摘要:

J. Chem. SOC., Faraday Trans. 1, 1986, 82, 3255-3274 The Thermodynamics of Solvation of Ions Part 1 .-The Heat Capacity of Hydration at 298.15 K Michael H. Abraham* and Yizhak Marcus*? Department of Chemistry, University of Surrey, Guildford, Surrey G U2 5XH Values of the standard partial molar heat capacities of aqueous electrolytes have been critically selected from the literature and have been divided into ionic contributions using the assumption that P (Ph,P+) = c; (BPh,). Combination of the single-ion values with <values for gaseous ions then yields single-ion values for the standard molar heat capacities of hydration, Ahyd c"p. Ions of various classes are considered : univalent and multivalent, monoatomic and polyatomic, hydrophilic and hydrophobic. The ionic values of A h y d q are analysed in terms of a model in which an ion is surrounded by a first layer of immobilised solvent, a possible second layer, and then the bulk structured solvent.The A h Y d q values are broken down into a neutral term, N , an electrostatic term, E, and a configurational term, C. Two possible modes of summation are discussed, stressing in the term C the effects of the orientation of the solvent near the ion, and the effects on the fluidity of the solvent in the second and outer layers. Our analysis is consistent with previous discussions by the authors on the standard molar entropies of hydration of ions, and with other parameters that contain structural information, such as viscosity B-coefficients and partial molal volumes of ions in water.The thermodynamics of ion solvation have been discussed by the present authors separately in several recent papers (Abraham et al.;1-9 Marcus et al.1°-15). Much of this discussion has been restricted to the standard temperature of 298.15 K, and in order to understand the behaviour of electrolyte solutions at other temperatures, data on their heat capacities are required. In this paper we consider electrolytes in aqueous solution, and we plan to deal with non-aqueous solutions subsequently. In order to be able to relate experimentally derivable quantities, in this case AhydCE for the transfer of ions from the gas phase to water, to properties of the ions and of water, it is essential to set up some model of ionic hydration constructed in terms of single ions.It is then necessary to split the total observed quantities for electrolytes into individual ionic contributions. To date, there have been only few attempts to interpret heat capaci- ties of single ions in aqueous 16-20 the most comprehensive schemes still being limited to the monoatomic univalent ions in the alkali-metal halide series.8$ l6 It is appropriate now to broaden the scope of the discussion of the heat capacity of hydration of ions to a much larger set. First, this is due to the availability now in the literature of reliable data for the standard partial molar heat capacities of many electrolytes, involving also polyatomic and multivalent ions. Secondly, this is due to the availability of literature data that are required for the calculation of the standard heat capacities of the gaseous polyatomic ions, obtained by Marcus and Loewenschuss.21$ 22 t Visiting from the Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.32553256 Thermodynamics of Solvation of Ions Thirdly, this seems to be a convenient starting point for discussion of the heat capacities of transfer of the ions to non-aqueous solvents and their solvation in them, as mentioned above. An examination of the heat capacity of hydration of ions over a wide temperature range would contribute much to our knowledge of the thermodynamic behaviour of electrolytes at elevated temperatures. Unfortunately, data on the heat capacities at such temperatures are limited to a small set of electrolytes, so that the only generalisation that can be made at present is that the values become highly negative, the more so as the temperature increases.** 17-19 This has been ascribed to the predominance of electrostatic over structural effects at these l9 Most of the data available now for dis- cussion pertain to room temperature only, however. The present paper is therefore devoted to the discussion of the standard partial molar heat capacity of electrolytes at 298.15 K, leading to the standard molar heat capacity of hydration of their constituent ions.Examination of ion-solvent interactions through the latter quantity excludes the study of ion-ion interactions that are of importance for electrolyte solutions at finite concentrations. Such a study might be the subject of further research.The standard molar heat capacity of hydration must be related to the properties of the ions, on the one hand, and to those of the solvent, water, on the other. Any model pro- posed for its interpretation must be compatible with results presented previously on other thermodynamic functions of hydration discussed by Abraham et al.lP9 and by Marcus et al.139 l4 In addition, since we shall consider not only hydrophilic ions such as the alkali and alkaline-earth metal halides, carbonates, sulphates etc., but also the hydrophobic ions, the model must take into account hydrophobic hydration. A starting point in a discussion could be the paper by Engel and Hertzz3 in which they examined the concept of negative hydration, i.e. the increase in fluidity of water brought about by certain ions generally classed as ‘structure breaking’.Thus large inorganic ions, such as Cs+, I- and Cloy, were characterised by negative viscosity B-coefficients and negative water proton relaxation rate B’-coefficients. Small inorganic ions (Li+, Mgz+, F-, COi-), on the other hand, have positive B- and B’-coefficients, as might be expected from the presence of a strong ionic electric field which should slow down the average motions of near-neighbour water molecules. Marcus and Loewenschu~s~~ have referred to this effect as translational immobility. Engel and observed that organic ions like (CD,),N+ also gave rise to positive B- and B’-coefficients, indicating a decrease in fluidity, but this effect certainly cannot be due to translational immobility brought about by the central electric field, because of the low charge density of Me,N+ compared to the inorganic ions.There is now considerable evidence that hydrophobic solutes decrease the fluidity of water by a mechanism unrelated to ionic charge effects. Both thermodynamic and spectroscopic studies indicate that there is an increase in the intermolecular water structure in the vicinity of an apolar molecule or the apolar parts of ions.l4? 24-28 This increase in the extent and strength of the water structure naturally leads to a decrease in fluidity. and Marcus et al.137 22 have related entropies of hydration to ‘ structure-making ’ and ‘ structure-breaking’ effects, but the discussion of Abraham et on heat capacities of hydration of the simple inorganic ions seems to be the only attempt to consider Ahyd values in terms of such effects in any quantitative way.The aim of the present paper is to devise a set of single-ion heat capacities of hydration for as many ions of as many classes as possible, using critically selected literature data, and then to discuss the set in an unified scheme that takes the above considerations into account. Both Abraham et aL47 6 v The Data Standard partial molar heat capacities CF, are available in the literature for many electrolytes. The most accurate and reliable values have been obtained by flow micro-M . H . Abraham and Y. Marcus 3257 calorimetry in recent years. This technique permits precise measurements to be made on solutions sufficiently dilute for safe extrapolation of the apparent molar heat capacities, 4Cp(m), against mi to infinite dilution to yield 4CF = cp.A further criterion that must be met, besides the availability of data for very dilute solutions, is the additivity of the standard partial molar heat capacity values of the cations and the anions to yield the values for the electrolytes. This is ensured by the selection of those values for two series of electrolytes, where the differences for, say, a given pair of anions is constant, irrespective of the cations. The CF data for electrolytes selected on this basis are shown in table 1 . Conformity with the additivity rule is within < 3 J K-l mo1-1 (see table 2). However, table 1 contains further data where these criteria could not be fully met.On the one hand these are data for salts of certain substituted ammonium ions such as H(CH,),NH,+, c-[(CH,),CH]NH; and (C,H,),N(CH,),N(C,H,)~+, and of carboxylic acids H(CH,),CO,. For most of these, data for only one counter-ion are available, so that the additivity criterion could not be applied. This also holds for salts of certain inorganic acids and their protonated anions such as MnO;, COi-, PO:-, HP0,2- and H,PO,. However, since these results have been obtained by flow microcalorimetry, we regard them as reliable. On the other hand, there are cases where the additivity criterion seems to hold, within perhaps wider limits than for the electrolytes discussed in the previous paragraph, but where the data do not extend to sufficiently low concentrations. The 4CP(m) data were obtained by the calorimetric determination of the specific heat of the solutions, which can hardly be applied for the present purpose below, say, m = 0.1 mol kg-'.In such cases the data for the most dilute solutions were fitted to the semi-empi rical equation 4C, = + wS(4Cp) mt -/- bm (1) where S(#Cp) = 25.6 J K-l mol-g kgi is the theoretical (Debye-Huckel) slope for a 1 : 1 electrolyte,29w = (0.5 Zviz$ is a valency factor, and b is an empirical fitting constant. This procedure could be followed for the lanthanide and uranyl salts, where data for salts with two or more anions showed the differences expected on application of the additivity criterion. A further group of data is included in table 1, which pertains to weak electrolytes, obtained as follows: - CP(H+A-) = CF(un-ionised HA) + ACi(ionisation).