“JBrIN AQUEOUS SOLUTIONS OF QUATERNARY AMMONIUM BROMIDES
Summary The origin and extent of the subtle errors possible for measurements of the emission lifetime of photoselected molecules have been delineated. These systematic
2805
errors can be siseable. They are expected to be more common in fluorescence lifetime determinations, especially for more viscous solvents or for larger solutes. Ways to reduce or avoid the error have been given.
Nuclear Quadrupole Relaxation of “Br in Aqueous Solutions
of Quaternary Ammonium Bromides by Bjorn Lmdman, Sture Forsen, Division of Physical Chemistry, The Lund Institute of Technology, Lund, Sweden
and Erik Forslind Nuclear Magnetic Resonance Croup, Division of Ph,ysical Chemistry, The Royal Institute of Technology, Stockholm, Sweden Accepted and Transmitted by The Faraday Society
(December 87, 196‘7)
Measurements of the line width of the 79Br magnetic resonance signal in aqueous solutions of tetraalkylammonium bromides are presented. It is found that the relaxation time of the 79Br nuclei decreases rapidly with increasing length of the alkyl groups on the cation and with increasing concentration of the electrolyte. The signal narrows with increasing temperature. Possible causes of the observed line-broadening effect are discussed, taking account of the known structure-stabilizing effect of the tetraalkylammonium ions on the water lattice. It is found that a simple model in which the bromide ions are rapidly exchanging between two sites, with different bonding properties for the bromines, provides a description of the observations. The two sites correspond to bromide ions in the water lattice in bulk and associated with a clathrate-like water lattice in the vicinity of the complex cations. The effect of local viscosity differences is also considered. Measurements were also performed with methanol and dimethyl sulfoxide as solvents. I n the methanolic solutions the signal narrows with increasing temperature, but it is only slightly affected by concentration changes or by changing the type of cation. Thus the observed effects on the band widths in aqueous solutions can be ascribed predominantly to anion-solvent interactions, since direct cation-anion interactions do not seem t o be important. With dimethyl sulfoxide (DMSO) as the solvent, the line width decreased with increasing temperature. Furthermore, the line width was increasing rapidly with increasing concentration and was highly dependent on the nature of the cation. Thus the line width of the 79Br signal in DMSO solutions of ammonium bromide was an order of magnitude greater than that of tetrabutylammonium bromide. Possible reasons for the marked differences between the three investigated solvents are discussed,
The structure of liquid water has been shown to be very sensitive to the introduction of solutes, the produced effect being strongly dependent on the nature of the solute. Two groups of solutes which have received special interest are strong electrolytes and substances containing lyophobic groups or molecules. The influence of dissolved strong electrolytes on the water lattice has been studied by means of several experimental methods. (A review of this and other subjects concerning solute-water interactions has been given by Kavanau.’) From, e.g., viscosity data, nuclear magnetic resonance spectroscopy, and infrared spectroscopy studies, it has been found that certain ions exhibit a structure-making effect on the water lattice, while other ions are structure breaking; ie.,
they reduce the stability of the water lattice. Contributions of interest for the elucidation of this question have, for instance, been given by studies of the proton magnetic resonance chemical shifts in aqueous solutions of strong electrolytes. Already, in 1954, Shoolery and Alder2 were able to resolve their measured molal shifts into ionic contributions, t,hereby obtaining information concerning the effect of the various ions on the degree of hydrogen bonding in the water lattice. Further studies of proton chemical shifts in aqueous solutions of alkali halides have since been published by (1) J. L. Kavanau, “Water and Solute-Water Interactions,” HoldenDay, Inc., San Francisco, Calif., 1964. (2) J. N. Shoolery and B. J. Alder, J . Chem. Phys., 2 3 , 805 (1955).
