GERALDR. STEVENSON AND JESUS GILBERTO CONCEPCT~N
2176
Thermodynamic Parameters for the Cyclooctatetraene Anion Radical Disproportionation as a Function of Ion Pairing in Hexamethylphosphoramide by Gerald R. Stevenson* and Jesus Gilbert0 Concepcih University of Puerto Rko, RW Piedras, Puerto Rico
00961
(Received February 4, 1972)
Publication costs assisted b y the University of Puerto Rico
The thermodynamic parameters controlling the cyclooctatetraene anion radical, dianion, neutral molecule disproportionation equilibrium constant have been studied in hexamethylphosphoramide. It has been observed that K,, varies with the counterion, and this has been attributed to the entropy and not the enthalpy term. The thermodynamic parameters show that the potassium cation is not solvated as well as the sodium cation by hexamethylphosphoramide. This is the first report of ion pairing for hydrocarbon anion radicals in hexamethylphosphoramide.
Electron spin resonance (esr) spectral parameters for organic anion radical solutions are strongly influenced by ion pairing. Conductivity measurements carried out on these solutions also are often indicative of ion pairing.2 However, when the esr spectral parameters (coupling constants and line widths) are independent of gegenion and there is no evidence for ion pairing in conductivity measurements, the ions involved are considered to be free ions or fully dissociated ions. Hydrocarbon anion radicals are considered to be fully dissociated in hexamethylphosphoramide (HMPA), since HMPA has been recognized to be the most powerful solvating agent for alkali metal ion^.^,^ Thermodynamic parameters controlling reaction equilibria and activation parameters controlling reaction kinetics might be more sensitive functions of ion pairing than esr parameters or conductivities. The equilibrium constant for the cyclooctatetraene (COT) anion radical disproportionation reaction (eq 1)has been quan-
titatively observed in tetrahydrofuran5and liquid ammoniaS6 In the latter solvent the equilibrium constant was found to vary by a factor of a million with the alkali metal. Here we report the equilibrium constants and the thermodynamic parameters controlling the disproportionation equilibrium (eq 1) as a function of counterion in HMPA to determine if hydrocarbon anion radicals in HRlPA are really free ions or if esr parameters are simply too insensitive to detect weakly associated ions. The energies of activation and the rate constants for the electron transfer reaction between the dianion and anion radical (eq 2) have also been investigated for
several COT-HMPA-metal systems. The Journal of Physical Chemistry, Vol. 76, No. 16, I978
Experimental Section X-Band esr spectra were recorded using a Varian E-3 esr spectrometer. The temperature was controlled using a Varian V-4557 variable temperature controller. Kmr spectra were recorded at room temperature using a Varian T-60 spectrometer. Line widths of the nmr line at half-height due to electron transfer were determined from the measured line width minus the line width of the dianion in the absence of anion radical. The HMPA was dried with potassium metal in bulb b (Figure 1) and was distilled into bulb a which contained a known amount of alkali metal. This distillation was carried out at 10-4 mm of Hg, and bulb a was kept in a Dry Ice-acetone bath (- 78"). A weighed portion of degassed COT was then distilled into bulb a from the vacuum line. With both stopcocks closed the mixture in bulb a was allowed to warm to room temperature, and the alkali metal dissolved to form the COT dianion and anion radical. Nmr and esr samples of this solution were made by taking an aliquot of the solution into the side arm (c). The anion radical concentration was determined using the system COTTHF-Li as a spin concentration standard as previously described.6 Results Solutions of COT in HMPA will dissolve small amounts of alkali metals to form the COT dianion and (1) (a) N. Hirota, J . Phys. Chem., 71, 127 (1967); (b) M . C. R . Symons, ibid., 71, 172 (1967); (c) N. Hirota, J . Amer. Chem. Soc., 8 9 , 32 (1967). (2) (a) E. Grunwald, Anal. Chem., 26, 1696 (1954); (b) S. Winstein, E. Clippinger, A . H . Fainberg, and G. C. Robinson, J . Amer. Chem. Soc., 76, 2597 (1954). (3) G. Levin, J. Jagur-Grodzinski, and M. Sswarc, ibid., 90, 6421 (1968). (4) H. Normant, Angew. Chem., Int. Ed. En&, 6 , 1046 (1967). (5) H . L. Strauss, T. J. Katz, and G. K . Fraenkel, J . Amer. Chem. SOC., 85, 2360 (1963). (6) F. J. Smentowski and G. R. Stevenson, J . Phys. Chem., 73, 340 (1969).