(2) With the aid of C,"(H+) = -71 J K-l mo1-1 (see below), the value of CF(A-) could be calculated, and this is shown in conjunction with the value calculated from the additivity criterion and data for other salts where available. Absent from table 1 are data for several electrolytes (AgF, AgNO,, NaNO, and KCNS), for which C; data have been presented in the critical compilation of Parker,29 but which are based on specific-heat data at too high concentrations and which either did not conform to the additivity criterion (AgF and AgNO,) or could not be checked according to it (NaNO, and KCNS). Thus values for the Ag+, NO; and CNS- ions could not be included in the list of (additive) individual ion values given in table 2. Nor could data be included on the ions T1+, Be2+, Ra2+, Pb", Sc3+, Cr3+, Fe"+, Zrl+ and U4+ given in the early paper of Criss and Cobble,30 nor on N,H: and S,Og- given in the - NBS Tables.31 The latter tables list values for ions on the conventional scale, Cp(H+, aq) = 0, which, however, do not add up to what we regard as the most reli- able electrolyte values.Part of the discrepancy is apparently due to the choice made in the NBS Tables concerning the value for HCI( - 136 J K-I mol-l as against - 127 J K-l mol-l, considered here to be the more reliable, following Desnoyers et a1.,:32 Singh et al.,33 Roux et af.,:54 Allred and W00lley~~~ and Tremaine et ~ 1 . : ~ ~ ) . Differences be-3258 Thermodynamics of Solvation of Ions Table 1. Values of F2 used to obtain single-ion quantities, together with the additive single-ion values (those in parentheses are based on a single electrolyte only), in J K-' mol-1 at 289.15 K electrolyte obs.calc. electrolyte obs. calc. ~- ~~ _ _ ~ ~ HF Li F NaF KF RbF CsF HCl LiCl NaCl KCl RbCl CsCl NH,Cl Me,NCl Et4NCI Pr4NC1 Bu,NC1 Pe,NCl Bu4PC1 Ph,PC1 Ph,AsCl CaCl, SrC1, BaCl, ZnC1, CdCl, MnC1, NiCI, AlCl, HBr LiBr NaBr KBr RbBr CsBr NH,Br Me,NBr Et,NBr Pr4NBr Bu,NBr Pe,NBr Bu,PBr Ph,PBr Ph4AsBr HI LiI NaT KI RbI CsI NH,I Me,NI MgCl, COC1, CUCl, - -116 - 54 - 75' - 73 - 104' - 103 - 125l - 125 - 136l - 139 - 127'' - 127 - 65' - 65 - 84l - 84 - 114' -114 - 136' - 136 - 149' - 150 - 57'9 3 - 57 108, 110 3894 387 796* 796 1 209, 1212 - (1 547) - (1 255) 1085' 1085 - 11 12' (1 112) - 269l - 270 - 282l -281 - 289l ( - 289) - 300' (- 300) - - 276 - 262 - 266 - 279s -281 - 2945 - 296 - 274 - 4996 - 500 - 1337 - 131 - 69l - 69 - 88l - 88 - 118l -118 - 139l - 140 - 155l - 154 -61' -61 - - - 1074* 106 380,~ lo+ '' 383 790'9 lo* l1 792 1 543, (1 543) 1251Y (1251) 1081' 1081 1108 - 121 - 59 - 77l - 78 - 109l - 108 - 1311 - 130 - 145l - 144 -51 12104.9~ 12 1208 - - I - 1 17, 116 392, 393 804, 802 12184 1218 - 7213 - 72 - 10 - 29 - 6013 - 59 - -81 - 95 - 214 -2 - 160" - 160 - 17015 - 171 - 165lS - 166 - 1 525 - 152 - 1 5615 - 156 - 170" - 171 - 1S715 - 186 - 16115 - 163 - 33Y - 335 - 2716 - 25 37 1714, 1 7 18 - 12 - 34 - 49 4714 45 - 665 - 66 - 77l' - 77 - 73'& - 72 - 5718 - 58 - 6218 - 62 --81'& - 77 - 9318 - 92 - 725 - 70 - 140' - 140 - 78" - 78 - 971Y - 97 - 1287- 19 - 127 - - 2913, 14 - - - - - -5120 (-51) 1 2 1 ( 1 ) 3722 (37) 11 134 (1 113) (-51) -5123 - 10 - 9 2 4 - 402* - 40 3424 32 124 2 - 1921 - 194 - 2 5 s - 254 - 21 525 (-215) - 17', - 15 - 43'4 - 45 - 51i4 - 49 - 77*, - 79 - 75 -~M .H . Abraham and Y. Marcus Table 1. (cont.) 3259 ~ _ _ _ _ _ _ _ . _ _ _ _ . ~ ____ ~ - ~ electrolyte obs. calc. electrolyte obs. calc. NaIO, KIO, "H2PO4) Na,(HPO,) H(HSO4) Na,P04 K3Fe(CN)6 K4Fe(CN)6 HC0,Na I-ICO;H+ CH,CO,Na CH,CO;H+'- C2H,C02Na C2H,CO;H+ C,H,CO;H+ o-HOC,H4C02Na m-HOC,H,CO,Na p-HOC6H4C02Na n-C3H7C02Bu4N n-C7Hl,C02Na n-C7Hl,C02Bu4N n-C,H,,CO,Na NH,+ MeNH3C1 EtNH,Cl MeNH3Br EtNH3Br PrNH,Br BuNH,Br PeNH3Br HexNH,Br HeptNH,Br OctNH,Br DodecylNH,Br c-PropylNH,Br c-PentylNH,Br c-HexylNH,Br c-HeptylNH,Br c-Oc tylNH,Br c-DodecylNH,Br Et3N(CH2),NEt3Br2 Et3N(CH2),NEt3Br2 Et3N(CH2),NEt3Br, Et3N(CH2),NEt3Br2 Et3N(CH2),,NEt3Br2 222H+ 222Hif C6H5C02Na - 2921 - 5914 925 - 16825 - 367', 2225 -2132g -4712, - 41 " - 85b 68'3 27c 1 58,' 1 12d 25328 210e 23Y8 20028 1 9728 1 550' 5941 1910' 77029 - '7f 6230 3' 97l 188l 2701 356l 44s 532l 622l 1 00331 1 35,l 26331 335,l 39231 45531 70231 54832 62532 83432 103432 I 18732 9199 7468 - 630 - 29 - 59 (9) (- 168) (- 367) (22) (-213) (-471) - 42 - 85 69 26 156 113 253 210 (235) (200) (197) (1 550) 604 1900 -1 (770) (+7) (101) (3) (97) (188) (270) (356) (445) (532) (622) (1 003) (135) (263) (335) (392) (455) (702) (548) (625) (834) (1034) (1137) (9 19) (746) 10939 1031g 9819 8549 9989 9399 - 46526 - 5414' - -5314' - S0740 - 479h - 49g4' - - 50340 - -4914' - - 49640 - 23441 - 34742 - 35442 - 34142 - 35542 - 32342 - 32942 - 32542 - 33742 - 34942 - 33942 - 35542 - 34342 - 129*' - 23943 - 27243 - 25803 - 25443 - 22543 - 22343 - 22643 - 20843 - -21143 - 22043 -21143 - 23043 -21543 (1 093) (1031) (981) (854) (998) (939) - 507 - 546 - 535 - 530 - 519 - 499 - 508 - 502 - 507 - 520 - 504 -518 - 508 - 237 - 342 -381 - 370 - 365 - 354 - 334 - 343 - 337 - 342 - 355 - 339 - 353 - 343 - 127 -201 - 240 - 229 - 224 -213 - 193 - 202 - 196 -201 -214 - 198 -212 - 202 - a From A"p (ionisation) = - 2 1 5.27 From AC., (ionisation) = - 180,33 C, (un-ionised HC0,H) = 95.34 AG (ionisation) = - 143,35r', (un-ionised CH,CO,H) = 170., AC., (ionisation) = - 141,35 C,, (un-ionised C,H,CO,H) = 253.34 Ac"p (ionisation) = - 162,36 cp (un- ionised C,H,CO,H) = 372.,' fAc"p (ionisation) = 1 1,38 Cp (NH,) = 753 and C,(H+) = - 71 (table -.2). g From AG of complexing of cryptate 222,39 together with CJ222) = 1050 J K-l m ~ l - ' , ~ ~ and Cp(H+, Mf, M2+) from table 2. Average from -43922 and -519.*O3260 Thermodynamics of Sohation of Ions References for table 1 I J. E. Desnoyers, C. DeVisser, G. Perron and P. Picker, J . Solution Chem., 1976, 5, 605. 2 P. R. Tremaine, K. Swag and J. A. Barbero, J . Solution Chem., in press (averaged from literature 3 G. C. Allred and E. M. Woolley, J . Chem. Thermodyn., 1981, 13, 155. 4 G. Perron, N. Desrosiers and J. E. Desnoyers, Can. J . Chem., 1976, 54, 2163. 5 J. J. Spitzer, P. P. Singh, K. G. McCurdy and L. G. Hepler, J . Solution Chem., 1978.7, 81. 6 J. K. Hovey and P. 'R. Tremaine, in press. 7 P. P. Singh, E. M. Woolley, K. G. McCurdy and L. G. Hepler, Can. J. Chem., 1976, 54, 3315. 8 P-A. Leduc, and J. E. Desnoyers, Can. J . Chem., 1973, 51, 2993. 9 C. Jolicoeur and P. Philip, J. Solution Chem., 1975, 4, 3. evaluated results). 10 C. Shin, I. Worsley and C. M. Criss, J. Solution Chem., 1976, 5, 867. 11 E. M. Arnett and J. J. Campion, J . Am. Chem. Soc., 1970, 92, 7097. 12 P. R. Philip and J. E. Desnoyers, J . Solution Chem. [quoted in ref. (6)]. 13 0. Enea, P. P. Singh, E. M. Wooliey, K. G. McCurdy and L. G. Hepler, J. Chem. Thermodyn., 1977, 14 A. Roux, G. M. Musbally, G. Perron, J. E. Desnoyers, P. P. Singh, E. M. Woolley and L. G. Hepler, 15 J. J. Spitzer, I. V. Olofsson, P. P. Singh and L.G. Hepler, J. Chem. Thermodyn., 1979, 11, 233. 16 P. P. Singh, K. G. McCurdy, E. M. Woolley and L. G. Hepler, J . Solution Chpm., 1977, 6, 327. 17 M. Mastroiani and C. M. Criss, J . Chem. Eng. Data, 1972, 17, 222. 18 J. J. Spitzer, P. P. Singh, I. V. Olofsson and L. G. Hepler, J. Solution Chem., 1978, 7, 623. 19 A. H. Roux, G. Perron and J. E. Desnoyers, Can. J. Chem., 1984, 62, 878. 20 V. B. Parker, Nut. Stand. Re6 Data Ser., April, 1965. 21 J. J. Spitzer, I. V. Olofsson, P. P. Singh and L. G. Hepler, Thermochim. Ada, 1979, 28, 155. 22 C. M. Criss and J. W. Cobble, J. Am. Chem. Soc., 1964,86, 5390. 23 J. A. Barbero, K. G. McCurdy and P. R. Tremaine, Can. J . Chem., 1982, 60, 1872. 24 J. A. Barbero, L. G. Hepler, K. G. McCurdy and P. R. Tremaine, Can. J .Chem., 1983, 61, 2509; the value of - 8.7 is a corrected one from Desnoyers et al., Can. J . Chem., 1979, 53, 1134 and J. Solution Chem., 1976, 5, 605, and is suggested to be the best value. 9, 731. Can. J. Chem., 1978, 56, 24. 25 J. W. Larson, K. G. Zeeb and L. G. Hepler, Can. J . Chem., 1982, 60. 2141. 26 J. J. Spitzer, 1. V. Olofsson, P. P. Singh and L. G. Hepler, Can, J . Chem., 1979, 57, 2798. 27 G. Olofsson and I. Olofsson, J. Chem. Thermodyn., 1981, 13, 437. 28 J. E. Desnoyers, R. Page, G. Perron, J-L Fortier, P-A. Leduc and R. F. Platford, Can. J . Chem., 29 R. De Lisi, G. Perron,and J. E. Desnoyers, Can. J. Chem., 1980, 58, 959. 30 H. Ruterjaus, F. Schreiner, V. Sage and T. Ackermann, J . Phys. Chem., 1969, 73, 986. 31 C . Jolicoeur, J. Boileau, S . Bazint and P.Picker, Can. J. Chem., 1975, 53, 7 16. 32 J. A. Burns and R. E. Verrall, J . Solution Chem., 1973, 2, 489; Thermochem. Acta, 1974, 9, 277. 33 M. J. Blandamer, J. Burgess, P. P. Duce, R. E. Robertson and J. M. W. Scott, J . Chem. SOC., Faraday 34 J. Konicek and I. Wadso, Acta Chem. Scand., 1971, 25, 1541. 35 G. Olofsson, J . Chem. Thermodyn., 1984, 16, 39. 36 L. E. Strong, C. Van Waes and K. H. DoolittIe, J. Solution Chem., 1982, 11, 237. 37 J. P. Guthrie, Can. J . Chem., 1977, 55, 3700. 38 G. Olofsson, J . Chem. Thermodyn., 1975, 7, 507. 39 N. Morel-Desrosiers and J-P. Morel, J. Phys. Chem., 1984, 88, 1023; 1985, 89, 1541. 40 F. H. Spedding, J. P. Walters and J. L. Baker, J. Chem. Eng. Data, 1975, 20, 438. 41 A. F. Kapustinskii and I. I. Lipilina, Dokl.Akad. Nauk SSSR, 1955, 104, 264. 42 F. H. Spedding, J. L. Baker and J. P. Walters, J. Chem. Eng. Data, 1979, 24, 298. 43 F. H. Spedding, J. L. Baker and J. P. Walters, J. Chem. Eng. Data. 1975, 20, 189. 1973, 51,2129. Trans. 1, 1981, 77, 2281. tween ionic values, e.g. CF(I-, aq) - CF(Cl-, aq) = - 6 J K-l mol--l in the NBS Tables as against 6 J K-l mo1-1 according to our analysis, are also significant and become worse the higher the charge, e.g. c;(Zn2+, aq) - 2c,"(Na+, aq) = -46 J K-l mol-1 us. - 108 J K-l mo1-1 for these two sets. For the lanthanides we did use the 4Cp data of Spedding et ~ 1 . ~ ~ 9 38 but not their set of fitting parameters, since these were chosen by them so as to accommodate the high concentration values too. Our recalculations according to eqn (l), using only the data at the lowest four concentrations, are re- garded as yielding better estimates for 4C; of the salts.These conform to the additivityM . H . Abraham and Y. Marcus 3261 Table 2. Single-ion values based on C,"(Ph,P+) = eF(Ph,B-), in J K-l mol-l at 298.15 K. The number of electrolytes used to obtain the given value is in parentheses ion value ion H+ Li+ Na+ K+ Rb+ Cs+ NH: Me,N+ Et,N+ Pr,N+ Bu,N+ Pe,N+ Ph,P+ Ph,As+ MeNH; EtNH; PrNH,f BuNH; PeNH; HexNHl HeptNHt OctNH; DodecylNHi c-PrNH; c-PeNHl c-HexNH; c-Hep tNH: c-DodecylNHt Mg2+ Ca2+ Sr2+ Ba2+ Zn2+ Cd2+ Mn2+ CO2+ Ni2+ cu2+ E t,N(CH,),NEt;+ Et,N(CH,),NEt;+ Et,N(CH,),NEt;+ Et,N(CH,),NEt;+ Et,N(CH,),,NEt;+ La3+ Pr3+ Nd3+ Sm3+ Bu,P+ c-OctNH,f UO22+ ~ 1 3 + - 7 1 f l - 9 f 1 -28f1 -58+1 -80f1 -94+1 -1+3 166+2 443f3 852 k 3 1268 3 1603 131 1 1141 & 1 1168 63" 157" 248 330 416 505 592 682 1063 195 323 395 452 515 762 58+ 1 69+ 1 77 88 64+2 50+ 1 54f 1 69f3 - 184i2 - 162f4 -125+3 668 745 954 1154 1307 -332f 1 -339+40 - 378 & 30 - 367 k 41 -362 30 Eu3+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Y b3+ Lu3+ 222H+ 222Hi+ 222Na+ 222K+ 222Rb+ 222Ca2+ 222Sr2+ 222Ba2+ HO- F- c1- Br- I- NO; NO; BrO; ClO, 1 0 , C10, ReO; MnO; HS- HSO; HSO, HCO; H2PO; Ph,B- HCO, CH,CO; C2H,CO; n-C3H,CO; n-C7H,,CO; n-C,W,,CB; C,H,CO; o-HOC,H,CO, m-HOC,H,CO, p-HOC,H,CO, c0;- sot- HPOt- PO:- Fe(CN):- Fe(CN)i- value - ~~ -351 f 17 -331 +27 - 340 + 21 -334f 17 -339f8 -352+8 -336f 13 - 350 & 25 -340+ 13 919 746 1093 1031 98 1 854 998 939 -69+1 -45f2 -5621 -60+2 -50+1 - 23? - 1 + 1 13*3 -21k3 - 1 + 1 46+ 1 65 59 - 23 60f3 93 18+ 1 37 1141 -1442 9722 184+_2 282 632k 17 798 281 & 1 263 228 225 - 159 - 138+2 -112 - 283 - 39 - 239 a Values using the results for the bromides only, table 1.3262 Thermodynamics of Solvation of Ions rules (established for chlorides, nitrates and perchlorates by the much more accurate data for the univalent and divalent cations) within the limit of & 30 J K-l mol-l (except for La3+ and Nd3+) as shown in tables 1 and 2.The ionic values given for the lan- thanides in table 2 are therefore considered to be