J. Phys. Chem. 1988, 92, 5823-5827
5823
Thermochemical Study of Tetramethyl- and Tetraethylammonium Halides: Nonionic Cohesive Energies in the Crystals and Hydration Enthalpies of the Cations Yatsuhisa Nagana,* Minoru Sakiyama, Chemical Thermodynamics Laboratory, Faculty of Science, Osaka University, Toyonaka, 560 Japan
Tadayuki Fujiwara, and Yasuhiko Kondo Department of Applied Chemistry, Osaka University, Suita, 565 Japan (Received: December 29, 1987)
Standard enthalpies of formation of crystalline tetramethylammonium (TMA) and tetraethylammonium (TEA) iodides were determined to be -203.9 i 2.7 and -300.2 f 3.2 kJ/mol, respectively, by oxygen bomb-combustion calorimetry. By use of these new data and the literature values of the enthalpies of solution, the standard enthalpies of formation of the other halide salts and of the cations in aqueous solution were determined: -276.4 i 2.8 kJ/mol for TMAC1, -251.0 f 2.8 kJ/mol for TMABr, -105.2 f 2.8 kJ/mol for TMA', -369.4 i 3.4 kJ/mol for TEAC1, -342.7 & 3.3 kJ/mol for TEABr, and -215.1 3.3 kJ/mol for TEA'. On the basis of thermochemical consideration,the crystal lattice energies and the hydration enthalpies in aqueous solution were evaluated. The large nonionic cohesive energies in these salts were found. Good continuity of the hydration enthalpies as a function of hydration radii was disclosed between these organic cations and the alkali-metal cations. Additivity was found to hold for the hydration enthalpies of methylammonium ions.
*
Introduction Tetraalkylammonium salts are one of the key compounds to clarify the structure of aqueous solution and the nature of hydrophobic solute-solvent interaction.]-* The hydration enthalpy (energy) is the most fundamental quantity in this respect. However, the determination of an exact hydration enthalpy has been prevented by the ambiguity and the lack of the energetic data of these compounds both in the crystalline state and in the gas phase, and, in addition, by the uncertainty in the hydration enthalpy of the proton? The tetraalkylammonium cations have recently been generated in the gas phase and complex formation with n- and ?r-donors was investigated.' However, for the crystalline state, no standard enthalpy of formation has been determined except for tetramethylammonium nitrate.l0 The tetraalkylammonium halide salts are interesting compounds also from the aspect of crystal cohesive energy. Their structures resemble those of alkali-metal LaddI3 and BoydI4 calculated the crystal energies in terms of the Coulombic energy and the energies due to short-range forces which were empirically estimated. Their results agree well with each other. On the other hand, however, Wilson estimated far larger lattice energies for the tetramethylammonium halides by the extrapolation method.l5 Although the lattice energies of neutral molecular crystals may be measured directly by sublimation calorimetry,l6 those for ionic (1) Wen, W. Y. In Water and Aqueous Solutions; Horne, R. A,, Ed.; Wiley-Interscience: New York, 1972, p 613. (2) Bhatnagar, 0. N.; Criss, C. M. J. Phys. Chem. 1969, 73, 174. (3) Johnson, D. A.; Martin, J. F. J. Chem. Soc. Dalton Tram. 1973, 1585. (4) Krivtsov, P. V.; Titova, K.V.; Rosolovskii, V. Ya. Zh. Neorg. Khim. 1976. 21. 1406. (5) Finch, A.; Gates, P. N.; Nwankwo, S. I.; Stephens, M. Thermochim. Acta 1980, 41, 387. (6) Castaanolo, M.; S a m , A.; de Gialio, A. J. Chem. Soc., Faraday Tram. I 1984,80, 2669. (7) Meot-Ner (Mautner), M.; Deakyne, C . A. J. Am. Chem. Soc. 1985, 107, 469. (8) Jorgensen, W. L.; Gao, J. J. Phys. Chem. 1986, 90, 2174. (9) Klots, C. E. J. Phys. Chem. 1981,85, 3585. (10) Medard, M.; Thomas, M. Mem. Poudres 1954, 36, 97. (11) Wyckoff, R. W. G. 2.Krist. 1928,67,91. Vegard, L.; Sollesnes, K. Philos. Mag. 1927,4,985. Bottger, G. L.; Geddes, A. L. Spectrochim. Acta 1965, 21, 1701. (12) Wait, E.; Powell, H. M . J. Chem. SOC.1958, 1872. (13) Ladd, M. F. C. 2.Phys. Chem. 1970, 72, 91. (14) Boyd, R. H. J. Chem. Phys. 1969, 51, 1470. (15) Wilson, J. W. J. Chem. Soc., Dalton Trans. 1976, 891.
