Hydrophobic hydration in mixtures of N,N-dimethylformamide and water enthalpies of solution and heat capacities of tetra-n-butylammonium bromide

J. Chem. Thermodynamics 1976,8, 8734350

Hydrophobic hydration in mixtures of N,N-dimethylformamide and water Enthalpies of solution and heat capacities tetra-n-butylammonium bromide W. J. M. HEUVELSLAND

of

and G. SOMSEN”

Department of Chemistry, Free University of Amsterdam, De Lairessestraat 174, Amsterdam, The Netherlands (Received 16 February 1976)

Enthalpies of solution of tetra-n-butylammonium bromide have been measuredcalorimetrically in mixtures of N,N-dimethylformamide (DMF) + water from 278 to 328 K at 10 K intervals covering the whole mole fraction range. All profiles of enthalpy of solution against composition show endothermic maxima. From a simple hydration model it is possibleto calculatethe number FJof water moleculeswhich surround a hydrophobic alkyl group and the enthalpic effect of hydrophobic hydration in pure water. The latter effect appearsto decreasestrongly with temperature,while n is almost temperatureindependent. In addition partial molar heat capacities,es, of n-Bu4NBr have beencalculatedin the DMF + water mixtures; Cz, hardly changesin the range from 0 to 0.6 mole fraction of water. In more water-rich regions CEa increasesvery rapidly towards its value in pure water.

1. Introduction The hydrophobic hydration of the larger tetraalkylammonium ions is expressed among other ways by a large negative enthalpy of solution of the corresponding salts in water. This hydration appearsto be characterized by an enhancedhydrogen bonding of the water molecules in the vicinity of the tetraalkylammonium ions. Accordingly the enthalpies of transfer of tetra-n-butylammonium bromide (n-Bu,NBr) from non-hydrogen-bonded solvents like N,N-dimethylformamide (DMF), dimethylsulphoxide, and propylene carbonate, to water are negative whereas the enthalpies of transfer of the hydrophilic salts RbBr and CsBr are positive.(‘* 2, In addition a marked difference between the partial molar heat capacities of tetraalkylammonium salts in water and those in nonaqueous solvents may be noticed.‘3) The hydrophobic hydration is strongly influenced by addition of non-hydrogen bonded co-solvents to water. Both the enthalpy of dilution(4$ ‘) and the enthalpy of solution@-‘) of n-Bu,NBr change substantially when the solvent water is replaced by mixtures of water + organic solvent. In water + DMF covering the whole mole fraction range we have interpreted (9) the change in the enthalpy of solution of n-Bu,NBr and n-Pr,NBr in terms of a cooperative hydration model, which involves only two 0 To whom correspondenceand requestsfor reprints should be addressed.

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W. J. M. HEUVELSLAKD

AND G. SOMSEN

parameters: the number of water molecules surrounding an alkyl group and the enthalpic effect due to hydrophobic hydration in pure water. Since a decreaseof the hydrophobic hydration with temperature might be expected, we felt it desirable to extend our measurementsto other temperatures. In the present paper we report the enthalpies of solution of n-Bu,NBr in DMF -t water at six temperatures ranging from 278 to 328 K. The results firstly provide a further test of the theory and secondly are used to calculate partial molar heat capacities at infinite dilution of n-Bu,NBr in the various solvent mixtures. In that respectthis paper can be considered as a continuation of earlier work presented in this Journal.(“) Heat capacities are of interest because their trend (or the transfer heat capacity from DMF to aqueous mixtures) reflects directly the influence of the ions on the solvent structure. As far as we know partial molar heat capacities in mixed solvent systems covering the total composition range have not been published before.

2. Experimental Dimethylformamide (Baker, Analyzed Reagent) was dried over molecular sieves (Baker, 4A) for at least 48 h and used without further purification. Its volume fraction of water, as determined by Karl Fischer titration, never exceeded5 x 10e5. Solvent mixtures were prepared by mass, using freshly distilled water. The solute n-Bu,NBr, supplied by Fluka (purissimum), was usedafter drying in vacuum at room temperature. Enthalpies of solution were measuredwith an LKB 8700-1precision calorimetry system. The experimental procedure and test of the calorimeter have been described previously!8p lo)

