The Journal of Physical Chemistry, Vol. 82, No. 1, 1978 29
Hydrophobic Hydration of Tetraalkylammonium Bromides
TABLE I:
R a t e C o n s t a n t Values at 573
R=H
Reaction ( 3 ) N,O t .CR,OH + N, t *OCR,OH (4) --OCH,OH* t H,O + HOCH,OH t O H ( 5 ) +OCH,OH t HCR,OH HOCR,OH t .CR,OH (7) B.CR,OH + P, (8) .CR,OH t *OCR,OH (9) B.OCR,OH -+ P,
2.5 X
lo4
+
R = CH, 2.9 X
10'
8.7 x
io3
38 -+
-+
P,
1 x 10'Oa 1 x 10'O
1x 1 x 1O'O
-
reactions in water a t 300 "C to be -1 X lo1" L/mol s, one obtains (AS*3 AS*5 - AS*8) = 0 in the propanol system and (AS*B-t &SI4 - ASS8) -32 cal/mol K in the methanol system. The values of AS* for reactions 3,5, and 8 are all probably near zero, which indicates a large negative value, --32 cal/mol K, for reaction 4. This supports the suggestion that solvent rearrangement (increase of solvation energy) makes a significant contribution to the driving force of reaction 4.
K
h(M-'s-')
a
References and Notes
a Assumed.
p r ~ p a n o l ] l demonstrated /~ the occurrence of reaction 5 in solutions where [HzO]/[2-propanol] 2 lo4, hence we for 2-propanol. conclude that h4/k5 I Figure 4 in ref 2 and the present Figure 4 may be used to estimate the sums of the entropies of activation of the propagation reactions in the propanol and methanol systems. Using the reaction sequence in Table I, and taking the diffusion controlled limit of radical/molecule
(4)
(5) (6) (7) (8) (9)
Financially assisted by the National Research Council of Canada. T. G. Ryan and G. R. Freeman, J . Phys. Chem., 81, 1455 (1977). E. C. Bricker and H. R. Johnson, Ind. Eng. Chem., Anal. Ed., 17, 400 (1945). R. L. Shriner, R. C. Fuson, and D. Y. Curtin, "The Systematic Identificationof Organic Compounds", Wiley, New York, N.Y., 1956. A. Kato and R. J. CvetanoviE, Can. J . Chem., 46, 235 (1968). J. G. Calvert and J. N. Pttts, "Photochemistry", Wiley, New York, N.Y., 1966, pp 824-826. Y. Ogata and A. Kawasaki in "Chemistry of the Carbonyl Group", Vol. 2, J. Zabicky, Ed., Interscience, Toronto, 1970, p 4. M.Sirnic, P. Neta, and E. Hayon, J. Phys. Chem., 73,3794 (1969). R. W. Gallant, "Physical Properties of Hydrocarbons", Vol. 2, Gulf Publishing Co., Houston, Tex., 1970, p 190.
Hydrophobic Hydration of Tetraalkylammonium Bromides in Mixtures of Water and Some Aprotic Solvents W. J. M. Heuvelsland, C. de Visser, and G. Somsen" Department of Chemistty, Free University, De Boelelaan 1083, Amsterdam, The Netherlands (Received July 26, 1977) Publication casts assisted by the Free University of Amsterdam
Enthalpies of solution of tetra-n-pentylammonium bromide in mixtures of water and N,N-dimethylformamide (DMF) and of tetra-n-butylammonium bromide in mixtures of water and dimethyl sulfoxide (Me2SO)and of water and N,N-dimethylacetamide (DMA) have been measured calorimetrically at 298.15 K over the whole mole fraction range. All profiles of the enthalpy of solution vs. solvent composition show endothermic maxima. The results are interpreted in terms of a simple hydration model with two parameters: the enthalpic effect of hydrophobic hydration in pure water, and the number of solvation sites of one alkyl group. After elimination of the influence of the Br- ion, both parameters are in good agreement with those found for some nonelectrolytes. Finally, the role of the cosolvent i s considered more systematically.
