Protonation of Potassium Anthracenide
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
1111
Kinetics of Protonation of Potassium Anthracenide by Ethanol in Tetrahydrofuran. Effect of Dicyclohexano-I 8-crown-6 and 2,2,2-Cryptand Nlcholas Papadakls and James L. Dye* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (Received August 29, 1977)
Previous work showed that the protonation of alkali metal anthracenides by ethanol in tetrahydrofuran follows mixed pseudo-first- and second-order kinetics (in total anthracenide) and that contact ion pairs play major roles in both pathways. The addition of either dicyclohexano-18-crown-6(DCC) or 2,2,2-cryptand (C222) to the solution drastically reduces both the first- and the second-order contributions. Complex-separated ion pairs do not contribute to the second-order pathway and are protonated by a pseudo-first-order process which is several orders of magnitude slower than the pseudo-first-order protonation of the contact ion pair. Quantitative treatment of the effect of DCC and C222 on the protonation rate is complicated by the large values of the cation complexation constants and the unknown effect of ethoxide ion pairs. However, the data permit estimates of -4 X lo5 and 1 5 X lo6 for the equilibrium constants for the reaction An.-,K+ + C e An.-CK+ with C = DCC and C222, respectively.
Introduction The overall stoichiometry of protonation of aromatic radical anions by proton donors such as water or alcohols is given by 2Ar.- + 2ROH ArH, t Ar + 2RO(11 In the case of anthracene, ArHz is 9,lO-dihydroanthracene.lpz Direct protonation of Ar.- to form ArH. followed by rapid electron transfer from Ar.- to yield ArH- which is rapidly protonated3 is in accord with the overall stoichiometry. The predicted pseudo-first-order disappearance of Are- is, indeed, observed in some system^.^^^ The mechanism of protonation of aromatic radical anions is more complicated than this, however. The fate depends strongly upon the solvent, the cation, and the protonating agent, and the order in Ar-- ranges from pseudo-first order to pseudo-second order, often showing mixed first- and second-order b e h a ~ i o r . ~The - ~ rate of protonation of a given species seems to depend upon the degree of charge localization, which in turn increases drastically as contact ion pairs, ion clusters, and dianions are formed. The pseudo-second-order pathway involves protonation of dianion contact ion pairs,8 Ar2-,2M+ and either dimers of contact ion pairs7 (Ar.-,M+)z or the kinetically indistinguishable cage complex,8 Ar2-, M2+,Ar. The pseudo-first-order pathway also involves primarily contact ion pairs with a much slower protonation of solvent-separated ion pairs and free ions.’ The pseudofirst-order pathway is further complicated by the fact that the order in alcohol varies between one and two. Szwarc and co-workerss have attributed this variation to the presence of alcohol dimers, (ROH)2. All of these studies emphasize the important role played by contact ion-pair formation. A direct indication of this effect was obtained by Minnich et ale7who showed that the addition of dicyclohexano-18-crown-6,9 1 (DCC), to the --f
coy
a:
Po /7,-7 N%O%OT/N L
0
”
d
bd 1
2
solution essentially eliminated the second-order component and drastically decreased the first-order component.