3. Results The enthalpy of solution measurements were carried out in very dilute solutions (0.01 to 0.001 mol kg-‘). In view of the experimental error the molality dependence of the enthalpies of solution was neglected. Hence, the enthalpy of solution at infinite dilution, AH”(soln) was taken to be the averageof three to five independent measurements agreeing within 150 J mol-‘. Values of A.H”(soln) of n-Bu,NBr with their mean deviations in mixtures of DMF + water at 278.15, 288.15, 298.15, 308.15, 3 18.15, and 328.15 K are given in table 1. The results in pure DMF have been reported earlier.(lo) In view of the consistency of the results we have measured ourselves the enthalpies of solution in pure water also, so that the values of AH”(soln, H,O) used throughout this paper differ from those adapted from literature in our previous report. (to) However the differences are slight and since we are more interested in trends than in absolute values of the enthalpies of solution, they do not affect the conclusions.

4. Discussion ENTHALPIES

OF SOLUTION

The enthalpies of solution of n-Bu,NBr at the various temperatures have been plotted as a function of the mole fraction of water in figure 1, which shows that all profiles

N(n-C4H&Br IN HCON(CH&f Hz0

875 TABLE 1. Enthalpiesof solutionat infinite dilution of tetra-n-butylammonium bromide in mixturesof DMF + waterat temperatures between278and 328K as a functionof the molefractionof water .u(HzO) ----~~

..-

AH “(soln) ~kJ mol-1

x(H,O)

~-

T = 278.15 K

0

i9.3 -t-16.31 &O.Ol +22.10+0.06 -t25.8610.03 $25.69*0.02 -L18.4510.01 +5.26*0.02 -8.1910.02 -m23.7610.03

0.224 0.421 0.601 0.676 0.806 0.890 0.949 1 T= 0 0.132 0.351 0.500 0.681 0.800 0.865 0.928 1

T = 288.15 0 0.219 0.422 0.612 0.720 0.780 0.890 0.949 1

308.15 K t13.7 +18.09*0.04 -t-24.46&0.03 +28.73*0.05 i-31.59&0.04 +28.12&0.05 i-22.68+0.07 i-13.99&0.03 --0.95iO.02

AH “(soin) ~___kJ mol-’

K

t10.8 +17.8OiO.O2 +23.85&0.04 t27.90f0.05 +26.9010.01 +23.95kO.03 +10.37*0.004 -1.88+0.01 -16.05+0.01

T = 298.15 0 0.192 0.311 0.488 0.623 0.695 0.760 0.869 0.945 1

T = 318.15 K 0 0.134 0.378 0.500 0.681 0.779 0.867 0.927 1

+14.8 +19.00*0.01 +26.44*0.03 +30.07.+0.04 +33.24iO.O4 +31.61+0.05 t26.OOi0.03 +19.2410.02 +5.s9rto.o5

AH “(soln) kJ mol-l

xW,O)

T= 0 0.124 0.321 0.519 0.681 0.778 0.874 0.930 1

K

+12.5 +18.48f0.05 +22.07&0.05 +27.12&0.04 1-29.63 ztO.05 $29.77~0.04 +27.89&0.03 +18.21&0.06 +5.26&0.02 -8.42kO.01 328.15 K +15.9 +19.88zkO.04 $25.6810.04 +31.78&0.05 +35.021lzO.O5 +34.31*0.04 +29.38+0.02 -i-23.92*0.03 +13.08&0.04

show a maximum value at mole fractions of water between 0.6 and 0.8. Below x(H,O) = 0.6 the curves are closely parallel and AH”(soln) changes linearly with solvent composition. In the region xmax< x(H,O) < 1 exothermic shifts occur which decreasewith temperature. As reported earlier (*) the enthalpies of solution of n-Bu,NBr in mixtures of DMF + N-methylformamide (NMF) change almost in proportion to the solvent composition. In this connexion we have defined an extra or excessenthalpy of solution in a mixture (M) of two solvents A and B by AIHE(soln) = AH”(soln, M) - (xAAHOo(soln,A) + x,AH O”(soln,B)}.