I. Introduction T h e hydrophobic hydration of larger tetraalkylammonium halides in water is strongly influenced by the addition of polar cosolvents. This is expressed among others by substantial changes of the enthalpies of dilution,l enthalpies of solution,24 and partial molar heat capacities5 of n-Bu4NBr when water is replaced as solvent by aqueous mixtures of N,N-dimethylformamide (DMF), dimethyl sulfoxide (MezSO), or dioxane. In earlier report^,^,^ we showed that the enthalpies of solution of n-Bu4NBr, nPr4NBr, and Et4NBr in mixtures of water and DMF can be interpreted in terms of a cooperative hydration model originated by Mastroianni, Pikal, and Lindenbaum.l From this cage model the experimental results can be described by two parameters, i.e., the number of solvation sites n surrounding an alkyl group and the enthalpic effect of hydrophobic hydration in pure water Hb(H20). In a recent study Lindenbaum, Stevenson, and Rytting7 have applied the same approach to some nonionic solutes. For the three tetraalkylammonium bromides mentioned before we found that both parameters increase with increasing number of 0022-3654/78/2082-0029$0 1.OO/O
C atoms. Since it might be expected that some leveling-off will occur a t larger chain lengths, we felt it desirable to extend our measurements to higher homologues. However, because of the slow rate of dissolution of n-Hex4NBr and n-Hep4Br in water we had to confine our measurements to n-Pen4NBr. As we have pointed out earlier4DMF is not essential for our model approach. According to the model the values of the parameters Hb(H20) and n ought to be independent of the choice of the cosolvent as long as the latter does not show specific interactions. In order to test the model on this particular point we have measured enthalpies of solution of n-Bu4NBr in mixtures of water and MezSO and water and N,N-dimethylacetamide (DMA). From the point of view of ion-solvent interactions the selected cosolvents MezSO and DMA are comparable with DMF. All three are dipolar aprotic solvents with Kirkwood correlation factors close to l,8v9 the same donor properties, and only slightly different acceptor pr0perties.l" This similarity in behavior is also expressed by the integral enthalpies of mixing with water. At 298.15 K DMF, 0 1978 American Chemical Society
30
The Journal of Physical Chemistry, Vol. 82, No. 1, 1978
MezSO, and DMA exhibit an exothermic enthalpy of mixing of about equal magnitude over the whole mole fraction range.11-13 Enthalpies of soluton of n-Bu4NBr in mixtures of water and Me2S0 have been measured earlier by Fuchs and Hagan.2 However their data cover only part of the mole fraction range and therefore hardly can serve as a test of the model.
PI. Experimental Section N,N-Dimethylformamide (Baker, Analyzed Reagent) and dimethyl sulfoxide (Merck, Zur Analyse) were stored over molecular sieves (Baker, 4A) for at least 48 h and used without further purification. N,N-Dimethylacetamide (Baker, Analyzed Reagent) was fractionated under reduced pressure; only the middle fraction was used. The volume fraction of water for these solvents was determined by a modified Karl Fischer titration14 and never exceeded 3 X The aqueous mixtures were prepared with freshly distilled deionized water by mass. The solutes n-Bu4NBr (Fluka, purissimum) and n-Pen4NBr (Organic Chemical Service, purum) were dried under vacuum at room temperature. Enthalpies of solution at 298.15 K were measured with a LKB 8700-1 precision calorimetry system equipped with a 100-cm3reaction vessel. The experimental procedure has been reported earlier.15 The calorimeter was tested by measuring the enthalpy of solution of Tham (tris(hydroxymethyl)aminomethane, Fluka, purissimum, dried under vacuum at room temperature) in 0.1 M aqueous HC1 at a concentration of about 5 g of Tham/dm3 solvent. From nine independent measurements we obtained an enthalpy of solution of 29.788 f 0.015 kJ mot1 a t 298.15 K (the uncertainty quoted is twice the standard deviation of the mean). This value is in fair agreement with the literature.16 111. Results All measurements of the enthalpies of solution were carried out at high dilution (0.003-0.01 mol kg-l). At this dilution a significant concentration dependence of the enthalpies of solution was not observed either in Me2S0 or in the aqueous-organic solvent mixtures. The enthalpy of solution at infinite dilution AHo(sol)was therefore taken to be the average of two to four independent experiments within 100 J mol-'. The enthalpies of solution in pure DMF and pure DMA showed a small but perceptible concentration dependence probably caused by incomplete dissociation of the s01ute.l~In these cases AH"(so1) was obtained by extrapolation according to a procedure reported earlier." Values of AHO(so1) for n-Bu4NBr in mixtures of water and Me2S0 and water and DMA and for n-Pen4NBr in mixtures of water and DMF at 298.15 K are given in Table I. Our value of AHo(sol) for n-Bu4NBr in MezSO (20.83 kJ molY1)is in close agreement with the results of Krishnan and Friedman'* (20.71 kJ mol-l) and in fair agreement with that of Fuchs, Bear, and Rodewaldlg(21.34 kJ mol-l). The values of AHo(sol)for n-Pen4NBr in pure water and pure DMF in Table I are 0.5-1 kJ mol-l more exothermic than those of Krishnan and Friedman.1s720 Since we are more interested in trends of the enthalpies of solution than in absolute values these differences do not affect the conclusions.
