578
J. Phys. Chem. 1983, 8 7 , 578-501
In the present paper the effect of various cations has been investigated; in the next paper we will consider the role of anions and X+-Y- ion pairs. Acknowledgment. We are indebted to Dr. M. Urban (Department of Chemistry, Comenius University, Bratis-
lava) and Dr. J. Sauer (Central Institute of Physical Chemistry, Academy of Sciences GDR, East Berlin) for valuable comments on the manuscript. Registry No.
Li',
17341-24-1; Na+, 17341-25-2; Mg2+,
22537-22-0;HCl, 7647-01-0;HF, 7664-39-3.
Thermodynamics of Ion-Pair Dissociation Involving the Dianions of [81- and [ 161Annulene Charles R. Wledrlch, Davld L. Catlett, Jr., James B. Sedgwlck, and Gerald R. Stevenson. Department of Chemlstty, Illlnols State Unlverslty, Normal, Illinois 6 176 1 (Received: June 16, 1982; I n Final Form: October 4, 1982)
The observed disproportionation equilibrium constant for the cyclooctatetraene (COT) anion radical in hexamethylphosphoramide (HMPA) has been algebraically related to the dissociation constant for the charged ion pair (COT2-,M+).Surprisingly, the systems COT2-,Cs+and COT2-,Li+were found to dissociate into the solvated ions (COT2-+ M') endothermically. This endothermic dissociation of the ion pair is explained in terms of solvation and Coulombic interactions between the dianion and the cation. The entropies of dissociation were found to be negative as expected. When [16]annulene was utilized in place of [8]annulene (COT), no ion association could be observed. This is explained in terms of the lesser charge density in the larger annulene dianion. The association of these dianions with M+ was studied via its effect upon the NMR resonances of the dianions. The internal protons of the [16]annulenedianion shift downfield by 0.4 ppm in HMPA relative to this dianion in tetrahydrofuran (THF).
Introduction Several years ago Szwarc and co-workers' reported a simple electrochemical technique that can be utilized to measure the enthalpies and entropies of anion radical disproportionation (eq 1). Some of the systems studied 2A-*,Mf A + A2-,2M+ (1) yielded very large values for A S ' due to the fact that desolvation of the cation takes place upon disproportionation. This desolvation by the tetrahydrofuran (THF) or dimethoxyethane (DME) is caused by the stronger Coulombic attraction that exists between the dianion (A2-) and the cation (M+)than exists between the anion radical (A'-.) and the cation. For systems where the solvation sheath around the cation remains intact upon disproportionation, the entropy changes are much smaller. Consequently, ASo is 68 eu for the sodium salt of tetracene in THF (where desolvation takes place upon disproportionation) vs. only 23 eu for the potassium salt (K+ remains appreciably solvated even in tetracene2-,2K+).lb In THF both the anion radicals and the dianions exist in the ion-associated state. In hexamethylphosphoramide (HMPA), on the other hand, the anion radicals of nonpolar hydrocarbons are free of ion association with alkali metal cations.2 However, hydrocarbon dianions can form ion pairs in HMPA as evidenced by the fact that the apparent disproportionation equilibrium constant for the cyclooctatetraene (COT) anion radical varies with the cation p r e ~ e n t . In ~ fact, it has been shown that the dependence of the apparent equilibrium constant (Kap= [C0T--l2/ ([COT][COT2-],,) is due to the formation of the charged (1) Jachimowicz, F.; Wang, H. C.; Levin, G.; Szwarc, M. J. Phys. Chem. 1978,82, 1371. (2) Levin, G.; Jagur-Grodzinski, J.; Szwarc, M. J. Am. Chem. SOC. 1970, 92, 2268. ( 3 ) Stevenson, G. R.; Concepcion,J. G. J.Phys. Chem. 1972, 76,2176.
