J . Chem. SOC., Faraday Trans. 1, 1986,82, 53-60 Cross Enthalpic Pair Interaction Coefficients with Water in N,N-Dimethylformamide and with N,N-Dimethylformamide in Water Michael Bloemendal, Aart C. Rouwt and Gus Somsen" Department of Chemistry, Free University, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands From earlier published enthalpies of solution of various organic compounds in binary solvent systems containing water and N,N-dimethylformamide (DMF), the enthalpic pair interaction coefficients (B:,) of these compounds with DMF in water as solvent, and with water in DMF as solvent have been evaluated. The organic solutes comprise urea, alkylsubstituted ureas, amides and alkanols. For water dissolved in DMF, enthalpic interaction coefficients have been obtained from microcalorimetrical dilution experiments.In water and DMF the various results differ considerably. In water a much larger variation in B!& is found than in DMF. In the former an almost constant CH, contribution to Bt,DMF is found for most homologous series. Branching of the alkyl chain in the organic compound hardly influences 132,DMF. The results indicate that hydrophobic interaction plays an important role. In DMF the results are less regular and branching effects are considerable. Hydrogen bonding has a large impact on Bt,H20. The relations between the enthalpic pair interaction coefficients on basis of the Savage and Wood additivity approach and the Barone method (square root rule) are tested. When sufficient functional groups are introduced, the Savage and Wood concept seems to work well for a large amount of molecules of different classes in water.The Barone approach seems to be more useful for the interaction between molecules with comparable functional groups. During recent years a number of reports have been published on the enthalpic interaction coefficients of solutes in dilute solutions on basis of the McMillan-Mayer In this approach, the enthalpic pair interaction coefficient, Bk, is related to the interaction between two solute molecules. As this interaction is mediated by the solvent, the values of Bk are influenced by the structure of the solvent, particularly that around the solute molecules. Values for the enthalpic pair interaction coefficient between similar solute molecules, Bkx, can be obtained from microcalorimetrically determined enthalpies of dilutionlo and calculated from the excess enthalpies of binary mixtures.l1 Values for the enthalpic pair interaction coefficients between unlike solute molecules, I?:&., have mostly been determined from the enthalpy of mixing of solutions of x and y in the same solvent.** 6 v 7 7 lo De Visser and coworkers12y l3 have shown that B:y values can also be obtained from data for the enthalpy of solution of a solute x in mixtures of the solvent with small amounts of a substance y (cosolvent), provided the enthalpies of solution are accurately known. Such enthalpies have been published by Rouw and Somsenl4~ l5 for several organic solutes in mixtures of water with DMF over the whole composition range. From these data it is possible to calculate the enthalpic pair interaction coefficients between these solutes with either DMF in the solvent water or with water in the solvent DMF. These B!& values are presented in this paper and compared with and B$y values obtained from enthalpies of dilution.Since the Bty value for H,O dissolved in DMF has t Present address : Sigma Coatings, Amsterdamseweg 14, 1422 AD Uithoorn, The Netherlands. 5354 Pair Interaction Coeflcients with DMF+ H 2 0 not been measured previously, we will also present microcalorimetrically determined enthalpies of dilution for H,O in DMF. In this paper the following abbreviations will be used: methanol, MeOH; ethanol, EtOH; propanol, PrOH ; butanol, BuOH ; pentanol, PeOH; formamide, FA; acetamide, AA; butyramide, BA; N-methylformamide, NMF; N-butylacetamide, NBA; N,N-dimethylformamide, DMF; N,N-dimethylacetamide, DMA; urea, U; methylurea, MeU ; dimethylurea, Me2U; tetramethylurea Me,U ; ethylurea, EtU.Experimental Results When a solute x is dissolved in a liquid mixture containing a large amount of a main solvent s and some cosolvent y, its standard molar enthalpy of solution, A,,,W(M) is dependent on the mole fraction of y, x,. De Visser et al." have shown that for xy -+ 0, the limiting slope b of the curve relating A,,,H"(M) to xs is related to B:y by b = 2 B;,/M, where M, is the molar mass of the solvent. De Visser et al. obtained values of b for different solutes by least-squares fitting of experimentally obtained As,, W(M) values in solvent mixtures with a low content of cosolvent y to the equation Asol W(M) = a + bx, + cx;.