0022-3654/88/2092-5823$01.50/0
crystals have to be determined by the thermochemical cycles, which need the standard enthalpies of formation of the compounds in the crystalline state. In the present study, the standard enthalpies of formation for tetramethylammonium (TMA) and tetraethylammonium (TEA) iodides were for the first time determined by oxygen bomb-combustion ~alorimetry.'~In conjunction with the literature value of enthalpies of solution of the salts, standard enthalpies of formation of TMA' and TEA' ions were derived, which in turn were used to derive standard enthalpies of formation of TMA and TEA chlorides and the corresponding bromides in the crystalline state. The lattice energies in the halide crystal were evaluated by the thermochemical consideration, and they are compared with the Coulombic lattice energies calculated by the Ewald's method'* to evaluate the magnitude of nonionic cohesive energies in the crystal. Finally, the hydration enthalpies of TMA' and TEA' cations in aqueous solution were reevaluated. Experimental Section Materials. Commercial tetramethylammonium iodide (TMAI) and tetraethylammonium iodide (TEAI) (Nakarai Chem. Co., specially prepared reagents) were twice recrystallized from the ethanol-water and ethanol-acetone mixtures, respectively. Both were kept in a vacuum over P20,for 3 days. After grinding, the dried materials were again kept in a vacuum over P205for 1 day. The reduction of the weights during the second drying was less than 0.02 %. The purities were determined to be 99.97% for TMAI and 99.96% for TEAI by the gravimetric method in which AgI was precipitated by adding silver nitrate solution to a solution of teraalkylammonium iodide under effective stirring and was filtered and dried over P2O5. Apparatus and Procedure. A rotating bomb calorimeter, described el~ewhere,'~ was used without rotating the bomb. The temperature was measured with a thermistor, which was calibrated against a quartz thermometer (HP 2801A). The resistance of the thermistor was sensitively detected with a Wheatstone bridge. (16) Murata, S.; Sakiyama, M.; Seki, S. J. Chem. Thermodyn. 1982,14, 707. (17) In the present paper, standard-state pressure is 100 kPa. (18) Ewald, P. P. Ann. Phys. 1921, 64, 253. Ziman, J. M. Principles of the Theory of Solids, 2nd ed.; Cambridge University: London, 1972. (19) Sakiyama, M.; Nakano, T.; Seki, S . Bull. Chem. SOC.Jpn. 1975,48, 705. Nishiyama, K.; Sakiyama, M.; Seki, S., Horita, H.; Otsubo, T.; Misumi, S. Bull. Chem. SOC.Jpn. 1980, 53, 869.
0 1988 American Chemical Society
5824
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
Nagano et al.
TABLE I: Auxiliary Data for the Calculation of Standard Energies of Combustion materials TMAI TEAI cotton fuse
p/g formula C4H1ZNI 1.83 CsHzoNI 1.56 CHI8600,93 1.5
C,/J K-lg-' 0.801 0.988 1.70
0 -
(dU/dP)T'/ J g-' MPa-l (-0.005 27) (-0.005 27) -0.029 0
'2 7
1
I
;
'Values in parentheses are estimated ones.
The data were fed to a personal computer. The calorimeter was calibrated by burning thermochemical standard benzoic acid (N.B.S. S R M 39i) under certificate conditions. Mean and standard deviation of the mean of observed energy equivalents for the empty calorimeter was 15 171.34 f 0.52 J/K (six experiments). The combustion was carried out at 3.0 MPa oxygen pressure. As a combustion aid, 0.88 g of standard benzoic acid (BA) was used for the combustion of 0.30 g of TMAI and 0.51 g of BA for that of 0.63 g of TEAI. The ideal combustion reactions to which energies of combustion refer are given in the following scheme:
-100
-
-200
-
s .
