J. Phys. Chem. 1985,89, 335-338 TABLE 11: Rate Constants for Quenching of (-)n-*[Ru(bpy)3]zt by ICo(edta)l- in 90%CHIOH as a Function of Temperature
k,(r)/(109 M-'s-' )
temp/OC
(+)D-
[Co(edta)]-
(-)D- [Co(edta)l-
9.7 11.8 14.4 16.7
15 25 35 45
AG' '/(kcal mol-') AH*/(kcal mol-') T U *"/(kcal mol-')
10.3 14.1 16.5 20.5
(+)D-[Co(edta)]-
(-)D-[Co(edta)]-
3.70 0.02 2.7 -1.0
3.59 i 0.05 3.4 -0.2
*
'At 25 'C.
+
335
dependent upon the assumed values of a, DA,and DQ, However, it should be noted that the kd in high ionic strength methanol media is lower than expected for the diffusion-controlled encounters of *[Ru(bpy),12+ and [Co(edta)]- in solution. A difference in the quenching cross section between (+)D- and (-)D-[Co(edta)]- is ascribed to a difference in the rate of electron transfer within the precursor ion pair, although the electrontransfer rates are reduced in methanol media. The A-(-)D-*[ R ~ ( b p y ) ~leads ] ~ + to preference for A-(-)D-[Co(edta)]- in the oxidative deactivation. A rather slow oxidation of rac-[Co(edta)]" by ~ i - ( + ) ~ - [ R u ( b p y ) ~also ] ~ +yields a slight excess of A-(+)D[Co(edta)]- in aqueous s01ution.I~ The rate constants for quenching of (-)D-* [ R u ( b p ~ ) ~ by ]~+ (+)D-[Co(edta)]- and (-)D-[Co(edta)]- in 90% C H 3 0 H were determined at a variety of temperatures from 15 to 45 OC. From the plot of In k,(r)/ T against 1/ T, AH*and AS*were evaluated. In Table 11, the observed rate constants are summarized as a function of temperature, and the thermodynamic parameters AG*, AH*, and AS* are also tabulated. The rate of electron transfer is increased when reorientation of the counterions in the precursor ion pair can yield closer contact of the reactants or provide a more effective path of electron transfer. (-)D-[Co(edta)]- can make closer contact with (-)D-*[R~(bpy)~]*+ than (+)D-[Co(edta)]-. The preference for (-)D-[Co(edta)]- is achieved only for a higher activation enthalpy barrier which is in turn compensated by a sizable increase in activation entropy. This is ascribed to a greater solvent reorientation accompanying the effective electron-transfer process.
in 11701 k,, and as high as lo9 s-l. Typical concentrations used in the present work were M for [ R ~ ( b p y ) ~ and ] ~ +(1-5) X lo4 M for [Co(edta)]-. For a value of the equilibrium constant of ion-pair formation K = 10, which is the case in aqueous solutions of lower ionic strengths, the fraction of [ R ~ ( b p y ) ~ forming ]~+ an ion pair with [Co(edta)]- is less than 0.2%. The fraction increases up to 2%if K = 40,which is obtained for 81% C H 3 0 H of lower ionic strength. It is inferred that only when the concentration of the nonluminescent ion pair is low, do the luminescence yield measurements give an intrinsic rate constant close to the value obtained from lifetime measurements. As shown in Table I, the quenching rate is larger in the media, in which the ion-pair formation is accelerated by an enhancement in the rate of diffusion-controlled association kd. The value of kd calAcknowledgment. We are grateful to Professor H. Ogino, culated for the diffusion-controlled encounters of * [ R ~ ( b p y ) ~ ] * + Tohoku University, for informative discussions on the reduction and [Co(edta)]-in 81% CH30H of = 0.126 M is 3.86 X lo9 potential of [Co(edta)]-. M-' s-l as shown in Table I. Assuming a = 11 A, the kd can be Registry No. (-)-[R~(bpy)~]~+, 52389-25-0;(+)-[Co(edta)]-, reevaluated as 2.56 X lo9 M-'s-l for the diffusion-controlled 18661-70-6; (-)-[Co(edta)]-, 27829-16-9. encounters of ( * [ R ~ ( b p y ) ~ ] B r )and + [Co(edta)]- in the same medium. The value yields K = kdJk4 = 2.4 M-I, k,/kd = 0.43, (15)Geselowitz, D. A,; Taube, H. J . Am. G e m . SOC.1980,102, 4525. and thus 11701 k,, = 0.36 X lo9 s-I. The results are not seriously
+
Ionizatlon of the Hydroxycyclohexadienyl Radical in Concentrated KOH: A Measure of the Actlvity of OH- in Highly Basic Media' Hitoshi Taniguchi and Robert H. Schuler* Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556, and Department of Chemistry, Yamaguchi University, Yamaguchi 753, Japan (Received: June 8, 1984)