Volume 78, Number 8 August 1968
2806
FIertz and Spalthoff ,8 by Bergqvist and Fors1indl4 and by HindmanS5 In accordance with what has been concluded from other experimental data, it was found that the smallest alkali ions exhibited a structuremaking effect, while the largest halide ions were strongly structure breaking. The properties of the ions in this respect could be correlated with their volumes and polarizing abilities.* A slightly different situation is encountered when the solute, for instance, consists of lyophobic or partially lyophobic molecules with nonpolar groups, A usually strong structure-forming effect is observed, which is due t,o water-lattice reorganization around the hydrophobic groups or molecules. This phenomenon has been reviewed recently by Scheraga16by Klotz,? and by Hertz . The complexity in the behavior of liquid water has caused many models for its structure to be proposed.’ One picture is the “defect ice lattice” model of Porslind,l,g~10 in which liquid water is treated as an essentially crystalline systcm, closely related to a slightly expanded ice lattice. This model is found to be in agreement with a recent X-ray diffraction study by Narten, et nZ.l1 According to the ideas presented by Forslind,’” the introduction of solutes affects the asymmetry of the intermolecular thermal vibrations and the probability of lattice-defect formation. The other common picture is the “flickering-cluster” model of Frank and Wen,l2,l8 which postulates that the formation of hydrogen bonds in liquid water is predominantly a cooperative phenomenon, thus producing short-lived clusters of highly hydrogen-bonded regions. According to this picture the introduction of solutes affects the initiation of clusters and cluster disruption. Dissolved hydrophobic molecules produce a water lattice of especially high hydrogen bonding and ~ r d e r , ~ as ~ ’shown ~ ~ ’ ~by the vcry large negative excess entropy change over the entropy change of ideal mixing arid by the high stability of a large number of crystalline hydrates. These hydrates contain polyhedra of hydrogen-bonded water molecules, the polyhedra forming large cavities in which the solute molecules are enclosed. This “clathration” shows a wide variation in the size and shape of the water ‘Lcages” enclosing a hydrophobic group or molecule. An X-ray investigation of the structure of a crystalline hydrate of tetraisoamylammonium fluoride performed by Feil and Jeff reyI4 revealed an interesting feature. The structure is of tbe clathrate type, the “host molecule” being B three-dimensional hydrogen-bonded water structure. The isoamyl groups are projecting tetrahedrally from the nitrogen atom into four cavities in the water lattice. One remarkable point is that the fluorine atoms are replacing water molecules in the water polyhedron lattice. The tetraisoamylammonium chloride and bromide were found to be isomorphous with the fluoride. l5 The Journal of Physical Chemistry
B. LINDMAN,S. F O R S ~AND N , E. FORSLIND I n aqueous solutions of tetraalkylammoninm halides, it can be assumed, from a knowledge of the interaction bettweenwater and hydrophobic groups in general, that the cation has a strong stabilizing effect on the water lattice, which is also confirmed by various experimental studies. Thus the nuclear magnetic relaxation rates of water protons, deuterons, and 170nuclei are much greater in these solutions than in pure water.la-l8 The stabilizing effect is also demonstrated by near-infrared studiosPJg by dielectric studies,20121 as well as by many other types of measurements. (See, e.g., ref 22-24, where additional references are given.) The above conclusions seem to be contradicted by earlier reported proton magnetic resonance chemical shiftsJSthe waterproton signal being shifted to higher fields. Separating the contributions from cations and anions, it appears that at least the larger complex cations give rise to an upfield shift of the proton resonance, corresponding to an over-all reduction of the hydrogen-bond strengths. However, anisotropy effects expected to occur in the water layers, which separate the large cations and which have not been taken into consideration, are probably of importance, making a direct comparison with data derived from small symmetrical ions inadmissible, since in this case the anisotropy effect is most certainly