Presumably, this effect results from the virtual elimination of contact ion pairs when DCC is added to the potassium anthracenide solution.lOJ1The present paper describes in more detail the effect of DCC and 2,2,2-cryptand,12 2 (C222), on the rate of protonation of potassium anthracenide (K+An.-) by ethanol (EtOH) in tetrahydrofuran (THF),
Experimental Section Since aromatic radical anions are air and moisture sensitive, all solutions were prepared and transferred in vacuo or under a helium atmosphere. All glassware, including the stopped-flow system, was cleaned with hot aqua regia followed by thorough rinsing with conductance water. In addition, the preparation vessels used for the kinetics experiments and the stopped-flow system were prerinsed with a solution of potassium anthracenide in T H F followed by extensive rinsing with THF. By using this method, recommended by Szwarc,13the K+An.- solutions were indefinitely stable and showed no change in absorbance with time either in the preparation vessels or in the stopped-flow cell. Solvent and solution preparation have been described el~ewhere.~ PAR grade anthracene from Princeton Organics and DCC from E. I. duPont de Nemours Co. were used without further purification. Zone-refined 2,2,2cryptand was synthesized in this laboratory as previously described.14 Anhydrous ammonia was condensed several times into break-seal tubes which contained the complexing agent (DCC or C222) and distilled out each time to complete the drying process.15 Spectral grade ethanol from Commercial Solvents Corp. was further purified as described previously.’ The computer-interfaced dual-beam rapid-scan stopped-flow system has been previously described.16J7The equations used were fitted to the data by a general non-linear least-squares program.ls Results and Discussion The approach used in this study was based upon the previous extensive study of the rate of protonation of K+An.- by EtOH in THF.’ By adjusting the total concentrations of K+An.- and EtOH, the reaction in the absence of the cation complexing agent can be forced to follow either an essentially pseudo-second-order or a pseudo-first-order pathway. For example, low concentrations of EtOH and high concentrations of K+An.- show
0022-3654/78/2082-1111$01.00/00 1978 American Chemical Society
1112
N. Papadakis and J. L. Dye
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
TABLE I: Pseudo-First- and Second-Order Rate Constants for the Protonation of Potassium Anthracenide by Ethanol in Tetrahydrofuran at 24 "C in the Absence of Complexing Agents 1 0 4 1 ~ + -104-
1.6
I .2
5.75 4.60 3.74 2.88 1.73 0.58 0.58 0.58 0.58
4.60 4.88 3.96 3.05 1.83 0.61 0.61 0.61 0.61
0.083 0.083 0.083 0.083 0.083 0.105 0.209 0.293 0.418
0.76(10)" 0.93( 3) 0.85(22) 1.37(5) 1.23(10) 1.78(9) 15.27(1 6 ) 27.6( 1 7 ) 62.9(35)
3.62(10) 3.68( 5 ) 3.71(13) 3.78(12) 3.36(13)
.--
0.8
at-
s"
0.4
0.c
Each entry represents the average of the results from four separate "pushes". The value in parentheses represents the standard deviation estimate for the last digit given. See ref 7 for details. a
primarily second-order decay of the absorbance of An.-, whereas the kinetics are pseudo-first order in the absorbance at high concentrations of EtOH and low concentrations of K+An--. By measuring the rate of decay of absorbance in the presence and absence of either DCC or C222 under the extremes described above, we were able to assess the effect of these complexing agents on both the first-order and the second-order pathways. The decay of the absorbance of An.- over the wavelength range 510-870 nm was followed by the scanning stopped-flow techniquel63l7at path lengths of 0.2 and 1.85 cm. The pseudo-first- and second-order rate constants were found to be independent of wavelength in agreement with the previous s t ~ d y The . ~ results in the absence of added complexing agent are given in Table I. For the short-path length data at [EtOH] = 0.083 M the pseudo-second-order rate constant k i is well-determined and is independent of the initial concentration of potassium anthracenide, [K+An.-Io. The pseudo-first-order rate constant kl' decreases slightly with [K+An.-Iobut this may not be significant because a small shift of the baseline or other systematic error could significantly affect the apparent first-order contribution since it is so small compared to the second-order contribution at the high values of [K+An.-Io used with the short-path cell. The average value of k2/, 3.63 X lo4 M-l s-l, agrees well with the value 3.14 X lo4 M-l s-l calculated from previous data7 for this concentration of ethanol. The pseudo-first-order rate constant, kl', is best determined from data at low concentrations of K+An.- (long path cell) and high concentrations of EtOH because under these conditions the pseudo-second-order pathway becomes less important. The data for kl' given in Table I agree reasonably well with previous data7 except that the scatter of the data is large at low concentrations of ethanol. Data from both sources are plotted in Figure 1. A non-linear weighted least-squares fit of these data to the equation
k I' = k [ EtOH]"
(2) yields n = 2.34 f 0.17. This compares with the value of n = 2 found by Rainis, Tung, and Szwarclg for the protonation of the contact ion-pair An--,K+,by methanol in THF. The value of k is 5.3 f 1.5 X lo2 M-2.34s-l. When n is forced to have a value of 2.0, kl becomes -3 X lo2M-2 s-l compared with the value of 1.0 X lo3 M-2 s-l obtained for protonation by methan01.l~ (It should be noted that this is twice the rate constant for protonation of An.-,K+ because of the stoichiometry of reaction 1.)
