2536
J. Phys. Chem. 1991,95, 2536-2540
Hydratlon Enthalpy of Tetra-n-butylammonlum Ion Yatsuhisa Nagana,* Hideki Mizuno, Minoru Sakiyama, Microcalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, 560 Japan
Tadayuki Fujiwara, and Yasuhiko Kondo Department of Applied Chemistry, Faculty of Engineering, Osaka University, Suita, 565 Japan (Received: August 27, 1990)
By means of oxygen bomb combustion calorimetry, the standard enthalpy of formation AfHoof crystalline tetra-n-butylammonium (TBA) iodide was determined to be -498.6 f 2.7 kJ/mol. By use of this and the literature values of the enthalpies of solution, the standard enthalpies of formation of TBA+(aq), of TBABr(cr), and of TBACl(cr) were derived to be -426.7 f 3.0, -540.3 f 3.2, and -564.8 3.1 kJ/mol, respectively. Good linear relationships were found between the length of the alkyl chains and the standard enthalpies of formation of tetraalkylammonium halide crystals as well as those of the cations in aqueous solution. By estimating AfHo(TBA+,g),the absolute hydration enthalpy of TBA' was evaluated to be -260 f 20 kJ/mol. The absolute hydration enthalpies of tetraalkylammonium ions were interpreted well in terms of the following two contributions: (1) the electrostatic term, which can be calculated by the Born model modified for nonspherical ions, and (2) the additive "hydrophobic" term due to hydration of the alkyl chains.
*
Introduction Tetraalkylammonium ions are the monovalent cations of large ionic radii that form no strong hydrogen bond to any solvent molecules in solutions. In early studies, the transport properties in aqueous solution, such as the viscosity B coefficients and the limiting ionic conductances, of tetraalkylammonium ions were found to show a temperature dependence very different from those of monatomic ions of smaller ionic radii.' This has been interpreted in terms of the 'structure making effect" of tetraalkylammonium ions in aqueous solution. Tetra-n-butylammonium (TBA) and tetraisoamylammonium compounds form the clathrate hydrate crystals below ambient temperature without applying high pressures. This fact suggests the ammonium ions with long alkyl chains have a strong tendency to enable the surrounding water molecules to form the clathratelike structure even in aqueous solution.* So far, many thermodynamic and spectroscopic studies have indicated the concept of "structure maker" appropriate for a TBA+ ion. However, the scarcity of established energetic data on the hydration interaction has hampered a detailed discussion. Recently, Nagano et al. derived the standard enthalpies of formation of crystalline tetramethylammonium (TMA) and tetraethylammonium (TEA) halides and the cations in aqueous solution, by means of oxygen bomb combustion calorimetry of the iodide crystal^.^ In addition, thL values of AfHo of the gaseous TMA+ and TEA' ions could be estimated by the extrapolation of recent experimental AfHO data of alkylammonium ions in the gas phase. By using these values of AfHofor the gaseous and aqueous states, the hydration enthalpies AhHoof TMA' and TEA' ions were determined: A,,HO(TMA+)= -251 kJ/mol, A&F(TEA+) = -239 kJ/m01.~ It should be remarked that hydration enthalpies determined in the series of our works are not the conventional quantities, but the absolute ones that have been calculated according to the equation
ventional hydration enthalpies are based on the assumption that AhHo(H+) = 0. Johnson and Martin5 estimated hydration enthalpies of tetraalkylammonium ions in aqueous solution, using the calculated lattice enthalpies by Ladd6 and Boyd:' AhHo(TMA') = -207 kJ/mol and AhHo(TEA+)= -180 kJ/mol, where the reference hydration enthalpy AhH0(H+)was shifted to -1 136 kJ/mol for comparison. There are serious disagreement between the AhHo values of TMA' and TEA' derived by Nagano et al. and those by Johnson and Martin. This discrepancy seems to be due to the underestimation by Ladd and Boyd of the magnitude of dispersion force terms in the evaluation of the crystalline lattice enthalpies of the tetraalkylammonium halides and also to their neglect of the effect of shift in the electronic energy of the cations caused by plausible geometry changes in the molecules on going from the crystalline state to the gaseous state. This fact shows that the calculation of lattice energy for ionic crystals with polyatomic ions is still