reduced to relative insignificance. A different interpretation has been given by Clifford, et ~ 2 . ~ ~ A great deal of effort has thus been devoted to the study of the interactions between the water lattice and (3) 13. G. Hertz and W. Bpalthoff, 2. Elektrochem., 63, 1096 (1959). (4) M. 9. Bergqvist and E. Forslind, Acta Chem. Scad., 16, 20691 (1962). (6) J. C.Hindman, J. Chem. Phys., 36, 1000 (1962). (6) H. A. Soheraga, Ann. N . Y. Acad. Sci., 125, 253 (1965). (7) I. M. Klotz, Federation Proc., 24, 8-24 (1965). (8)H. G. Hertz, Ber. Bunsenges. Phys. Chem., 68, 907 (1964). (9) E. Forslind, Acta Polytech., Chsm, Met. Ser., 3, No. 5 (1962). (10) E. Forslind, Proc. Int. Congr. Rheol., and, Oxford, 1063,50 (1954). (11) A. H . Narten, M. D. Danford, and H. A. Levy, Discussiwne Faraday SOC.,43, 97 (1967). (12) H. 8. Frank and W. Y. Wen, ibid., 24, 133 (1957). (13) H. 8. Frank, Proc. Roy. SOC.,A247, 481 (1958). (14) D. Feil and G. A. Jeffrey, J . Cham. Phys., 35, 1863 (1961). (15) R. McMullitn and G. A. Jeffrey, ihld., 31, 1231 (1959). (16) H. 6. Hertz and M.D. Zeidler, Ber. Bunsengea. Phys. Chem., 68, 823 (1964). (17) F. Fister and H. G. Hertz, ibid., 71, 1032 (1967). (18) S. S. Dnnyluk and E. S. Gore, Nature, 203, 748 (1964). (19) K. W. Bunzl, J. Phus. Chem*,71, 1358 (1967). (20) G . H. Haggis, J. B. Hasted, and T. J. Buchanan, J . Chem. Phys., 20, 1452 (1952). (21) R. Pott,el and 0.Lossen, Ber. Bunrten,gen. P h p . Chem., 71, 185 (1967). (22) R. E. Conway and R. E, Verrall, J . Phys. Chem., 70, 3962 (1966). . . (23) R. L. Kay, T. Vituocio, C. Zawoyski, and D. F. Evans, ibid., 70, 2336 (1966). (24) R. L. Kay and D. F. Evans, ibid., 70, 2325 (1966). (25) J. Clifford, B, A. Pethioa, and W. A. Benior. Ann. N . Y . Acad. Sci.. 125, 458 (1965).
79Br
IN
2807
AQUEOUS SOLUTIONS OF QUATERNARY AMMONIUM BROMIDES
the tetraalkylammonium ions, Very little, however, seems to be known about the interactions between the anions and the water lattice, in particular, whether the anions are relatively unaffected by the ordering of the water lattice or whether they are subjected to bonding similar to that found in the crystalline hydrates. A convenient way of examining the state of binding of an atom is by measuring the nuclear magnetic relaxation rates. We have undertaken a study of the rate of relaxation of .79Br in aqueous solutions of some tetraalkylammonium bromides. The results reported here concern the influence on the nuclear magnetic relaxation rate of the carbon-chain length, salt concentration, and; qualitatively, temperature. The effect of introducing a double bond into the hydrocarbon chain has also been examined, To make possible a separation of anion-cation interactions from wateranion interactions, we also performed measurements using two other solvents. Experimental Section A Varian V-4200 B nmr spectrometer equipped with a 12-in. V-4012 A magnet was used for the measurements, The magnetic field was controlled by a Varian Fieldial, The derivative of the absorption curve was recorded and the line width was estimated directly from the recorded curve as the distance between the maximum and minimum slopes of the absorption curve. The field modulation frequency was 40 HZ and the field-modulation amplitude was kept less than 0.3 of the line width (except in the case of the most dilute solution of tetraamylammonium bromide where, owing to the low signal intensity, it was set at nearly 0.5 of the line width). The radiofrequency field was optimized to avoid saturation. The resonance frequency was stabilized at 10 MHz by means of a Hewlett-Packard 5245 L electronic counter. The value of the magnetic-field inhomogeneity was obtained by recording the 23Nasignal for an aqueous sodium chloride solution, since 23Naresonates a t approximately the same magnetic field as 79Br. The field inhomogeneity was found to be less than 20 mG. All of the reported line widths are at least 15 times the magnetic field inhomogeneity. The time for passing the resonance was chosen sufficiently long not to produce any appreciable distortion of the recorded curve. Sample temperature was 25 i 1," if not otherwise stated. The reported line widths are usually the arithmetic means of two to four measurements. Individual measurements were ordinarily within 5% from the average, although the deviation could exceptionally amount to a value between 5 and 8%.