-0.4 I
I
I
L
I
-1.0
-1.4
-0.6
-0.i
log [EtOH]
Figure 1. log-lo plot of the pseudo-first-order rate constant for the protonation of KQAn.- in THF by ethanol at 24 OC in the absence of complexing agent: circles, this work; squares, ref 7.
0.31 0
I
I
I
0.2 0.4 0.6
I
0.8
I
1.0
I
1.2
I
1.4
1
1.6
I
1.8
i 3
TIME ( s e d M K+An.- in the Figure 2. First 2 s of the protonation of 4.6 X M: DCC (circles) or 1.79 X M C222 presence of 1.76 X (squares). (See the text for the meanings of the solid and dashed lines.)
The most pronounced effect of the addition of DCC or C222 in excess is the virtual disappearance of the second-order c ~ m p o n e n t .When ~ less than the stoichiometric concentration of complexing agent (C) is present, the kinetics of decay behave as if an amount of the ion pair An.-,K+ equivalent to the amount of added C were removed from the solution. For example, Figure 2 shows the first 2 s of the data obtained at 752 nm with [K+An.-Io M, [C] = 1.76 adjusted, but nominally equal to 4.6 X X lo4 M (for DCC) and 1.79 X lo4 M (for C222), [EtOH] = 0.083 M, and [Anlo = 4.9 X M. The solid line through the data was calculated by using k2' = 3.63 X lo4 M-l s-l and /q' = 0.93 s-l as measured in experiments without complexing agent present. It was assumed that the equilibrium constant for the reaction K,
An--,K++ C eAn.-CK+
(3)
is so large that the concentration of An--CK+ was equal to the total initial concentration of the complexing agent. I t was also assumed that the complex-separated ion pair is not protonated a t a significant rate during this period of time. The excellent agreement, obtained without adjusting any parameters, confirms our supposition that the effect of C is to decrease the concentration of contact on pairs.
The Journal of Physical Chemistty, Vol. 82, No. 10, 1978
Protonation of Potassium Anthracenide
1113
TABLE 11: Pseudo-First-OrderRate Constant for the Protonation of the Complex-Separated Ion Pair (Ana-CK') by Ethanol in Tetrahydrofuran at 24 "C and the Value of the Complexation Constant, K, 1O4 [An*-],,
1O4 [An],,
1O4 [ DCC 1,
1O4 [C22 2 1,
M 4.60 3.74 2.88 1.73
M 4.88 3.96 3.05 1.83 1.83 0.61 4.88 3.96 3.05 3.05 1.83 1.83 0.61
M 1.76 3.08 4.4 6.16 6.16 7.9
M
1.73 0.58 4.60 3.74 2.88 2.88 1.73 1.73 0.58
1.79 3.13 4.48 4.48 6.27
7.9 8.06
[EtOH], M 0.083 0.083 0.083 0.083 0.418 0.418 0.083 0.083 0.209 0.209 0.209 0.418 0.418
102h,", s-l 2.4( 6)' 1.20(6) 1.15(9) 1.19(9) 42(10) 95(4) 0.21(9) 0.16(5) 2.0( 3) 2.8(8) 3.9(2) 32(5) 56(3)
1 0 - 5 ~M-, , 16(5) 6.0(15) 6.0( 5 ) b b C
47(31)" 71(22)d 50(12)" 114(47)" b b C
No. of pushes 6 6 3 4 3 5 5 4 3 2 4 4 5
The value in parentheses represents the standard deviation estimate for the last digit given. See ref 7 tor details. I , At high [C]/[An.-], ratios, K cannot be determined. In evaluating h,", the value of K was fixed at 4.0 x lo5M-l for DCC and At these concentrations only protonation of An-CK' is significant so that h," was obtained 5.0 x l o 6 M-'for C222. The large standard deviations in K result from the small contribution of the disfrom a pseudo-first-order fit of the data. sociative pathway when C222 is used.
