March, 1963
NOTES
If magnesium or barium bicarbonate complexing occurs, and is assumed to be due to the formation of one or more complexes of the type M(HC03)n2” (M = Mg or Ba) ; the total extent of the complexing may be derived from the equation for electrostatic balance
0.37. The corresponding pK value for the thermodynamic dissociation constant is 0.86; a value within the limit of error of the present determination.
5
nmhr(HcoI),2-n
n=l
= 2maB,
+
m1i+
- rnIlc0,- (3)
mHCOI - was calculated directly from measured pH values by assuming PCO,= fco, = 1 atm., and using Latimer’s6pKl value of 6.38 for carbonic acid. Activity coefficients for H + and Mg++ were calculated from published T~ values for KCl16HCl,? and MgC12,7using the assumption that T&KC1 = yc1- = TK+. Values used for 7 ~ ~ 0are , -those determined by Walker, et aL18 from KIIC03 solutions. Complexing of magnesium with bicarbonate was found to occur because the sum expressed by the righthand side of eq. 3 (column 7, Table I) was positive, even with the initial absence of Ba(OH)2. From Table I the following data may be noted as Ba(OH)2was added: (a) No significant variations in p , ( b ) m B a , , m H c o I - , and e n m M ( I I C O I ) n l - n increased n=1
by more than two orders of
~
ON T H E ORIGIN OF T H E DIPOLE MOMENT OF TETRAZOLES BY JOHNB. LOIJNSBIJRY~ Deparfment of Chemzstry. IUtnoia Institute of Technology. Chtcaoo 16. lllanois, and I B M Development Laboratoru, Pouahkeepeie, New York
Received September 64, 195.8
The various substituted tetrazoles have received much attention with regard to activity upon the central nervous system.2 I n an examination of possible relationships betwecn dipole moments of these compounds and their physiological activities, it has been rcmarkcd that (‘ . . . the origin and nature of the tetrazole ring moment still is incompletely under~tood.”~With regard to this comment, a theoretical examination of the dipole moment of tetrazole has been undertkcken. A further point of consideration for the present study has The been the uncertainty of the tetrazole ~ t r u c t u r e. ~ location of one of the hydrogens is not known, either of the structurcs I or I1 being possible. It is concciv-
magnitude a t approximately the same rate, and, (c) slightly by dilution. Since, a t constant
H \1 5 Tu’-C
m h f g b decreased
1 ?nbf (HCOl).2-n
a
(mbr + +)( m t l c o ,
-1
n
MgHCOd+J_ hIgC030
+ H+
(5)
Grcenwald’s2experiments were conducted a t a nearly constant p of 0.15, and a t this p ((YH+) ( m M ~ O P ) / ( m g H C O , + )
= 10-8*oo (6)
The corresponding value of (6) assumed by Greenwald2 was 10-8Jo,which he used to calculate a concentration quotient for MgHCOa+of 0.17. If the value of 10-8JQis used instead, the concentration quotient is (6) W. M. Latimer, “Oxidation Potentials,” Second Ed., Prentice-Hall, New York. N. Y.. 1952, pp. 135, 355. (7) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” Third Edition, Reinhold Publ. Corp., New York, N. Y. 1958, pp. 252, 716, 738. (8) A. G. Walker, V. B. Bray, and J. Johnston, J . Am. Chem. Soc., 49, 1236 (1927).
/
(4)
and m M + + E V L M ~ (the ratio of complex M to hl, is low), it can be seen that only an MgHC03+ model and no Ba(HCOJn2-n model nor Mg(HC03)n2-n (n > 1) model is consistent with conditions (b) and (c) and proportionality (4) above. The PKdiss values for MgHC03+ given in Table I are calculated thermodynamic dissociation constants. It was assumed that for these relatively dilute solutions ~ M ~ I I C O=~ +T H C O ~ - . The six tabulated values yield an average pKdlssvalue of 1.00,but the last pK valuc shown (pK = 1.24), corresponding to the largest amount of added Ba(OH)2, is significantly higher than the othcr five values, and may reflect thc formation of a modest amount of BEL(HCO~),~-”.hvcraging the five othcr values leads to a PKdiss value of 0.95 f 0.1. Using a pKdiss value of 3.406 for MgC030 yields an equilibrium constant of 10-7.sG for the reaction
721
7
\
2N
N4
1 5 N=C
\
2 / H-N
\/
7 N4
\/
N 3
N 3 I1
I
able that a tautomeric equilibrium might exist between structures I and 11. Both of these structures have been considered in the prcscnt study.