0
2
0
1
2 n
3
4
Figure 1. Standard enthalpies of formation of gaseous alkylammonium ions and isostructural alkanes as a function of the number of alkyl substitutents: closed circles, NHh(CH3),+ (from ref 26); open circles, NHk(C2H5),+ (from ref 26); closed square, TMA+ (extrapolated); open square, TEA+ (extrapolated); closed triangles, CHen(CH3), (from ref 21); and open triangles, CHkn(C2HS), (from ref 21).
Actually, the iodine is converted substantially to elemental iodine and the nitrogen is partly oxidized. Six combustion experiments were carried out for each material. After the calorimetric measurements were completed, the combustion products were analyzed. The bomb gases were tested
for carbon monoxide. The internal surfaces of the bomb were washed out with water. The nitric acid in the washings was titrated with squeous sodium hydroxide. In all the cases, no nitrous acid wts detected with the Griess-Romijn reagent, so that its contribution was safely neglected for the combustion energy calculation. Finally, the washings were evaporated. The residuals were dissolved in D 2 0 for 'H N M R measurements in order to check the completeness of the combustion reactions. The reduction of standard states and the correction for combustion were carried out by using the literature method for organic nitrogen and iodine compounds.20
TABLE II: Summary of Combustion Calorimetric Results on "MAP 1 2 m(compd)/g 0.29578 0.29883 m(benzoic acid)/g 0.88736 0.88378 0.00212 0.00230 m(fuse) / a mi(H20j/g 1.oo 1.oo p'(gas)lMPa 3.040 3.040 23.18119 (TJK) - 273.15 23.18 182 25.04542 (Tf/K) - 273.15 25.04386 ATcUrlK 0.01831 0.01923 nf(HN03)/mmol 0.229 0.218 A u i g n lJ 2.7 2.8 A W J 17.0 16.9 J 12.8 AUd"O&/ 12.1 17.3 t'(cont)/J K-I 17.3 &cont)/J K-I 18.8 18.8 -AulBP/J 28035.2 27986.8 15.3223 -{AUO,/M(compd))/kJ g-' 15.3 129 -AVO,( compd)/ kJ mol-' 3080.54 3078.65
3 0.29145 0.88835 0.00267 1.oo 3.040 23.18237 25.04539 0.01925 0.225 2.8 17.0 12.5 17.3 18.8 28001.7 15.3147 3079.03
4 0.30198 0.88480 0.00218 1.oo 3.040 23.181 52 25.04820 0.01894 0.218 2.9 17.0 12.1 17.3 18.8 28062.7 15.3218 3080.44
5 0.29504 0.88932 0.00275 1.oo 3.040 23.18 142 25.04939 0.01916 0.217 2.9 17.1 12.0 17.3 18.8 28080.5 15.3057 3077.21
6 0.28948 0.88478 0.0021 8 1.oo 3.040 23.1 8079 25.03487 0.01 897 0.286 2.7 16.9 16.1 17.3 18.7 27871.0 15.3093 3077.93
3 0.61862 0.52453 0.00296 1.oo 3.040 23.18016 25.01993 0.01969 0.419 2.7 12.2 23.9 17.3 19.0 27642.6 22.1 506 5696.20
4 0.63178 0.51181 0.00300 1.oo 3.040 23.18032 25.0 1729 0.02017 0.413 2.7 12.0 23.6 17.3 19.0 27592.1 22.1409 5693.72
5 0.63480 0.49832 0.00262 1.oo 3.040 23.181 17 25.0001 5 0.02154 0.435 2.8 11.7 24.9 17.2 19.0 27297.4 22.1409 5693.71
6 0.63380 0.50820 0.00296 1.oo 3.040 23.18 120 25.01559 0.02076 0.408 2.7 12.0 23.3 17.3 19.0 27543.6 22.1459 5695.01
C4H12N1(cr) + 702(g) 4C02(g) + 6H20(1) + ( 1 / 2 N ( g ) + (1/2)12(cr) (1) C8HZ0NI(cr)+ 1302(g) 8CO,(g) + 10H20(1) + (1/2)N,(g) + (1/2)12(cr) (2) +
-
"The symbols are similar to those used in ref 20.