IV. Discussion 1. R4NBr in Water-DMF. First we will discuss the results of n-Pen4NBrin connection with the corresponding results for tetraalkylammonium bromides reported ear-
W. J. M. Heuvelsland, C. de Visser, and G. Somsen
TABLE I: Enthalpies of Solution AH" (sol) in kJ mol-' for n-Bu,NBr and n-Pen,NBr in Some Binary Mixtures as a Function of the Mole Fraction of Water XH,O at 298.15 K n-Bu,NBr in
n-Bu,NBr in H,O-DMA
H,0-Me SO
n-Pen,NBr in H,O-DMF
XH,O AH"(So1) XH-O AH"(so1) 0 20.83 0 15.7 0.061 21.53 0.056 18.28 0.164 23.19 0.132 20.65 0.334 26.22 0.265 24.89 0.500 29.65 0.380 28.54 0.601 30.86 0.487 32.36 0.650 31.06 0.630 36.40 0.735 28.57 0.701 36.94 0.802 23.04 0.770 35.04 0.851 16.51 0.840 28.62 0.900 8.76 0.902 17.74 0.950 0.18 0.951 6.23 1 -8.42 1 -8.42
I
-10;
"
"
'
"
0. '2
"
'
XH-O AH"(so1) 0 22.9 0.170 0.321 0.439 0.612 0.760 0.850 0.928 1
28.98 34.28 39.01 45.55 46.72 40.71 26.80 2.68
'
04 '
'
0.6 '
'
0.8 '
'
xHP
Figure 1. Enthalpies of solution AHo(sol) for tetraalkylammonium bromides in mixtures of water and DMF as a function of the mole fraction of water XHIOat 298.15 K.
lier.4s6 All enthalpies of solution involved are depicted in Figure 1.21In previous papers4* we have shown that the enthalpies of solution of larger tetraalkylammonium bromides in mixtures of water and DMF, AHo(M),can be expressed as a function of the mole fraction of water, X , by AH" (M) = (1- X)AH"(DMF) + XAHO(II20) + (X" - X)Hb ( H 2 0 ) (1) In this equation which is based on the cage model already mentioned, n denotes the number of solvation sites of one alkyl group and Hb(H20)the enthalpic effect of hydrophobic hydration in pure water. Exactly the same equation can also be derived by employing a different model which has some analogy to the one used by B$je and H ~ i d for t~~ the interpretation of volumetric data. In this chemical
The Journal of Physical Chemistry, Vol. 82, No. I, 1978 31
Hydrophobic Hydration of Tetraalkylammonium Bromides
TABLE 11: The Enthalpic Effect of Hydrophobic Hydration Hb(H,O), the Number n of Solvation Sites per Alkyl Group, and the Mean Deviations between Calculated and Experimental Values of AH”(sol) of Some Tetraalkylammonium Bromides in Mixtures of Water and DMF at 298.15 K Hb(H,O), 6 Solute kJ mol-’ n kJ mol-’ Et,NBr n-Pr,NBr n-Bu,NBr n-Pen,NBr a 6
= (AH”(ca1cd)-
- 29.3 - 39.6
- 52.8 - 58.0
2.3 4.2 6.4 8.6
401
1
0.52 0.17 0.23 0.37
AH”(obsd)).