underdeveloped? partly because of the scarcity of reliable ArHo(g) data of polyatomic ions. In the present study, the values of AfHo of tetra-n-butylammonium (TBA) halide crystals and the aqueous TBA' ion were derived for the first time by the oxygen bomb combustion calorimetry of the crystalline TBA iodide. The AhHo of TBA+ was evaluated by using AfHo(TBA+,aq) and the estimated value of the gaseous ArHoof TBA+. The hydration enthalpy of TBA' ion was found to be of magnitude similar to those of TMA' and TEA' ions. The values of AhHo of TMA', TEA', and TBA' ions were discussed in terms of the electrostatic hydration, which were calculated by the Born model modified for the nonspherical ion shape, and the hydration of the alkyl chains. Experimental Section Materials. Purification and purity determination of tetra-nbutylammonium iodide (TBAI) were carried out in the following
AhHo(TMA+)= AfHo(TMA+,aq) - ArHo(TMA+,g) + by using the adopted value of hydration enthalpy of proton AhHo(H+),-1 136 kJ/mol recommended by K l o t ~ . ~The con(1) Kay, R. L. In Water A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 3. (2) Wen, W . Y. In Water and Aqueous Solurions; Horne, R. A.,Ed.; Wilev-Interscience: New York. 1972. (f)Nagano. Y.; Sakiyama, M.;Fujiwara, T.; Kondo, Y. J. Phys. Chem.
1988, 92, 5823.
0022-3654/91/2095-2536$02.50/0
(4) Klots, C . E. J . Phys. Chem. 1981,85, 3585. ( 5 ) Johnson, D. A.; Martin, J. F. J . Chem. Soc., Dalron Trans. 1973, 1585. ( 6 ) Ladd, M. F. C. 2.Phys. Chem. 1970, 72, 91.
(7) Boyd, R. H. J . Chem. Phys. 1%9,51, 1470. ( 8 ) Recently, Marcus reported the hydration enthalpies of individual ions
based on the calculated lattice enthalpies by use of Ladd's equation and on the TATB extrathermcdynamic assumption. (Marcus, Y. J . Chrm. Soc., Faraday Trans. 1 1987,85339). However, the derived values of A@ for H* extends over a region of about 50 kJ/mol, the dependence on the countercation species for the tetraphenyl ion being more significant than that on the counteranion species. This demonstrates the incompletentgs of Ladd's equation for polyatomic ions. The hydration enthalpies derived by Marcus do not seem to be conclusive.
0 1991 American Chemical Society
Hydration Enthalpy of Tetra-n-butylammonium Ion
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2537
TABLE I: Auxiliary Data for the Calculation of Standard Energies of Combustion
materials TBAI benzoic acid cotton fuse
formula
P/8
cm-j C I ~ H ~ ~ N II.23 C7H602 1.32 CH1,8600.93 1.5
cy/ -I
(dU/dP)Ta/
J K- x
J x-' MPa-'
(1.200)
(-0.005 27) -0.005 27 -0.029 0
1.21
1.70
OValues in parentheses are estimated. way: Commercial TBAI (Nacalai Tesque, a special reagent for polarography) was twice recrystallized from the acetone-ether mixture and then was kept under vacuum over P205for 3 days. After grinding, the dried material was again kept under vacuum over P205for 1 day. The reduction of the weight during the second drying was less than 0.02%. The purity of the material was determined to be 99.96% by the gravimetric method previously described.' Since TBAI is hygroscopic, the pellets for combustion experiments were prepared under dry nitrogen flow, after keeping the material under vacuum at 100 O C for 2 days. Apparatus and Procedure. A rotating bomb calorimeter, described elsewhere: was used. The calorimeter was calibrated by burning thermochemical standard benzoic acid (N.I.S.T. SRM 39i) under certificate conditions. Mean and standard deviation of the mean of observed energy equivalents for the empty calorimeter was 15 381.49 f 0.56 J/K (eight experiments). The combustion was carried out at 3.0 MPa of oxygen pressure. As a combustion aid, 0.12-0.47 g of the standard benzoic acid (N.I.S.T. S R M 39i) was used for the combustion of 0.51-0.83 g of TBAI. Seven combustion experiments of TBAI were carried out. The ideal combustion reaction to which the energy of combustion refer is given in the following scheme: C16H36NI(~r) + 2502(g) = 16C02(g) + 18H20(1) + 1/2N2(g) + ?212(cr) (1) Actually, the nitrogen was partly oxidized, while the iodine was converted substantially to elemental iodine. After the calorimetric measurements were completed, the combustion products were analyzed. The bomb gases were tested for carbon monoxide by a commercial CO detection tube (Gastec). The internal surface of the bomb was washed out with distilled water. The endpoint in the sodium