Theory
It is customary to construct molecular dipole moments by vectorial summations of dipoles associated with bonds, those associated with the polarization of non-bonding electrons and the dipolcs arising from asymmetry of the distribution of delocalized (pi) electrons.6 I n this study the bond moments for the sigma bonds in the ring have been taken to be zero. This has been done previously for the C-N and C-C bonds in pyridinea and pyrrole.’ This is esscntially an assumption that electronegativity differences of ring atoms are accommodated exclusively by the mobile pi electrons. The moment of the C+-H- bond has been taken as 2.23 D., which is the value calculated by Hameka and Liquorie for pure sp2 hybridization on carbon. The value of the N+-H- dipole moment used is the 1.64 D. value calculated by Hamano and Hameka7 for the N-H bond in pyrrole. (1) IBM Predoctoral Fellow at I.I.T. (2) F. W. Schueler, 9. C. Wang, R. M. Feathetone. and E. G. Gross,
J. Pharmacol. Ezptl. Therapy, 97, 266 (1949). (3) A. I. Popov and R. D. Holm, J. Phye.
Chcm.,
66, 158 (1962). (4) M. H. Kaufman, F. M. Ernsherger, and W. 8. McEwan, J. Am. Soc., 78, 4197 (1956). (5) See, for example, R. Daudel, R. Lefebvre, and C. Moser, “Quantum Chemistry,” Interscience Publ., New York, N. Y., 1959, pp. 201-213. (6) H. F. Hameka and A. M. Liquori, Mol. Phua., 1, 9 (1958). (7) H. Hamano and E. F. Eameka, Tetrahedron. 18, 985 (1962).
Chem.
NOTES
722
The lone pair dipole moments on the pyridine type nitrogens has been handled by the procedure developed by Hameka and Liquori.61* If the hybridized lone pair orbital is normalized to unity and defined by eq. 1, then the lone pair dipole will point in the x-direction,
+ bpXN
(1) and the moment is given by eq. 2. The functions SN ~ L P= a S N
= 4ab
f .siyxpx~d r
):(
'/z
(2) and p , ~ are the Slater type orbitals defined by eq. 3. PLP
pxN
=
x exp (--
Hameka and Liquori take bN = 1.95 according to the Slater-Zener r u l e ~ . ~Thus ~ l ~ p ~ is p found to be given by eq. 4. If it is assumed that the state of hybridizapLP
=
4ab
2fN
dii-(4.80) (0.5292) = 7.521ab D.
(4)
tion of the two bonding orbitals on the nitrogen of interest are equal and that these hybrids lie along the lines connecting this nitrogen with the two bonded neighboring nuclei X and Y, Hameka and Liquoris have shown how the values of a and b depend on the state of hybridization of the lone pair orbital. The values of a and b are given by eq. 5, where # is the X-N-Y angle. When 4 = 120' there is pure sp2 hy-
bridization on the nitrogen and pLP = 3.55 D. The p obtain is 3.76 D. at 4 = 109' largest value p ~ can 28' 15". The value of PLP is not a very sensitive function of # around this maximum, and the value may be taken as 3.69 f 0.07 D. for 103' 6 4 6 116'. The pi electron distributions were calculated using the I.I.T. SCF-MO Univac 1105 computer program.11 The details of this program and the parameters it utilizes are thoroughly discussed in the indicated references and will not be repeated here. It is worthwhile to note that, using the pi electron distributions obtained by WIiller, et aZ.,ll" very good theoretical values for the dipole moments of pyridine and pyrrole are realized. I n the case of pyridine, a dipole moment due to the pi electrons p, = 0.60 D. is found, which points in the same direction as the lone pair moment and opposes the net C +-H- moment (calculated using the pyridine geometry of Bak, et a1.I2)of 2.18 D. Thus p = pr PULPJLCH = 0.60 3.69 - 2.18 = 2.11 D. This compares favorably with the experimental valuel8 of 2.15 f
+
+
(8) H. F. Hameka and A. M. Liquori, Proc. Koninlcl. Ned. Akad. Wetenschap., BS9, 242 (1956). (9) J. C. Slater, Phys. Rev., 36, 57 (1930). (lo) C. Zener, ibid., 36, 51 (1930). (11) (a) 0. W. Adams, Ph.D. Thesis, Illinois Institute of Technology, 1961; (b) 0. W. Adams and P. G. Lykos, J. Chem. Phys., 84, 1444 (1961); ( c ) R. L. Miller, P. G. Lykos, and H. N. Sohmeising, J. Am. Chem. Soc., 84, 4623 (1962). (12) B. Bak, X. Hansen-Nygaard, and J. Rastrip-Andersen, J. LMoZ. Spectru., 2, 361 (1968). (13) B. B. DeMore, W. S. Wilcox, and J. H. Goldstein, J. Chem. Phgs., a2, 876 (1954).
