of kobs with pH, which shows that 2k35 is not smaller than 2k33 (or k34) by a factor of up to 20 as might be inferred from the comparison of the respective rate constants for other related semiq~inones.~~ The faster rate of disproportionation of TBQ'- (2k35 = 7.5 x lo8 M-l s-l) than of the benzosemiquinone anion (BQ'-, 2k = 5.5 x lo7 M-' s-l 37) can be rationalized as follows. Marcus theory predicts that for electron transfer between identical anions the reorganization energy, 2, decreases with increasing ionic radius, if AGO