hydroxide titration of nitric acid was not clear owing to the low concentration of the nitric acid and to the interference from iodine dissolved in the washings. Therefore, nitric acid in the washings was determined by using an ion chromatographic analyzer (Yokogawa, IC500) equipped with an electric conductivity detector and PAXI-035 and SAXI-205 columns. The analyzer was calibrated by standard N a N 0 3 solution. The possible error of nitric acid determination is 1%, which is negligibly small for the present work, because the correction of nitric acid contributes to the final standard molar combustion energy of TBAI only by 0.1% of the total. In every case, no nitrous acid was detected with the Griess-Romijn reagent, so that its contribution was safely neglected for the combustion energy calculation. Reduction to standard states was carried out by combining the literature methods for organic nitrogen and iodine c o m p o ~ n d s . ~ The J ~ standard molar combustion energies of TBAI after the correction did not depend on the ratio of the amount of TBAI to that of the combustion aid. This fact also suggests the reliability of the whole procedure.
Results Auxiliary data for the calculation of the standard molar energies of combustion are listed in Table I. Details of the combustion calorimetric results are presented in Table 11. Most of the symbols in Table I1 are essentially the same as those used by Hubbard (9) Sakiyama, M.; Nakano, T.; Seki, S . Bull. Chem. Soc. Jpn. 1975,48, 705. Nshiyama, K.;Saluyama, M.; Seki, S.;Horita, H.; Otsubo, T.;Misumi, S . Bull. Chem. Soc. Jpn. 1980,53, 869. (10) Hubbard, W. N.; Scott. D.W.; Waddington, G. In Experimental Thermochemistry; Rossini, F. D., Ed.; Interscience: New York, 1956.
t.' 0
3 4 n Figure 1. Standard enthalpies of formation of tetraalkylammonium ((CnHwl)4N) halides (chloride, open squares; bromide, closed squares; open circles, iodide) and the aqueous cations (closed circles). 1
2
et al.IO The mean and standard deviation of the mean for the observed standard molar energies of combustion AJ"'(cr) of TBAI at 298.15 K were -10921.5 f 0.48 kJ/mol. The final overall uncertainty of &uD(cr) of TBAI, which is defined as twice the combined standard deviations of the mean, was determined to be f1.5 kJ/mol by using the equation of the error propagation."
Discussion The standard enthalpy of formation ArHo(cr) of TBAI at 298.15 K and 100 kPa was derived from the observed 4 u D by using the CODATA recommended values of AfHo(H20,1) (=285.830 f 0.042 kJ/mol)12 and AfHo(C02,g)(=-393.51 f 0.13 kJ/mol) .l 2 The conventional standard enthalpy of formation of aqueous TBA+ ion was evaluated by the equation AfHo(TBA+,aq) = AfHo(TBAI,cr) + AwlHo(TBAI)- AfHo(I-,aq) (2) where L I H o is the standard enthalpy of solution in water, and ArHo(I-,aq) is the conventional standard enthalpy of formation of the aqueous I- ion. The values of the auxiliary quantities are &,Ho(TBAI) = 15.0 f 1.0 kJ/mol13 and AfHo(I-,aq) = -56.90 f 0.84 kJ/mol.I2 Using the value of AfHO(TBA+,aq), we can determine the standard enthalpies of formation of the other tetra-n-butylammonium halides in the crystalline state on the basis of the relation AfHo(TBAX,cr) = ArHo(TBA+,aq) + AfHo(X-,aq) - L I H 0 ( T B A X ) (3) where X stands for CI and Br. The following values were employed: AJP(TBAC1) = -28.9 f 1.0 kJ/mol," $dHO(TBABr) = -7.9 i 1.0 kJ/mol,I3 ArHo(C1-,aq) = -167.080 f 0.088 kJ/ mo1,I2 and ArHo(Br-,aq) = -121.50 f 0.15 kJ/mol.12 Derived standard thermodynamic quantities are summarized in Table 111. With the results on TMA and TEA,3 we can examine the dependence of the standard enthalpies of formation of tetraalkylammonium halide crystals and of the aqueous cations upon the length of the alkyl chains. Surprisingly, good linear relationships were found for every series as shown in Figure 1, Le., the standard enthalpies of formation are the linear functions with (1 1 ) Olofsson, G. In Combustion Calorimetry; Sunner, G., Mansson, M., Eds.; Pergamon Press: Oxford, 1979. (12) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Shumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.;Nuttall, R. L. J . Phys. Chem. Re/. Dura
982, I I ( 2 ) . CODATA Task Group on Key Values for Thermodynamics, 1977; CODATA Bull. 1978.28; J . Chem. Thermodn. 1978,10,903. (13) Ahrland, S.;Ishiguro, S.; Portanova, R. Ausr. J . Chem. 1983, 36,
1805.