Vol. 67
0.07 D. For pyrrole p, = 1.25 D. is obtained which is in the opposite direction of the N+-H- moment and in the same direction as the net C+-H- moment of 2.24 D. (calculated using the pyrrole geometry of Bak, et ~ 1 . l ~ ) Thus . p = 1.25 - 1.64 2.24 = 1.85 D., in good agreement with the measured value15 of 1.84 f 0.08 D.
+
Results and Discussion The tetrazole geometry was approximated by a regular pentagon with sides of 1.32 A. since no experimental information regarding the geometry of unsubstituted tetrazole was found in the literature. The molecule is assumed to be planar, although this may not be correct for the N-H bond. The pi electron distributions found for structures I and I1 are given in Table I. This leads to values of the pi moment of pnl = 1.17 D. and prll = 0.49 D. If the x-axis selected passes through ring positions 2 and (3 and the y-axis through ring position 1, then the directions of pi moments are such that the 2 and y components are those given in Table 11. Also given in Table I1 are the x and y components of the C+-H- moment, the net lone pair moment, and the N*-H- moment. The individual x and y components are summed to give those components of the total dipole moment. The total dipole moments calculated for the two tetrazole structures are PI = 5.22 D. and = 1.63 D. The experimental dipole moment of tetrazole is 5.11 D. TABLE I SCF-MO PI ELWTROX DISTRIBUTIONS IN TETRAZOLE~ Position
Structure I
Structure I1
1.7447 1.2489 1 1.7050 2 1.2260 0.9331 1.0767 3 4 1.2412 1.1367 0.8328 5 0.8550 a Tetrazole assumpd to be planar and to have a regular pentagon geometry with 1.32 A. sides.
TABLE I1 COMPONENTS OF THE DIPOLEMOXENT OF TETRAZOLE~ --Struoture x-Component
--I y-Component
--Structure x-Component
I1-y-Component
0.69 0.69 2.12 2.12 -1.56 0.51 1.64 0 -2.29 -4.84 0 -3.51 PLP Plr -0.49 -1.06 0.45 -0.19 -1.28 -5.21 I .01 -0.24 Ptotal a x-Axis taken to pass through ring positions 2 and 5, y-axis to pass through ring position 1. Tetrazole assumed Lo have a regular pentagon geometry and to he planar. PGH
#NH
It is felt that these results are of considerable value in representing the gross features of the origin of the dipole moment of tetrazole. The close agreement of the theoretical and experimental dipole moments of pyridine and pyrrole should not be taken to indicate that a similar close agreement necessarily exists between the theoretical and experimental values for tetraeole. This is especially true considering the uncertainty in the tetrazole geometry. The results show that a large (14) B. Bak, D. Christensen, L. Hansen, and 3. Rastrip-Andersen, ibid., a4, 720 (1956). (15) A. D. Buokingham, B. Harris, and R. J. LeFevre, J. Chem. Soe., 1623
(1953). (16) X. A. Jensen and A. Friediger, Kgl. Danske Videnslcab. SeZskab. Mat.-Fys. Medd., 20, (20) 1 (1943).