DISPROPORTIONATION 1~ N I O NRADICAL CYCLOOCTATETRAENE
2177
to vacuum l i n e
L eC
\
1
Figure 1. High-vacuum apparatus for reducing COT in HMPA. Inlets e and d allow addition of the alkali metal; they are subsequently sealed off.
'%T
Figure 2. Plot of In (ZAw2) us. 108/RT for the system COT-HMPA-Li.
anion radical. These solutions yield the expected nineline esr pattern for the COT anion radical. The proton coupling constant of 3.18 f 0.01 G is independent of the alkali metal used (K, Na, or Li). The disproportionation equilibrium constant is a function of the alkali metal counterion. For the systems COT-HMPA.-Li, COT-HMPA-Na, and COT-HMPAK the equilibrium constants are 5 X 2 X and 2 X lob5,respectively. It is surprising that the value for sodium does not lie between those for lithium and potassium. Rieger, et a1.,7 have shown that ion pairing shifts the disproportionation equilibrium to the left (eq 1 ) . Since the value for sodium is larger than that for the other two metals, the sodium ion must be better solvated in HMPA. There is less ion pairing for the sodium reduction than for either the potassium or lithium reduction. Assuming a Lorenzian line shape, the anion radical concentration is proportional to the esr peak height ( I ) times the square of the extrema to extrema line width (Aw). The equilibrium constant can then be expressed as shown in eq 3, where B is simply a proportionality IC
-
1 0 1Dl L
- I L
(3)
4
Table I : Thermodynamic Parameters for the COT Disproportionation Equilibrium in HMPA a t 25" Metal
Li Na K a
AGO,
AH',
ASO,
kcal/mol
kcal/mol
cal/deg mol
4.5 i 0.3a -7.8 f 1 3 . 6 k 0 . 3 -4.233 0.3 6.3 zk 0.2 -4.6 f 0.7
Kes
-29 i 2 (5.0 i 2) X low4 - 2 6 i 1 (2.3 f 1) X 10-8 -46 zt 1 (2.3 f 1) X lom6
All errors are standard deviations.
units. The entropy term for the sodium reduction is larger than for either of the other two systems. This indicates that the sodium ion does not associate with the dianion and anion radical as strongly as does the potassium ion. The equilibrium constants indicate that ion pairing follows the order: K > Li > Na. When two moles of potassium react with one mole of COT in HMPA, no esr signal is obtained, but this solution gives a sharp singlet upon nmr analysis at 5.9 ppm due to the dianion. Addition of small amounts of COT neutral molecule broadens the dianion line. The rate constant for the electron transfer (eq 2) can be estimated with the use of eq 4, where 6w is the esr
constant.