2538 The Journal of Physical Chemistry, Vol. 95, No. 6,1991
Nagano et al.
TABLE II: Summary of Combustion Calorimetric Results 011 TBAI' m(compd)lg m(benzoic acid)/g m(fuse)lg mYHiO)/g p'(gas)lMPa (Ti/K) - 273.15 (Tf/K) - 273.15 ATCorrIK nf(HN03)/mmol
WgnlJ 4 l J
4ud,(HNo3)/J cl(cont)/J K-l c'(cont)/J K-I
-W,,lJ
-(AUO,/M(compd)J/kJ g-I -AUO,(compd)/kJ mol-'
0.639 25 0.331 38 0.002 47 1 .oo 3.040 23.18354 25.007 88 0.023 94 0.333 2.5 10.1 19.9 17.2 19.1 27 722.8 29.5644 10920.3
0.77062 0.183 37 0.002 13 1.oo 3.040 23.181 17 25.00408 0.024 02 0.401 2.5 8.2 23.9 17.2 19.2 27 698.9 29.5713 10 922.8
0.5 12 97 0.470 56 0.002 27 1.00 3.040 23.18193 25.00262 0.024 00 0.314 2.6 11.9 18.7 17.2 19.0 27 665.0 29.5687 10921.9
0.83083 0.11530 0.001 99 1.00 3.040 23.181 26 25.002 22 0.023 69 0.408 2.7 7.3 24.4 17.2 19.3 27 673.8 29.5653 10920.6
0.677 93 0.289 15 0.002 15 1 .00 3.040 23.18047 25.005 95 0.023 21 0.373 2.6 9.5 22.3 17.2 19.1 27751.0 29.5697 10922.2
0.771 88 0.183 24 0.002 03 1.00 3.040 23.18086 25.004 84 0.023 36 0.409 2.6 8.2 24.4 17.2 19.2 27 725.0 29.5627 10919.7
0.696 98 0.26472 0.00203 1.oo 3.040 23.17937 24.998 38 0.022 14 0.370 2.7 9.2 22.1 17.2 19.2 27 677.4 29.57 10 10922.7
#The symbols are similar to those used in ref 10.
TABLE III: Derived Molar Standard Thermodynamic Quantities at 298.15 K
-4'Jm"l
TBAI(cr) TBABr(cr) TBACl (cr) TBA+(aq)a
kJ mol-l 10921.5 & 1.5
- U m o /
kJ mol-' 10942.5 1.5
-4Hm0/ kJ mol-l 498.6 i 2.7 540.3 i 3.2 564.8 f 3.1 426.7 3.0
*
"Based on the convention that AfHo(H+,aq) = 0.