The absolute line widths were checked by comparative measurements carried out at the Varian Research Laboratory, in Zurich, by the courtesy of Dr. L.-0. Andersson. The chemicals were of purum or pro analysi grade.
i i i Number of carbon atoms in the chain, R.
1
6
Figure 1. The line width, AB, for 79Br as a function of R in 0.100 and 0.500 M aqueous solutions of RaN+Br-: 0, 0.100 M ; 0 , 0.500 M . (The lines serve merely as an aid to the eye.)
Spectra of samples prepared from salts purified by recrystallization in chloroform-ethyl ether or acetoneethyl ether showed the same line widths as samples prepared from the bottled compounds. Experimental Results The values of the line width of the 79Brresonance for 0.100 and 0.500 M solutions of five tetraalkylammonium bromides in water are given in Figure 1. Owing to limited solubility, the line width for the 0.500 M solution of tetraamylammonium bromide could not be obtained. Instead the value for a 0.200 M solution was measured and was found to be 3.8 G. In the case of still longer carbon chains, the solubility was too low t o permit any measurements of the line width. In Figure 1 are also included the corresponding values for ammonium bromide and tetraallylammonium bromide solutions. The variation of line width with salt concentration was investigated in greater detail and over an extended concentration range for tetraethylammonium bromide. The results are given in Table I.
I
I
2.80.
3.00
3.10
3,20
3.30
3.40
1/~.10~ OK-' ,
Figure 2. The temperature dependence of the 78Brresonance line width in 0.5 M solutions of (C2H5)4NBrv The logarithm of the line width is given as a function of the inverse absolute temperature. (The line merely serves as an aid to the eye.)
Volume 78, Number 8 August 1968
B. LINDMAN, S. FORS~N, AND E. FORSLIND
2808
A preliminary study of the temperature dependence of the 79Br line width was undertaken for a 0.500 M solution of tetraethylammonium bromide. I n Figure 2 the logarithm of the line width is plotted as a function of the inverse absolute temperature. The effect on the 79Brline width of changing the concentration of bromide ions while keeping the concentration of tetrabutylammonium ions constant was also investigated (Table 11). Some further measurements undertaken to test our assumptions for the interpretation of the data are reported below. Table I: Concentration Dependence of the ‘OBr Resonance Line Width in Aqueous Solutions of Tetraethylammonium Bromide (25 =!= 1’) 112,
mo1/1000 g of H20
Line width, G
0.040
0.58
0.087
0.71 0.74 0.97 1.93 2.33 2.8 5.4 6.9 9.9 21.3
0.102
0.176 0.472 0.549 0.841 1.69 2.41 3.51
6.84
Table 11: 7BBrLine Widths in Aqueous Solutions Containing Both Tetrabutylammonium Bromide and Ammonium Bromide“ Concn of NHaBr, M
0
0.497 0,999
Line width,
G
6.0 4.6 4.6
a The concentration of tetrabutylammonium bromide is constant (0.500 M ) , while the concentration of ammonium bromide is varied.