more reliable than those given in the NBS Tables,32 which are too positive by 110-160 J K-l mol-l. - Values of CF for individual ions were calculated according to the Cp(Ph4P+, aq) = CF(BPh;, aq) extrathermodynamic assumption and are shown in table 2.The con- formity of the selected electrolyte data presented in table 1 to the additivity rule is shown by the column of values calculated from the data of table 2, to be compared with the experimental values. The number of electrolytes on which the individual ionic values in table 2 are based is shown there in parentheses, and in cases where this is larger than one, the estimated limits of error are given with the individual ionic value of CF. The choice of the extrathermodynamic assumption appropriate for splitting standard partial molal heat capacities of electrolytes into the individual ionic contributions has been discussed by Jolicoeur et aZ.39 Conway40 and French and Criss.20 We use the assumption that CF(Ph4P+, aq) C;(Ph,B-, as), which is very straightforward to apply, but defer further consideration of this issue until the Discussion.In any case, the single-ion values in table 2 can always be transformed into values based on any other assumption or convention. Once a set of individual cF values is available (table 2), the standard heat capacity of hydration of the ions is obtainable from For the monoatomic ions the value of q ( g ) is simply the ideal gas translational heat capacity, iR. For polyatomic ions the rotational contribution, R for a linear ion and $It for a non-linear one, and the vibrational contribution, C",vib) = R gi u: exp (ui) [exp (ui) - 1]-2 (4) must be added. For each vibrational frequency, vi, the degeneracy is gi and 24% = l.4388vi/T. The summation extends over all the vibrational degrees of freedom 3n - 6 (or 3n - 5 for a linear ion) where n is the number of atoms in the ion.However, frequencies vi > 2000 cm-1 can be ignored, since they do not contribute apprreciably to q(vib). In ions where internal rotation of one polyatomic part against another can occur freely, a vibrational mode is transformed into an internal rotational one, contributing 4R to C;(g). The non-availability of the complete set of vibrational frequencies, in particular those pertaining to bending, rocking, wagging, twisting and torsion modes, and ignorance of the barrier height to internal rotation, limits the calculation of q.(g) to relatively simple polyatomic ions. The calculated values, based on the vibration frequencies selected for polyatomic ions by Loewenschuss and Marcus,21 are presented in table 3 along with the values of Abyd q.Table 3 also lists values of CE(g) and Ahyd for the tetra-alkylammonium and tetraphenyl-phosphonium, -arsonium and -borate ions. For the former, the values of q(g), for [H(CH,),],N+ (n > 1) were obtained from that of (CH3),N+ for which all the required vibrational frequencies are known, by means of the average slope, 23.0 J K-l mot1, for the methylene increment for uncharged homologous series (see table 4). Rihani and Dorai~warni~l give 24.1 J K-l mol-1 for the methylene increment at 298.15 K based on general group additivity values, For the tetraphenyl-type ions, the values given by Marcus and Loewenschuss,22 based on published or estimated vibration frequencies, were used.A possible measure of self-consistency of the data for the long-chain ions is provided through plots of Cp against n, the number of methylene groups in the ion. These plots are shown in fig. 1 for the series H(CH,),NH;, [H(CH2)n,4]4N+, Et,N(CH,),-,NEt:+ and H(CH,),CO;, and can be seen to be linear, surprisingly perhaps down to n = 0 inM . H. Abraham and Y. Marcus Table 3. The Standard molar heat capacities of hydration of ions in J K-l mol-l at 298.15 K 3263 'hyd Li + Na+ K+ Rb+ Cs+ H,O+ NH: Mg2+ Ca2+ Sr2 + Ba2+ Zn2+ Cd2+ Mn2+ co2+ Ni2+ cu2+ La3+ Pr3+ Nd3+ Sm3+ Eu3+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Yb3+ Lu3+ uo;+ 0.059 -9 0.102 -28 0.138 -58 0.149 -80 0.170 -94 0.130 -71 0.148 -1 0.072 -158 0.100 -169 0.113 -177 0.136 -188 0.075 -164 0.095 -150 0.083 -144 0.075 -169 0.069 -184 0.073 -162 0.210 -125 0.105 -339 0.100 -378 0.098 -367 0.096 -362 0.095 -351 0.094 -331 0.092 -340 0.091 -334 0.090 -339 0.089 -352 0.088 -336 0.087 -350 0.086 -340 21 21 21 21 21 35 35 21 21 21 21 21 21 21 21 21 21 49 21 21 21 21 21 21 21 21 21 21 21 21 21 - 30 - 49 - 79 - 101 - 115 - 106 - 36 - 179 - 190 - 198 - 209 - 185 - 171 - 175 - 190 - 205 - 183 - 174 - 360 - 399 - 388 - 383 - 372 - 352 - 361 - 355 - 360 - 373 - 357 -371 -361 F- c1- Br- I- OH- SH- NO, c10, TO, c10, BrO; MnO, ReO; HCO; HSO; HSO, H,PO, HP0;- Fe(CN)i- Fe(CN):- Me,N+ Et,N+ Pr,N+ Bu,N+ Pe,N+ Ph,P+ Ph,As+ BPh; c0;- so;- Poi- 0.133 0.181 0.196 0.220 0.133 0.207 0.179 0.200 0.191 0.181 0.240 0.250 0.260 0.156 0.170 0.190 0.200 0.178 0.230 0.200 0.238 0.440 0.450 0.280 0.337 0.379 0.413 0.443 0.424 0.425 0.420 - 45 - 56 - 60 - 50 - 69 - 23 -1 13 - 21 -4 46 60 65 18 60 93 37 - 159 - 138 -112 - 283 - 39 - 239 166 443 852 1268 1603 1141 1168 1141 21 21 21 21 29 29 45 58 60 62 62 72 75 51 53 71 63 44 62 68 65 217 21 1 99 191 283 375 467 369 372 367 - 66 - 77 -81 -71 - 98 - 52 - 46 - 45 -81 - 66 - 16 - 12 - 10 - 33 7 22 - 26 - 203 - 200 - 180 - 348 - 256 - 450 67 252 569 893 1136 772 796 774 some cases.Intercepts and slopes of the plots are given in table 4, together with corresponding values for a number of homologous series of non-electrolytes using data compiled by Cabani et aZ.42 Except for the series cycloalkyl-NH:, where the slope is only 63 J K-l rnol-l, the methylene increments to CF are all reasonably constant, averaging (90+3) J K-l mol-1 for the 10 remaining electrolyte and non-electrolyte series.Also in table 4 are details of corresponding plots of c",(g) and Ahyd c", against n: the methylene group constancy is still observed. It is of interest that in the two series of quaternary ammonium salts, for cations with the same number of carbon atoms, the divalent ion has a much less positive ZF value than has the univalent ion: cf. cF values for the C,, compounds Et,N(CH,),NEt:+ (745 J K-l mol-l) and Bu,N+ (1268 J K-l mol-l). Discussion Single-ion Values of C,"(aq) The relative values of C;(aq) within a given valence set, such as univalent anions or divalent cations, are quite independent of the choice of the extrathermodynamic - assumption made in order to arrive at the single-ion values in table 2, namely that Cp(Ph,P+, as) = CF(BPh4, as).However, the relative values of anions and cations3264 Thermodynamics of Solvation of Ions Table 4. Slopes and intercepts of plots of heat capacities against the total number of methylene groups in the solute, in J K-l mo1-1 at 298.15 K" solute slope 90+7 90+3 92f 1 87f 1 9 5 f 3 86f4 9 2 f 3 88f 1 63+ 1 94+3 89+ 1 23.1 + 0.2 23.0 f 0.0 22.7 f 0.1 22.5 +0.2 23.0 +O.O 23.1 + 0.0 67f7 67+3 69f 1 65+ 1 72+3 63k6 intercept _ _ _ _ ~ (A) q ( a s > 106f 18 72+7 52k4 88+3 146f6 173+9 - 243 f 45 -21+2 11&5 - 180+20 2 k 7 (B) Cp(gas> 4.5 + 0.6 46.8 f 0.0 27.7k0.4 20.0 f 0.4 70.4 f 0.0 66.2 f 0.1 (C) Ah,& 101 + 18 25+7 25f4 67*4 75f6 107+9 no. of solutesb 4(3-6) 3(2-4) 4(3-6) 4(2-5) 3P-4) 3(2-4) 5(4-20) 8( 1-8) 6(3-6, 8, 12) 5(9, 10, 12, 14, 16) 5(0-3, 7,9) 4(3-6) 4(3-6) 4(2-5) 3(24) 3(2-4) 3C-4) 4(2-5) 3(2-4) 4( 3-6) 4(2-5) 3 C 4 ) 3C-4) standard deviation ~ ~___ 15 4 3 3 4 6 43 3 5 17 6 0.4 0.0 0.2 0.5 0.0 0.0 15 4 3 3 4 6 a All heat-capacity values for non-electrolytes from ref.(42); values for ionic solutes from table 2. Parenthesised values denote the actual values of n used. depend crucially on the particular choice. French and Criss20 have recently discussed the various single-ion assumptions that have been made. They preferred a modification of ours, leading to CF(H+, as) = -63 30 J K-l mol-l, as against our value of -71 J K-l mob1. However, our assumption is more readily applicable and simpler. If the alternative of C2(Ph4As+, aq) = c?(BPh;, aq) were employed, the resulting ionic values would change by - 142 J K-l mol-l, yielding CF(H+, aq) = -85 J K-l mol-l.The phosphonium value is preferred by us over the arsonium value (used more generally as the extrathermodynamic assumption for splitting electrolyte values into ionic contributions), since for the heat capacities the phosphonium data pertain to two electrolytes (Ph,PCl and Ph,PBr) that show excellent conformity to the additivity rule, whereas only Ph,AsCl was measured, and since the phosphonium ion is closer in size to the tetraphenylborate ion than is the arsonium ion.22 A different approach was taken by Tremaine et al.43 who measured the initial thermoelectric power of the cell Ag I AgCl 1 KCl(aq) 1 AgCl(aq) I Ag from 303 to 363 K.Their conclusion, dependent on assumptions concerning the transported ionic entropy is that 0 > C;(H+, as) 2 -57 J K-l mol-l. The lower limit, -57 J K-l mol-l, was adopted by Abraham et aZ.8 but this is still not quite as negative as our present value of -71 J K-l mol-l.M. H. Abraham and Y. Marcus 3265 1500 - 1 c1 ; 1000 - 4 b4 ‘L, h \ E Q 500 0 I I I I I 1000 500 0 5 10 15 20 n Fig. 1. The standard partial molar heat capacities of aqueous long-chain ions plotted against the total number n of the methylene groups in their alkyl chains. (1) H(CH,),NH,+, (2) ordinate) : H(CH,),CO;. c-[(CH,),-,CH”,+; (3) [H(CH,),,,I,N+, (4) (C,H,),N(CH,),_,N(C,H~)~+ ( 5 ) (right-hand Finally, we point out that use of the extrathermodynamic assumption employed by us has the corollary that cations and anions of the same size are treated alike.Since the heat capacities of the gaseous ions, and the contributions due to cavity effects and electrostatic effects on our hydration model (see later) do not depend on the sign of the charge of the ion, z, the result that heat-capacity-related functions for cations and anions should fall on the same curves in plots against ionic radii is expected, and indeed found, see later (fig. 3 and 5). This result would not be obtained if the splitting of cF values for electrolytes were done by some other assumption that required our single-ion values for univalent ions to be adjusted by > k30 J K-l mol-l. This limit of self-consistency of the assumption used by us is, incidentally, the same as that estimated by French and Criss20 for their assumption.The difference between ionic values on our assumption and that of French and Criss20 is only 8 J K-l mol-l, and between our values and those of Abraham et aLs is only 14 J K-l mol-l, so that these three sets of single-ion values will lead to essentially the same results. Since we wish to compare our analysis of heat-capacity data with those of the entropy data we have discussed before, our single-ion heat-capacity data should be compatible with the single-ion entropy data. The standard partial molar entropies of electrolytes cannot, unfortunately, be split according to the tetraphenylphosphonium (or arsonium) tetraphenylborate assumption, because of lack of data on the entropy of a crystalline tetraphenylphosphonium (or arsonium) salt.22 The single-ion assignments