TABLE 111: Summary of Combustion Calorimetric Results on TEAI' 1 2 m(compd)/g 0.63340 0.63091 m(benzoic acid)/g 0.51335 0.51404 m(fuse)/g 0.00248 0.00283 m'(H,O)/g 1.oo 1.oo p'(gas)/MPa 3.040 3.040 (T,/K) - 273.15 23.18088 23.18069 (Tf/K) - 273.15 25.02173 25.0198 1 0.01943 0.01960 ATCnrIK nf(HN03)/ mmol 0.442 0.401 2.7 2.7 Auipl J 12.0 12.0 A.udJ 25.3 22.9 Audec("o3)/J c'(cont)/J K-I 17.3 17.3 r'(cont)/J K-l 19.0 19.0 27663.0 21634.7 -AulBP/J -(AUO,/M(compd)J/kJ g-l 22.1429 22.1511 -AUO,(compd)/kJ mol-' 5694.23 5696.32 "The symbols are similar to those used in ref 20.
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 5825
Thermochemical Study of TMA and TEA Iodides TABLE IV: Derived Standard Thermodynamic Quantities at 298.15
TABLE V: Lattice Energies of the TMA and TEA Halide Salts
K species TMAUcr) TMABr(cr) TMACl(cr) TMA+(aa) TMA+(gj' TEAI(cr) TEABdcrl
-&,UO/kJ mol-I 3079.0 f 2.6
5694.9 f 3.0
-A$P/kJ mol-I 3085.2 f 2.6
5706.1 f 3.0
AfH"/kJ mol-' -203.9 f 2.7 -251.0 f 2.8 -276.4 f 2.8 -105.2 f 2.8" 546b -300.2 f 3.2 -342.7 & 3.3 -369.4 f 3.4 -215.1 f 3.3' 424b
OBased on the convention that AfH"(H+,aq) = 0. bBy extrapolation.
Results and Discussion 1 . Standard Enthalpies of Formation AfHo. Auxiliary data for the calculation of molar energies of combustion are listed in Table I. Details of the combustion calorimetric results are presented in Table I1 and Table I11 for TMAI and TEAI, respectively. Most of the symbols in these tables are essentially those used by Hubbard et a1.20 Mean and standard deviation of the mean for the observed molar energies of combustion k u " ( c r ) at 298.15 K for TMAI and TEAI were -3079.0 f 0.55 and -5694.9 f 0.48 kJ/mol, respectively. The proton N M R measurements of the residuals of TMAI combustion showed that the amount of trimethylamine, which would be formed by the thermal decomposition of TMAI and would be present as trimethylammonium nitrate in the bomb solution, was less than 10 nmol. Therefore, this side reaction would introduce the error less than 0.02 kJ/mol to 4u". However, in the case of TEAI combustion, the ethyl proton signals were more apparently observed. By quantitative measurements of the intensity of these signals, the amount of triethylamine was estimated to be 0.3-1.2 pmol, which gives errors of +2.8 kJ/mol at most to A , V . In three of six TMAI experiments CO gas was detected. The largest amount of CO, 10 pmol, gives an error of +2 kJ/mol to the 4u". In the present study, the corrections for the competing decomposition reaction and the CO gas formation were introduced into the final overall uncertainties of ~ W S which , were defined as twice the standard deviation of the mean, by using the equation of error propagation. Finally, the molar energies of combustion were determined to be -3079.0 f 2.6 kJ/mol for TMAI and -5694.9 f 3.0 kJ/mol for TEAI. The standard enthalpies of formation AfHo at 298.15 K and 100 kPa were evaluated by using the observed ku"s and the literature values of AfHO(H20,1)(-285.830 f 0.042 kJ/mol) and AfHo(C02,g)(-393.51f 0.13 kJ/mol),2i and presented in Table IV. AfHo(TMAI) was previously estimated by Wilson by the extrapolation of AfHos of methylammonium halide salts to be -203.5 kJ/mol,15 which agrees very well with the present result. The standard enthalpies of formation of aqueous TMA' and TEA+ ions were evaluated by the equation:
+
AfHo(TMA+or TEA+,aq) = AfHo(TMAI or TEAI) $,,,Ho(TMAI or TEAI) - AfHo(I-,aq) (3) where AmlnHois the standard enthalpy of solution in water, AfHO(I-,aq) is the standard enthalpy of formation of the aqueous I- ions. AmInH0(TMAI)= 41.8 f 0.2 kJ/mol,2 $olnHo(TEAI) = 28.2 f 0.3 kJ/mol: and AfHO(1;aq) = -56.90 f 0.84 kJ/mol,2' so that AfHo(TMA+,aq) = -105.2 f 2.8 kJ/mol (4) AfHo(TEA+,aq)= -215.1 f 3.3 kJ/mol
(5)
(20) Hubbard, W. N.; Scott, D. W.; Waddington, G. In Experimental Thermochemistry; Rossini, F. D. Ed.; Interscience: New York, 1956; p 75. (21) Wagman, D. D.; Evans, W. H.; Parker, V. E.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J. Phys. Chem. Ref. Data 1982, ll(2). CODATA Task Group on Key Values for Thermodynamics, 1971. CODATA Bull. 1978,28;J. Chem. Thermodyn. 1978,10,903.
