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Thermodynamic Quantities for the Ionization Reactions of Buffers

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Thermodynamic Quantities for the Ionization Reactions of Buffers Thermodynamic Quantities for the Ionization Reactions of Buffers Robert N. Goldberg,a… Nand Kishore,b… and Rebecca M. Lennen Biotechnology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 ͑Received 21 June 2001; accepted 16 September 2001; published 24 April 2002͒ This review contains selected values of thermodynamic quantities for the aqueous ionization reactions of 64 buffers, many of which are used in biological research. Since the aim is to be able to predict values of the ionization constant at temperatures not too far from ambient, the thermodynamic quantities which are tabulated are the pK, standard ⌬ ؠ ⌬ molar Gibbs energy rG , standard molar enthalpy rH°, and standard molar heat ca- ؠ ⌬ pacity change rC p for each of the ionization reactions at the temperature T ϭ298.15 K and the pressure pϭ0.1 MPa. The standard state is the hypothetical ideal solution of unit molality. The chemical name͑s͒ and CAS registry number, structure, empirical formula, and molecular weight are given for each buffer considered herein. The selection of the values of the thermodynamic quantities for each buffer is discussed. © 2002 by the U.S. Secretary of Commerce on behalf of the United States. All rights reserved. Key words: buffers; enthalpy; equilibrium constant; evaluated data; Gibbs free energy; heat capacity; ionization; pK; thermodynamic properties. Contents 7.19. CAPSO.............................. 263 7.20. Carbonate............................ 264 7.21. CHES............................... 264 1. Introduction................................ 232 7.22. Citrate............................... 265 2. Thermodynamic Background.................. 233 7.23. L-Cysteine............................ 268 3. Presentation of Data......................... 234 7.24. Diethanolamine........................ 270 4. Evaluation of Data. ........................ 235 7.25. Diglycolate........................... 272 5. Acknowledgments.......................... 235 7.26. 3,3-Dimethylglutarate................... 275 6. References for the Introductory Discussion...... 236 7.27. DIPSO............................... 276 7. Tables of Thermodynamic Quantities for 7.28. Ethanolamine......................... 277 Ionization Reactions......................... 237 7.29. N-Ethylmorpholine. .................... 279 7.1. ACES............................... 237 7.30. Glycerol 2-phosphate................... 280 7.2. Acetate.............................. 238 7.31. Glycine.............................. 281 7.3. ADA................................ 241 7.32. Glycine amide......................... 286 7.4. 2-Amino-2-methyl-1,3-propanediol. ....... 243 7.33. Glycylglycine. ....................... 287 7.5. 2-Amino-2-methyl-1-propanol. ........... 244 7.34. Glycylglycylglycine.................... 289 7.6. 3-Amino-1-propanesulfonic acid.......... 245 7.35. HEPBS.............................. 292 7.7. Ammonia............................. 245 7.36. HEPES.............................. 292 7.8. AMPSO.............................. 247 7.37. HEPPS............................... 294 7.9. Arsenate............................. 248 7.38. HEPPSO............................. 295 7.10. Barbital.............................. 251 7.39. L-Histidine............................ 296 7.11.BES................................. 253 7.40. Hydrazine. ........................... 300 7.12. Bicine............................... 255 7.41. Imidazole............................. 302 7.13. Bis-tris............................... 257 7.42. Maleate.............................. 305 7.14. Bis-tris propane........................ 258 7.43. 2-Mercaptoethanol..................... 308 7.15. Borate............................... 259 7.44. MES................................ 309 7.16. CABS............................... 260 7.45. Methylamine.......................... 310 7.17. Cacodylate............................ 261 7.46. 2-Methylimidazole..................... 312 7.18. CAPS................................ 262 7.47. MOBS............................... 313 7.48. MOPS............................... 313 a͒Electronic mail: [email protected] 7.49. MOPSO.............................. 315 b͒Guest research scientist from the Department of Chemistry, Indian Institute 7.50. Oxalate.............................. 316 of Technology, Powai, Bombay 400-076, India; electronic mail: 7.51. Phosphate............................ 321 [email protected] © 2002 by the U.S. Secretary of Commerce on behalf of the United States. 7.52. Phthalate............................. 326 All rights reserved. 7.53. Piperazine............................ 