The ESR spectrum of the hydroxycyclohexadienyl radical has been examined in aqueous solutions containing up to 10 M KOH. In strongly basic solution the radical exists, as a result of ionization of the OH proton, predominantly in an anionic form where the hyperfine constant of the c6 proton (a(H,))is -4 G greater than that of the neutral radical. The other ESR parameters are virtually unaffected by ionization. At pH values above 12, equilibration of the neutral and anionic forms is rapid with respect to the frequency of the hyperfine interaction so that the observed hyperfine constant represents the weighted average of the two forms and directly provides information on the equilibrium composition. From the dependence observed up to 1 M OH- the pKb for deprotonation of this radical by base is found to be -0.58 i 0.05. At higher base concentrations a(H6),because it can be accurately measured even in the presence of reaction products, provides a good measure of the apparent activity of OH-. While the present measurements indicate that the activity coefficient of OH- in strong base considerably exceeds one, the values obtained are substantially less than those given by the spectrophotometricmeasurements of Yagi1 using indoles as indicators. Implications of the differences noted on the significances of any given basicity scale are discussed.
@-Hydroxyradicals ionize considerably more readily than do aliphatic alcohols and, in general, undergo acid dissociation of the O H proton in the pH range of 13-16.24 Because acid-base equilibria of these radicals can be readily examined by in situ
* Address correspondence to this author at the University of Notre Dame. 0022-365418512089-0335$01SO10
radiolysis-ESR techniques these radicals are potentially very valuable indicators for determining the activity of OH- in con(1) The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Document No. NDRL-2598 from the Notre Dame Radiation Laboratory.
0 1985 American Chemical Society
336 The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 centrated base. At pH values above 12 equilibration between the acidic and basic forms of this type of radical is rapid compared to the frequency of the hyperfine interaction of the proton undergoing exchange so that the ESR spectrum corresponds to the appropriately weighted average of the two forms of the radical rather than being the superposition of separate spectra, as is the case in spectrophotometric studies. Thus the information required to determine the ratio of the acidic and basic forms of these radicals is contained in the hyperfine data. The equilibrium composition can be accurately determined even though impurities or reaction products are present, as can readily be the case in concentrated base. Given that the hyperfine constants of the two forms are separately available from limiting measurements, the dependence of the ionic equilibrium on OH- concentration can be examined in detail as long as the ESR spectrum can be identified. We have used an approach based on this principle to examine the acid-base equilibrium of hydroxycyclohexadienyl radical up to KOH concentrations of 10 M and report the results here. Yagi15has effectively shown, by intercomparing acid-base equilibria of a number of indole derivatives having pK, values in the range of 12-15, that the activity coefficient of OH- in concentrated KOH is appreciably greater than unity. Based on these studies he has suggested a H.. basicity scale that effectively extends the pH range normally available for studies in aqueous solutions.6 Currently there is very little additional information on the activity of OH- in strong base.’ The present measurements provide a detailed and coherent picture of an acid-base equilibrium over a wide range of base concentrations determined with a single indicator. It is found, in agreement with Yagil, that with increased base concentration the activity coefficient of OH- appears to increase appreciably above unity. However, the magnitudes found here are somewhat lower than given by Yagil’s study. Whether or not the basicity scale derived from the present measurements has significance in an absolute sense will, as discussed below, depend on correlations with additional measurements using other indicators.