that have been made by us, equivalent to P(H+, aq, 1 mol dm-3) of 6 , - 35 J K-l mol-l or 1 3 3 40 - 22 J K-l mol-l, lead to entropy values for univalent cations and anions being located on the same curve in plots against ionic radii, and are both compatible with the present assumption on heat capacities.3266 Thermodynamics of Solvation of Ions Analysis of the AhydCpO Results The thermodynamics of hydration of ions have been discussed by many authors in terms of models that have a great deal in cornmon.ly 9 v 1 3 9 44-46 On these models, the standard thermodynamic functions for hydration are considered to arise from the sum of a number of contributions as follows: (i) a correction for standard states in the gas and in solution, where applicable, (ii) the creation in the solvent of a cavity of suitable size, (iii) interaction of the ion with near-neighbour solvent molecules by dispersion forces, (iv) (electrostatic) interaction of the ion with the solvent within its solvation layer(s), (v) electrostatic interaction of the ion with the bulk solvent, (vi) non-electrostatic inter- actions of the ion with the solvent, which might include hydrogen-bond formation (for anions), coordinate bond formation (for cations) and various specific ion-water inter- actions (for organic ions) and (vii) the reorganisation of solvent molecules around the ion, with concomitant increase or decrease in fluidity.When applied to Ahyd Ci values, no standard-state correction is requircd, so that only contributions (iik(vii) need be considered. Although it is possible to calculate a cavity contribution, term (ii), 4.g.by scaled particle theory (SPT), there is some advantage to be gained by including terms (ii) and (iii) together in a 'neutral term', designated as N in the following, and calculated as the heat capacity of hydration of a neutral solute of the same size as the ion. Indeed, it has been shown that for a one-centre ion the polarisation charge induced in the solvent around the ion is exactly the opposite of the ionic charge, so that the ion is screened by the polarisation charge and behaves like a neutral molecule. The electrostatic effects, denoted as E, are calculated by continuum theory in which the solvent is characterised by its relative permittivity (dielectric constant) E and temperature derivatives of E .This applies to both terms (iv) and (v), with appropriate values of the radii of the ion and of the solvent layers. The remaining interactions cannot be estimated independently and are grouped together in a 'configurational term', C, obtained by difference : ( 5 ) Ahyd ci = N+E+ c. Following the general method of Abraham and Liszi,' and the analysis by Marcus and Loewen~chuss~~ of entropies of hydration of ions, we set up two summations of the contributions to the heat capacity of hydration according to eqn ( 5 ) : the summations are distinguished in the following by subscripts 1 and 2. We note that these are not the only possible summations of N, E and C terms in eqn (5), but we feel that these particular summations enable us to interpret usefully the Ahyd (l"p values for single ions.The summations are ultimately based on the same model of ionic hydration, in which an ion is surrounded by a first layer of immobilised solvent, then by a possible transitional layer and finally by the bulk structured solvent.g* 44 The ionic radii needed for the calculations were taken from Marcus and L o e w e n s c h ~ s s ~ ~ ~ ~ and from King4s and Mi1ler0~~ for the tetra-alkylammonium and tetraphenyl ions, and are listed in table 3. In the first summation the neutral term, N,, is calculated from A h y d q for the rare gases, dataS for which are given in table 5 and fig 2. Values of N , are obtained from a fit of the rare-gas data to a linear equation in Y, the rare-gas radius [eqn (6)], for which the correlation coefficient p = 0.9446: N , = - 55 + 1380(r/nm) J K-l mo1-l.(6) The rare-gas radii range from 0.13 to 0.205 nm; beyond these limits N , must be obtained by extrapolation. For ions with Y < 0.13 nm, no appreciable error is introduced, since the neutral term is small in absolute magnitude and relatively unimportant, but for ions with large values of Y a more serious error may be introduced. Use of eqn (6) to obtain the neutral term excludes, of course, any hydrophobic effects observed for ions such asM . H . Abraham and Y . Marcus 3267 Table 5. The heat capacity of hydration of neutral solutes [in J K-l mol-1 (rounded to nearest 5)] solute ~~ ~ helium 0.131 145 20 125 neon 0.139 165 20 145 argon 0.170 190 20 170 krypton 0.180 210 20 190 xenon 0.205 255 20 23 5 methane 0.190 240 35 205 ethane 0.221 300 50 250 propane 0.253 370 75 295 n-butane 0.276 470 95 375 n-pentane 0.289 570 120 450 n-hexane 0.301 63 5 145 490 c-hexane 0.283 515 105 410 a Rare gas radii from R.A. Pierotti, Chern. Rev., 1976, 76, 717 and E. Wilhelm and R. Battino, J. Chern. Phys., 1971, 55, 4012. Alkane radii from ref. (1) or from molar volumes using the Stearn-Eyring formula. Rare-gas values from M. H. Abraham and E. Matteoli, unpublished survey. Alkane values from ref. (42). D. R. Stull, E. F. Westrum and G. C . Sinke, The Chemical Thermodynamics of Organic Compounds (Wiley, New York, 1969). ~ ~~~ R,N+. Heat-capacity contributions due to such effects, which may be quite large (as seen in fig.2) for the alkanes, are then incorporated in the configurational term. The electrostatic term in the first summation, El, is calculated as the total electrostatic heat capacity of solvation and is obtained from the ‘one-layer’ solvation model of Abraham et aZ.* through the equation -2 BE = A Z 2 T [ ( T ) ($+(i) (31 (;-;) In this equation z is the ionic charge, E, is the solvent bulk dielectric constant, E , is the dielectric constant of the first hydration shell of thickness (b - r ) and r is the ionic radius. As before, we take E, = 1.87, &,/ST = - 1.60 x K-l and B2~,/BT2 = 0. The bulk water values are 50 E, = 78.36, 6~,/6T = -0.3595 K-l and B2&,/ST2 = 1.553 x K2, and the thickness of the layer, (b - r ) is taken as 0.15 nm (i.e. approximately the radius of a water molecule).The constant A has the value 69454 J mol-1 nm-1 at 298,15 K. is termed the ‘configurational contribution’, C,. Values of C, are plotted as a function of r in fig. 3, and are seen to fall into four families: trivalent cations and anions, divalent cations and anions, univalent cations and anions and the tetra-alkyl or -aryl ions. If C,/ I z I is plotted instead of C,, the first three families collapse into one, and a more-or-less parabola-shaped single curve results, with the hexacyanoferrate anions being obvious outliers. In this first summation the entire electrostatic term El is subtracted out; this term includes implicitly the solvent immobilisation effect. Hence the ‘configuration contribution, ’ C,, should be related to effects on solvent fluidity, or structure-making and -breaking effects.Abraham What is left after N , and El are subtracted from Ahyd3268 1000 800 600 3 I 4 z - I M h O Q . 400 3 U 200 0 Thermodynamics of Solvation of Ions I I ' I I I I I I I I I I I / 0 0.1 0.2 0.3 0.4 rlnm Fig. 2. The standard molar heat capacities of hydration of the rare gases (filled symbols) and the lower alkanes (empty symbols), plotted against their radii (data from table 3). The straight line represents eqn (6) and the dashed curved line eqn (8). et al.6 showed that an electrostatic entropy term, ASE, was quantitatively connected to structure-making and -breaking effects of simple univalent inorganic anions and cations. A plot (not shown) of C, against ASE is a smooth curve for both anions and cations with an intercept of ca.- 170 J K-l mol-l, corresponding to ASE = 0, the null point6 between structure-making and structure-breaking. Since Abraham et aZ.8 used different ionic radii to those in this work, we have recalculated ASE values using the same ionic radii as used to obtain C,. There is again a smooth plot of C, against ASE, but the null point is changed only slightly to - 150 J K-l mol-l. As in the case of ASE, a quantitative connection can be established between C , and measures of fluidity, the viscosity B-coefficient and the proton relaxation %-coefficient. A plot of C, against the B-coefficient for ions, with the latter assigned according to B(Ph,P+) = B(BPh,), is shown in fig. 4. The hydrophilic ions fall into two distinct quadrants: ions with positive B-coefficients and with C, more positive than ca.- 170 J K-l mol-l (cf. the same value for the C, against ASE plot), and ions with negative B-coefficients and with C, more negative than ca. - 170 J K-l mol-l.t We can therefore t There is no significance to be attached to the 'null-point' of ca. - 170 J K-' mo1-I other than as an empirical structure-making and -breaking measure. Alteration in the constants used to calculate El could lead to the 'null-point' being more positive or more negative.M . H. Abraham and Y. Marcus 3269 1000 500 4 I + z G o 3 I * c, 1 -500 I U 0 0 0 0.1 0.2 0-3 0-4 0-5 rlnm Fig. 3. The fluidity-related structural contribution to the standard molar heat capacity of hydration of ions, C,, plotted against their radii r.Symbols: 0, univalent cations; A, divalent cations; 0, trivalent cations, 0, univalent anions; A, divalent anions; ., trivalent anions, x , tetra-alkyl and tetra-aryl ions. take C, as a measure of structure-making and structure-breaking: if C, is more positive than ca. - 100 J K-l mol-l the ion is a structure-maker, if C, is more negative than ca. -250 J K-l mol-1 the ion is a structure-breaker, and with C, between, say, - 100 to - 250 J K-l mol-1 an ion would be a borderline case. The hydrophobic ions form a quite separate category, even though they fall into the quadrant with positive B-coefficients and with C, > - 170 J K-l mol-l. These ions are hydrophobic structure-makers and, like apolar solutes, lead to large positive heat capacities of hydration (see values for alkanes in table 5).Of all the ions plotted in fig. 4, only SO:- and (CH,),N+ lie outside the two quadrants. To conclude, according to our first summation of terms, the configurational contri- bution to the heat capactity of hydration, C,, is due mainly to the effect of the ion on the fluidity of the solvent. For the hydrophilic ions C, is > - 170 or < - 170 J K-l mol-l, depending on whether the ions are structure-makers or structure-, breakers, and become less positive or more negative as the size of the ion increases or as its charge (irrespective of sign) decreases. For hydrophobic ions C, is > - 170 J K-l mol-l, becoming more positive as the ions increase in size. The signs of these effects are opposite to those of the structural contribution to the entropy of hydration (ASstr of Marcus and Loewens~huss~~) and opposite to those of the ASE term of Abraham et aZ.6 but show the same trends with size and charge.The more disordered is the solvent around an ion, the larger will be the entropy and the less will be the heat3270 Thermodynamics of Solvation of Ions 600 7 400 d 0 E M CI I h 1 G 200 0 - a structure breakers -40( / structure makers I 1.5 .