(2) Some years ago we measured accurate values of Asol W(M) for alkano1s,14 amides15 and substituted urea in mixtures of water and DMF over the whole composition range. A fit of the values at low DMF content (x,,, < 0.15) to eqn (2) and combination with eqn (1) yields enthalpic pair interaction coefficients between several organic molecules and DMF molecules in water. In an analogous way Bty values between those organic molecules and water in the solvent DMF have been obtained from data at low water content (xHz0 < 0.189). Both sets of BZy values are presented in table 1. We estimate the uncertainty of these coefficients at 15 . The value obtained for DMF in water as solvent (620 J kg molF2) refers to the interaction between two like molecules and may be compared with values obtained from enthalpies of dilution by Wood and Hiltziklg (578 J kg mol-2) and by Tasker and Wood20 (737 J kg mol-2).Table 1 also presents enthalpic interaction coefficients between like molecules, B;x, calculated from enthalpies of dilution in both water and DMF. Most data have been taken from the literature. Only the enthalpy of dilution of water dissolved in DMF has been determined experimentally by microcalorimetry . The experimental procedure has been described before.9$ 29 In table 2 we present the enthalpic change, AH, when nA moles of H 2 0 in DMF at molality mA,i are mixed with n, moles at H,O in DMF at molality rnB,i to give a solution with final molality m,.The relation between AH and the McMillan-Mayer enthalpic interaction coefficients is given by where Bh, is the nth enthalpic interaction coeffi~ient.~.~~ Values of Bh, can be obtained from a least-squares analysis of the results of table 2 in terms of eqn (3) to yield Bt = (- 160 & 1) J kg mo1-2 and Bk = (14.2 0.3) J kg2 molt3. The uncertainties'are the standard deviations. Only for these coefficients the Student's t-test indicated a probability of more than 95% that their values were not zero. Discussion Interaction Coefficients in Water In water all values of the enthalpic pair interaction coefficients between unlike molecules, Bty, except that for urea are positive. They become more positive when more or largerM. Bloemendal, A . C . Rouw and G.Somsen 55 Table 1. Enthalpic pair interaction coefficients in water and DMF", solute (4 solvent : water - - MeOH EtOH PrnOH Pr'OH BunOH BuiOH BusOH ButOH PenOH PetOH H2O FA NMF DMF AA DMA NBA BA U MeU 1,l -Me,U 1,3-Me2U Me,U EtU 530 [ 141" 760 [14] 1020 [14] 1020 [14] 1300 [14] 1240 [14] 1300 [14] 1270 [14] 1520 [14] 1580 [14] - 140 [IS] 420 [ 151 620 [ 151 190 [15] 750 [ 151 1270 [15] 660 I151 - 160 [23] 100 [ 151 280 [ 151 380 [15] 1180 [15] 340 [ 151 ( A ) alkanols 247 [16] 243 [17] 561 [17] 339 [ 181 1004 [17] 1000 [18] 916 [18] 657 [ 171 1757 [18] 0 (B) amides 272 [22] 12 [19] 962 [22] 1477 [22] - -77, - 115 [19, 201 578, 737 [19, 201 - (C) ureas -348 [13] -85 1251 38 [26] 35 [27] 2032 [28] 160 [27] solvent: DMF ____ - 80 [ 141' -20 [14] 10 [14] 70 [ 141 70 [14] 50 [14] 10 [14] 170 1141 70 [14] - 10 [14] - 100 [15] 0 [151 - -40 [15] - 180 [15] -60 [15] 30 [15] -230 [23] -230 [15] - 160 [15] -370 [15] - 10 [15] - 130 [15] - - - - - - - - - - - 160 100 [21]" 4 [211 0 -350 [13] 4 ~ 3 1 - 302 [ 1 31 -313 [9] - 5552 [24] -2200 [24] - 171 1 [24] -595 [24] - 17 [24] -2108 [24] - a Units J kg mol-2; Bxy from enthalpies of solution; B,, from enthalpies of dilution.in brackets denote references. Numbers In view of the accuracy of the data round values are given. alkyl groups are introduced into the molecules. Similar positive values for compounds containing alkyl groups were found in other investigation^.