respect to alkyl chain length n (n = 1 for TMA, 2 for TEA, and 4 for TBA). In all the cases, the deviation from the linear relationship is less than 3.0 kJ/mol, which is within the magnitude of the uncertainty of each datum. It is also remarkable that Figure 1 shows that all the halide crystals have the same slope. Analogous linear relations have been found by Wilson for the standard enthalpies of formation of methylammonium halide crystals as functions of the number of methyl groups,14 although the slopes of the chloride, bromide, and iodide crystals are significantly different from each other. Absolute hydration enthalpy of the TBA' ion AhHo(TBA+) is defined by the equation AhHo(TBA+) = AfHo(TBA+,aq) - AfHo(TBA+,g) + AfHo(H+,g) + AhHo(H+) (4) where AfHo(H+,g) is the standard enthalpy of formation of gaseous proton, and A,,P(H+) is the hydration enthalpy of proton. The last two terms were used to derive a value of AhHO free from the &HO(H+,aq) = 0 convention. 4HO(H+,g) = 1536.2 kJ/mol,'2 in the thermal electron convention. For AhHo(H+)the Klots' value, -1 136 kJ/mol,4 is used. No method has been known for the direct experimental determination of the values of AfH0 of the gaseous tetraalkylammonium ions. Therefore, 4W(TBA+,g) was estimated by the extrapolation of the experimental values of AfW for the gaseous protonated amines. A modem thermodynamic table of the gaseous ionsI5 shows that the differences in the enthalpy between ethylammonium ion and butylammonium ion, 4W(N(C2H,)flH,+,g) - AfW(N(C4H9)xHCx+rg),are 50.95, and 142 kJ/mol for x = 1,2, and 3, respectively. These figures suggest that an additivity rule holds for the A&O(NRXHcx+,g) with R = C2H5, n-C3H7, and n-C4H9, the increment per CH2group being -23.75 kJ/mol with the maximum deviation of 1.3 kJ/mol per CH2 group. The additivity was assumed to be applicable to the corresponding tetraalkylammonium ions. Using A,W(TEA+,g) = 424 kJ/mol,' A,W(TBA+,g) was estimated as follows: AfHO(TBA+,g) = AJP(TEA+,g) + 84W(-CH2:) = 234 kJ/mol. The uncertainty due to this extrapolation is estimated to be f 1 0 kJ/mol. (14)Wilson, J. W.J . Chem. Soc., Dalton Trom. 1976, 891. (IS) Lias, S.G.;Bartmess, J. E.;Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Re/. Data 1988, 17, 1.
Accordingly, AhHo(TBA+)was evaluated to be -260 kJ/mol by using eq 4. The uncertainty associated with the proton affinities for every amine used in this extrapolation has been estimated to be f 1 2 kJ/mol.I6 Hence, final overall uncertainty of AhHo(TBA+) is estimated to be f20 kJ/mol. In spite of the uncertainty, which is not negligibly small, this is the first quantitative determination of hydration enthalpy of TBA+ ion based on experimental data. Let us compare this value with AhHO(TMA+) = -251 f 17 kJ/mol and with AhP(TEA+) = -239 f 17 kJ/moL3 After excluding common uncertainties about proton affinity of NH3 and AhP(H+), the net uncertainties for comparison are f 12, f12, and f16 kJ/mol for TMA+, TEA+, and TBA', respectively. It should be noticed that the numerical value of AhHo(TBA+) is not less than AhHo(TMA+) and AhHo(TEA+). This conclusion is quite in contrast to the naive expectation that an increase in ionic radius would decrease the magnitude of electrostatic hydration enthalpy, which is a dominant factor in the total hydration enthalpy. As a first-order approximation, the hydration enthalpy of an ion would be divided into the two contributions, Le., the electrostatic (el) and nonelectrostatic (ne) quantities: AhH0 = AhHo(el) + &Ho(ne) (5) The first term is due to long-range charge-dipole interaction and short-range multipole-dipole interactions, while the second term is composed of local interactions between the alkyl chain and water molecules in the first hydration sphere. The second term may be considered to have the same magnitude as the hydration enthalpies of the neutral alkanes. In fact, recent studies of hydration energy of the protonated amines indicate that the hydrophobic hydration enthalpy evaluated as the total hydration enthalpy minus the electrostatic term due to the charge of ions is close to those of neutral nonprotonated amines."*'* Olofsson et al. recently reported on the calorimetric measurement of the enthalpies of hydration for rare gases and several alkanes.'9 These values agree with those tabulated by Krishnan and Friedman,20although the latter values seem to have large uncertainties. For alkanes of CnH2n+2(n = 2-8), as a general trend, a linear relationship holds between the hydration enthalpies and the carbon number n, as shown in Figure 2. Therefore, it would not be unreasonable to assume that a linear relation holds between the hydration enthalpies and the carbon number up to 17 and that the hydration enthalpies have the same value within the series of structural isomers. Although these (16) Lias, S.G.; Liebman, J. F.;Levin, R. D. J . Phys. Chem. Re/. Data
1984, 13, 695.