. .
TMACl TMABr TMAI TEAI
546 546 546 424
-233 -219 -197 -197
-589 -578 -553 -527
-554 -542 -506 -478
(-5441' (-531)c (-510)' (-481)'
(-527)' (-523)' (-506Id (-477)'
kJ mol-i. -5 1 -52 -47 -49
'
The Coulombic energies calculated by Ewald's method. Reference 21. Reference 13. Reference 14.
'
All the single ion values in aqueous solution were calculated on the basis of the convention AfHo(H+,aq) = 0. The present AfHO(TMA+,aq)agrees well with the value -103.3 f 3.0 kJ/mol which has been evaluated by Krivtsov et a1.4 through the combination of enthalpy of solution for TMA nitrate with standard enthalpy of formation which was determined by Medard and Thomas by means of oxygen bombcombustion calorimetry.I0 Finch et aL5 estimated AfHO(TEA+,aq) to be -246.5 f 5.0 kJ/mol, which is much more negative than the present value, by extrapolation of AfH0[(C2H5),NH4-,+,aq] (n = 0-3) data to n = 4. This value was subsequently used for the determination of standard enthalpy of formation of N(C2H5)4C104(~r),22 N(C2H5)4Cl(cr),22N(C2Hs)4Br(cr),22 N(C2Hs)41(~r),22 N(C2H5)4PC16(~r),5 and N(C2H5)4PBr4.23However, a survey of the literature shows that AfHO[(CzH5),NHh+,aq] data (n = 1-3) given in ref 21 appear to be considerably less certified as compared with those for AfHo[(CH3)nNHen+,aq] data.2i Firstly, the data are not those at the infinite dilution. Secondly, the data appear to be based, at least partly, on the enthalpy of combustion data by Cottrell and Gill,24which have been reported only briefly and on the reliability of which no mention has been made. An extrapolated value based on such seemingly less scrutinized data would have to be taken with great care. Using the value of AfHo(TMA+ or TEA+,aq), we may determine the standard enthalpies of formation of other halides in the crystalline state on the basis of the relation AfHo(TMAX or TEAX) = AfHo(TMA+or TEA+,aq) + AfHo(X-,aq) - &,,HO(TMAX or TEAX) (6) where X stands for C1 or Br. The following values were employed: &I,Ho(TMACl) = 4.08 f 0.3 1 kJ/rn01,~~ L I n H 0 ( T M A B r )= 24.27 f 0.42 kJ/m01,2~AwI,H0(TEACl) = -12.82 f 0.95 kJ/ P,,,HO(TEABr) = 6.05 f 0.45 kJ/mo1,22 AfHo(C1-,aq) = -167.080 f 0.088 kJ/mol,21 and AfHo(Br-,aq) = -121.50 f 0.15kJ/moL2' The derived standard thermodynamic quantities are summarized in Table IV. 2. Crystal Lattice Energies. We define here the standard lattice enthalpy AIHoat 298.15 K by the equation AiHo(TMAX or TEAX) = AfHo(TMAX or TEAX) AfHo(TMA+or TEA+,g) - AfHo(X-,g) (7) where AfHO(TMA+or TEA+,g) and A&P(X-,g) are the standard enthalpies of formation of the gaseous TMA+, TEA', and X- ions. Since AfHO(TMA+ or TEA+,g) were unknown, they were estimated by the linear extrapolation of the recent literature values of AfHo(g) of the protonated amines (NR,H4-,+, R = CH3 or C2H5) with n = 2 and 326to n = 4 (tetraalkylammonium ion). The plot of AfHoof gaseous alkanes (CR,Hen, R = CH3 and C2H5),which are isostructutal to the alkylammonium ions, against n shows good linear correlation over the range of n = 2-4 (Figure 1).