model we consider the hydration of the tetraalkylammonium ion (R4N+)by n cooperatively interacting water molecules as a chemical process, which can be described by the equilibrium R,Nt
+ nH,O
K
~R,N+*-*(H,O),
(2)
In this equation R4N+-.(HzO), denotes the resulting hydrophobic “complex” and K its association constant. The enthalpic effect of hydrophobic hydration in mixtures of water and DMF, Hb(M), can now be considered as the result of the formation of this hydration “complex”, so that
(3) where a is a constant independent of the solvent composition. In terms of mole fractions eq 3 can be written as Hb(M) = a K X n
(4)
Since Hb(HzO) = aK for X = 1, eq 4 can be written as H b (M) = H b (H2O)X”
(5)
Introduction of eq 5 into the derivation given in our previous paper4 yields an expression similar to eq 1. However in the present case the meaning of the parameter n is not as strictly defined as in the first model. The quantity n merely represents a certain number of water molecules in the vicinity of the hydrophobic particle without further specifications. Previously we have fitted the experimental data for n-Bu4NBr, n-Pr4NBr,and Et4NBr with eq 1by optimizing both parameters n and Hb(H20).4@These results, together with the present ones for n-Pen4NBr, are listed in Table 11. The mean deviations given in this table show that also for n-Pen4NBr a very satisfactory fit is obtained. Moreover, Table I1 shows that the parameters n and Hb(H20)increase gradually with the number of C atoms in the solute, while in the case of Hb(H20) a leveling-off seems to occur. In contrast to our results, Lindenbaum et al. did not find a significant dependence of n on the number of C atoms for trialkyl phosphate^.^ Moreover, they observed larger values for the contribution to Hb(H20) per C atom. In their opinion this is caused by the influence of the Br- ion in our case. In an attempt to eliminate this influence we have calculated differences in enthalpies of solution over the whole mole fraction range between pairs of tetraalkylammonium bromides and fitted them to eq 1. The values of n obtained by this procedure are 9.0,9.8, and 11.7 for the pairs Pr4NBr-Et4NBr, Bu4NBr-Et4NBr, and Pen4NBr-Et4NBr, respectively. The corresponding results for the contributions to Hb(H20)per C atom are -4.6, -4.5,
401 0
,
,
0.2
,
,
,
0.4
,
0.6
,
, 0.8
,
J 1
HO ,
Figure 2. Enthalpies of solution AHo(sol) for n-Bu,NBr in mixtures of water with DMA, DMF, and Me2S0 as a function of the solvent composition at 298.15 K.
and -3.8 kJ mol-’. These results are now in better agreement with those of Lindenbaum et ala7 (For trialkyl phosphates they calculated n = 9.4,8.9, and 10.1 and for the contribution to Hb(H20)per C atom -4.8, -4.4, and -3.9 kJ mol-l.) Therefore, after correction for the contribution of the Br- ion the value of n becomes less dependent of the number of C atoms indeed and the value for the contribution to Hb(HzO) per C atom increases. This confirms the idea in which the Br- ion is conceived of as a so-called “structure breaker” in water.7J8~20~24 2. n-Bu4NBr in Water-MezSO and Water-DMA. Enthalpies of solution of n-Bu4NBr in mixtures of water and MezSO and of water and DMA are plotted in Figure 2. For the sake of comparison those in mixtures of water and DMF are given too. As this figure shows the curves representing aH”(s01) for n-Bu4NBr in the various mixed solvent systems seem rather similar. All curves reach a maximum value at about X = 0.65. Below X = 0.6, AHo(sol) increases almost proportionally with the mole fraction of water, while in the region X , < X < 1strong exothermic shifts occur. In addition we have analyzed the experimental data in the various solvent systems with our model approach. The results for the parameters Hb(H20) and n, together with the mean deviation for the enthalpies of solution calculated from eq 1 and the experimental values, are given in the upper part of Table 111. Two striking features can be deduced from this table. (a) The mean deviation listed in the last column shows that the description of the experimental data with our model approach in water-MezSO and in water-DMA becomes less accurate than in water-DMF. This can be deduced already from Figure 2, since the curve in water-Me2S0 (and in water-DMA) is too sharp to fit eq 1 as good as in the case of water-DMF. (b) The values of the calculated parameters Hb(H20) and n vary with the choice of the cosolvent, whereas according to the model these values should be independent