^? l2, 19* 22* 2 6 q 28 They are supposed to be due to a partial destruction of the hydrophobic hydration structures (cospheres) around the alkyl groups when these cospheres ~ v e r l a p . ~ ~ ~ 31 This process is accompanied by an increase in enthalpy, resulting in a positive contribution to the enthalpic pair interaction coefficient.Fig. 1 gives B!& in relation to the number of C atoms for sets of related compounds containing n-alkyl groups. For the n-alkanols, the unsubstituted amides AA and BA, and the monoalkyl ureas the slopes are nearly equal, suggesting that for each set of compounds the interaction between an additional CH, group and a DMF molecule is essentially similar. For these compounds the mean CH, increment is 244 & 22 J kg mo1-2. Within the experimental uncertainty this value equals the one obtained by Heuvelsland et a1.13 from their study on tetra-alkylammonium bromides (250f 14 J kg mol-2).However, it differs from the CH, increment between acetamides and corresponding formamides. From the results on FA, AA, DMF and DMA, we calculate a mean CH, increment of 90 J kg mo1k2 in the B:y values. On the other hand, it can be observed that the substitution of N-protons by methyl groups in56 Pair Interaction Coeficients with DMF+ H,O 1500 Table 2. Enthalpies of dilution of H,O dissolved in DMF at 25 "C" - pen7 mA,i n A mB,i nB mf AH 1200 N I - 8 900- Do Y c-, 1 600- sc aq 300 0- 0.3850 0.5507 0.6337 0.7329 0.9730 0.9349 1.2304 1.3276 1.4997 1.4377 1.8822 2.4994 2.1443 3.1926 - - 0.8232 1.7761 2.0458 3.0793 1.2238 3.9567 3.9432 5.61 19 6.3 130 2.7410 7.8222 10.0758 8.9360 11.3984 0 0 0 7.55 5.77 9.63 0 16.43 18.69 23.58 25.94 0 0 0 0 0 0 16.57 21.35 21.05 29.69 33.44 41.69 47.28 0 0 0 0 0.1377 0.3276 0.3800 0.4840 0.25 1 1 0.6 196 0.7329 0.9349 1.0580 0.4989 1.3276 1.8822 1.4997 2.1443 29.86 56.70 74.84 108.66 124.03 170.38 262.10 283.18 338.28 342.63 497.71 615.74 622.77 995.98 - 4.0 -3.1 - 1.0 + 0.4 - 0.9 + 0.2 + 1.1 + 1.9 -0.5 +0.5 + 1.8 + 1.3 + 1.4 - 0.7 a Units of mA,i and m,, mol kg-l; mB,i, mmol kg-l; nA, mmol; ng, pmol; AH, mJ.ArA) = 100 [AH(exptl) -AH(calc)/AH(exptl), where AH(ca1c) is calculated from eqn (3). NBA BunOH D, / / Prn OH / NMF, EtU McOH ,' MeU ' d' / / d -300' I I I I 1 I 0 1 2 3 4 5 6 7 nC Fig. 1. 13&F in relation to the number of C atoms for several compounds in water. formamide leads to a 'normal' CH, increment in Bgy (mean value 240 J kg moF2).Apparently the contribution to Bt as a result of the introduction of a CH, group in formamides to obtain acetamides is markedly different from that due to other methylene groups. It may be argued that this is caused by the acidic character of the formyl proton. However, this would mean that the difference in hydrophobicity, and hence in B$,M . Bloernendal, A . C . Rouw and G. Sornsen 57 Table 3. Contributions to BE,,,, of several functional groups in water" compound functional group ~~ alkanols OH formamides HCONH, ace tamides H,CCONH, unsubstituted amidesd H,CCONH, N-alkylureas H,NCONH, a Units: J kg rnol-,. This paper. Ref. estimated value6 calculated valueC 230 44 151 70 185 25 1 185 25 1 - 135 - 268 (22). Formamide not included. between acetamides and formamides is larger than that between other compounds differing by one CH, group.This is contrary to what is found. Since it is well known that the CH, group adjacent to the carbonyl group has a strong inductive influence on the electronic structure of the carbonyl we contribute the deviating CH, increment to a different interaction of the carbonyl group, when higher amides are compared with formamides. The broken lines in fig. 1 show the effects of alkyl substitution at the N atom on the pair interaction coefficients. Generally the increments are comparable to those in the previously mentioned homologous series. This is clearly demonstrated by the BtY. values of the two isomers DMA and BA which correspond within experimental error. It implies that in water the interaction of DMF with the functional groups CON, CONH and CONH, is more or less equal, indicating that the contribution of the N-bonded protons is negligible.A similar conclusion has been obtained by Wood and of substitution of N-protons by methyl groups is considered for the urea compounds, it appears that a