-
Experimental Section Because of the short lifetime of hydroxycyclohexadienylradicals the required ESR measurements must be made during continuing production of the radical, such as is possible with in situ-radiolysis techniques as previously d e ~ c r i b e d . ~Hydroxycyclohexadienyl ,~ radicals were prepared by addition of radiolytically produced .OH and -0radicals to benzene. Samples were irradiated directly in the ESR cavity with a 10-kA beam of 2.8-MeV electrons as in previous studies of hydroxycyclohexadienyl radicals in aqueous sol~tions.~ Our spectrometer sensitivity has recently been improved by addition of a microwave amplifier and computer control of the magnetic scanning systemlo to allow use of somewhat greater electronic time constants than previously. As a result it has become possible to observe signals of the hydroxycyclohexadienyl radical up to very high base concentrations. Aqueous solutions saturated
-
(2) Kirino, Y. J. Phys. Chem. 1975, 79, 1296. (3) Kirino, Y.; Taniguchi, H. J . Am. Chem. SOC.1976, 98, 5089. (4) Taniguchi, H.;Kirino, Y. J. Am. Chem. SOC.1977, 99, 3625. (5) Yagil, G. J. Phys. Chem. 1962, 71, 1034. (6) In highly basic media acid-base reactions are controlled entirely by OH‘ activity and it is not appropriate to discuss equilibria in terms of pH since the relationshipof the pH scale to OH-activity involves considerations of both the temperature and ionic strength dependence of water dissociation. Discussions can be carried out more readily and explicit considerations of the ionic dissociation of water can be avoided if one related the measurement to an appropriate basicity scale such as the H-scale used by Yagil (ref 5). In the present study we take H- as 14.0 at an OH-activity of 1 and define the Hscale as 14.0 + log (-y*[OH-]). Conceptually this scale can be thought of as an extension of the pH scale to highly basic solutions. (7) Rochester, C. H. ‘Acidity Functions”; Academic Press: New York, 1970; Chapter 7. Cox, R. A.; Yates, K. Can. J. Chem. 1983, 61, 2225. (8) Eiben, K.; Fessenden, R. W. J. Phys. Chem. 1971, 75, 1186. (9) Eiben, K.; Schuler, R. H. J . Chem. Phys. 1975, 62, 3093. (10) We acknowledge the developmental work of Drs. R.W. Fessenden and K. P. Madden in markedly improving the characteristics of the spectrometer used in the in situ radiolysis experiment. This developmental work has made the present measurements possible.
H20
--
erq;OH ,.-.
+ NO,
e; .OH
Taniguchi and Schuler
+ OH-
N,
+*O-
pK,=11.9
.O-+ HZO
t
t
0 ...
....* 0 9 -I -I
k=8x10 M s
I -I -I
k=8xlO M s
F I1. Radiolytic reactions which produce the hydroxycyclohexadienyl radical and its conjugate base in highly basic media. TABLE I: ESR Parameters of the HydroxycyclobexadienylRadical and Its Conjugate Base” acidic formb basic form 9.3 16.1 16.8 2.00227 8.92‘ 2.71 13.02 38.55 “Protons H I , H3, and H5 are on the conjugated system of the ring at positions of high spin density and H2 and H 4 at positions of low negative spin density. The ESR data do not directly give the sign of the hyperfine constants. Only the hyperfine constant of the methylenic proton (H6) at the site of .OH addition is sufficiently sensitive to ionization to probe the equilibrium. Limiting values of n(H6) in the acidic and basic forms are 34.32 and 38.67 G, respectively (see Figure 2). bExcept for a(H,) the parameters are within experimental error as given by Eiben and Schuler (ref 9 where a(H6) was reported as 34.54 G). Additional splitting of 0.47 G by the O H proton is observed below p H 11. CMeasured in 6.2 M KOH (H-= 15.3). dThis hyperfine constant increases to 34.55 on additional of 1 M Na2S04.
with benzene (Fisher, Certified ACS spectranalyzed) and containing the desired concentration of KOH (Fisher, Certified ACS) were purged of dissolved air, saturated with N,O to convert eaqto .OH, and irradiated in a flat 0.5-mm quartz cell in a flow system. Flow rates of N 1 cm3/s were used and residence times of the sample in the cavity were -50 ms. Water was prepared with a Millipore Q system. Base concentrations were determined by titration with standard HCl. Baker Analyzed Reagent Grade sodium and potassium sulfate were used for ionic strength studies. Magnetic field measurements were made with a N M R probe locked to the field and the computer-controlled scanning system automatically corrected for any drift in the cavity frequency. Hyperfine constants are, in general, accurate to 0.01 G. The g factors were determined by reference to a value of 2.00306 for sulfite radical” and are accurate to 0.00001. Most measurements were made at -16 OC. Results and Discussion The hydroxycyclohexadienyl radical and its conjugate base are rapidly produced in the radiolysis of aqueous solutions of benzene produced from the water, as is inby addition of .OH and -0dicated in Figure 1. Because the rate constant for -OH addition is more than an order of magnitude higher than that for .O-, reaction of .OH dominates up to at least pH 13 but at higher pH side reactions of -0become more important and appreciably reduce the intensity of the signals of interest. We were, however, (11) Behar, D.; Fessenden, R. W. J. Phys. Chem. 1972, 76, 1706.