32
The Journal of Physical Chemistry, Vol. 82, No. 1, 1978
TABLE 111: T h e E n t h a l p i c E f f e c t of H y d r o p h o b i c Hydration Hb(H,O), t h e N u m b e r n of Solvation Sites p e r Alkyl Group, a n d t h e M e a n Deviations b e t w e e n Calculated a n d E x p e r i m e n t a l Values of AH"(so1) of n-Bu,NBr a n d T r i m e t h y l p h o s p h a t e ( T M P ) in M i x t u r e s o f Water a n d Some A w o t i c Cosolvents a t 298.15 K Solvent system
H,O-DMA H, 0-DMF H;O-Me,SO
HbW, 01, kJ mol-' n-Bu,NBr - 59.9 -52.8 - 51.5
6 ,a
n
k J mol-'
7.0 6.4 5.1
0.64 0.23 1.12
9.4 7.6
0.16 0.28
TMP H,O-DMF~ H,O-Me,SOC
-14.5 -16.6
a 6 = (AH"(ca1cd) - A H " ( o b s d ) ) , D a t a from r e f 7. Calculated from e x p e r i m e n t a l data from r e f 26.
of the nature of the cosolvent as long as the latter does not show specific interactions. Especially the value of Hb(H20) in water-DMA is considerably more negative than the corresponding one in water-DMF and water-Me2S0. In Figure 2 the latter can be seen too since extrapolations of the linear parts of the curves below X = 0.6 do not reach the same value at X = 1. When protic cosolvents such as formamide and N-methylformamide are used25 this phenomenon becomes much more pronounced. Analogous conclusions can also be drawn from a comparison of the enthalpies of solution of trimethylphosphate in water-DMF and water-Me2S0 as reported in the lite r a t ~ r e . ' #The ~ ~ calculated values of the parameters are given in the lower part of Table 111. Consequently, the model cannot describe the experimental results quite satisfactorily and therefore the assumptions made in the derivations of our model should be reconsidered carefully. Let us take these points in the same sequence.27 (a) It had been assumed that in aqueous solutions each alkyl group of a hydrophobic particle is surrounded by a subcage of n cooperatively interacting water molecules. However the calculated number of water molecules is in most cases much too small to form a real network by hydrogen bonding as is necessary in the cage model. On the other hand, in the chemical model this problem does not occur, since then the value of n is not directly related to a special solvation structure. (b) In order to calculate the influence of cosolvent on cage formation we had to assume that the distribution of solvent molecules in the vicinity of a solute particle is random. This assumption of course is wrong, since especially around hydrophobic particles the distribution of water molecules and nonaqueous molecules is not random, as might be deduced from the word "hydrophobic" alone. However, we still used this approximation since it is very difficult to quantify the degree of randomness. (c) Probably the supposition that the formation of a subcage around one alkyl group will not affect the structure of the subcages around the other alkyl groups is not too unrealistic. Preliminary measurements with unsymmetrical tetraalkylammonium bromides show that the magnitude of the hydrophobic effect roughly is additive with the number of alkyl groups. Finally it should be noted again that the basic assumption to apply the calculation is that in the absence of hydrophobic hydration the enthalpies of solution would
W. J. M. Heuvelsland, C. de Visser, and G. Somsen
change proportionally to the solvent composition, as in mixtures of two nonaqueous solventseZ6In water-DMF we found this type of behavior for Me4NBr,6alkali halides,27 and ureaz8indeed. Also the results for Me4NClBand alkali halidesZt3Oin water-Me2S0 support this assumption. In water-DMA however sufficient experimental data to check this point are lacking. All these aspects clearly show that the outlined cage model approach can only be considered as a first approximation in the interpretation of the enthalpic behavior of hydrophobic solutes in mixed solvent systems. For the selected solvent systems the results are nevertheless quite acceptable and show that in any case eq 1provides a good mathematical description of the AH"(so1) data. The mutual differences both for the values of the parameters and for the accuracy of the fit are probably a reflection of the extent to which the assumptions hold for each individual system. Investigations with other aqueousorganic solvent systems, preferably systems which differ more from water-DMF than those used here, are necessary to study the influence of the cosolvent in more detail.