(17) Aue, D. H.;Webb, H. M.; Bowers, M. T. J . Am. Chem. SOC.1976, 98, 318. (18) Meot-Ner (Mautner), M. J . Phys. Chem. 1987, 91, 417. (19) Olofsson, G.; Oshodj, A. A.; Qvarnstrom, E.;Wadso, I. J. Chem. Thermodyn. 1984, 16, 1041. (20) Krishnan, C. V.; Friedman, H. L. In Solute-Solvent Interactions; Coetzee, J. F., Ritchie, C. D., Eds.;Marcel Dekker: 1976, New Yorlt; Vol. 2.
Hydration Enthalpy of Tetra-n-butylammonium Ion
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2539
(a 1 (b) Figure 4. Orientational change of a water molecule in the first hydration shell of a TMAt ion. (a) A water molecule in the first hydration shell is attached to TMAt ion by charge-electric dipole interaction. (b) Orientational change of a water molecule in the first hydration shell is complemented by formation of another hydrogen bond to an outer water
1
3
5
7
molecule.
9
n
Figure 2. Hydration enthalpies of alkanes (C,,HM2). Open circles from ref 19, closed circles from ref 20. The regression line, -AhHo/W mol-' = 13.7 + 3.03n, was used in text to estimate the A h p values of neopentane, 3,3-diethylpentane,and 5,5-dibutylnonane.
+
2ml Figure 3. Hydration enthalpies of tetraalkylammonium ions (closed circles). The solid line indicates AhHD[el,(CnHMI),Nt] derived by subtracting the value of A@(ne), which is assumed to be equal to that of AhHo(~4,,+~Hn,,+~), from AhHo [(cnH~,),N+l.
assumptions would have to be reevaluated in future on the basis of more accurate calorimetric data, it is remarkable here that these assumptions depend on a clear physical image: the hydration energy of alkyl chains is governed by short-range two-body interactions such as dispersion forces between the chain components (CH,) and water molecules, so that the hydration enthalpies are additive. Recent theoretical studies on the hydration of alkalimetal ions shows the importance of the three-body interaction,2' and the sealled structure-making effect might have a contribution from any interactions extending over the several chain components. Therefore, if such nonadditive terms are significant, these would be observed as a deviation from the above-mentioned linear relationship for alkanes. From the linear relation assumption we tentatively have AhHo(neopentane) = -29 kJ/mol, AhHO(3,3-diethylpentane) = -41 kJ/mol, and AhH0(5,5-dibutylnonane) = -65 kJ/mol. By substitution of these values into AhHo(ne) terms of the tetraalkylammonium ions, the values of A h P ( e l ) have been evaluated to be -222, -198, and -195 kJ/mol for TMA+, TEA+, and TBA+, respectively, which are shown in Figure 3 as a function of the length of the alkyl chains. Let us assume at first that the water molecule in the first hydration shell has the fixed configuration with the electric dipole being colinear with the ion-oxygen axis. The electrostatic hydration enthalpy of an ion by water molecules in the first hydration shell is expressed in terms of the charge-dipole interaction AhH(el, 1)/NA= -nqc(o/(47ft/)
(6) where n is the number of water molecules in the first hydration (21) Migliore, M.; Corongiu, G.;Clementi, E.; Lie, G. C. J . Chem. Phys. 1988, 88. 7766. Corongiu, G.; Migliore, M.;Clementi, E. J. Chem. Phys. 1989, 90.4629.