ion pair (COT2-,M+).4 From this it is clear that the original observations provided only an apparent equilibrium constant, with the following relationship between Kapand the ion-pair dissociation constant (Kd)lbv4
K,, = Kf(1 + Kd-'[M+])
(2)
where Kf refers to the disproportionation involving only the free ions (eq 3). On the basis of these considerations,
+
2COT-- COT COT2(3) Szwarc and co-workers1have suggested that the thermodynamic parameters for the disproportionation of the potassium salt of COT4 should be recalculated. His published suggestion represented part of our motivation to carry out this study. In HMPA the COT dianion is completely free of ion association with the sodium ~ a t i o n .Thus, ~ when Na+ is the only cation present, the disproportionation of COT. is as described in eq 3. After the COT anion radical and the dianion are generated in HMPA with sodium metal, the addition of alkali metal salts (LiC104, KC1O4, or CsC104)should result in an increase in the observed or apparent disproportionation equilibrium constant as predicted by eq 2. This prediction was born out when KC104 was added to solutions of the COT anion radical in HMPA, and Kd = [COT2-][K+]/[COT2-,K+]was found to be (13 f 3) X lo-*. Neither enthalpies nor entropies of ion-pair dissociation were determined as temperature-dependent studies were not carried Further, K+ was the only cation included in the study. Here the wish to report the complete set of thermodynamic parameters controlling the ion-pair dissociation, reaction 4,for all three cations mentioned above. The (4) Stevenson, G. R.; Ocasio, I. J. Am. Chem. SOC.1976, 98,890.
0022-3654/83/2Q87-0578$01.5O/O 0 1983 American Chemical Society
The Journal of Physical Chemktty, Vol. 87, No. 4, 1983 579
Thermodynamics of Ion-Pair Dissociation
TABLE I: Representative Data for Some Cesium and Lithium Systems
results of this work should allow us to draw conclusions concerning the relationship between ion association involving the dianion only and disproportionation. Further, we will be able to evaluate, for the first time, thermodynamic parameters controlling the dissociation of a dianion-cation complex. The thermodynamic parameters controlling reaction 4 should yield insight as to the role of solvation and Coulombic attraction between the dianion and the cation in ion-pair dissociation. By replacing COT with [16]annulene, one can ascertain the effect of diffusing the charge density in the dianion. Experimental Section The anion radicals were generated via sodium reduction in freshly distilled HMPA under high vacuum as previously described! After complete dissolution of the sodium an ESR sample was sealed off from the apparatus and a portion of alkali metal perchlorate added to the anion radical solution. After this salt had dissolved in the HMPA solution, a second ESR sample was taken. The apparatus, procedure, and purification of the solvent and salts have been described previ~usly.~ The two samples (one containing dissolved salt) from the same reaction mixture were compared for spin concentration by using a Varian E-4 ESR spectrometer interfaced with a MINC 11 64 K computer. The ESR data were collected with the maximum modulation amplitude as described by Goldberg5 to minimize the error in obtaining the anion radical concentration from the double integral of the ESR signal. The ESR data were sent directly into the computer, where double integrations were performed, software available from Digital. The anion radical concentration is proportional to the double integral of the overmodulated ESR line, A. Kapcan be expressed as shown in eq 5 , where B is simply a proportionality ~ o n s t a n t . ~
Kap= [COT][COT2-],,/(B2A2)
= [COT]([COT2-,M+]+ [COT2-])/(B2A2)( 5 )
Since the ion-pair dissociation constant is given by
Kd = [COT2-][M+]/[COT2-,M+]
(6)
a simple relationship exists between the ion-pair dissociation constant (Kd) and Kf (eq 2). In the absence of ion association, the disproportionation is controlled by Kf = [COT2-][COT]/[COT-*]2= [COT2-][COT]/(B2Af2) (7) Further, since Kap/Kfis simply equal to the ratio of the intensities of the ESR spectra squared (Aa,2/Af2), the double integrals of the overmodulated ESR spectra for the sample containing salt (A, ) and that without added salt (eq 8). (Af) can be used to find
&
Kd
= [M+]/ [ (A,p/AJ2 - 11
(8)
The values for (A,p/Af)2 were taken directly from the computer after the ESR data were taken and the double integrations performed. A value for Kdwas f i s t calculated by assuming that the concentration of M+ was identical with that added to the solution. This first value for Kd is actually a bit large, since some of the M+ ions are as( 5 ) Goldberg, I.
