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4 Standard Entropies of Hydration of Ions View Article Online / Journal Homepage / Table of Contents for this issue 4 Standard Entropies of Hydration of Ions By Y. MARCUS and A. LOEWENSCHUSS Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, 9 I904 Jerusalem, Israel 1 Introduction Since ions are hydrated in aqueous solutions, the standard thermodynamic functions of the hydration process are of interest. Of these, the standard entropy of hydration is expected to shed some light on the state of the ion and the surrounding aqueous medium. In particular, the notion of water- structure-breaking and -making is amenable to quantitative expression in terms of a structural entropy that can be derived from the experimental standard molar entropy of hydration. The process of hydration of an ion X', where z is the algebraic charge number of the ion, consists of its transfer from the ideal gas phase to the aqueous phase at infinite dilution: X'(g) - X'(aq) (1) A thorough discussion of the general process of solvation, of which hydration Published on 01 January 1984. Downloaded by FAC DE QUIMICA 27/07/2015 16:16:07. is a particular case, was recently published by Ben-Naim and Marcus,' with a sequel on the solvation of dissociating electrolytes by Ben-Naim.2 Provided that the number density concentration scale or an equivalent one (e.g., the molar, i.e., mol dm-') is employed, the standard molar entropy change of the process, conventionally determined experimentally and converted appro- priately to an absolute value, equals Avogadro's number NA, times the entropy change per particle.'-2The conventional standard states are the ideal gas at 0.1 MPa pressure (formerly at 0.101 325 MPa = 1 atm pressure) for the gas phase (g) and the ideal aqueous solution under 0.1 MPa pressure and at 1 mol dmP3concentration of the ion for the aqueous phase. Most discussions are limited to the entropies of hydration at 298.15 K, although the entropies of hydration at other temperatures, in particular elevated temperatures, are expected to provide interesting information too. Recently a large amount of information was published that is pertinent to ' A. Ben-Naim and Y. Marcus, J. Chem. Phys., 1984, 81, 2016. * A. Ben-Naim, J. Phys. Chem., 1985, 81, in the press. 81 View Article Online 82 Y. Marcus and A. Loewenschuss the present topic, in a compilation by Wagman et aL3 and in a review by Loewenschuss and Mar~us.~The former contains conventional standard partial molar entropies of aqueous ions at 298.1 5 K, the latter the standard molar entropies of polyatomic gaseous ions, again at 298.15K. These sources, supplemented by the readily calculated standard molar entropies of monoatomic gaseous ions, provide the bulk of the information presented and discussed in the present report. These data are further supplemented by data from other sources or by values estimated in the present work. Sources have been scanned through the years 1979 to 1983 inclusive, and further back where necessary. A previous survey of the entropy of hydration of ions that may be con- sulted is that of Friedman and Krishnan,' who discussed this subject within the framework of a discussion of the thermodynamics of ion hydration. 2 Conventional Entropies of Hydration at 298.15K The Available Data. - The conventional standard molar entropy of hydration is reported in Table 1 for nearly 200 ions. This quantity is given, in view of equation (l), by -0 AhydrConv = &o,,(as) - SP<d (2) where the subscript i stands for an ion X' and the quantities on the right hand side are defined below. The conventional standard partial molar entropy of the aqueous ion, sEon,(aq), is obtained from the actual standard molar entropy change A(3)So for the reaction (3) which is accessible experimentally. The hypothetically ideal state of 1 mol (kgwater)-' is generally used for the aqueous ions, the pure substance Published on 01 January 1984. Downloaded by FAC DE QUIMICA 27/07/2015 16:16:07. (unionized) in its standard state (ss) for X(ss), and the