March, 1963
COMMUNICATION TO THE EDITOR
part of the difference in the dipole moments of 1- and %substituted tetrazoles lies in the difference in the vectorial sums of the lone pair moments and the sigma bond moments, these moments more nearly canceling each other in the case of 2-substitution. A much smaller part of the difference is due to the reduced pi moment of the 2-substituted compounds. Although the accuracy of the calculated dipole moments does not warrant it, and although the existence of a tautomeric equilibrium between structures I and I1 has never been demonstrated, it is of interest to calculate an equilibrium constant between structures I and 11, if for no other reason than it is not known that this has ever been done before for tetrazole. It is found that, for a mixture of I and I1 to produce an apparent dipole moment of 5.11 D., K,, = [I]/[II]= 31.3, which corresponds to tetrazole existing as 97% in form I. Considering the probable numerical accuracy, this calculation may be considered consistent with tetrazole existing exclusively
723
in the 1-protonated tautomer. This predominance of structure I is in agreement with the results of a recent n.m.r. study17 of the chemical shifts of the carbon bound proton on the tetrazole ring in tetrazole and N-alkylated tetrazoles. It is also consistent with the observation4 that 1-ethyltetrasole has a dipole moment of 5.64 while 2-ethyltetrazole has a moment of 2.64 D. Acknowledgment.-Thc author is indebted to Dr. P. G. Lykos of this Laboratory for suggesting this problem and for encouragement and advice during the study. The author wishes to thank Drs. It. L. Flurry and R. L. Miller of this Laboratory for many stimulating discussions, This work was carried out with a generous grant of computer time by the Illinois Institute of Technology. The author is especially indebted to the International Business Machines Corporation for a fellowship from the IBM Special Education Program. (17) 13. W. Moore and A . G. Whittaker, J . A m . Chem. Soc., 81, 5007 (1060).
COMMUNICATION TO THE EDITOR RELATIVE MOBILITIES O F LIKE-CHARGED IONS I N FUSED SALTSa
Sir: We wish to call attcntion to an observation, based on results of other workers as well as our own experimental data, that appears sufficiently general to warrant consideration in any attempt to understand the mechanism of ionic transport in fused salts. Our experiments were initiated in an effort to throw light on the reasons for the characteristic behavior of conductivity isotherms in fused salt mixtures. The equivalent conductance generally is found to deviate negatively from additivity of the pure salt values. l b Because this behavior is particularly striking in the case of LiC1-KC1 mixtures, we have been running Hittorf-type transference experiments to determine the relative mobilities of the two cations a t various concentrations. Electrolysis between chlorine electrodes is carried out in accordance with experimental procedures analogous to those described elsewhere for this type of experiment.2 By choosing the common ion (in this case chloride) as reference, we can use the results of such experiments t o compare the two cation m~bilities.~A useful quantity for this purpose is the per cent mobility difference 10O(pl3- p 2 3 ) / p 2 3which is equal to [100(4] - E1)/4,E1],and thus indepcndeiit of the conductivity of the mixture. Here El is the equivalent fraction of the faster-moving ion and 42 (= 1 - 41) is the quantity designated 4 by h i x aiid Wetmore.2b The latter quantity has been represented by P el~ewhere.~ (1) (a) This work is supported by a contract with the U. S. Atoiiiic Energy Commission. Financial assistance from a National Science Foundation pre-doctoral fellowship is also gratefully acknowIedged. (b) See, for example, R. W. Laity, J . Chem. Bduc., 39, 67 (l902), and references cited therein. (2) (a) A. IClemm, 11. IIintenberKer, and 1’. lioernes, Z. h’alur/uwch., 2% 245 (1947); (b) P. M. Aziz and F. E. W.Wctinoro, Can. J . Chem., 30, 770 (1952). (3) R. W.Laity, J . Chem. I’hyx., 30, 082 (1959); A n n . A’. Y . Acad. Sci.. 79, 997 (19GO).
Our preliminary results (described below) immediately recalled the corresponding observations of Duke and Victor4 on the system LiNOS-.KNO3, and prompted a search of the literature for all data indicative of relative mobilities of like-charged ions in binary fused salt mixtures. What follows is summary of our findings. Hittorf-type experiments have yielded the following results. LiC1-KC1.-At 2.2 mole per cent KCl Klemm and co-workers2a found the lithium ion more mobile than potassium by about 15%. Our results are in good agreement here, but are also consistent with the rather surprising observation of Chemla and coworkers5 on relative cation mobilities in the LiBr-KBr and NaBrKBr systems. These workers reported that in spite of the substantially highcr conductances of the pure salts LiBr and NaBr, I