--A so,*- Fig. 4. The correlation of the fluidity-related structural contribution to the standard partial molar heat capacity of hydration of ions, C,, with their viscosity B-coefficients.sT 23, 51 Symbols as in fig. 3. capacity, relative to that for hydrogen-bonded bulk water, and vice versa for ordered solvent. In the second summation based on eqn ( 9 , hydrophobic effects are included in the neutral term, N,, by calculating this term from data on Ahyd C; for hydrophobic solutes; see results in table 5 and fig.2 for alkanes. The Ahyd values in table 5 were therefore fitted, for r 2 0.25 nm, to an equation in r3, for which p = 0.9953: (8) For values of r d 0.25 nm, N , values equalling those of Nl were used. However, considerable differences between N , and N , arise on extrapolation to larger values of r. The configurational term, C,, will then also differ from C, because the former will exclude and the latter will include hydrophobic structure-making effects. In this second summation these hydrophobic effects are included in the neutral term N,. Because we have excluded outer-layer hydrophobic effects, it is appropriate also to exclude outer-layer or bulk electrostatic effects, so that C, then refers to the total structural effects within a solvent layer of given thickness.We therefore calculated E, as the electrostatic contribution to the heat capacity of hydration of the bulk solvent outside a radius that we as r+0.28 nm, the addend being the diameter of a water molecule. Eqn (7) then reduces to N2 = 1 + 18 140(r/11m)~ J K-l mol-l. with b = (r+0.28) nm. Values of E, are much less negative than E, for ions of a givenM. H. Abraham and Y. Marcus 327 1 0 -1 00 -200 - N - \ G -300 -400 -500 0 0.1 0 0.20 0.30 rlnm Fig. 5. The orientation-related contribution to the standard partial molar heat capacity of hydration of ions, C,/ 1 z 1, plotted against the ionic radius, r.Symbols: 0, all cations; 0 , all anions, irrespective of charges. charge and radius, and the difference becomes larger the smaller is r and the larger is z. Values of C, are obtained from N , and E, through eqn (5). In fig. 5 is plotted the quantity C,/ 1 z I against r, yielding a straight line common to singly, doubly and triply charged cations, and to singly charged anions, mono- or poly-atomic, given by C,/ I z I = 15 - 1350(r/nm) J K-l mol-' (10) with p = -0.9614 and a standard deviation of 20 J K-' mol-1 for 42 ions. Not lying on this straight line are the doubly and higher-charged anions and protonated anions. These ions seem to have specific structural effects in water, owing to strong hydrogen bonding with the highly charged or protonated anions, terms (vii) and (vi), respectively.This mode of summation stresses in the configurational contribution C, the central orientation of the solvent near the ion, i.e. in the region between r and ( r + 0.28 nm) from its centre, term (iv). For ions larger than Li+ (i.e. for 0.07 6 r/nm 6 0.30) the volume of this region is nearly proportional to r (within+7%), so that the number of water molecules affected by the ion in this region (not taken into account in the E, term) would also be proportional to r . A centrally orientated water molecule does not partici- pate in the normal tetrahedral hydrogen bonding of bulk water, and has therefore a lower heat capacity, The strength of this orientation, i.e. the extent to which the heat capacity3272 Thermodynamics of Solvation of Ions is decreased per mole of water molecules orientated, is expected to be proportional to the charge of the ion causing it, and interfering thus with its hydrogen bonding.This reasoning then explains the dependence of the configurational contribution C,, see eqn (lo), on the product r I z I and its negative sign. Note that the number of water molecules that are immobilised, i.e. have lost all their translational degrees of freedom relative to the ion, is not the same as the number of water molecules that are prevented from participation in the normal hydrogen bonding of water. The former number, playing a role in the immobilisation entropy of hydration,13 is proportional to 1 z 1 r - l , whereas the latter number, playing a role in the orientational heat capacity of hydration, is proportional to I z I r.Conclusions Two single-ion assumptions are involved in our summation of effects through eqn (5). The assumption that cF(Ph,P+) = C,"(BPh;) leads, through values of C(g), to Ahyd q(Ph,P+) at 772 J K-l mol-l being essentially the same as that of Ah.yd <(BPh;) at 774 J K-l mol-l. On the other hand, our calculations of N and E involve ions of equal radii (and equal 121) being treated similarly, which is in effect also a single-ion assumption.? That these two assumptions are compatible is shown by the plots in fig. 3 and 5 and also by eqn (lo), in which values for ions of equal radii and equal I z I lie on the same line or curve. These assumptions, leading to values of C, and C,, are also compatible with previous divisions of entropies of hydration into single-ion values,6T l3 as shown, for example, by plots of C, against AS, in which values for univalent anions - and cations again lie on the same curve.The C, values, derived ultimately from Cp(Ph,P+) = cF(BPh;), are also perfectly compatible with viscosity B-coefficientsderived from B(Ph,P+) = l?(BPh~),~l as seen from the plots shown in fig 4. A plot of C, for univalent anions and cations against p values based20 on p(Ph,P+) = 287 cm3 mo1-I and p(BPh;) = 283 cm3 mol-1 also yields a single curve (not shown) for both anions and cations. Thus, although the numerical values of C, and C, will depend on exactly how the respective N and E values are calculated, the general relationship of these configurational contributions to other parameters that contain structural information cannot be doubted.Our interpretation of single-ion Ahydcp values through the parameters C, and C, draws on three major types of ionic effect: (a) the electrostatic immobilisation of near-neighbour solvent molecules, (b) stuctural changes amongst the transitional-layer solvent molecules (either structure-breaking/fluidity increasing or structure-making/ fluidity decreasing) and ( c ) a hydrophobic structure-making or fluidity decrease due to the effect of hydrocarbon groups. A summary of these effects in terms of increase or decrease in heat capacity is shown in table 6, together with the concomitant effects on entropies and viscosity B-coefficients. Aside from the hydrophobic structure-making effect (c), it can be seen that only a quite detailed analysis will distinguish effects due to electrostatic immobilisation (a) and any increase in fluidity (b), since both lead to negative heat capacities.The situation in terms of the entropy function is not so complicated because effect (a) leads to a decrease in entropy, whereas (h) leads to an increase in entropy. t Note that the assumption Cp(Ph,P+, aq) = C,(BPh,, aq) and hence that Ahyd C,(Ph,P+) = C,(BPh;) does not by itself lead to values of Ahya C; being the same for small ions of equal radii but of opposite charge. Short-range ion-water interactions such as ion-quadrupole effects could conceivably be different for anions and cations, but would rapidly be diminished with increase in ionic radius.Table 6.A summary of ionic effects on Ahyd ci, Ahyd So and the viscosity B-coefficient for univalenta ions hydrophilic ions, small r hydrophilic ions, large r hydrophobic ions, large r ‘ h y d q ‘hydS0 B ‘hydC; ‘hydSO B ‘hyd ‘hyd so B neutral term first layer electrostatic immobilisation transitional layer bulk solvent overall effect description + ve - ve - ve - ve + ve + ve - ve + ve - ve - ve - ve - ve + ve net decrease in fluidity ‘ structure-maker ’ + ve - ve + ve - ve small - ve - ve + ve small - ve + ve - ve - ve } +ve - ve + ve - ve - ve - ve - ve + ve - ve + ve net decrease in fluidity ’ hydrophobic-structure-maker ’ net increase in fluidity ‘ structure-breaker ’ a For hydrophilic multivalent ions, the effect on the first-layer electrostatic immobilisation is much larger, leading to more negative values of Ahyd and Ahyd So and to more positive B-coefficients.Indeed, for multivalent ions of large radius, e.g. SO:- and CO$-, the observed B-coefficients are now positive. Q x 9 w h, 4 w3274 Thermodynamics of Solvation of Ions References 1 M. H. Abraham and J. Liszi, J . Chem. SOC., Faraday Trans, 1, 1978, 74, 1604. 2 M. H. Abraham and J. Liszi, J . Chem. SOC., Faraday Trans. I , 1978, 78, 2858. 3 M. H. Abraham, J. Liszi and L. Meszaros, J. Chem. Phys., 1979, 70, 249. 4 M. H. Abraham and J. Liszi, J. Chem. SOC., Faraday Trans. I , 1980, 76, 1219. 5 M. H. Abraham and J. Liszi, J . Inorg. Nucl. Chem., 1981, 43, 143. 6 M. H. Abraham, J. Liszi and E. Papp, J . Chem. Soc., Faraday Trans. I, 1982, 78, 197. 7 M. H. Abraham, J.Liszi and E. Kristof, Aust. J. Chem., 1982, 35, 1273. 8 M. H. Abraham, E. Matteoli and J. Liszi, J . Chem. SOC., Faraday Trans. I, 1983, 79, 2781. 9 M. H. Abraham, Acta Chim. Hung., in press. 10 Y. Marcus, Pure Appl. Chem., 1983, 55, 977; 1985, 57, 1103. 11 S. Clikberg and Y. Marcus, J. Solution Chem., 1983, 12, 255. 12 Y. Marcus, Aust. J . Chem., 1983, 36, 1719. 13 Y. Marcus and A. Loewenschuss, Annu. Rep., Sect. C, (Royal Society of Chemistry, London, 1984), 14 Y. Marcus and A. Ben-Naim, J. Chem. Phys., 1985,83,4744. 15 Y. Marcus, J . Solution Chem., 1985, 14, in press. 16 P. R. Tremaine and S. Goldman, J. Phys. Chem., 1978,112, 2317. 17 D. Smith-Magowan and R. H. Wood, J . Chem. Thermodyn., 1981, 13, 1047. 18 R. H. Wood, J. R. Quint and J-P. E. Grolier, J.Phys. C‘hem.. 1981, 85, 3944. 19 J. W. Cobble, R. C. Murray Jr and U. Sen, Nature (London), 1981, 291, 566. 20 R. N. French and C. M. Criss, J. Solution Chem., 1982, 11, 625. 21 A. Loewenschuss and Y. Marcus, Chem. Rev., 1984,84, 89. 22 Y. Marcus and A. Loewenschuss, J . Chem. SOC., Faradajj Trans. I, 1985, 81, in press. 23 G. Engel and H. G. Hertz, Ber. Bunsenges. Phys. Chem., 1968, 72, 808. 24 L. R. Pratt and D. Chandler, J. Chem. Phys., 1977, 67, 3683. 25 K. Hallinga, J. R. Grigera and H. J. C. Berendsen, J. Phys. Chem., 1980, 84, 2381. 26 P. J. Rossky and D. A. Zichi, Faraday Symp. Chem. SOC., 1982, 17, 69. 27 H. Leiter, C. Albayrak and H. G. Hertz, J. Mol. Liq., 1984, 27, 21 1. 28 A. Ben-Naim, J. Phys. Chem., 1965,69, 3240; 1968,72, 2998; A. Ben-Naim, Hydrophobic Interactions (Plenum, New York, 1978). 29 V. B. Parker, Thermal Properties of Uni-Univalent Electrolytes, (NSRDS-NBS-2, Natl Bur. Stand., Washington, 1965). 30 C. M. Criss and J. W. Cobble, J. Am. Chem. Soc., 1964,86, 5394. 31 D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney and R. L. Nuttall, NBS Tables on Chemical Thermodynamic Properties, (Am. Chem. SOC. and Am. Inst. Phys., Washington, 1982). in press; Y. Marcus, J. Chem. SOC., Faraday Trans. 1, 1985, 81, in press. 32 J. E. Desnoyers, C. De Visser, G. Perron and P. Picker, J. Solution Chem., 1976, 5, 605. 33 P. P. Singh, E. M. Woolley, K. G. McCurdy and L. G. Hepler, Can. J . Chem., 1976, 54, 3315. 34 A. Roux, G. M. Musbally, G. Perron, J. E. Desnoyers, P. P. Singh, E. M. Woolley and L. G. Hepler, 35 G. C. Allred and E. M. Woolley, J. Chem. Thermodyn., 1981, 13, 147. 36 P. R. Tremaine, K. Swag and J. A. Barbero, J . Solution Chem., 1985, 14, in press. 37 F. H. Spedding, J. P. Walter and J. L. Baker, J. Chem. Eng. Data, 1975, 20, 438. 38 F. H. Spedding, J. L. Baker and J. P. Walters, J. Chem. Eng. Data, 1975, 20, 189; 1979, 24, 298. 39 C. Jolicoeur, P. R. Philip, G. Perron, P-A. Leduc and J. E. Desnoyers, Can. J. Chem., 1972, 50, 3167. 40 B. E. Conway, J. Solution Chem., 1978, 7, 721. 41 D. N. Rihani and L. K. Doraiswami, Znd. Eng. Chem. Fundam., 1965,4, 17. 42 S. Cabani, P. Gianni, V. Mollica and L. Lepori, J . Solution Chem., 1981, 10, 563. 43 P. R. Tremaine, N. H. Sagert and G. J. Wallace, J. Phys. Chem., 1981,85, 1977. 44 H. S. Frank and M. W. Evans, J. Chem. Phys., 1945, 13, 507. 45 H. L. Friedman and C. V. Krishnan, in Water, A Comprehensive Treatise, ed F. Franks (Plenum, New York, 1973), vol 3. 46 M. Yu. Matuzenko, S. N. L’vov and V. I. Zarembo, Geokhimiya, 1982, 720; S. N. L’vov and V. I. Zarembo, Zh. Prikl. Khim., 1982, 55, 2674. 47 R. Constanciel and R. Contreras, Theor. Chim. Acta, 1984, 65, 1. 48 E. J. King, J . Phys. Chem., 1970, 74, 4590. 49 F. J. Millero, J . Phys. Chem., 1971, 75, 280. 50 D. J. Bradley and K. S. Pitzer, J . Phys. Chem., 1979, 83, 1599. 51 A. Sacco, A. de Giglo and A. Dell’Atti, J . Chem SOC., Faraday Trans. I , 1981, 77, 2693. Can. J. Chem., 1978, 56, 24. Paper 6/270; Received 7th February, 1986

