c
I
0
2.00
I
I
400
I
I
I
I
I
I
I
I
I
600
800 1000 1200 1400Trn,OK Fig. 1.-Energies of activation for diffusion against melting temperature. Sources of data: Nitrates, $, S. Dworkin, R. B. Escue, and E. R. Van Artsdalen, J . Phys. Chem., 64,872 (1960) ; T1 in TlCI, E. Berne and A. Klemm, 2. Natigjorsch., 8a, 400 (1953); PbClZ, G. Perkins, R. B. Escue, J. F. Lamb, and J. W. Wimberley, J . Phys. Chem., 64, 1792 (1960); Na, Rb, CsC1, reference 1; Ca, Sr, BaCI,, S. R. Richards, Ph.D. thesis, University of Pennsylvania; NaI, S. B. Tricklebank, L. Nanis, and J. O'bl. Bockris, to be published; Ar, Kr, Xe, J. Naghizadeh and S.A. Rice, J . Chem. Phys., 36, 2710 (1962); Hg, Ga, N. H. Kachtrieb and J. Petit, ibid., 24, 746, 1027 (1956); K, J. Rohlin and A. Lodding. Z. iyaturforsch., 17a, 1081 (1962); Na, R. F. Meyer and N. H. Kachtrieb, J . Chem. Phys., 23, 405, 1861 (1955); In, A. Lodding, Z. Naturforsch., lla, 200 (1956); Sn, G. Careri, A. Paoletti, and XI. Vicentini, Nvoz;o Cimento, 10, 1088 (1958); Zn, W Lange, W. Pippel, and F. Bendel, 4. physik. Chem. (Leipzig), 212,238(1959); Ag, L. Yang, S. Kado, and G. Derge, Trans. Am. lnst. X i n i n g , M e t . Petrol. Eng., 212, 628 (1958); Cu, J. Henderson and L. Yang. ihid., 221, 72 (1961); CO in Fe, D. W. Morgan and J. A. Kitchener, Trans. Faraday Sac., 50, 5 i (1954).
where T , is the melting temperature. Evidence in support of this relation was adduced in terms of the data available for molten salts. The available data for a wide class of materials have been now used to test eq. 1. Results are shown in Fig. 1. (The data for cobalt in iron, m.p. 1808'K., also fit the relation.) It should be noted that no empirical factors are involved. The numerical constant in eq. 1 is bounded from theoretical considerations3 by the limits 3.5 to 3.8. The relation in eq. 1 implies that the heat of activation for movement of particles from one site to the next is insignificant in comparison with that necessary for hole formation. Hence, it would not be expected t o apply to associated liquids. For virtually all the molten salts examined, the cations and anions have equal energies of activation within experimental error for 9 out of 12 cases. The several theories of self-diffusion in liquids yield the result that the pre-exponential factor in theoretical equations for D is independent of the model and of the substance considered to within f100%. Hence, an order of magnitude calculation for any nonassociated liquid may be made from F. H. Stillingrr in "SPlected Topics in Nolten Salt Cheniistry," M. Blander, Ed., Interscience Publishers, Inc., New York, Ii.Y . , 1963. (3)
The widespread nature of the consistency shown by experimental data with eq. 2 offers strong support for the applicability of Fiirth's theory for transport properties in nonassociated liquids. Acknowledgment.-The authors wish to thank the Atomic Energy Comniission for financial support of this work under Contract No. AT (30-1)-1769. RATE OF ELECTRON EXCHANGE BET\Y'EES B,B'-BIPYRIDINE AND B,%'-BIPYRIDINE NEGATIVE ION1 BY RARREX L. REYNOLDS Chemzstrg DepaTtment, UnwersPtpl of Mtnnesota, Mznneapolm, IM7nnesofa
Recezved July 16,1963
A number of electron transfer reactions between various organic radicals and their parent compounds in the presence of inorganic cations, usually alkali metal ions, have been studied The activation (1) Work performed a t ITashinston University. St. Louis, $50. ( 2 ) R. L. Waid and S.I. Weissman, J. A m . Chem. Sac., 79, 2080 (1957) ( 3 ) P. 1. Zandetra and S. I. Weissnlan, zlrzd., 84, 4408 (1962).