It is noticeable that, over the whole region n = 0-4, the dependence of n of AfHo[(C2H5),NH4-,+,g] is not linear. This (22) Nwankwo, S. I. Thermochim. Acta 1981, 47, 157. (23) Nwankwo, S. I. J. Chem. Thermodyn. 1981, 13, 301. (24) Cottrell, T. L.; Gill, J. E. J. Chem. SOC.1951, 1798. (25) Parker, V. B. Thermal Properties of Aqueous Uni-univalent Electrolytes; National Bureau of Standards: Washington, DC, 1965. (26) Lias, S. G.; Liebman, J. F.; Levin, R. D. J. Phys. Chem. Ref. Data 1984, 13, 695.
Nagano et al.
5826 The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
implies that there is no a priori reason to state that AfHo((C,H,),NH,,+,aq) should linearly depend on n, as was assumed by Finch et al.s Thus, we obtain 546 and 424 kJ/mol for AfHo(TMA+,g) and AfHo(TEA+,g), respectively, which are corrected for the "stationary electron" convention.26 The following values were used for the calculation of the standard lattice energies: A,Ho(CI-,g) = -233.1 3 kJ/mol,21 AfHo(Br-,g) = -219.09 kJ/mol,21 and AfHo(I-,g) = -197 kJ/ Derived standard lattice energies are presented in Table V. The crystal lattice energy at 0 K, Uowas evaluated by the equation
uo= A'HO(TMAX TEA+,g)
TABLE VI: Hvdration Enthaldes of Univalent Cations r(A+-OH2) / AfHo(A+,aq)/ A,Ho (A+& / AhHo(A') nm kJ mol-' kJ mol-l kJ mol-l
Li+ Na+
K+ Rb'
cs+ NH4+ TMA+
TEA' a
0.218 0.242 0.271 0.285 0.3 13 0.281 0.376 0.394
-278.49' -240.12" -252.38" -251.17' -258.28" -132.51" -105 -215
685.183" 609.358' 514.26' 490.10 1" 457.964" 636.7b 546 424
/
-564 -449 -366 -34 1 -316 -369 -25 1 -239
Reference 21. Reference 26.
298
or TEAX)
+ J0
{C,O(TMA+ or
2.8,
I
+ Cpo(X-,g) - Cpo(TMAX or TEAX)] d T (8)
where Cpodenotes the molar standard heat capacity. The heat capacity of gaseous TMA+ ion was evaluated by a statisticalmechanical calculation in which the skeletal vibrational frequencies were determined by using those of Y(CH3)4type molecules27and a hindered rotation ( V = 18.7 kJ/mol) was assumed for the methyl groups. The calculated heat capacity of gaseous TMA+ ion was 119.8 J K-' mol-' at 300 K, which is equal to that of neopentane. The first and the second heat capacity terms in eq 8 were evaluated to be 21.7 and 6.2 kJ/mol, respectively. The third term was evaluated to be 27.7, 28.2, and 28.6 kJ/mol for TMACl(cr), TMABr(cr), and TMAI(cr), respectively, on the basis of the heat capacity data.28%29Therefore, the contribution from the heat capacity terms is of the order of 1 kJ/mol, so that this correction was not taken into account in the following discussions. It is noted that the crystal lattice energy thus evaluated includes the intramolecular distortion energy of the cation. The Coulombic energies in the crystals were calculated by Ewald's method'* for the model in which unit charges are located on nitrogen and halogen atoms, for TMACl, TMABr, TMAI, and TEAL The crystal structure data reported by Wyckoff" and Bottger and Geddes" were used for TMAX. That reported by Wait and Powell12 was adopted for TEAI. For TEACl and TEABr, the calculation was not performed owing to the lack of crystal structure data. The calculated Coulombic energies are presented in Table V, with those of LaddI3 and Boyd14 for comparison. The present results for TMAI and TEAI agree well with those of Boyd. The Coulombic energies for TMACl and TMABr by Boyd are the least negative. This may be due to the fact that they were evaluated by direct summation in the limited number of cells. An ab initio calculation of TMA+ ion showed that the charge on N atom is negative of -0.16e.8 The Coulombic energies of TMAI were calculated to be -503 kJ/mol, which is only 3 kJ/mol higher than that of the first model, on the basis of the charge distribution model of -0.16e on N atom and +0.29e on C atom. Thus, no sophistication at this level seems to introduce a significant variation in the crystal lattice energy. 