ISSN:0300-9599    

DOI:10.1039/F19868203255

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. 1, 1986,82, 3275-3285 Thermodynamic Parameters of Electrolyte Solutions in Ni tromet hane Angela F. Danil de Namor" and Lily Ghousseini Department of Chemistry, University of Surrey, Guildford, Surrey G U2 5XH Standard enthalpies of solution of eighteen 1 : 1 electrolytes in nitromethane derived from heats of solution measured calorimetrically at 298 K are reported. Combination of these data and those in water yields enthalpies of transfer, A e , for these electrolytes from water to nitromethane. The Ph,AsPh,B convention has been used to derive single-ion AHp contributions for seven cations and six anions. These data and those previously reported for single-ion free energy of transfer from water to nitromethane enables the calculation of the transfer single-ion entropies based on the Ph,AsPh,B convention.As in transfers from water to other non-aqueous solvents AG(M+ + X-) from water to nitromethane is approximately independent of Mi and X- when M+ = Li+, Na+, K+, Rb+ and Cs+ and X- = ClO;, I-, Br- and perhaps CI-. The results obtained indicate that A% for the alkali-metal cations between dipolar aprotic solvents derived from heat of complexing data of cryptand 222, and these cations in these solvents yield single-ion values for transfer among dipolar aprotic solvents that are chemically reasonable and in accord with values obtained by the Ph,AsPh,B convention. The calculation of the thermodynamic transfer functions, AG:, A K and A K of a dissociated (M+ +X-) electrolyte from a reference solvent (A) to another solvent (B) requires data on the standard parameters of solution (AG;, AK and A$') for that electrolyte in the two solvents in their pure state.Several accounts for the methods used to obtain these parameters can be found in the Single-ion transfer data are useful in the study of interactions between ions and solvents. No less significant is the generation of data in solvent systems which are relevant to industrial processes. Our recent work on the water-nitrocompound solvent system^^-^ encourages us to measure the heats of solution of 1 : 1 electrolytes in nitromethane. Since a number of electrolytes are sufficiently soluble and their rate of dissolution is relatively fast in this solvent, the calorimetric techniques was used for these measurements.In this paper we report the standard enthalpies of solution of 1 : 1 electrolytes in nitromethane, the enthalpies for the transfer, AG(M+ + X-) of the dissociated electrolytes from water to nitromethane and the single-ion A% parameters based on the Ph,AsPh,B convention. Combination of these data and single-ion AG,O values based on the same convention previously reported by us enables the calculation of the entropies for the transfer of single ions from water to nitromethane. Criss et ~ 1 . ~ 9 found that the entropies for the transfer of (M+ + X-) electrolytes from water to non-aqueous solvents when M+ is an alkali-metal cation and X- is a halide is independent of the cation and the anion. The availability of more data on entropies of transfer to other solvents revealed that A,!$(M+ + X-) is also approximately constant for transfers involving other anions such as perchlorates and nitrate^.^, lo The calculation of A$(M++X-) for the transfer of alkali-metal halides and per- chlorates is of particular interest in the water-nitromethane system, since this could help 108 3275 FAR 13276 Thermodynamics of Electrolytes in Nitromethane in reaching a more definite conclusion regarding the values previously reported6 for the single-ion A% of alkali-metal cations obtained from heats of complexing data between these cations and cryptand 222 in the dipolar aprotic solvents.Experimental The tetra-n-alkylammonium tetraphenylborate salts were prepared and purified as described elsewhere.ll Tetra-n-methyl-and tetra-n-ethyl-ammonium picrates were ob- tained by neutralisation of the appropriate hydroxide with picric acid (Hopkins and Williams Ltd).The compounds were recrystallised from water and dried in a vacuum oven at room temperature for several days. Tetra-n-ethyl- and tetra-n-propyl-ammonium perchlorates (Fluka) were dried under vacuum for several days prior to use. Tetra- n-butylammonium perchlorate was prepared from Bu,NOH (Aldrich, 40 % solution in water) and aqueous perchloric acid. The salt was purified by recrystallisation from water and dried under vacuum for several days. Tetraphenylarsonium perchlorate was prepared from Ph,AsCl and KClO, and recrystallised from an acetone-water solution. Tetra-n-methylammonium iodide (A.R. reagent) was recrystallised from water and dried at 333 Kin a vacuum oven for several days.Tetra-n-ethyl- and tetra-n-propyl-ammonium iodide (A.R. grade reagents) were recrystallised from aqueous acetone and dried in a vacuum oven at 328 K for several days. Tetra-n-butylammonium iodide (A.R. reagent) was recrystallised from a water-methanol mixture and dried over P,O,, at 323 K in a vacuum oven for a few days. Tetraphenylarsonium iodide was prepared from aqueous solutions of Ph,AsCl and NaI. The compound was recrystallised from water containing a small amount of acetone and dried under vacuum for several days before use. Tetra-n-ethylammonium chloride (Fluka purum) was recrystallised from absolute ethanol, then from ethyl acetate and dried in vacuo at 373 K for several days. Tetra-n-ethylammonium bromide (A.R.reagent) was recrystallised from aqueous and dried in a vacuum oven at 328 K for several days. Tetraphenylphosphonium bromide (Fluka) was recrystallised from water and dried in vacuo for one week prior to use. Sodium tetraphenylboron (B.D.H.) was purified as described elsewhere.12 Nitromethane (Aldrich Chemical Co., 98 % ) was twice fractionally distilled. The water content checked by gas-liquid chromatography and Karl Fisher titration was 0.005 % . Heat-of-solution measurements were made by using the Tronac 550 calorimeter equipped with a chart recorder to obtain a continuous readout. The accuracy of the instrument was periodically checked by using the standard reaction of tris(hydroxy- methy1)methylamine (THAM) with HCl (0.01 mol dmP3) suggested by Irving and WadsO.l3 Results are expressed in terms of the defined calorie, 1 cal = 4.1840 J, and refer to the isothermal process at 298.15 K.Results and Discussion Heats of solution, AH,, for eighteen 1 : 1 electrolytes in nitromethane were measured calorimetrically at 298.15 K. Measurements were made in the 10-3-10-4 mol dm-3 concentration range as detailed in table 1. The variation in AHs (after correction for the heat of breaking of empty ampoules in nitromethane) with the electrolyte concentration is small in this solvent. Nitromethane is a relatively polar solvent, and electrolytes listed in table 1 are almost fully dissociated in it., Standard enthalpies of solution, AG, have been obtained by (a) extrapolation of AHs values (table 1) vs. ci to c = 0, where c is the final molar concentration of the electrolyte in solution and (b) by applying to the AH, values (table 1) a correction for the heat of dilution of the electrolyte by using the extended Debye-Huckel equation.Both sets of data are included in table 1. Indeed, inA. F. Danil de Namor and L. Ghousseini Table 1. Heats of solution of I : I electrolytes in nitromethane (in cal mol-') at 298 K 3277 NaPh4B (A% = - 3737 f 28)" (A% = -3788, K, = 5, H = 5.7)' Et4NPh4B (A% = 6850 84)' (AK = 6822; K , = 2; ri = 5.2)' c/mol dm-3 AHsd c/mol dmP3 AHsd 5.58 x 10-3 -3781 4.35 x 10-3 - 3742 3.71 x - 3759 2.98 x 10-3 - 3800 1.48 x 10-3 - 3744 2.67 x lop3 6845 2.36 x 6878 1.77 x lop3 6808 1.43 x lop3 6975 1.28 x 6748 9.45 x lop4 6869 Pr,NPh,B ( A x = 7405 f 74)" (A% = 7358; K, = 2; h = 5.1)' Bu,NPh,B(A% = 9540 1 17)' ( A X = 9584; K , = 1 ; H = 4.85)' c/mol dm-3C AHsd c/mol dmP3 AHsd 3.10 x 7330 2.29 x 10-3 7460 1.59 x 10-3 7475 1.17 x 10-3 7348 7.56 x 10-4 7380 3.02 x 9789 1.96 x lop3 9705 9 . 8 5 ~ lop4 9530 5.84 x 9737 Me4NPi (A% = 3365 & I 82)' (A% = 3183; K, = 10, H = 6.3)b Et4NPi(A% = 63 I5 & 25)" (A% = 6298; K, = 1; B = 6.5)' c/mol dm-3c AHsd c/mol dm-3 AHsd 2.71 x 10-3 3218 1.36 x 10-3 3483 1.11 x 10-3 3522 6.65 x 10-4 31 15 4.76 x 10-4 3366 2.75 x lop3 6342 1.83 x lop3 6353 1.30 x lop3 6344 8.82 x 6359 7.13 x lop4 6292 6.69 x 6348 Et4NC10, (A% = 2503 f 26)" ( A K = 2468 ; K, = 2; H = 4.3)' Pr4NC104(A~ = 4658 f 68)u (A% = 4787; K, = 1 ; H = 4.4)' c/mol dm-3c AHsd c/mol dm-3c AHsd 5.92 x 10-3 2552 4.68 x 10-3 2536 4.04 x 10-3 2560 2.40 x 10-3 2502 2.25 x 10-3 2559 4.75 x 5154 4.01 x 5050 3.29 x 5167 1.80 x 4924 1.66 x 4963 108-23278 Thermodynamics of Electrolytes in Nitromethane Table 1.(cont.) Bu4NCI04(AX = 28 I8 f 89)" Ph4AsC104(AS = 6701 & 76)" ( A S = 2772; K, = 1 ; H = 4.3)b ( A S = 6758; K , = 1 ; H = 4.2)b c/mol dmP3" AHsd 4.02 x 10-3 2815 2.31 x 10-3 2885 1.92 x 10-3 2714 1.30 x 10-3 2902 9.44 x 10-4 2783 c/mol dmP3 AHsd 2.15 x lop3 6824 1.83 x lop3 6982 1.72 x lop3 6936 9.26 x 6812 4.08 x 6795 Me,NI (A% = 5043 & 35)" ( A S = 5049; K , = I ; H = 3.5)b Et4NI (Ax = 441 2 ? 