B.J. Mugn. Reson. 1978, 32, 233.
salt added
M'
LiC10, LiC10, LiC10, LiClO, CSClO, CSC10, CSC10, NaC10,
0.070
0.004 5 0.070 0.049
0.0044 0.009 0.0088 0.1
AnIAf 0.11 0.83 0.12 0.15 0.21 0.16 0.12 1.0
Kd 8.6 X 9.9 x 8.4 x 1.1 x 1.9 x 2.4 x 1.2 x
10-3 10-4
10-3 10-4 10-4
10-4
TABLE I1 : Thermodynamic Parameters Controlling the Dissociation of the COT", M+ Ion Pair (Reaction 4 ) in HMPA at 25 "C ~~
M' Li' Na'
K' CS'
Kd
(1.1i 0 . 5 ) x 10-3 >lo-' ( 1 . 5 * 0.6) x (1.6+ 0.7) x low4
A H , kcalimol AS, eu
0.0k 0 . 9
-14
t 1 . 2 i 0.4
-9 -9
+2.5 k 1.2
sociated with the COT2- (total cation concentration ([M+],) is not identical with [M']). This initial value for Kd was then placed into eq 9 and a new value for [M+] [M+] = l/~([M+)t - [COT2-], - & + (([COT2-],4- Kd [M+1J2- 4Kd[M+])1'2) (9) calculated. The new value for [M+]was then placed into eq 8, and the process was repeated until & did not change with further iterations (usually four or five). NMR spectra were recorded on a Perkin-Elmer R-32 90-MHz NMR. For each experiment a sample was taken without added salt; then salt was added and the second sample taken. Several hours were allowed for complete dissolution of the salt before the second sample was sealed off from the apparatus (Figure 1). Before the standard (sample without salt) was taken, complete reduction of the COT to the dianion was assured by monitoring the ESR signal as the reduction proceeded. Once the dianion was completely formed, as indicated by the absence of an ESR signal, the standard was taken and the salt mixed with the remainder of the solution. The fact that the COT dianion NMR chemical shift varies with ion association has been demonstrated in other solvents.6 Results and Discussion Sodium reduction of COT in HMPA results in a solution yielding the well-known nine-line ESR pattern for COT.. Both the dianion and the anion radical are known to be free of ion association with Na+, and the addition of sodium perchlorate does not result in a change in the anion radical concentration. However, the addition of cesium perchlorate or cesium iodide to the solution causes a dramatic decrease in the ESR spectral intensity due to the association of Cs+ with COT2- (eq 4). Similarly, the addition of lithium perchlorate also results in a decrease in the magnitude of the double integral of the ESR spectrum, but this decrease is not as dramatic as that caused by the Cs+ addition (Table I). Each experiment can be utilized to evaluate &, and the errors reported for & in Table 11represent the standard deviation taken from 10-12 measurements for a given cation. Although the error in Kd is rather large, this error does not have to be reflected in AH'. This is the case since each sample with its standard (containing no added salt) can be studied as a function of temperature and a van't (6) Cox, R. H.; Harrison, L. W.; Austin, W. K. J. Phys. Chem. 1973, 77, 200.
580
The Journal of Physical Chemistv, Vol. 87, No. 4, 1983
Wiedrich et al.
3.
Chemical Shiit in ppm from HMPA
2. 1
COT
1
or [ 1 6 l a n n u l e n e
I
1' ci1 ' ,
NMR
2.
tubes
Flgure 1. Apparatus used to generate the dianion of COT and [ 161annulene for NMR anaysis. The HMPA was distilled Into the apparatus from the vacuum line and the apparatus sealed from the line. The annuiene solution was then piaced in contact with the alkall metal mirror, which was previously produced by dlsMng the sodium from bulb A to bulb B and sealing A from the apparatus. The ESR signal could be monitored as the reduction proceeded wlthout dlslodglng the alkall metal salt by using the ESR tube. After complete formation of the dlanion, an NMR sample was taken, and bulb B was sealed from the apparatus. The apparatus was then inverted to mix the salt wlth the solution. After dissolution of the salt, the second NMR sample was taken.
012
O! 4
[K'lx 10
Flgure 3. Plot of the chemical shift of the COT dianion relative to the high-field line of HMPA vs. the concentration of added potassium perchlorate.
3.01 ppm
i
-5
I n Kd
-6
Figure 4. 'H NMR spectra of the COT dlanlon free from ion association (upper) and a sample containlng 0.2 M potasslum cation. Note the upfield shift due to the formatlon of COT2-,K+.
-7
1.6
1.8 IO~IRT
Flgurr 2. Representative van't Hoff plots for the dissoclation of the COT2-,K+ complex. Each line was obtained from a separate sample and standard. The enthalpy reported in Table I1 is an average of 10 such plots.