reasonably constant CH, increment is found going from U through MU to 1,3-DMU. 1,l-DMU and Me,U seem to be at variance with this trend. However, in view of the uncertainty of the data all urea compounds may lie on a common line with a CH, increment close to the increments of the other sets of compounds. The constant CH, contribution to Bk,UMF for most homologous series makes it possible to estimate the contribution of the functional groups of these series to by extrapolating the linear relations in fig.1. Since the values of B!,DMF for the branched alkanols are more or less the same as those of their normal isomers they are included in the estimation of the contribution of the functional group in the alkanols. The results are collected in table 3 and will be discussed later. Generally the observations mentioned so far indicate that there is no preferential site for the interaction between DMF and alkanols, amides, monoalkyl urea and tetra-alkylammonium ions in water. The interaction enthalpy seems to be determined by the number of groups only. This suggests that the Savage and Wood additivity approach22 will be applicable for these compounds. In this approach each molecule is considered to be composed of a limited number of functional groups and a certain BiY value is assumed to be the sum of the interaction of all functional groups in the solute molecule x with all functional groups in the solute molecule, y, resulting in 20, 22 When the influence on Bk, = x.4d%J%i (4) 2 ,I where nXai is the number of groups i in molecule x, n y , j is the number of groups j in molecule y and hij is the enthalpic group interaction coefficient between the groups i and j [for details, see ref. (22)]. Tasker and Wood36 give a survey of group interaction coefficients based on experimental work of several authors. When, as in the original paper of Savage and Wood,22 a CH group is counted as 0.5 and a CH, group as 1.5 CH, groups, a value for BtH2,DMF of 200 J kg mol-2 is predicted on basis of their data set for amides.58 Pair Interaction Coeficients with DMF+ H,O Table 4.Prediction of BE,DMF from BEx and Bk,," in H,Ob according to Barone solute Bh,,(exptl) BFJcalc.) solute Bh,,(exptl) B:,(calc.) MeOH EtOH PrOH Pr'OH BunOH BuiOH BuSOH ButOH 530 760 1020 1020 1310 1240 1300 1270 _____ 380 380 570 440 760 760 730 620 NMF AA DMA NBA 1,l-Me,U 1,3-Me2U Me,U EtU 420 190 750 1270 280 380 1180 340 400 260 750 920 150 140 1080 300 " Ref. (19). Units J kg mol-,; rounded values are given. This value is comparable with the value of 244 22 J kg mo1P2 reported in this paper. From eqn (4) and the data of ref. (36) we have also calculated the enthalpic interaction coefficients between DMF and several functional groups. These coefficients are compared with the functional group contributions given in table 3 as a result of the extrapolation procedure mentioned above.The values are comparable, but definitely not similar. However, it should be realized that the group interaction coefficients used for the Savage and Wood prediction are based on data for different types of compounds. The OH interactions, for example, are based on a number of both hydroxy and polyhydroxy compounds. This, together with the different influence of the CO group in formamides as compared with acetamides, leads us to the conclusion that an important reason for less satisfactorily predictive results of the Savage and Wood approach lies in the simplification of functional group contributions. The almost constant CH, increment for most sets of compounds points to strong additivity as long as sufficient functional groups are introduced.For positive enthalpic pair interaction coefficients, Franks and coworkers37 have suggested using the expression BkY = (BixB;Y)$ in order to relate like and unlike pairs.? In table 4 we present values predicted according to eqn (5) together with the experimental ones. It is obvious that the empirical rule holds fairly well for compounds with related functional groups (DMF + amide or substituted urea), but fails for compounds with more different functional groups (DMF + alkanol). For many alkanols the experimental B!