Acknowledgment. The valuable assistance of K. J. Terpstra and R. P. Tito in the experimental work is gratefully acknowledged. References and Notes (1) M. J. Mastroianni, M. J. Pikal, and S. Lindenbaum, J. Pbys. Cbem., 76, 3050 (1972). (2) R. Fuchs and C. P. Haaan. J. fbvs. Cbem., 77, 1797 (1973). i3i 0. N. Bhatnagar, Can. 2. Cbem., 54, 3487 (1976). (4) C. de Visser and G. Somsen, J . fbys. Chem., 78, 1719 (1974). (5) W. J. M. Heuvelslandand G. Somsen, J. Cbem. Tbermodyn., 8, 873 (1976). (6) C. de Visser, W. J. M. Heuvelsland, and G. Somsen, J. Solution Cbem., 4, 311 (1975). (7) S.Lindenbaum, D. Stevenson, and J. H. Rytting, J. Solution Cbem., 4, 893 (1975). (8) S.J. Bass, W. I. Nathan, R. M. Meighan, and R. H. Cole, J. fbys. Cbem., 68, 509 (1964). (9) R. L. Amey, J . fbys. Chem., 72, 3358 (1968). (10) V. Gutmann, Electrochim. Acta, 21, 661 (1976). (11) M. F. Fox and K. P. Whittingham, J . Cbem. Soc., Faraday Trans. I , 71, 1407 (1975). (12) J. Bougard and R. Jadot, J . Cbem. Tbermodyn., 7, 1185 (1975). (13) P. Assarsson, N. Y. Chen, and F. R. Eirich, Adv. Cbem. Ser., No. 142, 288 (1975). (14) J. C. Verhoef and E. Barendrecht, J . flectroanal. Cbem., 75, 705 (1977). (15) C. de Visser, E. van Netten, and G. Somsen, Electrochim. Acta, 21, 97 11976). (16) E. j .Prosen and M. V. Kilday, J . Res. Natl. Bur. Stand., Sect. A , 77, 581 (1973). (17) C. de Visser and G. Somsen, Red. Trav. Cbim. fays-Bas, 91, 942 (1972). (18) C. V. Krishnan and H. L. Friedman, J. Pbys. Cbem., 73,3934 (1969). (19) R. Fuchs, J. L. Bear, and R. F. Rodewald, J . Am. Cbem. Soc., 91, 5797 (1969). (20) C. V. Krishnan and H. L. Friedman, J. Phys. Cbern.,75,3606 (1971). (21) AHo(sol) of Me,NBr in pure DMF given in Figure 1 differs from the value reported earlier.' The value adopted now has been calculated from the results of Bhatnagar and Criss.** In view of the enthalpies of solution in DMF-rich mixtures we consider this value as more reliable than that given in ref 6. (22) 0. N. Bhatnagar and C. M. Criss, J . Pbys. Cbem., 73, 174 (1969). (23) L. Bee and A. Hvidt, J . Cbem. Tbermodyn., 3, 663 (1971). (24) C. de Visser and G. Somsen, J . Cbem. Soc., Faraday Trans. 7 , 69, 1440 (1973). (25) C. de Visser and G. Somsen, J . Solution Cbem., 3, 847 (1974). (26) B. G. Cox, J . Cbem. Soc., Perkin Trans. 2, 607 (1973). (27) C. de Visser and G. Somsen, Adv. Cbem. Ser., No. 155, 289 (1975). (28j C. de Visser, H. J. M. Grunbauer, and G. Somsen, Z . fbys. Cbem. (Frankfurt am Maln), 97, 69 (1975). (29) M. E. Estep, D. D. Macdonald, and J. B. Hyne, J . Solution Cbem., 6, 129 (1977). (30) A. F. Vorob'ev, A. S. Monaenkova, and I. D. Padfinova, Moscow Univ. Cbem. Bull., 29, 14 (1974).