25)" ( A S = 4453; K, = 2; H = 2)b c/mol dmPSr AHsd 6.73 x 1 0 - 4 5234 6.51 x 5192 6.25 x 1 0 - 4 5139 4.78 x 10-4 5162 2.95 x 10-4 5149 ~~ ~ -~ Pr4NI (A% = 3487 & 70)" ( A R = 3613; K , = 1; H = 4.1)* c/mol dm-3 AHsd 6.38 x 4668 4.33 x lop3 4652 3.52 x lop3 4607 2 .9 9 ~ 4641 1.95 x lop3 4536 Bu4NI ( A S = 740 1 IfI 30)" ( A S = 7357; K, = 1 ; H = 4.5)b c/mol dmP3' AHSd c/mol dm-3 AHsd 6.46 x 4014 4.23 x lo-:$ 3940 3.29 x 398 1 2.94 x 3838 2.37 x 3765 4.75 x 10-3 7408 2.49 x 10-3 7357 2.92 x 7380 1.63 x 7425 Ph4AsI (A% = 4550 & 42)" (AX = 4547; K, = 1 ; H = 4.3)' Et,NCl(AG = 1627 f 2)' (A% = 1471 ; K, = 2; H = 3.4)b c/mol dm-3 AHSd 4.04 x 10-3 4680 2.21 x 10-3 4697 2.06 x 4595 1.55 x lo-" 4602 1.09 x lo-" 4639 c/mol dm-3c AHsd 1.10 x 1327 9.63 x 1349 5 . 8 9 ~ lop3 1403 3 . 2 2 ~ lop3 1467 ~~A . F. Danil de Namor and L. Ghousseini 3279 Table 1. (cont.) Et,NBr ( A e = 2688 f 33)" Ph,PBr (A% = 2025 & 37)a (A% = 2587; K, = 1.7; H = 3.3)b ( A e = 1951; K, = 1; H = 4.4)b c/mol dm-3C AHsd c/mol dm-3C AHsd 5.91 x 10-3 2438 6.23 x lop3 1939 4.10 x 10-3 2501 4.83 x 1948 3.15 x 10-3 2476 3.86 x lop3 1917 2.44 x 1980 3.67 x 10-3 2535 4.36 x 10-3 2002 ~~ -~ ~ -~ a A 6 obtained at c = 0 from least-squares plot of AHs us.ci. Value obtained at u = 1 from AH,,,,, (AHs corrected for heat of dilution by use of the extended Debye-Huckel equation) against a (degree of dissociation of electrolyte). K, and d (A) are the ion-pair association constant and ion-size parameter, respectively, used in the calculation [ref. (4)] and R. Fernandez Prini, Physical Chemistry of Organic Solvent Systems, ed. A. K. Covington and T. Dickinson, (Plenum Press, New York, 1973). Heat of solution corrected for heat of breaking of empty ampoules in nitromethane (0.01447 cal; average of 11 measurements).Final concentration of electrolyte in solution. most cases both methods of calculation led to very close A% values. However, considering the theoretical nature of the Debye-Huckel, equation, as well as possible uncertainties in the parameters used in the calculation (solvent density and dielectric constants at the different temperatures are not all that well established in nitr~methane),'~ we recommend as the standard enthalpies of solution of these electrolytes in nitromethane the A E values obtained at c = 0 from a plot of AHs us. ck The standard deviation from the points is also included in table 1. As a result of the limited solubility and slow dissolution rates of various electrolytes containing alkali-metal cations in nitromethane, heats of solution for these electrolytes could not be measured calorimetrically.Although electrolytes such as NaI, KI, RbI and CsI are sufficiently soluble in nitromethane to enable calorimetric measurements of the heats of solution, these electrolytes dissolve at a very slow rate in this solvent. Consequently, the enthalpy of solution of one compound containing sodium could be measured by the calorimetric method, that of NaPh,B. To ensure that a pure sample of this salt was used for heats of solution measurements in nitromethane, we determined the heat of solution of NaPh,B in water, and a value of 4.78 kcal mol-l for the enthalpy of solution was obtained. This value is in good agreement with previously reported data.'* Other salts containing alkali-metal ions were tested.In the case of LiClO,, which is appreciably soluble in this solvent, the heats of solution obtained calorimetrically varied considerably, partly because the electrolyte did not dissolve instantly during the experimental runs. No data on the standard enthalpies of solution of 1 : 1 electrolytes in nitromethane at 298 K have been reported in the literature, with the exception of the standard enthalpy of solution of AgBr, obtained by Cox and Parker.15 Hence the standard enthalpies of solution for the series of electrolytes in nitromethane obtained in this work cannot be compared with literature data. Askew et aZ.16 reported the standard enthalpies of solution for Me,NBr (A% = 4.12 kcal mol-l); Et,NCl (AK = -0.59 kcal mol-l); Et,NBr (AG = 2.59 kcal mol-l); Et,NClO, (A% = 2.43 kcal mol-l) and Et,NPi (A% = 5.78 kcal mol-l); however, these data are referred to 293 K.Having obtained a set of A% values for a series of electrolytes in nitromethane, the enthalpies of transfer from water to nitromethane are calculated. Details are given in table 2.3280 Thermodynamics of Electrolytes in Nitromethane Table 2. Enthalpies of transfer of 1 : 1 electrolytes from water to nitromethane in kcal rno1-I at 298 K A$'(H,O+MeNO,) electrolyte AS"(MeN0,) AS(H20) obs.8 calc. NaPh,B Et,NPh,B Pr,NPh,B BuNPh,B Me,NPi Et,NPi Et,NClO, Pr,NClO, Bu,NC10, Pr,AsC10, Me,NI E t,NI Pr,NI Bu,NI Ph,AsI Et,NCl Et,NBr Ph,PBr - 3.74 6.85 7.41 9.54 3.37 6.32 2.50 4.66 2.82 6.70 5.04 4.4 1 3.49 7.40 4.55 1.63 2.69 2.03 -4.78b 9.12c 6.1 2c 6.06" 7.61d 7.65d 7.40b 6.54-f 2.51e 1 2.80b 10.07b 6.72b 2.76' 3.90b 8.28b 1.49 2.2w - 3.0b 1.04 1.29 3.48 - 2.27 - 4.24 - 1.33 - 4.90 - 1.88 0.3 1 -6.10 - 5.03 - 2.30 0.73 3.50 - 3.73 4.63 1.26 -0.17 - - 2.09 1.10 3.48 -4.18 - 1.39 - 5.03 - 1.84 0.54 - 6.24 - 5.09 - 2.30 0.89 3.27 -3.51 - 1.25 -0.17 a This work, see table 1.Ref. (13). Ref. (7). A. Finch and E. Smith, Therrnochirn. Acta, 1983, 53, 349. Ref. (9). f M. H. Abraham, A. F. Danil de Namor and R. A. Schulz, J. Solution Chern., 1977, 6, 49 1. AH,"(M+ + X-)H,O -, MeNO,) = AHi(M+ + X-)(MeNO,) - AHz(M+ + X-)(H,O). From single- ion AH"t values given in table 3. As enthalpies of transfer of electrolytes are made of additive ionic contributions, it is useful to discuss trends for single-ion enthalpies that may exemplify the dominant interactions.Also, ionic contributions will be useful in testing the self-consistency of the data. Enthalpies of transfer of 1 : 1 electrolytes (table 2) from water to nitromethane are used to calculate single-ion enthalpies of transfer of cations and anions using the extrathermodynamic convention proposed by Parker and coworkers : l2 AG(Ph,As+) = A%(Ph4B-). (1) We were unable to measure calorimetrically the AX of Ph,AsPh,B in nitro- methane owing to the low solubility of this electrolyte in this solvent. Then, Ae(Ph,AsPh,B)(H,O -+MeNO,) was obtained indirectly by combination of A% values for electrolytes containing this particular cation or anion. Derived single-ion A% values from water to nitromethane for seven cations and six anions based on the Ph,AsPh,B convention are reported in table 3.Cations and anions AK combinations yield the calculated A% values for 1 : 1 electrolytes (table 2). Comparison between calculated and observed A% values (table 2 ) enables testing for self-consistency of this set of data. An average of 0.10 kcal mol-1 between observed and calculated A e values for these electrolytes in transfers from water to nitromethane is found, showing excellent consistency for this set of data, Among the single-ion values given in table 3 are data previously reported by us6 forA . F. Danil de Namor and L. Ghousseini 328 1 Table 3. Single-ion enthalpies of transfer from water to nitromethane based on the Ph,AsPh,B convention at 298 K cation Aqlkcal mol-l anion Aq/kcal mol-' Li+ Na+ K+ Rb+ cs+ Me,N+ Et,N+ Pr,N+ Bu,Nf [Li+222] [Na+222] [K+222] [ R b+22 21 Ph,P+ Ph,As+ [Cs+222] - 6.169 6.52h Cloy -4.59 If: 0.Mb 2.69" 2.749 3.07h I- - 1.86&0.10b - - 3.229 -2.70h Br- 1 .69e - - 4.229 -4.32h C1- 5.07f - - 3.979 - Pi- - 0.95 If: 0.05b - 3.23 _+ 0.1 Ob - Ph,B- - 1.65 f 0. lob - 0.44 & 0. lob 2.75 0. lob 5.13 f 0 . w 7.2OC 3.61" 3.Ogc 2.92c 2.3Y - 1 .86d - 1.65+0.15b a Single-ion A% value obtained from Aq(NaPh,B)(H,O-+MeNO,), table 2. From data given in table 2. Ref. (6). Single-ion A G value obtained from Aq(Ph,PBr)(H,O-,MeNO,), table 2. Single-ion A% value obtained from AK(H,O+MeNO,) of Ph,PBr and Et,NBr, table 2. f Single-ion A q value obtained from A~(Et,NCl)(H,O-+MeNO,), table 2. 9 From heat of complexing of metal-ion cryptates [ref.(6)]. Using a thermodynamic cycle [ref. (6)]. A% of the alkali-metal cryptates and A% of alkali-metal cations. The latter values were obtained from heat of complexing data and via a thermodynamic cycle.6 Excellent agreement is found between the A~[Na+](H,O-,MeNO,) as obtained from A%(NaPh,B)(H,O+MeNO,) and that derived from heat-of-complexing data between the sodium cation and cryptand 222 in the dipolar aprotic solvents. Single-ion enthalpies for the transfer from water to a number of dipolar aprotic solvents based on the Ph,AsPh,B convention (table 4) show that the enthalpies for transfer of the alkali-metal cations are generally exothermic. This is the result of the cations being enthalpically more stable in the non-aqueous solvent than in water.This stability (in enthalpic terms) decreases appreciably in nitromethane with respect to any of the solvents listed. This is particularly enhanced for ions such as lithium and sodium. For transfers from water to nitromethane, AK[Li+] and Aq[Na+] are positive as a result of the highest stability in terms of enthalpy of these two cations in water with respect to nitromethane. Comparison between the A% values for the transfer of these two cations from water to nitromethane and to acetonitrile shows that the stability of Li+ and Na+ decreases by ca. 6 kcal mol-1 in the former solvent, reflecting somehow the differences in the coordinating abilities of the two solvents. Like transfers from water to each of the dipolar aprotic solvents, A% values for the tetra-alkylammonium ions become more positive in the series Me,N+, Et,N+, Pr,N+ and Bu4N+.The hydrophobic behaviour of the metal-ion cryptates is again reflected in the A% values which, (with the exception of [Li+222]) depending on the solvent, are close to the A% values of the Pr,N+ or Bu,N+ ions. For transfers from water to nitromethane A% for the Ph,As+ and Ph,B- are negative. Although the A%(H,O+MeNO,) values are less negative than those for the transfer of the same ions from water to other dipolar aprotic solvents, the A% for Ph,As+ and3282 Thermodynamics of Electrolytes in Nit rome t hane Table 4. Single-ion enthalpies of transfer (in kcal mol-l) from water to dipolar aprotic solvents based on the Ph,AsPh, convention at 298 K. ion H,O-+DMF H,O+Me,SO H,O-+AN H,O+PC H,O+MeNO, Li+ Na+ K+ Rb+ cs+ Me,N+ Et,N+ Pr,N+ Bu,N+ [Li+222] Na+222] [K+222] [Rb+222] Ph,P+ Ph,As+ I- Br- c1- Pi- Ph,B- [Cs+222] ClO, -7.71" - 7.89" - 9.44" - 9.03" - 8.50" -4.15" - 0.23" 2.2 1 a 3.58" 4.35b 3.2tjb 3.67b 3.42b ~ - 4.25" - 4.69" - 5.4" - 2.94" 0.98a 5.06" - 4.69" -6.31" - 6.62' - 8.34" - 8.01 " -7.71' - 3.66" 1.01" 4.02' 6.0Y 4.75b 3.02' 4.04b 3.40b ~ - 2.23" - 2.84" - 4.60" - 3.05' 0.83' 4.49" - 2.84' 0.1 5d - 3.26d - 5.40e - 5.50e - 6.00d - 3.50d -0.12d 2.55d 4.20d 8.2Id 3.57b 3.19b 3.27b 2.57b - - 2.42d -4.19d 1 .84d 4.68d - 2.42d - 2.42d - 0.73c - 2.44" - 5.24' - 5.87' - 6.40' - 3.89" 0.1 7" 2.79" 4.39c 7.58b 4.02h 3.29b 3.75b 3.08b - 3.22" - 3.49" - 3.93' - 3.49" 3.24" 6.31' - 3.49" 6. 