ideal gas state for the hydrogen, all at the standard pressure of 0.1 MPa. The convention that SPconv(aq)= 0 for H+(aq) is then employed to convert the A(3,S0value to a value of $&(aq) for the ion XZ(aq). The conversion from the 1 mol (kg water)-' (molal) concentration scale to the 1 moldm-3 (molar) one is done by noting that 1 kg water occupies 1.002964dm3 at 298.15 K,6hence the amount - R In (1.002964 dm3/ldm3) = 0.024 J K-' mol-' must be added to the con- ventional values on the molal scale (tabulated, e.g., in ref. 3). This correction is entirely negligible in view of the accuracy and precision claimed for the reported sEonv(as) data. The uncertainties of these values reported in Table 1 follow the code of being 8 to 80 times the unit of the last digit rep~rted.~ D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Balley, K. L. Churney, and R. L. Nuttal, 'The NBS Tables of Chemical Thermodynamic Properties', American Chemical Society and American Institute of Physics, Washington, DC, 1982. A. Loewenschuss and Y. Marcus, Chem. Rev., 1984, 84, 89. H. L. Friedman and C. V. Krishnan, in 'Water, A Comprehensive Treatise', ed. F. Franks, Plenum Press, New York, NY, Vol 3, 1973. K. S. Kell, J. Chem. Eng. Dara, 1975, 20, 97. View Article Online Standard Entropies of Hydration of Ions 83 Table 1 Conventional standard molar entropies of hydration of ions, at 298.15 K, arranged according to the order in the NBS Tables (in J K-' mol-') No. Ion s? (g) si%v (aq) ~hydr$on, 0 e- * 20.98 35.2 14.2 1 O2- * 143.32 - 86. - 229. 2 O2- * 203.8 100. - 104. 3 0;- * 199.6 - 100. - 300. 4 H+ * 108.84 0.00 - 108.84 5 OH- 172.3 - 10.7 - 183.0 6 H30+ * 192.8 0.00 - 192.8 7 HOT 228.6 23.8 - 204.8 8 F- 145.59 - 13.8 - 159.4 9 HF; 21 1.3 92.5 - 118.8 10 c1- 154.40 56.5 - 96.9 11 c10 - 215.7 42. - 174. 12 ClO, 257.0 101.3 - 155.7 13 ClO; 264.3 162.3 - 102.0 14 clod 263.0 184.0 - 79.0 15 Br- 163.57 82.4 -81.2 16 Bry 326.6 215.5 - 111.0 17 BrO- 227.2 42. - 185. 18 BrO; 278.7 161.7 - 117.0 19 BrO; 282.1 199.6 - 82.5 20 I- 169.36 111.3 - 58.1 21 1; 334.7 239.3 - 95.4 22 IOj 288.2 118.4 - 169.8 23 10; 297.0 222. - 75. 23a At - * 167.47 126. -41. 24 S2- 152.14 - 14.6 - 166.7 25 s;- 223.1 28.5 - 194.6 26 s: ~ 285.4 66.1 - 219.3 27 so: ~ 264.3 - 29. - 293. 28 so;- 263.6 18.8 - 244.8 29 s20:- 291.1 67. - 224. Published on 01 January 1984. Downloaded by FAC DE QUIMICA 27/07/2015 16:16:07. 30 S,O,z- 319. 92. - 227. 31 s,o; ~- * 337.3 125. -212. 32 s20;- * 341. 244.3 - 97. 33 s,o; - 356. 257.3 - 99. 34 HS - 186.2 66. - 120. 35 HSO; 266.8 139.7 - 127.1 36 HSO, 283.0 131.8 - 151.2 37 Se2- * 163.42 0. - 163. 38 SeO:- 284.0 13. -271. 39 SeO:- 28 1.2 54.0 - 227.2 40 HSe- 203.8 80. - 124. 41 HSeO; 283.0 135.1 - 147.9 42 HSeO; 295.8 149.4 - 146.4 43 TeO: - 294.5 13.4 -281.1 44 TeOi- * 295.7 46. - 250. 45 N; 212.2 107.9 - 104.3 46 NO+ * 198.4 - 103. -301. 47 NO: 214.1 - 93. - 307. 48 NO; 236.3 123.0 - 113.3 49 NO; 245.2 146.6 - 98.6 View Article Online 84 Y. Marcus and A. Loewenschuss No. Ion SP (g) con"(aq) Ahydr sp0fl" 50 N20i- * 256.9 28. - 229. 51 NH: 186.3 96.9 - 89.4 52 N2H: 230.5 151. - 80. 53 N2Hi+ * 225.2 79. - 146. 54 NH,OH+ * 235.4 155. - 80. 55 Po: - 266.4 - 222. - 488.0 56 P,O': - 342.8 - 117. - 460. 57 HPOi- 283.0 - 33.5 - 3 16.5 58 H, PO; 280.7 92.5 - 188.2 59 AsO; * 268.2 40.6 - 227.6 60 AsOj- 282.9 - 168.9 -451.8 61 HASO:- 302.9 - 1.7 - 304.6 61a SbO+ * 23 1.6 22. - 210. 62 Sb0:- * 298.5 - 155. - 454. 63 Bi3+ * 175.90 - 151.8 - 327.7 64 co: - 246.1 - 43.5 - 289.6 65 c,o: - 295.1 45.6 - 249.5 66 HCO; 238.2 92. - 146. 67 HCO, 257.9 98.4 - 159.5 68 CH3CO; 278.7 86.6 - 192.1 69 CN- 196.7 94.1 - 102.6 70 CNO- 218.9 106.7 - 112.2 71 SCN- 232.5 144.3 - 88.3 72 CH3NH: 327.7 142.7 - 90.0 73 (CH3),N+ * 331.9 210. - 122. 74 (C,H,)4N+ * 483. 283. - 200. 75 (C3H7)4N+ * 641 * 336. - 305. 76 SiFi- 309.9 122.2 - 187.7 77 Sn2+ 168.52 - 17. - 186. 78 Sn4+ 168.52 - 117. - 286. 79 SnFz- * 354.0 220. - 134. 80 Pb2+ 175.49 10.5 - 165.0 81 BO; 215.8 - 37.2 - 253.0 82 BH; 187.7 110.5 - 77.2 83 BF; 267.9 180.
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