TABLE I V Cartesian Coordinates of Skeletal Atoms in Tetraalkylammonium Ions Used in the Calculation of Electrostatic Hydration Enthalpies species (sym) atom Y/nm z/nm x/nm 0.0 TMA+(Td) N 0.0 0.0 C -0.0842925 0.084 292 5 0.084 292 5 0.0 0.0 TEAt (D2) N 0.0 C( 1) -0.084 292 5 0.084 292 5 0.084 292 5 C(2) 0.00397 0.162 15 0.18361 0.0 0.0 TBA'(D2) N 0.0 C( 1) -0.084 292 5 0.084 292 5 0.084 292 5 C(2) 0.00397 0.162 15 0.18361 C(3) -0.083 0.262 02 0.262 19 0.339 89 C(4) 0.00526 0.361 51
shell and pD is the dipole moment of a water molecule (1 -84 D).22 The hydration radius of TMA+ was estimated to be 0.376 nm from the interionic distance in the iodide crystal (0.458 r(I-) = 0.206 nm, and r ( 0 ) = 0.124 nm for the water oxygen. The electric dipole will be located on the bisector of the HOH angle 0.044 nm from the oxygen toward the H atoms by the TIP4P potential,24so that the charge-dipole distance is estimated to be 0.420 nm. Thus, AhH(el,l)/n is calculated to be -30 kJ/mol for TMA+ and -65 kJ/mol for Na+. In fact, the dissociation energy of TMA+H20 complex was found to be -38 kJ/mol by a highpressure mass spectroscopic meas~rement.~' The former is comparable to the vaporization energy of water a t 25 OC, 41 kJ/mol. Water forms a tetrahedral network by hydrogen bonds, so that 41 kJ/mol is divided into two hydrogen bonds. Therefore, the unfavorable electrostatic energy change accompanying the reorientation of the water molecule in the first hydration shell of TMA+ ion (Figure 4) would mostly be compensated for by forming newer hydrogen bonds with outside water molecules. The orientational change, while decreasing the chargedipole attraction, promotes exchange of water molecules between the first hydration shell and the outer shells. In fact, Monte Carlo simulation showed that the hydration of TMA' is less specific and involves weak interactions with 20-30 water molecules in the first hydration The smaller solvation number, 7.4 (which has been derived through the discussion of the experimental enthalpy, AhHo(el) = -222 kJ/mol by the theoretical value, AhH(el,l)/n = -30 kJ/mol), than the Monte Carlo value can be rationalized by invoking the reorientational feature discussed above. The electrostatic hydration enthalpy can be approximately given by the Born model:' in which the solvent is treated as a dielectric continuum. The Born model is more relevant for the tetraalkylammonium ions as compared with alkali-metal ions, because ~~~
Dyke, T. R.;Muenter, J. S . J . Chem. Phys. 1973,59. 3125. Wyckoff, R.W. G. 2.Krystallogr. 1928,67, 91. Vergard, L.; Sollesnes, K. Philos. Mag. 1927, 4 , 985. Bottger, G. L.; Geddes, A. L. Spec(22) (23)
trochim. Acta 1965, 21, 1701. (24) Chandrasekhar, J.; Spellmeyer, D. C.; Jorgensen, W. L. J. Am. Chem. Soc. 1984, 106, 903. (25) Meot-Ner (Mautner), M.; Deakyne, C. A. J . Am. Chem. SOC.1985, 107. 469. (26) Jorgensen, W. L.;'Gao, J. J. Phys. Chem. 1986, 90, 2174. (27) Born, M. Z.Phys. 1920, I , 45.
Nagano et al.
2540 The Journal of Physical Chemistry, Vol. 95, No. 6,1991
u
100
3
2
4
n Figure 5. Calculated electrostatic hydration enthalpies of tetraalkylammonium ions ((C,H,,),Nt). The solid lines (a) and (b) were obtained on the basis of the Born model modified for nonspherical ions with a CH, cavity diameter of 0.225 and 0.278 nm, respectively, while the dashed line (c) was obtained by using the Born model for spherical ions. The shaded area indicates those evaluated by using the present experimental hydration enthalpies and eq 5.