A simple revised van't Hoff plot of In should yield a straight line with a slope of -AH0/2 (Figure 2). For all three systems a straight line was obtained. The corresponding thermodynamic parameters are shown in Table I. From Table I it is clear that the variance of K,, with counterion is mainly due to the entropy and not the enthalpy term. Comparing the systems COT-HMPAK and COT-HMPA-Na, we see that the enthalpies are almost identical, but the entropies differ by 20 entropy
(law2)vs. 1/RT
2xAv =
(4)
hyperfine splitting constant in radians per second, (7) R. D. Allendolfer and P. H. Rieger, J. Amer. Chem. SOC.,87, 2336 (1965). The Journal of Phgsical Chemistrg, Vol. 76, No. 16, 1978
T. DRAKENBERG, K.-I. DAHLQVIST, AND S.F O R S ~ N
2178
Av is the half-height line width due to electron transfer, and k is the second-order rate constant.8 The rate constant for the system COT-HMPA-K is about lo4 l./mol sec. This is a very slow electron transfer relative to the vaIues found in liquid ammonia9 and for the system COT-THF-K,5 all of which have a rate constant greater than lo8. The slow rate of electron transfer for the HMPA system is presumably due to the,relatively high viscosity of this solvent. The energies of activation for all three systems were obtained from a plot of In ( w ) us. l/RTIO and are 0.92 0.03, 1.2 f 0.1, and 1.51 f 0.1 kcal/mol for the systems COT-HMPA-Li, COT-HMPA-Na, and COT-HMPA-K, respectively.
function of metal ion association. Ion association has been found even in HMPA where only free ions were thought to exist. No set of esr spectral parameters or conductivity measurements has been able to detect this ion association of cation and hydrocarbon anion radical in HMPA. Further, small differences in the energies of activation for the electron transfer reactions have been observed as a function of the counterion.
Conclusions
(8) T. J. Katz and G. K. Fraenkel, J . Amer. Chem. SOC.,82, 3784, 3785 (1960). (9) F . J. Smentowski and G . R . Stevenson, ibid., 91, 7401 (1969). (10) F . J. Smentowski and G . R . Stevenson, ibid., 89, 5120 (1967).
The disproportionation equilibrium constants for the COT-solvent-metal systems are a very sensitive
Acknowledgments. The authors gratefully acknowledge support of this work by Research Corporation. We wish to thank Dr. Luis Lizardi for helpful discussion.
The Barrier to Internal Rotation in Amides.
IV. N,N-Dimethylamides;
Substituent and Solvent Effects by Torbjorn Drakenberg,* Kjell-Ivar Dahlqvist, and Sture Forsen Division of Physical Chemistry, The Lund Institute of Technology, Chemical Center, P.O.B. 740, 8-290 07 Lund 7 , Sweden (Received November 17, 1971) Publication costs assisted by The Lund Institute of Technology
Activation parameters for internal rotation about the N-CO bond in several N,N-dimethylalkylamides, in various solvents, have been determined by the pmr total line shape technique. The effect on the torsional barrier of variations in the alkyl group as well as the solvent have been found to be significant; the origin of these effects is discussed. Additionally, the results of extended Huckel theory calculations of the N-CO torsional barrier are presented.
Introduction The hindered internal rotation of the dimethylamino group in substituted amides (X = 0) and thioamides (X = S) has been shown by nuclear magnetic resonance (nmr) spectroscopy to be strongly dependent on
the nature of the substituent, R.’j2 Thus, the magnitude of the torsional barrier is found to be lowered when R is electron donating (for example, CHIO-, CH&-, or R-C=C-) and raised when R is electron withdrawing (for example, K=Cor EtCO-). For N,N-dimethylamides the major influence of R , The Journal of Physical Chemistry, Vola76, No. 16, 1972
where R is an alkyl group such as CH,-, CH,CHZ-, (CHa),CH-, or (CH&C-, on torsion about the N-C(0) bond may be assumed to arise from the following interactions: inductive, steric, and hyperconjugative. Relative to N,N-dimethylformamide, each of these effects is expected to lower the amide rotational barrier. Inductive and steric influences increase while hyperconjugative influences decrease, in the order: CHa-, CHaCHr, (CH,)ZCH-, (CHa)sC-. The purpose of the present work was to study quantitatively the influence of various alkyl groups, and addi(1) C. W. Fryer, F. Conti, and C . Franconi, Ric. Sci., Parte 9,Sez. A , 35, 788 (1965). (2) J. Sandstrom, J . Phys. Chem., 71, 3218 (1967).