3. Nonionic Crystal Energies. The difference between Uoand the Coulombic energy is attributable to the contribution from the ionionic bondings to the crystal lattice energies. Therefore, in these crystals, the additional stabilization due to the nonionic interaction which are contributed by the short-range attractive and repulsive forces was found to be ca. -50 kJ/mol. This is numerically far larger than those estimated by Ladd13and Boyd,I4 so that it seems that the potential parameters adopted by Ladd and Boyd were inadequate for these compounds. For the alkali-metal halide crystal, Tosi evaluated such nonionic crystal cohesive energies, which are numerically less than the present results, by the Born-type treatmentg0 (27) Siebezt, V. H. 2.Anorg. Chem. 1952, 268, 177. (28) Chang, S.S.; Westrum, E. F. J. Chem. Phys. 1962, 36, 2420. (29) Coulter, L. V.;Pitzer, K. S.; Latimer, W. M. J. Am. Chem. SOC.1940, 62, 2845. (30) Tosi, M. P. In Solid Stare Physics; Seitz, F., Turnbull, D., Eds.; Academic: London, 1965; Vol. 16, p 1.
2.2
0.3
04
05
06
1 +log(r/nm)
Figure 2. Hydration radius dependence of hydration enthalpies of univalent cations: closed circles, present results; and open triangles, data from ref 3.
It is noticeable that the nonionic cohesive energy of TMA and TEA halides may be composed of two interaction energies. The first is the interactions between the tetraalkylammonium cation and halogen anion. The second is the interaction between the cations. The X-ray diffraction studies indicate that the shortest distance between methyl groups of the nearest-neighbor cations is 0.39 nm or less for the TMA and TEA halides.",12 Therefore, van der Waals interaction between cations could be invoked as one of the major components of nonionic energy. The sphere-to-sphere contact between the ions with a similar charge is also observed in the alkali-metal halide crystals having large anions and small cations. In fact, in the LiI crystal, which has the largest nonionic cohesive energy, -36 k J / m ~ l , ~inO alkali-metal halide salts, the ionic radius ratio is the almost same as the critical ratio 0.41 of the NaCl structure, at which the contact between anions is significant. 4. Hydration Enthalpies of TMA' and TEA'. Johnson and Martin3 have determined the hydration enthalpies of TMA+ and TEA+ ions by using the calculated lattice energies of Ladd13 and of Boyd.14 However, the present experimental study showed these theoretical lattice energies were numerically underestimated so that the hydration enthalpies would have to be reevaluated. The hydration enthalpies, AhW, were calculated by the equation AhHo(TMA+or TEA') = AfHo(TMA+or TEA+,aq) AfHo(TMA+ or TEA+,g) + AfHo(H+,g) + AhHo(H') (9) where AfHo(H+,g) = 1536.2 kJ/rnol:' and the hydration enthalpy of proton, AhHo(H+) = -1 136 kJ/m01.~ The last two terms were used to derive a value of AhHofree from the convention that AfHo(H+,aq)= 0. The calculated hydration enthalpies for TMA' and TEA' ions are -25 1 and -239 kJ/mol, respectively. For comparison, those for the alkali-metal and ammonium ions were also calculated similarly, using the literature values of standard enthalpies of formation of these ions.21 The results are summarized in Table VI, where the hydration radii shown in the second column were estimated by first subtracting the ionic radius of the iodide (0.206 nm) from the interatomic distances in the alkali-metal or ammonium iodide crystals to obtain the ionic radii of the cations in these crystals, and then adding to it the radius
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 5827
Thermochemical Study of TMA and TEA Iodides
I9 L
-
2ooo
1
2 n
3
4
Figure 3. Hydration enthalpies of methylammonium ions as a function of the number of methyl substituents.
