962
ALECGRIMISOX
Vol. 67
THE D E U T E R I U M ISOTOPE E F F E C T IS THE HYDROGEN BONDING OF 1R.lIDAZOLE IS S A P H T H A L E S E SOLUTIOSS BY ALEC GRIMISON Chemistry Department, Uniaersity of Puerto Raco, Rio l'ieclras, P. K . Received June 16, 1.968 A study has been made of the self-association of imidazole and I-d-imidazole in naphthalene solution a t 80". Under these conditions imidazole forms linear oligomers through X-H-N hydrogen bonding. The deuterium compound is found to be less associated, b j about 8%. than the hydrogen analog. This difference is analyzed in terms of the equilibriiim constants and free-energy changes for the various association equilibria. For, e.g., dimerization the results give a AF" of -1100 cal./mole for imidazole, and a AFO of -1020 cal./mole for 1-dimidazole. This implies weaker hydrogen bonding by deuterium.
Introduction associated through X-H-N bonds in solvents which do not compete effectively for hydrogen bonding,12 and a The question of the relative strengths of the hydrogen careful spectroscopic study of the association of imidand deuterium bonds is one which has been discussed azole in carbon tetrachloridel3 has recently proved that recently in several papers, without any general linear oligomers are formed, as would be indicated on conclusion being reached. This problem is of interest steric grounds, and as previous cryoscopic work in napliin fields varying from purely cheniical kinetic and thalene14 has suggested. Also, it is known that while niechaiiist8ic studies, where deuterium substitution in deuterium exchange of the 1-position is extremely solut'e or solvent is often used to aid interpret'ation, to rapid, as expected for mi N-H proton, the exchange biological studies of the inhibition of mitosis by deuterates of the remaining C-H protons are very slovv, parrium o~ide.~-*OSome of the most importaxit recent ticularly in neutral solution. The possibility of iiievidence of quantitative significa,iiceis t,hat of Potter, ternal exchange can therefore be ignored. The associaBender, and Ritter,2Dahlgren and and P l ~ u r d e . ~ tion of imidazole and 1-d-imidazole mas therefore These data will be discussed later. studied in naphthalene solution by a cryoscopic method, The technique used by Potter, Bender, and Ritter was which satisfies the dual requirements of simplicity and to study, by means of vapor densit'y measuremeiit,s, the in the concentration range used. accuracy, relative extent of dimerization of acetic acid and deuterated acet'ic acid (actually acetic-& acid-d). The Experimental major difficult,ylies in the small magnitude of the effect Molecular weights were measured by an adaptation of the Beclimann f. p t . depression technique, but with certain alterafor the syst,ems studied, often of the same order as the tions, specifically designed to exclude moisture. Stirring was experimental error. It was felt that a more effective found to be best accomplished manually, the spiral glass stirrer approach t,o the problem was through the study of the being raised and lowered by a nichrome wire passing through a relative self-association of a highly associated system, closely fitting polytliene seal. A Beckman f. pt. thermometer forming oligomers through hydrogen bonding. It was m-as used, pasaing through a rubber bung, and capable of being read to 0.002". The freezing point cell was surrounded by an preferable for the mathemat,ical analysis of results that air jacket, this heing immersed in an oil bath, which was thermothe model system should show a linear iiicrease of assostated to within 0.05' by