Discussion The 79Br nucleus has a spin quantum number I = 3/z and an electric quadrupole moment. The interaction between the latter and the fluctuating electric field gradients at the nucleus will, under most circumstances, provide the dominant nuclear magnetic relaxation mechanism in fluid systems. The relaxation of nuclei having quadrupole moments has been studied previously for electrolyte solutions by several worker^.^^-^^ A theory of quadrupole relaxation in liquids has been developed by Abragam and P ~ u n d , ~who ~ J derived ~ the following expression for the inverse spin-lattice relaxation time The Journal of Physical Chemistry
where e& is the electric quadrupole moment of the 2, is the mean-square electric-field nucleus, ((b2V/bz2) gradient at the nucleus, and T~ is a correlation time describing the random molecular motions producing the electric-field gradients, while A = h/2n (h is Planck’s constant), Experiments performed at three different resonance frequencies (10.0, 13.9, and 15.0 MHz) showed that the line width is independent of the magnetic-field strength, thus proving that the present situation is described by the case of extreme narrowing. TI is then equal to Tz, the spin-spin relaxation time. The equality between TI and Tzhas been verified for some electrolytic soluti0ns.3~ The nuclear magnetic resonance line width, AB, is, in this case, proportional to the inverse spinlattice relaxation time. According to eq 1, the variable factors that determine the width of the resonance line of a given nucleus should be the mean-square electricfield gradient and the correlation time. For ordinary electrolytic solutions, it has been shown that both factors play a ro1e.32*34As is shown by the now reported results, the leBr line width in aqueous solutions of tetraalkylammonium bromides increases rapidly with the size of the cation and with the concentration of the salt. The broadening effect observed can be due either to an increase in the electric-field gradient or to a decrease in the rate of motion of the species in the solution. Since the field gradients at a given nucleus produced by neighboring ions or molecules decrease very rapidly with increasing distance to the species, giving rise to the electric field,26 the effect of the highly shielded charge at the nitrogen atom can be neglected. Furthermore, in the crystalline state it has been shown that the cation-anion interaction cannot be important. Thus the bromide ion is built into a water lattice that has no direct chemical coupling to the cation, the effect of which is only to polarize the water molecules and, consequently, to force the protons of the water molecules into orientations pointing away from the alkyl groups. (That cation-anion interactions are really of (26) H. G. Hertz, 2. Elektrochem., 65, 20 (1961). (27) H. G. Hertz, ibid., 65, 36 (1961). (28) J. C. Eriksson, b. Johansson, and L.-0. Andersson, Acta Chem. Scand., 20, 2301 (1966). (29) M. St. J. Arnold and K. J. Packer, Mol. Phys., 10, 141 (1966). (30) J. Itoh and Y. Yamagata, J . Phys. SOC.Jap., 13, 1182 (1958). (31) R. E. Richards and B. A. Yorke, Mol. Phys., 6, 289 (1963). (32) C. Deverell, D. J. Frost, and R. E. Richards, ibid., 9, 565 (1965). (33) D. E. O’Reilly, G. E. Schacher, and K. Schug, J . Chem. Phys., 39, 1756 (1963). (34) M. Eisenstadt and H. L. Friedman, ibid., 44, 1407 (1966). (35) A. Abragam and R. V. Pound, Phys. Rev., 92, 943 (1953). (36) A. Abragam, “The Principles of Nuclear Magnetism,” Clarendon Press, London, 1961.