& value is even larger than either h,, or hYY. Comparing the predicting power of the method of Barone with that of Savage and Wood in aqueous systems, it seems that the former is more useful for interactions between molecules with comparable functional groups, whereas that of Savage and Wood gives better results for a large amount of molecules of different classes.Interaction Coefficients in DMF The B$,H20 values in DMF as solvent are presented in table 1 also. They show smaller variations in magnitude than those with DMF in water as the solvent. However, branching effects seem to be more important and the CH, increments are less constant, which suggests that in the solvent DMF a simple additivity approach will be more approximative. In fig. 2 we have plotted Bk,H20 of alkan-1-01s in relation to the number of C atoms in the alkan-1-01. The value of Bk20,H20 is also given in this figure. It fits onto the curve t This equation has been applied extensively by Barone and c o ~ o r k e r s .~ ~M . Bloemendal, A . C. Rouw and G. Somserz 59 200 100 P( 3 z r“ - 0 O? 7 --. G X cq -1 00 -200 I 1 1 1 1 1 PeOH Me0 I I I I I I 0 1 2 3 4 5 nC Fig. 2. B&z, in relation to the number of C atoms for alkan-1-01s in DMF. of the alkan-1-01s very well. Apparently, in this respect a water molecule at high dilution in DMF is comparable with other OH containing solutes. A similar conclusion was reached by Zegers and S ~ m s e n ~ ~ with respect to the partial molar volume of H,O at infinite dilution in DMF. Since water behaves as a ‘normal’ alkanol, we conclude that the interaction between a water and an amide molecule occurs predominantly along one hydrogen bond. It has been found for alkanols in polar solvents that an increase in chain length results in a decrease in the number and/or the strength of OH*-.OH hydrogen bond~,~O-~, which may also be the reason for the positive shift in with increasing chain length of the alkan-1-01s.It has been found also that branching of the alkyl chain has a strong influence on the OH-OH interaction^,^^-^^ which corresponds to the observed sensitivity of B~lkanol,H20 for branching. However, since Bk, HzO approaches zero for propan-1-01 with molar volume close to that of DMF, the results may also be related to volume effects. The values of Be,H20 of the amides are relatively small and do not show special trends. The cross enthalpic interaction coefficients represent the enthalpy change when solutes x and y interact with each other in a solvent.The comparatively small and scattered values for the amides may indicate that an important part of the H,O-amide interaction occurs via the CON group which solute and solvent molecules have in common. It has been found that in mixtures of alkanols and amides the OH*-.O=C interaction is indeed d ~ m i n a t i n g . ~ ~ BtY for the interaction between Me4U and H,O is almost zero. The 13k,H20 values for compounds with one or more NH groups are negative and comparable in magnitude ( - 160 to - 320 J kg mol-2). In this case the interaction is apparently dominated by the NH * * - OH hydrogen bond. As the proton-donating character of different ureas may differ con~iderably,~~-~~ differences in B!& values are not improbable. Since both Be, and B& are negative in DMF the Franks-Barone approach according to eqn ( 5 ) becomes in this case BEY = - (BEx B!,)a.( 6 )60 Pair Interaction Coeficients with DMF+ H,O Also with this modification the method appears to be unsuccessful. However, we have noticed that in water the Barone method applies best for related solute compounds. The same may be true in the solvent DMF and in that case the Barone equation should hold for interactions involving alkanols and water. Unfortunately data for alkanol-alkanol interactions in DMF are not yet available. This work was carried out under auspices of the Netherlands Foundation for Chemical Research (SON) and with financial aid from the Netherlands Organization for the Advancement of Pure Research (ZWO).We thank one of the referees for helpful comments. References 1 P. J. Rossky and H. L. Friedman, J . Phys. Chem., 1980, 84, 587. 2 L. R. Pratt and D. Chandler, J . Solution Chem., 1980, 9, 1. 3 F. Franks, M. Pedley and D. S. 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