a Sunvic unit and intermittent heater. ciation with increasing concentration, indicating that The use of a large 11.5 kw.) main heater through a rheostat linear, rather than cyclic, polymers are being formed. allowed rapid changes in the thermostating temperature of the bath. Further, the protons other than those involved in hyThe stoppered freezing point cell, containing a weighed amount drogen bonding should be resistant to exchange by deuof naphthalene, was quic'.ly heated to about 10" above the terium, or internal deuterium exchange may necessitate melting point of naphthalene by a small auxiliary oil bath, then the study of a completely deuterated compound, as in the thermometer and stirrer assembly replaced, and the whole placed in the air jacket in the bath, which was thermostated a t t'he work of Potter, Bender, and Ritter.2 According to about 1.5" belpw the freezing point of naphthalene. The naphthe work of Halevil11this introduces tthe possibility of thalene mas allowed to cool T.T hile stirring gently, until a superchanges in t'he acid or base strength of the compound cooling of about 0.02' had occurred, when slightly more vigorous (and thus in t,he strength of the hydrogen bonding), alstirring produced crystallization, and the highest steady temperathough the existence of this effect has been disputed. ture reached under stirring was Wcorded as the freezing point. No supercooling difficulties or correction proved necessary as is A system satisfying these requirements was imidazole found for certain other solvents, particularly sulfuric acid. and 1-d-imidazole, as it is known that imidazole is highly Subsequent measurements could be effected simply by warming up (1) J. H. Wan& J . A m . Chem. Soc.. 7 8 , 510 (1951). ( 2 ) A . E. Potter, J r . , P. Bender, and H. L. Ritter, J . Phys. Chem., 5 9 , 250 (1955). (3) G. Dahlgren, J r . , and F. A. Long, J . Am. Chem. Soc., 82, 1303 (1960). (4) G . R. Plourde, Dissertation Abstr., 22, 1400 (1961). (5) J. Hermans. J r . , and H. A . Soheraga, B i o c h i m . B i o p h y s . Acta, 86, 534 (1959); see also PI.Calvin, J. Hermans, Jr.. and €1. A. Scheraga, J . Am. Chern,. Soc.. 81, 5048 (1959). (6) A. M. Hughes, B. M. Tolbert, K. Lonberg-Holm, a n d X. Calvin, Biorhim. B i o p h v s . Acta, 28, 58 (1958). (7) V. Moses, 0. Holm-Hansen. and &I. Calvin, ibid., 28, 62 (1958). (8) A . RI. Hughes and AI. Calvin, Science, 127, 1445 (1958). (9) A. AI. Hughes, E. L. Bennett, and h1. Calvin, Proc. XatZ. d c a d . Sci., 45, $81 (1959). 110) See, e . g . , P. R . Gross and W. Spindel, Ann. N . Y . Acad. Sci., 90, Seoond Conference on t h e Mechanisms of Cell Division (19601, p. 500. (11) E. A. Halevi, Tetimhedron, 1, 174 (1957).
the cell in the auxiliary oil bath, then replacing in the air jacket in the thermostated bath, and myere generally reproducible to 10.002O. This procedureis much more rapid and rigorous than the alternative of raising the cell temperature by means of the main bath, then re-equilibrating the bath and cell a t the correct thermostating temperature. Solid samples were introduced through a stoppered glass tube passing into the cell, by means of a specially designed weight bottle and glass tube. ( 1 2 ) K. Hofmann, "'Imidazole a n d its Derivatives," P t . I, Interscience Publishers, New York, N. Y . , 1953, p . 24. (13) D. "I TV. Anderson, J. L. Duncan, and F. J. C. Rossotti, J . Chem. Soc , 2165 (1961). (14) L. Hunter a n d J. A. Marriott, ibid., 777 (1941). (15) R. J. Gillespie, A. Grimison, J. H. Ridd, and R. F. AI. White, ibid., 3228 (1958); A. Grimison. Ph.D. Thesis, London, 1958.