329 Õ Õ Õ Õ Õ 0047-2689 2002 31„2… 231 140 $35.00231 J. Phys. Chem. Ref. Data, Vol. 31, No. 2, 2002 232 GOLDBERG, KISHORE, AND LENNEN 7.54. PIPES............................... 331 7.64. TES................................. 350 7.55. POPSO.............................. 333 7.65. Tricine............................... 351 7.56. Pyrophosphate......................... 333 7.66. Triethanolamine. ................. 353 7.57. Succinate............................. 340 7.67. Triethylamine......................... 355 7.58. Sulfate............................... 344 7.68. Tris................................. 357 7.59. Sulfite............................... 344 8. Summary of Selected Values of Thermodynamic 7.60. TABS. ............................ 345 Quantities for the Ionization Reactions of 7.61. TAPS................................ 345 Buffers in Water at Tϭ298.15 K and 7.62. TAPSO. ............................. 346 pϭ0.1MPa................................ 359 7.63. L͑ϩ͒Tartaric acid...................... 347 9. References to the Tables. .................... 360 Nomenclature Symbol Name Unit a activity dimensionless 1/2 Ϫ1/2 Am Debye–Hu¨ckel constant kg mol B parameter in Debye–Hu¨ckel equation kg1/2 molϪ1/2 c concentration mol dmϪ3 or Ma ؠ Ϫ1 Ϫ1 ⌬ rC p standard molar heat capacity of reaction at constant pressure J K mol ex Ϫ1 Ϫ1 Ci excess heat capacity of species i J mol K ⌬ Ϫ1 rG° standard molar Gibbs energy of reaction kJ mol ⌬ Ϫ1 rH° standard molar enthalpy of reaction kJ mol ex Ϫ1 Hi excess enthalpy of species i kJ mol I ionic strength, molality or concentration basis mol kgϪ1 or Ma Ϫ3 Ic ionic strength, concentration basis mol dm Ϫ1 Im ionic strength, molality basis mol kg K equilibrium constantb dimensionless m molality mol kgϪ1 p pressure Pa pK Ϫlg Kb dimensionless R gas constant ͑8.31451 J KϪ1 molϪ1͒ JKϪ1 molϪ1 T temperature K ͑ ͒ Tr reference temperature usually 298.15 K K z charge number dimensionless ␥ activity coefficientb dimensionless ⌫ ratio of activity coefficients dimensionless ␳ density kg dmϪ3 aThe symbol M has been used as an abbreviation for mol dmϪ3. bWhen needed, a subscipt c or m has been added to these quantities to designate, respectively, a concentration, or molality basis. 1. Introduction measurements on biochemical reactions require a knowledge of the molar enthalpy changes for the ionization reactions. Thermodynamic data on the ionization reactions of acids Corrections for the enthalpy of buffer protonation can be and bases are needed to predict the extent of these reactions quite significant in the treatment of calorimetric data for bio- and the position of equilibrium for processes in which these chemical reactions.4 reactions occur. Acid-base chemistry is a particularly large The aim of this study is to survey the available literature area of chemical research and extensive tabulations1,2 of that leads to values of the equilibrium constants, standard thermodynamic data ͑primarily pKs͒ currently exist for a molar enthalpies, and standard molar heat-capacity changes very large number of acids and bases. Of the many thousands for the ionization reactions of a variety of commonly used of acid and base reactions which have been studied, the ion- buffers at the temperature Tϭ298.15 K. This is the data that ization reactions of those substances that are used as buffers is needed to predict the value of the ionization constant over in aqueous solutions assumes a particular significance in that the temperature range that is generally encountered in the a knowledge of these ionization constants plays an important vast majority of biochemical studies. The selection of buffers role in the establishment and use of the pH scale.3 Also, in was done by first constructing a list of those buffers identi- order to maintain the pH at a constant value, biochemical fied in previous reviews5–10 to have been used in thermody- reactions are generally studied in buffered solutions. Thus, namic studies on enzyme-catalyzed reactions. To this list we one needs the values for the pertinent ionization constants to have added the commonly used buffers of the type suggested properly analyze the results of any equilibrium measure- by Good et al.11–13 as well as several other buffers that have ments which have been performed. Additionally, calorimetric often been used in much of general chemistry. J. Phys. Chem. Ref. Data, Vol. 31, No. 2, 2002 IONIZATION REACTIONS OF BUFFERS 233 2. Thermodynamic Background ϩ0.001 27) and can be neglected except for the most accu- rate work. While values of the standard molar enthalpy of ⌬ ͑ ͒ reaction rH° are identical for different standard states, val- Of primary interest to this review is the thermodynamic ⌬ equilibrium constant ues of rH° are often determined by use of the van’t Hoff equation ϭ ͕ ϩ͑ ͖͒ ͕ Ϫ͑ ͖͒ ͕ ͑ ͖͒ ͑ ͒ Ka,m a H aq •a A aq /a HA aq 1 ͒ ͑ ͒ ץ ץϭ 2͑ ⌬ for the ionization reaction rH° RT ln K/ T p . 11 ϩ Ϫ HA͑aq͒ϭH ͑aq͒ϩA
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