79Br IN AQUEOUS SOLUTIONS OF QUATERNARY AMMONIUM BROMIDES
2809
hedra.I4 A possible explanation of the now-reported small importance was experimentally confirmed by perresults would be that even in the solutions at least part forming measurements in methanolic solutions. This of the Br atoms are built into a clathrate-like water will be discussed below.) The implication is that, at lattice. With a slow exchange of Br atoms between least in the case of the largest cations, the dominant the clathrate structure (which we denote as site A) and nuclear magnetic relaxation mechanism must depend the water lattice in bulk (site B), the resulting signal on the water molecules. The water molecules can afshould be determined by the relaxation rates of the two fect the rate of relaxation of the bromines by a change sites and of the rate of chemical exchange. Expresof the correlation time or a change of the electric field sions for the relaxation rate have, for this case, been gradients. The correlation time, which in our case et u ~ . , ~ O by Hertz,27and by Pearson, given by Pople, depends on the rate of motion of the water molecules, et a 2 . 4 1 can be altered by changes in the viscosity or by changes I n the limit of rapid exchange, only one resonance in the state of binding between bromine and water. signal can appear. Here the following approximate The magnitude of the electric-field gradients is, on the expression is valid for the “effective” relaxation other hand, highly dependent on the type of bonding time37,40 and on the intermolecular distances. We first consider the “viscosity effect.” For the rotations6~87of a rigid sphere of radius a in a fluid of viscosity 7, r0 = 4 ~ q a / 3 k T . It has been verified for many electrolytic solutions that the correlation time at where P A and P B denote the fractions of the nuclei under constant temperature is roughly proportional to the consideration in sites A and B. Since the bromines in macroscopic viscosity. This is shown by the fact that both sites are coupled to water molecules, the difference the dependence of nuclear magnetic relaxation rates being merely one of thermal amplitudes, it can be on viscosity has often been found to be linear.*9~31~32~34~as assumed that Au ‘v 0. Thus the last term in eq 2 may Viscosity data,a9 however, prove that this cause for be neglected. This is enhanced by the fact that the line broadening can only be of secondary importance. lines are rather broad and that PAis rather small. Thus the viscosity of a 0.5 M aqueous solution of tetraA further support for our neglect of the last term in ethylammonium bromide exceeds that of pure water eq 2 is given by the observed frequency independence with less than 20%, while the 79Brline width of the of the line widths and also by the applicability of eq 4 same solution is about 7 times that of an aqueous 0.5 (see below). Thus, in the case of a rapid exchange, M NH4Br solution, where the viscosity effect is neglithe relaxation time should be given by the expression gible. Local viscosity effects might, however, offer an explanation, as discussed below. (3) We next consider the changes in the electric-field gradients effected by the water molecules. Bergqvist The question now arises whether the present situation and Forslind4 showed that in solutions of alkali broshould be described by the slow-exchange or the fastmides, covalent bonding constitutes part of the interexchange case. There are three observations that exaction between a bromide ion and the water lattice. clude the slow-exchange case. I n the slow-exchange As was remarked above the electric-field gradients are case, the observed signal should correspond to 79Brions very sensitive to changes in the intermolecular disin bulk water, since the effective relaxation processes of tances. A change in the distances between a bromide the bromine atoms in clathrate-like regions would most ion and the surrounding water molecules should, howlikely render these signals too broad to be observed ever, also greatly affect the bonding properties and, if under the present experimental conditions (cf. the rewe disregard the local viscosity effects for the moment, sults on covalently bonded halogen nuclei).42 An init does not seem possible to account for the observed creased exchange rat’e of bromine ions between the two 20-fold increase in line width, effected in the 0.500 M sites would then manifest itself as a broadening of the solutions by replacing the hydrogens in NH4Br by butyl groups, without assuming that a change in the state of (37) J. W.Emsley, J. Feeney, and L. H. Sypliffe, “High Resolution Nuclear Magnetic Resonance Spectroscopy, Vol. 1, Pergamon Press binding for at least part of the bromide ions occurs. Ltd., London, 1965. The change in state of binding should increase both the (38) D. Herbison-Evans and R. E. Richards, Mol. Phys., 7 , 615 electric-field gradients and the correlation time. Our (1964). (39) E. W.Washburn, Ed., “International Critical Tables,” Vol. V, experiments, however, do not reveal which effect is McGraw-Hill Book Co., Inc., New York, N. Y.,1929,p 13. the most important. (40)J. A. Pople, W. G. Schneider, and,,H. J. Bernstein, “HighIt has already been mentioned that the hydrophobic Resolution Nuclear Magnetic Resonance, McGraw-Hill Book Co., Inc., New York, N. Y.,1959. groups in the tetraalkylammonium cations produce an (41) R. G. Pearson, 3. Palmer, M. M. Anderson, and A. L. Allred, ordering of the surrounding water lattice and that in the 2.EZektrochem., 6 4 , 110 (1960). crysta11ine hydrates the ions can water (42) D, E. 09Reilly and E, Schaoher, J . phys., 39, 1768 molecules and can be incorporated in the water poly(1963). Volume 78, Number 8 August 1968
B. LINDMAN, S. FORS~N, AND E. FORSLIND
28 10 observable signal. The experimental signal is, however, narrowing with increasing temperature. (This question has been discussed by Hertz4aand by Loewenstein and C ~ n n o r . ~On ~ ) the other hand, it does not seem possible that a mere change in the carbon-chain length should have such a profound influence on the slow rate of exchange as is indicated by the results. That the case of rapid exchange is appropriately describing the present situation was demonstrated by recording the 8lBr resonance for a 0.5 M tetrabutylammonium bromide solution. The slBr line width is 3.8 G, which should be compared with 6.0 G for 79Br. Hertzz6has shown that the ratio of the line widths for the two Br isotopes in ordinary aqueous solution is given by the expression
where y is the magnetogyric ratio. The same expression should obviously hold true also when chemical exchange occurs and eq 3 is valid. The ratio calculated from our observations is 1.58, thus in good agreement with the predicted value. I n the case of slow exchange, this ratio should be smaller, the magnitude being dependent on the rate of chemical exchange. In an oversimplified model of our solutions of tetraalkylammonium bromides, we may consider the clathrate-like regions in the solutions to be formed by water and salt L+.R/I- according to the reactions
+
L+free nHzO M-free
+ L+w.nHzO If
L+w'nHzO
L+w*IVI-W*(n - 1)H20
+ HzO
(1)
(5) if activity coefficients are omitted. The concentration of water outside the clathrate-like water lattice is at moderate concentrations practically independent of reaction I1 and is included in the equilibrium constant. Let Co be the total salt concentration and c = [L+w. M-W.nH20]. Then M-free = Co - c, which makes
K = (11)
Here L+freeand M-free denote the ions in the water lattice in bulk and L+w.nH20denotes a clathrate-like water lattice containing the cation, while L+w.M-w. (n - 1)H20 denotes a clathrate structure containing also the anion. It must be emphasized that reaction formulas I and I1 should be regarded only as formal representations of the processes which are taking place in the solutions. Thus the number of water molecules in the clathrate-like regions in the solutions cannot be stated, since the structure-stabilizing effect of the cations is gradually diminishing with increasing distance from the cations. (An experimental proof of this distance-dependent structure-stabilizing effect is referred to below. It should, on the other hand, be observed, that for large cations, the spacing, measured in water molecule diameters, is only about 5 diameters or less at unit molality.) The question is, obviously, to what degree a certain water molecule is affected by the waterlattice stabilization brought about by the tetraalkylammonium cations, rather than whether it belongs to the clathrate-like regions in the solutions or not. The absolute value of n will, however, not enter the followThe Journal of Physical Chemistry
ing discussion. It is only concluded that the structurestabilizing effect of the tetraalkylammonium cations is highly significant (this is demonstrated by the measurements of the relaxation rates of protons, deuterons, and 170nuclei in aqueous solutions of tetraalkylammonium bromides, which have been presented by Hertz, et ~ 1 . ~ ~ 8which ' ~ ) guarantees that n >> 1 and consequently n N n - 1 (in the following we will always write n even when n - 1 might be more appropriate). As was concluded above, our results show that the state of binding of the bromide ions is changed when certain cations are present which we interpret as being due to reaction 11. Reaction I is describing the process of clathrate-like water ordering around a cation and is, of course, a result of many steps. Reaction I1 describes the substitution of one bromide ion for a water molecule in the clathrate-like lattice. According to the well-known fact that clathrate formation is very readily achieved, it can be assumed that reaction I is very far on the right side. It is thus only necessary to consider reaction 11, t,he equilibrium constant of which can be written
C
(CO - C l 2
I n the case when K is small (