Hoff plot generated for it (Figure 2). The errors reported for the enthalpies of ion-pair dissociation represent the standard deviations from the several van't Hoff plots generated. The thermodynamic parameters controlling the dissociation of the COT2-,M+complex are given in Table 11. The addition of alkali metal salts did not result in any change in the ESR parameters (g value or coupling constant) for the anion radical. This, of course, should be the case since the cation only ion associates with the dianion.
The fact that the cations are indeed complexing with the dianion of COT was verified by monitoring the chemical shift of the COT dianion as alkali metal cations were added to the solutions. Figure 3 shows that the chemical shift of the COT dianion measured from the high-field line of HMPA decreases as the concentration of potassium perchlorate is increased in the solution. This decrease in the lH NMR chemical shift verifies the formation of the COT2-,M+complex (Figure 4). The addition of lithium perchlorate or potassium perchlorate to solutions of the [16]annulene anion radical does not result in a change in the ESR signal intensity nor is there any change in the proton chemical shifts for the dianion (Figure 5). This means that the equilbrium shown (7)Szwarc, M.In 'Ions and Ion Pairs in Organic Reactions";Szwarc, M.,Ed.; Wiley: New York, 1974;pp 94-6. (8) Hirota, N. J. Phys. Chem. 1967, 71, 127.
The Journal of Physical Chemlstty, Vol. 87, No. 4, 1983 581
Thermodynamics of Ion-Pair Dissociation HMPP
internal
protons
8.77
1
7.39
-7.97
'; I
Figure 5. 'H NMR spectrum of the dianlon of [ ldlannubne In HMPA and free of ion associatlon. Neither the internal nor the external proton chemical shifts vary with the addition of alkali metal salt. However, the external protons are shifted upfiekl and the internal protons shifted strongly downfield relatlve to this system in tetrahydrofuran where ion associatlon takes p1ace.l'
is shifted far to the right. This is especially true, since the internal protons at -8.37 ppm relative to MelSi should be very sensitive to ion-pair formation. Clearly, the large ring system of [16]annulene has such a small charge density that the Coulombic attraction between it and the cation is not sufficient to result in ion association.
T h e most surprising aspect of the results shown in Table I1 is the fact that the enthalpies of ion-pair dissociation ~~~~
(9) (a) Stevenson, G. R.; Echegoyen, L.; Lizardi, L. R. J. Phys. Chem. 1972, 76,2058. (b)Stevenson, G. R.; Alegria, A. E. Ibid. 1973,77,3100. (10) Stevenson, G. R.; Alegria, A. E.; Block, A. McB. J. Am. Chem. SOC.1976,97,4859. (11) The internal protons are 0.4 ppm downfield from where they are found in tetrahydrofuran, where the dianion is associated with cations.I2 (12) Oth, J. F. M.; Bauman, H.; Gilles, J. M.; Schroder, G. J. Am. Chem. SOC.1972,94, 3498.
are positive. For the systems where anion radicals are associated with the cations, the ion-pair dissociations are exothermic without exception.''^^ This is also the case in HMPA.SJOThe negative enthalpies of ion-pair dissociation result from better solvation of the unassociated ions relative to the associated species. This increase in solvation is more than enough to make up for the Coulombic energy gain due to the separation of the cation and the anion. However, when a dianion replaces the anion, the loss of Coulombic relaxation due to separation of the dianion and the cation cannot be offset by the better solvation of the unassociated ions. The explanation for this is twofold (1) the negatively charged ion associated species (COT2-,M+) is appreciably solvated, even in comparison with the unassociated ions; and (2) the Coulombic relaxation obtained for the interaction between the dianion and the cation is much greater than that obtained between an anion radical and a cation. The fact that there is more ordering of the solvent by the unassociated ions is evident by the negative entropies of ion-pair dissociation. This effect of solvent ordering upon ion-pair dissociation is greater for the lithium system than for the potassium or cesium systems. This is consistent with the observation that the lithium complex dissociates in a thermoneutral fashion as opposed to the endothermic nature of the other ions. The very small endothermic enthalpies of dianion-cation dissociation are not sufficient to necessitate a meaningful correction of the disproportionation and comproportionation values previously reported for the COT systems in HMPAS3
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this work. We also thank the National Science Foundation (Grant CDP-8000535)for the purchase of the computer and data acquisition system. Registry No. [BIAnnulene, 629-20-9; [16]annulene, 3332-38-5; COT2-,Cs+,84170-83-2; COT2-,Li+, 84170-84-3.