(1) In contrast to the behaviour in the nonaqueous mixture DMF + NMF, AHE(soln) deviates substantially from zero in mixtures of DMF -t water.“’ We have explained”) this deviation as a result of two effects: one that would appear if the tetra-n-butylammonium ion were not hydrated hydrophobically in water and aqueous DMF and another which is due to hydrophobic hydration. Accordingly the excessenthalpy of solution in DMF + H,O could be representedby AHE(soln) = (x” - x)AH,,dH,O),

(2)

in which x is the mole fraction of water, II is the number of water molecules which hydrate one butyl group, and AH,,(H,O) represents the enthalpic effect of the

W. J. M. HEUVELSLAND AND G. SOMSEN

876 36

21

18

t

I

4

0.2

0.4

I

t

0.6

I

I

0.8

x (H&V

FIGURE 1. Enthalpies of solution, AH”(soln), of n-Bu,NBr in mixtures of DMF + water as function of composition at six temperatures.0,278X K; B, 288.15K; A, 298.15K; Q308.15 K; x, 318.15K; 0, 328.15K.

hydrophobic hydration of the n-Bu,N+ ion in pure water. Very recently Lindenbaum, Stevenson,and Rytting cl ‘) showed that equation (2) can be applied with equal success to somenon-ionic solutes. Values of AHE(soln) for n-Br,NBr in the temperature range 278 to 328 K are shown in figure 2. They can be reconciled easily with equation (2). In addition figure 2 demonstrates clearly that the position of the maximum of the excess enthalpy of solution is almost independent of temperature. This means that the value of II hardly changes.Further, figure 2 showsthat the heights of the maxima decreaseregularly from 278 to 328 K. Since the height of a maximum can be related to the magnitude of AHhb(HZO), this corresponds to a strong reduction of mhb(HZO). By optimizing both parameters n and AI!I,,(H20) the experimental mE(soln) data can be fitted to equation (2). The resulting best values of n and AHhb(HZO) are presented in table 2. Moreover this table lists the mean deviations of the calculated

N(n-C*Hp),Br IN HCON(CH&+HaO

877

FIGURE 2. Dependenceof excessenthalpiesof solution, AH&(soln),of n-BthNBr in DMF + water mixtures on the mole fraction of water at various temperatures,0, 278.15K; X, 288.15K; 0, 298.15K; A, 308.15K; n , 318.15K; 0, 328.15K.

TABLE 2. The enthalpic effect of hydrophobic hydration, AHhs(HaO),the number II of hydrating water moleculesper butyl group, and the mean deviations betweencalculated and experimental values of fiE of n-BuJVBr in DMF + water mixtures at d&rent temperatures TIK

AHhb(HzO)/kJmol-1

R

(AH&-AH&)/W

278.15 288.15 298.15 308.15 318.15 328.15

-65.6 -59.7 -52.8 -46.3 -40.5 -34.4

6.0 6.1 6.4

0.38 0.31 0.23 0.19 0.12 0.15

2 6:7

mol-’

W. J. M. HEUVELSLAND AND G. SOMSEN

878

AHE values from the experimental ones, indicating the good fit. Table 2 makes quantitative again that a temperature change affects only the enthalpic effect of hydrophobic hydration of the n-Bu,N+ ion. In our opinion the slight change in the values of n is hardly significant. Anyhow it makes highly unlikely a possible stepwiseincreasing hydration of the n-Bu,N+ ion in DMF + water mixtures. HEAT CAPACITIES

Another way to discuss the present results is based on a calculation of the partial molar heat capacities Cz z of n-Bu,NBr in mixtures of DMF + water by means of the integral enthalpy of solution method.“*) At one particular solvent composition the enthalpies of solution at different temperatures can be representedwithin experimental error by the equation AH”(soln) = A+BT+CT*, (3) in which the parameters A, B, and C are calculated by a least-squares procedure. TABLE 3. The changein molar heat capacity at dissolution, AC?, and the partial molar heat capacity at infinite dilution Cm P.a of tetra-n-butylammoniumbromide in mixtures of DMF + water as a function of the mole fraction x(HzO) of water, at temperaturesbetween 278and 328K

x0&D) 0 0.2 0.4 0.6

0.1 0.8 0.9

1

:2 0:4 0.6 0.7 0.8 0.9

1 0 0.2 0.4 0.6 0.7 0.8 0.9

1

AC JK-lmol-l T= 278.15 K 169 167 168 188 231 330 524 787

T= 298.15 K 139 139 140 162 204 297

480 746

T= 318.15 K 109 110 113 135 176 264 436 705

CZ2 JK-‘mol-l 620 618 619 639 682 781 975 1238

615 615 616 638 680 773 956 1222 613 614 617 639 680 768 940 1209

xW,O)

AC,” JK-lmolP1

0

T = 288.15K 154 153

0.2 0.4 0.6 0.7 0.8 0.9

1

154 175 217 313 502 766

0

T= 308.15 K 124

0.2 0.4 0.6 0.7 0.8 0.9

1 0 0.2 0.4 0.6 0.7 0.8 0.9

1

125 127 149

190 280 458 725

T= 328.15 K 94 96

AC22 JK-lmol-1 617 616 617 638 680 776 965 1229

613 614 616 638 679 769 947 1214

613 615 618

192;

641

162 248 414 684

681 767 933

1203

N(n-GH&Br IN HCON(CH&SHaO

879

Hence the change in molar heat capacity at dissolution, AC,“, is given by AC; = B+2CT.