NOTES
Dec., 1963
2867
6,6
6,4
6,2
u'
g
-
6,O
5,8
5.4 3,4
36
35
3.7
3,8
3,9
103 WT).
Fig. 2.--Plut
H--+ Fig. I.-Central-lines in K + bip- spectra, 0": (a) absence of bip; (b) 0.468 M bip; (e) 1.00 M bip.
energies found have varied from a few kcal. inole-l to approximately 18-19 kcal. mole-I. Those reactions with low activatioiz energies have rates which are near those expected for diffusion controlled proce~ses.~J Those which have larger activation energies and which involve an ion pair are thought to proceed through a metal ion bridged activated ~ o m p l e x . ~I n this respect it was of interest t o study ai1 analogous electron transfer reaction using ai1 organic inolecule with strong chelating properties such as reaction 1
K + bip-
+ bip + bip 3. E(+ bip-
(1)
between 2,2'-bipyridine and the ion pair formed by K + and 2,2'-bipyridine negative ion, K + bip-. Experimental Reagents.-The solvent 1,2-dimethoxyethane (DMIE) was prepared as described by Jones and Weissman.* 2,2'-Bipyridine, obtained from Matheson Coleman and Bell, from G. Frederick Smith Chemical Co., and from Eastman Organic Chemicals, (4) M. T. Jones and S. I. Weissman, J . Am. Chem Soc., 84, 4269 (1962). ( 5 ) hTorboru Hirota, Ph.D. dissertation, January, 1963, Wafihington University, St. Louis, Mo.
of log IC us. lo3(l/T).
was twice recrystallized from water-ethanol mixtures and dried in an oven a t approximately 55". Procedure.-The negative ion was formed by pouring the 2,2'bipyridine in DME onto a K mirror under vacuum. The tube containing the metal mirror was then sealed off and the radical concentration diluted until highly resolved spectra were obtained on a 100 kc. modulation frequency e.8.r. spectrometer designed by Prof. J. Towsend of the Department of Physics, Washington University, and operated near 9000 Me. with an applied field of approximately 3200 gauss. The K+ bip- spectra were identical regardless of the source of the 2,2'-bipyridine. The K+ is regarded as associated with the bip- ion because when Na+ and Rb+ were used the spectra showed splitting by the Na+ and Rb+ nuclear magnetic moments. It may be mentioned here that the Na+ bip- spectrum obtained in DME was completely different from that which has been reported as belonging to Naf bip- ion pair in DME.6 The spectrum of K+ bipshowed no K splitting. The central line had a width between points of maximum slope of approximately 73 mgauss at O", and was sufficiently isolated to be usable for line-broadening measurements. The rate constant k of reaction 1 was calcutated,2 using eq. 2, from the line broadening produced when neutral bipyridine was added t o the K+ bip- solution from behind
k
=
1.6 X 107AH/[M]
(2)
an evacuated break seal. I n eq. 2 AH is the increase of line width, measured between points of maximum slope, produced by a neutral molecule concentration [MI. Temperatures below 20" were maintained by boiling liquid Nz through a quartz dewar surrounding the sample in the microwave cavity.*
Results Typical center lines obtained in the presence and absence of a neutral molecule are shown in Fig. 1. Each line width used in a rate determination was the average value of no less than four measurements. Seutral molecule conceiitrations of 0.183, 0.468, and 1.00 M were used except a t - 10' where only the last two conceiitrations were used, and a t -15' where only the last concentration produced a reliable increase of line width. The line width was linearly dependent on [MI. The line width was independent of negative ion (6) A. Zahlan, F. W. Heineken, 37 683 (1962).
PI.Bruin, and F. Bruin, J . Chem. Phys.,
NOTES
2868
concentration up to the point where line broadening also occurred in the absence of a neutral molecule. Therefore the reaction was first order with respect to each of the two reactants in eq. 1. The results obtained a t -1.3, -10, 0, 10, and 20" are plotted in Fig. 2. I n Fig. 2 a point gives the average rate constant and the vertical line spans the extreme values obtained a t each temperature. The activation enthalpy and entropy were 10 kcal. mole-1 and + S cal. deg. -I inole-l, respectively. It is tempting to postulate that the activated complex for electron transfer involves zt I