HYDROGEN BOSDISGOF IMIDAZOLE IN XAPHTHALEXE SOLUTIONS
May, 1963
Materials.-Deuterium oxide was >99.8Yc, obtainedfrom BioRad Labs. B. D . H. cryowopic naphthalene was dried by resubliming twice over phosphorus pentoxide in uacuo at 60' and was stored oyer P z O in ~ a vacuum desiccator. The freezing point of the pure naphthalene provided a purity check, being usually constant t o within =to005". Samples varying more than 0.01" from the mean were discarded, or resublimed. Imidazole was purified by a preliminary recrystallization from benzene, followed by vacuum sublimation a t ea. 60'. 1-&Imidazole was prepared by equilibrating 2 g. of imidazole pith two 15-ml. portions of 99.8% D20, removing the solvent by means of a vacuum oil pump at room temperature each time, then subliming the product to purify, without transfer from the original vessel. This technique and associated apparatus has previously been described.l6 Analysis of the Data. --The data from experimental cryoscopic measurements consists initially of a series of values for the apparent molecular weight of the solute a t different solute concentrations. This is customarily expressed in terms of an association factor given b y j = &/AT, where Q = stoichiometric concentration of single molecules, L e . , in terms of formula weights, and ,V = apparent concentration from measurement of any colligative property, both expressed in the same units. The first step of an analysis of the data is a calculation of the equilibrium constants, K L for the self-association reactions LA F! AL, = polymer of order I,, and K L = AL/AL. where A = monomer, 41, Also of interest may be the equilibrium constant KL' for the nddition of a monomer unit to a polymer of order L; i.e., the association reaction AL A e AL + 1, given by KL' = K L + l/Kr. From these equilibrium constants the free-energy changes for the above reactions can be calculated. The basic assumption necessary for a calculation of the equilibrium constants is that all deviations from ideality are due to the presence of associated molecules. This is certainly not strictly correct a t the concentrations normally used in cryoscopic work, and precautions need to be taken when making precise calculations.16 However, the deviations will be of no significance in a relative study on tA o closely similar molecules as reported here, i.e., it is assumed that the solute-solvent interactions are not significantly changed by the substitution of deuterium for hydrogen in this system. It is appropriate to mention here that no assumptions are made that some very weak hydrogen bonds are not formed with the solvent naphthalene, but only that these interactions are so weak in comparison with the predominant solute-solute hydrogen bonding that any changes in this solute-solvent bonding by substitution of deuterium for hydrogen must be negligible. -4s demonstrated in the work of Martin and Kilpgtricli,'6 the first essential step 7s the establishment of a relationship between f and A- or &. Three somewhat different methods of calculating the equilibrium constants are those of Lassettre,'7~*8 Dunlien, 19,ao and Rierrum and Fronaeus.2lnaa See also Rossotti and R o ~ s o t t i . ~ The ~ method of Lassettre, although less generally applicable than the others, is accurate and convenient for suitable systems, and has been s h o m to give good results for compounds with a similar type of association behavior t o imidazole,le it was therefore used exclusively. Lassettre considered a general equation for association behavior
+
f
==
1
+ a& + pN
where LY and p are constants. It is obvious that in the limit 17 = 0 the aquation describes a compound in which f is a linear function of Q. It can be seen from Fig. 1 that this is true for imidazole, so that a is easily determined from the slope of the straight line plot. Lassettre goes on to prove that the equilibiium constants K L are given by KL = (aL)L-l/L!,and the equil)L-'/L for the limiting librium constants KL' by KL' = a l L case with /3 = 0. Equilibrium constants KL and KL' were therefore determined from the slope of a plot of f against (3 as above. The free energg
+
(16) N. E. White and hf. Kilpatrick, J . Phgs. Chem., 59, 1044 (1955). (17) E. N. Lassettre, Chem Rev., 20, 269 (1937). (18) E. N. Lassettre, J . Am. Chem. Sac., 59, 1383 (1937). (19) H. Dunken, 2. phgsilc. Chem., 45B, 201 (1940). (20) K. L. Wolf, H. Dunkem, and K. Merkel. ibid., 46B, 287 (1940). (21) J. Bjerrum, K e n . Ma,anedsbZad, 24, 121 (1943).
(22) S. Fronaeus, Dissertation. "Komplexsystem hos Koppar," Lund, 1948. (23) F. J. C. Rossotti and 17. Rossotti, J . Phys. Chem., 86, 1376 (1961).
963
changes ini-oh ed in the more physically meaningful reaction A AL $ - 4 ~ + 1, AFLO', for both normal and 1-d-imidazole were calculated from the relation AFLO' = - R T In (Y - RT ( L - 1) in ( L I)&
+
+
Results and Discussion The results for the association of imidazole are shown in Table I and plotted in Fig. 1. The slope of the graph agrees very well with the results of Hunter and h4arriott14 (l.SyOdiff.), although their graph was displaced slightly to the right, and in fact failed to extrapolate to the point f = 1, Q = 0. This might be due to the neglect of drying the naphthalene used, resulting in some competition for hydrogen bonding by water. TABLE I ASSOCIATIONO F IMIDAZOLEQ R u n no.
Concn. ( m )
Assn. factor
ATf. OC.
H. 2 0.0612 0.337 H. 2 ,1174 ,531 H. 1 ,1300 ,567 H. 2 ,1625 ,645 H. 3 ,3705 ,915 H. 4 ,3960 ,940 H. 3 .4.781 1.014 H. 5 ,6117 1,095 uI