of the hydrating oxygen atom of water (0.124 nm). Figure 2 shows an empirical correlation between the present hydration enthalpies and the hydration radii of cations, where the literature values for TMA+ and TEA+ ions are also indicated for comparison. According to the regression line drawn through the present values, the cations seem to be classified into two series: Li+, Na+, and K+ belong to the first series with a slope of -2.0, while K+,Rb+, Cs+, TMA+, and TEA+ belong to the second series with a slope of -1.1. An only exception is ammonium ion, NH4+. The deviation of the value for NH4+ from the regression line amounts to ca. -20 kJ/mol and would be attributed to the extra stabilization due to the N-He-0 hydrogen bonding between the ion and water. This view is supported by the fact that the enhanced formation of specific-size protonated ammonia-water clusters was observed in the supersonic beam experiment^.^' The slope of the first series (-2.0) is an expected trend, if a charge-dipole interaction, which is proportional to the reciprocal square of the hydration radius, is the major contributor in the hydration enthalpy. In terms of the charge-dipole interaction, the average coordination number x could be calculated to be 5.1 for the first series of ions. where 1.84 D was used for the diPole moment of water pD,32 by using the equation
The K+ ion, which is a t the cross point of the two lines, has a hydration radius similar to the 0-0distance in ice, 0.275 nm. Therefore, the hydration of the ions larger than K+ would break the structure of water. This effect should reduce the stability of these ions in aqueous solutions. On the other hand, the larger hydration number and the larger polarizability would lead to increasing stabilization, so that the slope of second series is due to the competitive effects of stabilization and destabilization. 5. Hydration Enthalpies of Methylammonium Ions. Finally, the hydration enthalpies of methylammonium ions were calculated by using eq 9, on the basis of the literature data.2'-26 The results are shown in Figure 3, together with the present data for TMA'. The hydration enthalpies are plotted against the methyl-substitution numbers. The plot indicates an almost linear dependence on the substitution numbers. This means that the enthalpy changes due to the hydration of H and methylsubstituents are additive. The hydration enthalpies of methylammonium ions may be expressed by the equation A,,Ho(NH+,,(cH~),,+) = (4 - n)AhHo(NH+) nAhH0( NCH3+) (1 1)
+
where AhHo(NH+)and AhHo(NCH3+)are the contribution to the hydration enthalpy from a H atom and a methyl group, respectively. From the present result, AT("+) = -92 kJ/mol and bhHo(NCH3+)= -63 kJ/mol. For ethylammonium ions, if the additivity of hydration enthalpies is assumed, then AhHo(NC2H5+)= -60 kJ/mol and AfHo[N(C2H5),He,+,aq] is estimated to be -1 56 kJ/mol for n = 1, -188 kJ/mol for n = 2, and -201 kJ/mol for n = 3, on the basis of AfHo[N(C2H5!,,He,,+,g] data.26 The tetraalkylammonium ions of longer alkyl chains are known to form the clathrate hydrates, in which the four alkyl chains of the cation occupy the four polyhedra of the water network.' Therefore, the tetraalkylammonium ions of long alkyl chains are expected to exist in a nonspherical form in aqueous solutions. The hydration enthalpies of such tetraalkylammonium ions would provide one with essential and fruitful information on the states of these ions in aqueous solution. In our laboratories, thermochemical studies on tetrapropyl- and tetrabutylammonium salts are going on.
(lo)
Acknowledgment. We thank Dr M. H. Abraham, University of Surrey, for stimulating our interest in the present work and Mr. Seiji Adachi for the N M R measurements.
(31) Shinohara, H.; Nagashima, U.; Tanah, H.; Nishi, N. J . Chem. p h p . 1985,83,4183. (32) Dyke, T. R.; Muenter, J. S.J . Chem. Phys. 1973, 59, 3125.
Registry No. TMAI. 75-58-1; TEAL 68-05-3: TMAC1. 75-57-0: TMAir, 64-20-0; TMA+, 51-92-3; TEACI, 56-34-8; TEABr; 71-91-0; TEA', 66-40-0; Li', 17341-24-1;Na+, 17341-25-2;K+, 24203-36-9; Rb+, 22537-38-8; CS', 18459-37-5; NH4+, 14798-03-9.