(4)

By repeating this procedure at other mole fractions we evaluated AC: as a function of solvent composition. Values of AC; in the various mixtures are given in table 3. On account of the mean deviations in AH”(soln) and the errors due to the curve fitting to equation (3) we estimate the uncertainty of these AC: values to be + 10 J K-’ mol-‘. When C:, 2 is the molar heat capacity of crystalline n-Bu,NBr, values of Cz 2 in the different solvent mixtures can be calculated from C;,=AC;+Cp*,2.

(5)

The most accurate data on the heat capacity of n-Bu,NBr have been reported by Burns and Verrall.“3’ Introduction of their values into equation (5) yields the partial molar heat capacities of n-Bu,NBr presented in table 3. The estimated uncertainty in CE 2 is + 14 J K- ’ mol- ‘. The results in water are in fair agreementwith those obtained by direct calorimetry. (14)For this reason and in view of the more reasonable temperature dependence we consider the present results as more accurate than those published previously!“’ 1200

---.,-1--7.----: __ 7-.--T-I----

3. The partial molar heat capacity at infinite dilution, C$a, of n-Bu4NBr in mixtures of + water as a function of the mole fraction of water at 298.15K.

FIGURE DMF

A representative plot of Cz 2 against x(H,O) is shown in figure 3. It must be borne in mind that the curve in figure 3 represents at the same time the change of the contribution to Cz 2 which arises from the influence of the ions on solvent structure. Passing through the mole fraction range from pure DMF to water Cz z remains constant in regions where the influence of hydrophobic hydration is absent. Beyond

x(H,O) = 0.6, when hydrophobic effectsbecomeimportant, Cz z increasesdrastically towards the value in pure water. This behaviour agrees fully with the description of

880

W. J. M. HEUVELSLAND AND G. SOMSEN

hydrophobic hydration presented above. In this approach the choice of the co-solvent is not essential as long as specific structural effects are absent. Analogous results of Mohanty and Ahluwalia(‘) in dioxan + water mixtures seemto confirm this. The valuable assistanceof Mr P. Pel and Mr J. J. van Norden in carrying out part of the measurementsis gratefully acknowledged. REFERENCES 1. Wen, W. Y. In Water and Aqueous Solutions, Structure, Thermodynamics and Transport Processes.

Horne,R. A.: ed. Wiley: New York. 1972. 2. De Visser,C. Ph.D. thesis, Free University, Amsterdam.1973. 3. De Visser, C.; Somsen,G. J. Chem. Sot. Faraday Trans. Z 1973, 69, 1440. 4. Mastroianni, M. J.; Pikal, M. J.; Lindenbaum, S. J. Phys. Chem. 1972,76, 3050. 5. Falcone, J. S.; Wood, R. H. J. Solution Chem. 1974, 3, 233. 6. Fuchs, R.; Hagan, C. P. J. Phys. Chem. 1973,77, 1797. 7. Mohanty, R. K.; Ahluwalia, J. C. J. Solution Chem. 1972, 1, 531. 8. De Visser,C.; Somsen,G. J. Solution Chem. 1974, 3, 847. 9. De Visser,C.; Somsen,G. J. Phys. Chem. 1974,78, 1719. 10. De Visser,C.; Somsen,G. J. Chem. Thermodynamics 1973, 5, 147. 11. Lmdenbaum,S.; Stevenson,D.; Rytting, J. H. J. Solution Chem. 1975, 4, 893. 12. Criss, C. M.; Cobble, J. W. J. Anrer. Chem. Sot. 1961, 83, 3223. 13. Burns, J. A.; Verrall, R. E. Thermochimica Acta 1974,9, 277. 14. Jolicoeur, C.; Philip, P. R. J. Solution Chem. 1975, 4, 3.