"
Figure 2 also shows that over this time interval, at the concentrations of K+An.- and EtOH used, most of the fast initial decay is the result of the pseudo-second-order (in total An-) pathway (dashed line). Attempts to include the species An.-CK+ as part of the second-order pathway yielded null results; the second-order contribution in all cases could be quantitatively accounted for by considering that it requires two contact ion pairs. Of course, if An;CK+ could not be protonated at all, we would expect the rate of disappearance of the absorbance to decrease continuously as the concentration of C is increased. That this is not the case, a t least when C = C222, is shown in Figure 3, which shows the shape of the absorbance decay a t 752 nm for [C222]/[K+An.-Io = 1.56 (circles) and 3.63 (squares and triangles) and [EtOH] = 0.209 M (circles and squares) and 0.418 M (triangles). Clearly, the species An--CK+ can be protonated a t a rate which, although much slower than the rate of protonation of An-,K+, increases with increasing ethanol concentration. The constancy of the protonation rate as the [C]/[K+An.-], ratio is increased (provided the ratio is larger than unity) shows that the bulk of the protonation proceeds by a direct route rather than by prior dissociation of An.-CK+ to form An--,K+ and C. While complexation of K+ by C seems to be complete at the 1:l stoichiometry when C = C222, this is apparently not the case when C = DCC. For the latter (weaker) complexing agent, the observed pseudo-first-order rate constant decreased by -30% when the ratio [DCC]/ [K'An-], was changed from 1.55 to 3.57. This indicates that the dissociation of An.-CK+ to form An.-,K+ which is then rapidly protonated probably contributes to the net rate of protonation. This made it possible to estimate the value of K3 when DCC was used as described below. I t is difficult to determine how much of the protonation occurs via dissociation of An.-CK+ without an independent determination of the equilibrium constant for reaction 3. However, by using hl' and k i from data obtained in the absence of cation complexing agents, and by adjusting [K+An.-]o,K3,and k r (where k 7 is the pseudo-first-order rate constant for the protonation of An.-CK+), it was possible to evaluate K3 and k7 separately when DCC was used but only an approximate minimum value of K3 could be obtained when the complexing agent was 2,2,2-cryptand. The value of kl" for the latter case when C222 is present in excess is insensitive to K3 so it was possible to evaluate this pseudo-first-order rate constant for the protonation
3
TIME (seconds) Figure 3. Shape of the absorbance decay in the presence of an excess of C222: [C222]/[K+An.-]= 1.56 (circles);[C222]/[K+An--]= 3.63 (squaresand triangles); [EtOH] = 0.209 M (circlesand squares);[EtOH] = 0.418 M (triangles). See Table I1 for the concentrations of other species.
of An.-C222K+ even without an accurate value for K3. All of the results are given in Table 11. At a low concentration of K+An.- (5.8 X 10" M), a high concentration of ethanol (0.418 M), and with a large excess of cation complexing agent (7.9 X lo4 M for DCC and 8.1 X M for C222) only the protonation of An.-CK+ was important. The results for this case are also given in Table 11. I t is clear that the rate of protonation of An.-CK+ is strongly dependent upon the concentration of ethanol. The protonation rate roughly parallels that of the contact ion pair An.-,K+. The "crown-separated ion pair" is protonated by ethanol 60 to 150 times slower than is the contact pair while the "cryptate-separated ion pair" is protonated 100-650 times slower than the contact pair. The dissociation of ion pairs to give free ions was ignored in the treatment of these data. At low concentrations of K+An.-, especially for the complex-separated ion pair An.-CK+ this assumption is probably not valid. Estimates of the ion-pair dissociation constant made by using the Fuoss e x p r e s s i ~ nindicate ~ , ~ that An.-CK+ may be as much as 50% dissociated at the lowest concentration used. Also ignored in this treatment is the effect of alkoxide formation. If complexing agent is removed from the solution by formation of RO-CK+ this will affect the treatment of the data when C is not present in excess. Because of these problems, the values of K3 and k