thermal orientational fluctuation of water molecules in the solvation shell diminishes the theoretical shortcoming arising from the neglect of the dielectric saturation effect.28 In the present study, the values of AhH"(el) of tetraalkylammonium ions were calculated by the method of Rashin and Namboodiri, which is the modified form of the Born model for molecules with arbitrary because crystallographic results indicate that tetraalkylammonium ions are oblate rather than spherical.30 The molecular geometries used for this calculation are shown in Table IV. The skelton of TEA+ was assumed to be a rigid oblate form because of the steric hindrance between the four ethyl groups. TBA+ was assumed to have a rigid core of the TEA+ structure with four outer ethyl groups, which are more flexible. Although the torsional rotation of the four ethyl groups about the C&, axes of TBA+ is actually free, the coordinates of all the carbon atoms of TBA+ were fixed at values consistent with an oblate shape for the AhH"(el) calculation, since the AhHo(el) value is not sensitive to the position of the outer methyl groups. In such oblate forms, a water molecule can be in contact with the a-methylenes of a TBA+ ion as readily as those of a TEA+ ion. A recent ab initio calculation of TMA+ ion shows that the positive charge is distributed on the C atoms rather than the N atom.26 In the present calculation, the positive charge was localized on the C atoms of the a-methylenes. Therefore, the present molecular model, which allows the relatively undisturbed contact of water molecule to the charged C atoms in the a-methylenes, would lead to the maximum estimate of electrostatic hydration. Calculated results for the hydration energy on the basis of the cavity radius of the methyl and methylene groups of 0.225 nm are shown in Figure 5 as a function of the carbon numbers n of an alkyl chain. For comparison, the results for the cavity radius (28) Noyes, R. M.J . Am. Chem. Soc. 1962, 84, 513. Millen, W. A,; Watts, D.W.J . Am. Chem. Soc. 1%7,89,6051. (29) Rashin, A. A,; Namboodiri, K. J . Phys. Chem. 1987, 91, 6003. (30) Alcock. N. W.;Harrison, W.D. J . Chem. Soc., Dulron Trum. 1983, 2015. Khan, M. A,; McCulloch, A. W.; McInnes, A. G. Con.J . Chem. 1985,
63, 21 19.
TMA' TEA' TBA' Figure 6. Schematic illustration of hydrated tetraalkylammonium ions with respect to their interaction with surrounding water molecules. TMAt and TEAt ions are composed of rigid cores, while TBA' ion is composed of a TEAt type core and four flexible alkyl chains. The electrostatic hydration is governed by the core components.
of 0.278 nm, which has been adopted by Rashin and Namboodiri,29 and also those for spherical ions with ionic radii that are equal to those used for tetraalkylammonium ions in the scaled particle model3' are shown. The values calculated by the present nonspherical ion model reproduce the observed trend very well, while the calculated values based on the spherical ion model do not. Although the magnitude of the values calculated on the basis of the nonspherical model depends on the selected radius of the methylene group, the small change of AhHo(el,TEA+) to AhHo(el,TBA+) is very similar to the observed tendency of AhHo(el) derived by using eq 5. Conclusions Standard enthalpies of formation of crystalline tetra-n-butylammonium (TBA) iodide, bromide, chloride, and aqueous TBA+ ions were determined as follows: -498.6 f 2.7, -540.3 f 3.2, -564.8 f 3.1, and -426.7 f 3.0 kJ/mol, respectively. Good linear relationships were found between standard enthalpies of formation and the length of alkyl chain. It is remarkable that this simple result is quite unexpected for such ionic species in the condensed phase because electrostatic cohesive energy might not have a linear dependence on the interionic distances. The hydration enthalpy of TBA+ ion was estimated to be -260 f 20 kJ/mol for the first time without recourse to any lattice enthalpy calculation. Hydration enthalpies of tetraalkylammonium ions can be interpreted by the two terms: (1) the electrostatic term, which can be calculated by the Born model modified for nonspherical ions and (2) the additive nonelectrostatic term due to hydration of the alkyl chains. This conclusion is schematically shown in Figure 6. The TMA+ and TEA+ ions are described as a respective core, which governs the electrostatic hydration and also the nonelectrostatic one, whereas a TBA+ ion is composed of both a core similar to TEA+ and flexible ethyl groups that contribute only to the nonelectrostatic ("hydrophobic") hydration. From the present energetic consideration, we could find no evidence of the extra "structure-making effect" besides that expected for the model, 5,5-dibutylnonane. However, the remarkable effect on the hydration entropies was indicated by Johnson and Martin.s Acknowledgment. We thank Dr.Ken-ichi Lee for the N M R measurements and Central Workshop of Osaka University for permission to use the ion chromatographic analyzer. (31) Barta, L.;
Hepler, L. G . J . Phys. Chem. 1989, 93, 5588.