The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 337
Ionization of Hydroxycyclohexadienyl Radical
immediately below, this latter value must be regarded as a lower limit. In strong base hyperfine interactions from the five protons on the conjugated system continue to be observed, demonstrating definitively that the radical does not undergo further deprotonation in strong base. The constancy observed for the ESR parameters is taken as a manifestation that the hydroxycyclohexadienylradical does not undergo any solvation or other reaction with the base. The acid-base equilibrium thus appears to be as indicated in Figure 1 . In view of this the increase observed in a(H6) should be simply interpretable in terms of this equilibrium provided one has a proper measure of the OH- activity. For a simple equilibrium the hyperfine constant should be given as a function of the base concentration by
3/ 38
I
a(H6) = I
341
111
12
I
13
I
I
15
14
H-=14.0+lop(l/x
I 16
I 17
DH-J)
F w e 2. Dependence of a(H6) on basicity (H-= 14.0 + log (y[OH-1)): 0,taking y = 1; 0, taking y as given by eq 2; A,H-as given by Yagil for KOH. Data for solute also containing 1 M Na$04 are given by X’s. Sigmoidal curves correspond to simple equilibria with pKb of hydroxycyclohexadienyl taken as -0.58.
able to observe lines from the hydroxycyclohexadienyl radical even up to 10 M KOH in N20-saturated solutions also saturated with benzene (0.02 M). The overall spectrum is complicated in the center by lies of highly conjugated radicals with low total splitting. Lines of the H-atom adduct, though weak, also appear on the periphery. Appropriate lines of the hydroxycyclohexadienylradical were, however, able to be identified at all base concentrations studied. As described below, appreciable change in the hyperfine constant of the proton on (26, a(H6), occurs in the region above pH 13 and is attributed to ionization of the OH proton. The initial experiments indicated that pKb for the ionization equilibrium is -0.5. The radical should, therefore, be predominantly in its neutral (acidic) form below H-= 13 and in its anionic (basic) form above 16. The ESR parameters observed in 0.01 and 9.3 M KOH are given in Table I. At the lower concentration the parameters are essentially as previously giveng except for a(H6) where the value previously observed was 0.2-G higher, apparently because of the effect of added ions described below. From the comparison at the two basicities it is seen that the g factor and hyperfine constants of the protons on the conjugated system are almost completely unaffected by the state of ionization, as is also the case for a number of the carboxylated derivatives.’* While this observation is perhaps somewhat surprising it demonstrates very clearly that there is no appreciable shift in electron population on ionization, i.e., that the distribution of spin density over the conjugated system is not sensitive to the presence of formal charge on the oxygen atom. In contrast to the above, the hyperfine constant of the proton at (26 increases by over 4 G upon the addition of base. The concentration dependence is illustrated by the open squares in Figure 2. It is seen that its value increases very rapidly above H-= 13. Taking the increase over the low concentration limit (ao = 34.32 G) as a measure of the amount of the anionic form of the radical, the degree of ionization can be determined if the high concentration limit (a=) can be estimated. The latter is clearly greater than 38.5 so that the midpoint of the equilibrium is at a KOH concentration in excess of 2.5 M. Yagil’s study shows that the activity coefficient of OH- in this region is greater than one so that the p& of this radical must be more negative than -0.4. His basicity scale suggests a value of --0.7 but because of questions about the applicability of this scale, as discussed (12) Taniguchi, H.; Schuler, R. H., to be published. The hyperfine constants of the protons on the conjugated system and g factors of various carboxylated derivatives of hydroxycyclohexadienyl radical are not appreciably affected by ionization of the OH proton. The value of a(H6), however, decreases by up to 4 G if there is an adjacent carboxyl group but increases in the other cases, showing that a(H6) is very sensitive to the local environ-
ment.