16b 2.74f - 3.22b -4.22b - 3.97b - 3.23f - 0.44f 2.79 5.13f 7.20b 3.6Ib 3.08b 2.92' 2.35b - 1.86f - 1.69 - 4.59f - 1.86f 1.69f 5.07f - 0.99 - 1.69 a C.V. Krishnan and H. L. Friedman, in Solute-Solvent Interactions, ed. J. F. Coetzee and C. D. Ritchie (Marcel Dekker, New York, 1976), Vol. 2. C. V. Krishnan and H. L. Friedman, J. Phys. Chern., 1969,73,3934. H. C. Ling, P h D . Thesis (University of Surrey, 1981). Ref. (13). f This work, table 3. Ref. (6). Ph4B- ions still opposes that of the large organic ions (Pr4N+, Bu4N+ and M+222). This effect has been attributed to the additional dispersion interaction between the non-aqueous solvents and the hydrophobic Ph4Asf, Ph4P+ and Ph4B- ions2 In the case of the anions, the transfer from water to nitromethane show the same pattern as for the transfer to other dipolar aprotic solvents.Transfers are enthalpically favourable (AG negative) or unfavourable (AG positive), depending on the nature of the anion. The picrate anion appears to be enthalpically more stable in nitromethane than in water, with a favourable enthalpy of transfer. Combination of free energies4 and corresponding enthalpies (table 3) yields single-ion entropies for transfer from water to nitromethane. Single-ion entropies of transfer based on the Ph4AsPh4B convention are given in table 5. An estimated error of ca. 1 cal K-l mol-l for single-ion values results when errors in AG: z 0.14 and AK z 0.1 kcal mol-l are combined. The lower precision in A q values is expected as the data contain the combined experimental error in AG: and A% values.For comparison with AK data for single ions for the transfer from water to nitromethane obtained in this work, representative single-ion AK data on the mole fraction scale based on the Ph,AsPh,B convention are included in table 6. The results show that in transfers from water to nitromethane Aq(M+ + X-) are approximately con- stant as the A% values for the transfer of electrolytes containing alkali-metal halides and perchlorates from water to the solvents listed in table 6. In transfers from water to nitromethane an average A,!$ value of -33 cal K-l molt1 is obtained for M+ = Li+,A . F. Danil de Namor and L. Ghousseini 3283 Table 5. Single-ion entropies of transfer, A% (molar scale) and A g *(mole fraction scale) from water to nitromethane at 298 K, based on the Ph,AsPh,B convention ion AG: A q e A K A g * f /kcal mol-1 /kcal mol-l /cal K-l mol-l /cal-l mol-l Li+ Na+ K+ Rb+ cs+ Me,N+ Et,N+ Pr,N+ [Rb+222] [Cs+222] Ph,P+ Ph,As+ I- Br- c1- Ph,B- ClO, 12.05" 7.Sb 3.69b 2.64' 1 -35' - l.lOb - 2.45b - 4.77' - 0.60' - 3.84' - 4.33" - 3 .94c - 1.95," -4.13d - 8.02' - 7.80b 1.12b 4Slb 6.92b 9.OOb - 7.80b 6.16 2.69 - 3.22 -4.22 - 3.97 - 3.23 - 0.44 2.75 7.20 3.6 1 3.08 2.92 2.35 - 1.86 - 1.65 -4.59 - 1.86 1.69 5.07 - 1.65 - 19.8 - 16.3 - 23.2 - 23.0 - 17.8 -7.1 6.7 25.2 26.2 25.0 24.9 23.0 14.4, 21.7d 20.7 20.6 - 19.2 -21.2 - 17.5 - 13.2 20.6 - 17.6 - 14.1 -21.0 - 20.8 - 15.6 - 4.9 8.9 27.4 28.4 27.2 27.1 25.2 16.6, 23.9 22.9 22.8 - 17.0 - 19.0 - 15.3 -11.0 22.8 a S.Glikberg and Y. Marcus, J. Solution Chern., 1983,12,255.Ref. (4). Ref. (5). Calculated through a thermodynamic cycle using values for the stability constants [Cs+222] in water given in ref. (19). Values from table 3. f Values in the mole fraction scale (Ph,AsPh,B convention) by adding 2.2 cal K-l mol-1 to the AT values (molar scale). Na+, KS, Rb+ and Cs+ and X- = C1-, Br-, I- and C10;. The ASt(M+ + X-) for X- = C1- is lower by at least 4 cal K-l mol-l than the A,!$ for the transfer of any other alkali-metal salt containing bromide, iodide or perchlorate. The value for A~(Cl-)(H,O+MeNO,) has been obtained from A% of only one electrolyte containing this particular anion, and therefore we have no internal check of A% (and consequently A$) for the chloride anion. These findings lead us to conclude that, provided there is no ion-pair formation of the relevant electrolytes in solution, single-ion A% values for the alkali-metal cations among the dipolar aprotic solvents can be successfully obtained from heats of complexing data between cryptand 222 and these cations in these solvents.The A$ values thus obtained show that the single-ion AK values previously reported for transfers among dipolar aprotic solvents of alkali-metal cations are chemically reasonable and in accord with values obtained by using the Ph,AsPh,B convention. New values for the single-ion entropies for the transfer of [Cs+222] from water to DMF, to Me,SO to PC and to AN based on the Ph,AsPh,B (mole fraction scale) are also included in table 6. These data have been derived from AG; and A% values for the transfer of these cryptates from water to the appropriate solvent. Values for the transfer enthalpy term are those reported by Danil de Namor and Ghousseini.l7, Values for the transfer free-energy term obtained through a thermodynamic cycle have been recalculated using the most recent data for the stability constant of [Cs+222] in water given by Morel and Morel-Desro~iers.~~ Obviously the recalculated value does not alter our previous conclusions regarding the thermodynamic parameters for the transfer of metal-ion cryptates among dipolar3284 Thermodynamics of Electrolytes in Nitromethane Table 6.Entropies of transfer (in cal K-l mol-l) for single ions from water to dipolar aprotic solvents as 298 K on the mole fraction scale based on the Ph,AsPh,B convention - ion H,O-+DMFa H20+Me2SOb H20+ANc - Lit Na+ K+ Rb+ cs+ Me,N+ Et,N+ Pr,N+ Bu,N+ [Li+222] [Na+222] [K+222] [ Rb+222] Ph,P+ Ph,As+ I- Br- c1- Ph,B- [Cs+222] c10, - 15.3 - 16.0 - 20.6 - 19.6 - 17.0 - 6.8 8.2 24.1 14.9 29.4f 28. lf 29.2f 21.lf 28.38 19.2 17.8 ~ - 18.4 - 23.6 - 22.9 - 19.1 17.8 - 6.4 - 8.8 - 14.8 - 15.8 - 12.9 - 8.0 16.2 - - - 30.9 25. if 26.9 19.3f 26.48 23.2 - -11.9 - 15.9 - 16.9 - 14.5 23.2 -21.5 - 20.3 -21.9 -21.6 -21.3 -11.2 7.7 24.4 36.8 29.3i 24.gh 27.7h 28.2h 18.0h 25.38 19.9 - - 13.3 - 18.7 - 17.2 - 16.4 19.9 H20-+PCd H,0+MeN02e ~ - 13.0 - 15.9 - 18.9 - 18.0 - 17.1 - 0.93 14.0 29.9 43.0 3O.gi 29Sh 29.4h 29.7h 20Sh 27.89 19.9 - 10.8 -11.0 - 9.9 - 8.0 19.9 - - 17.5 - 14.1 -21.0 - 20.8 - 15.6 - 4.9 8.9 27.4 28.4 27.2 27.1 25.2 16.6 23.9 22.9 22.8 - - 17.0 - 19.0 - 15.3 -11.0 22.8 a AG: values from S.Glikberg and J. Marcus, J. Solution Chem., 1983, 12,955 and A% (table 4) converted to mole fraction scale by adding 2.9 to A G (molar scale). As in footnote (a), converted to mole fraction scale by adding 2.7 to A G (molar scale). As in footnote (a), converted to mole fraction scale by adding 2.1 to A G (molar scale). From A G given by M. H. Abraham, Monatsh. Chem., 1979, 110, 517. From table 5. f From ref. (17). g From AG, values obtained through a thermodynamic cycle using values for the stability constants of [Cs+222] in water given in ref. (19) and A% given in table 3. These values slightly differ from those given in ref. (18). The AG: [Li+222](H20+AN) and [Li+222](HZO-+PC) were recalculated through a thermodynamic cycle using AGE [Li+222](H20) = - 1.34 kcal mol-l, derived from data given by B.G. Cox, Annu. Rep. C (Royal Chemical Society, London, 1981). From ref. (18). aprotic solvent^.^? 6 y 1 7 9 la On the contrary, the new A$' value for [Cs+222] in the dipolar aprotic solvents lends support to our recent work on the partition of cryptand 222 in water-alcohol systems.20 Along the [Li+222] to [Cs+222] series there is not much variation in A$[M+222] in transfers from water to the dipolar aprotic solvents. It is quite clear (table 6) that there is no variation in Ag[M+222] among the dipolar aprotic solvents. In addition, the A$ values for transfers among these solvents appear to be close to 0 cal K-l mol-l. Similar conclusions were obtained in terms of the free energy and enthalpy parameters.5* 6+ 1 7 9 l8 These observations support the suggestion that the differ- ence found in the thermodynamic parameters for the transfer of [M+222] from water to dipolar aprotic solvents with respect to the transfer of these cryptates among dipolar aprotic solvents could be mainly attributed to interactions between the ligand cryptand 222 and water rather than to interactions between the alkali-metal cryptates and For the highly hydrophobic ions (Pr,N+, Ph,P+, Ph,As+, Ph,B-, [M+222]) there is a net increase of entropy which ranges from 23 to 28 cal K-l mol-1 in transfers from water to nitromethane. It is interesting to observe that in transfers from water to most dipolar 21A .I;. Danil de Namor and L. Ghousseini 3285 aprotic solvents, the A% values for the alkali-metal cryptates are very close to the AS: values for the transfer of the tetra-n-propylammonium ions.We are investigating this further. References 1 C. M. Criss, Physical Chemistry of Non-aqueous Solvents, ed. A. K. Covington and T. Dickinson 2 0. Popovych and R. P. T. Tomkins, Non-aqueous Solution Chemistry (Wiley, New York, 1981), 3 A. F. Danil de Namor, T. Hill and E. Sigstad, J. Chem. SOC., Faraday Trans. 1, 1983, 79, 2713. 4 A. F. Danil de Namor and L. Ghousseini, J. Chem. SOC., Faraday Trans. 1, 1984, 80, 2843. 5 A. F. Danil de Namor, L. Ghousseini and W. H. Lee, J. Chem. SOC., Faraday Trans. 1, 1985,81,2495. 6 A. F. Danil de Namor, L. Ghousseini and T. Hill, J . Chem. SOC., Faraday Trans. I , 1986, 82, 349. 7 C. M. Criss, R. P. Held and E. Luksha, J. Phys. Chem., 1968, 72, 2970. 8 C. M. Criss, J. Phys. Chem., 1974, 78, 1000. 9 M. H. Abraham, J. Chem. Soc., Faraday Trans. 1, 1973,69, 1375. (Plenum Press, London, 1973). chap. 4. 10 M. H. Abraham and A. F. Danil de Namor, J. Chem. SOC., Faraduy Trans. 1, 1978, 74, 2101. 11 A. F. Danil de Namor, L. Ghousseini and R. A. Schulz, J. Chem. SOC., Faraday Trans. 1, 1984, 80, 12 B. G. Cox, G. R. Hedwig, A. J. Parker and D. W. Watts, Austr. J. Chem., 1974, 27, 477. 13 R. J. Irving and I. Wadso, Acta Chem. Scand., 1964, 18, 195. 14 G. J. Janz and R. P. T. Tomkins, Nonaqueous Electrolytes Hundbook (Academic Press, New York, 15 B. G. Cox and A. J. Parker, J . Am. Chem. SOC., 1973,95,402. 16 F. A. Askew, E. Bullock, H. T. Smith, R. K. Tinkler, 0. Gatty and T. H. Wolfensen, J. Chern. SOC., 17 A. F. Danil de Namor and L. Ghousseini, J. Chem. SOC., Faraday Trans. I , 1984, 80, 2349. 18 A. F. Danil de Namor and L. Ghousseini, J. Chem. SOC., Faraday Trans. 1 , 1985, 81, 781. 19 J. P. Morel and M. Morel, Desrosiers, Nouv. J. Chim., 1982, 6, 547. 20 A. F. Danil de Namor, H. Berroa de Ponce and E. Contreras Veguria, J. Chem. SOC., Faraday Trans. 21 B. G. Cox, J. Garcia Rosas and H. Schneider, J. Am. Chem. SOC., 1981, 103, 1384. 22 A. F. Danil de Namor and H. Berroa de Ponce, to be published. 1323. 1972). 1934, 1368. 1, 1986, in press. Paper 6.448; Received 5th March, 1986

ISSN:0300-9599    

DOI:10.1039/F19868203275

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1986, 82, 3287 CORRIGENDUM The Interaction of Aromatic Compounds with Poly(vinylpyrro1idone) in Aqueous Solution Part 6.-Polymer Precipitation and Viscosity Studies with Phenols and @Substituted Phenols Philip Molyneux" Macrophile Associates, 53 Crestway, Roehampton, London S W15 5DB Sudhe Vekavakayanondha Faculty of Pharmaceutical Sciences, Chulalongkorn University, Bangkok 10500, Thailand J. Chem. SOC., Faraday Trans. I, 1986, 82, 635-661 On p. 658, the line below eqn (C 7) should read: where a = 0.63 and K, = 3.0 x cm3 g-l for PVP in water at 25 0C.20 This correction does not affect the remainder of the text. 3287

ISSN:0300-9599    

DOI:10.1039/F19868203287

出版商:RSC    

年代:1986

数据来源: RSC