aO
+
- aO)K(y[OH-l)/(l + K(y[OH-]))
(1)
where K is the equilibrium constant and y the appropriate activity coefficient. On a given H-scale one should, therefore, observe 9 and 91% of the overall change 1 unit below and above the pKb of the equilibrium. The present results are plotted as the open triangles in Figure 2 according to Yagil’s H- basicity scale. Inspection shows that on this scale the observed increase occurs over too wide a range in H-to be described by a simple equilibrium. We conclude that at least in the present case Yagil’s scale exaggerates the activity of OH-. It should be noted that Yagil does not explicitly discuss his H-scale in terms of OH- activity but rather considers the equilibria to involve free water in addition to OH-. If such an approach is applicable generally then any particular H-scale is, at least to some extent, ad hoc and it would not be surprising if the present example is not properly fitted on Yagil’s scale. We proceed here to construct an alternative H- scale based on the present data. To do so one must proceed iteratively. If one accepts that the activity coefficient of OH- increases above one at KOH concentrations above 1 M then an appropriate description of the dependence must lie somewhere between the squares and triangles of Figure 2. When Yagil’s scale is used it is clear that as a first approximation the measurements of a(H6) at the highest base concentrations are within a few percent of a,. Reasonable extrapolation gives 38.67 f 0.10 G as the limiting value in strong base so that a. - a, is 4.35 G. The midpoint of the increase m u r s at a KOH concentration of 2.7 M. From the data up to 1 M KOH, where the activity coefficient does not increase significantly above one, the sigmoid of Figure 2 was constructed. This sigmoidal curve corresponds to a pKb of -0.58. Since the slope of eq 1 in the region of the inflection point is 3 G / H , errors in determining a(H6) do not contribute significantly (CO.01). The principal uncertainty arises from errors in estimating a, and y in the region of 2.7 M base. Since the latter is, from the arguments given below, 1.67 it is reasonably estimated to be accurate to lo%, corresponding to an uncertainty of only 0.04 in pK,. Any increase in the value taken for a, will be partially compensated for by an accompanying decrease in y so that the uncertainties possible from this source are -0.05. If these various factors are taken into account in the data of Figure 2 the probable error in p& is f0.05. We are now in a position to determine the activities of OHfrom a comparison of the observed data with the sigmoid of Figure 2. Taking the activity coefficient as the ratio of the apparent OHactivity to the actual concentration we obtain the plot given in Figure 3. It is seen that in the region to 5 M KOH y increases relatively modestly to a value of -2. A similar plot from Yagil’s data shows a much more pronounced increase with his H-scale effectively corresponding to a y of -5.5 at this concentration or a difference in the two basicity scales of -0.4 units. Since our studies were carried out at 16 O C and Yagil’s at 25 O C it was thought that the observed difference might reflect a strong temperature dependence of the activity. However, measurements carried out at 5.6 M KOH show only a trivially overall increase of 0.03 G on increase of the temperature to 26 “C. This increase corresponds to an increase of only 3% in the activity coefficient or 0.01 in the value of H-. Sorting out the source of the difference in the two scales remains for further experimentation. We note
-
338 The Journal of Physical Chemistry, Vol. 89, No. 2, 1985
15
-
I
I
0 0.0 2.0 4.0
6.0 8.0 [KOH] - M
10.0
Figure 3. Dependence of activity coefficient of OH- on concentration of KOH as obtained in the present study (0)and from the work of Yagil (0, ref 5).
here only that Yagil’s scale for N a O H does, in fact, correspond very closely with the activity coefficients as measured here for KOH so it is possible that the cation may play a fairly direct role in the spectrophotometric studies. We are currently exploring this aspect. The data of Figure 3 can be fitted quite well up to 9.3 M by the fourth-order polynomial
+ 0.2043[OH-I2 0.05861 [OH-]) + 0.005802[0H-]4 (2)
y = 1.0050 - 0.08410[OH-]
Equation 2 was obtained by polynomial regression methods so the different terms compensate to some extent and the coefficients should not be interpreted separately. The experimental data are plotted as the solid circles in Figure 2 on a basicity scale defined by H- = 14.0 log (y[OH-]) = 14.0 - pOH (3)
+
withy given by eq 2. The fit here, of course, only reflects the fit in Figure 3. The difference between the H- scale used for this display and Yagil’s scale is exemplified by the horizontal differences between the triangles and the solid curve in Figure 2. These differences are small at low base concentrations (
