Thermodynamic Quantities for the Ionization Reactions of Buffers

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232 GOLDBERG, KISHORE, AND LENNEN 7.54. PIPES............................... 331 7.55. POPSO.............................. 333 7.56. Pyrophosphate......................... 333 7.57. Succinate............................. 340 7.58. Sulfate............................... 344 7.59. Sulfite............................... 344 7.60. TABS. . . . ............................ 345 7.61. TAPS................................ 345 7.62. TAPSO. ............................. 346 7.63. LTartaric acid...................... 347 Nomenclature 7.64. TES................................. 350 7.65. Tricine............................... 351 7.66. Triethanolamine. . . . . . ................. 353 7.67. Triethylamine......................... 355 7.68. Tris................................. 357 8. Summary of Selected Values of Thermodynamic Quantities for the Ionization Reactions of Buffers in Water at T298.15 K and p0.1MPa................................ 359 9. References to the Tables. .................... 360 Symbol Name Unit a activity dimensionless A m Debye–Hückel constant kg 1/2 mol 1/2 B parameter in Debye–Hückel equation kg 1/2 mol 1/2 c concentration mol dm 3 or M a rC p ex Ci standard molar heat capacity of reaction at constant pressure J K 1 mol 1 excess heat capacity of species i J mol 1 K 1 rG° standard molar Gibbs energy of reaction kJ mol 1 rH° standard molar enthalpy of reaction kJ mol 1 excess enthalpy of species i kJ mol 1 ex Hi I ionic strength, molality or concentration basis mol kg 1 or M a Ic ionic strength, concentration basis mol dm 3 Im ionic strength, molality basis mol kg 1 K equilibrium constant b dimensionless m molality mol kg 1 p pressure Pa pK lg K b dimensionless R gas constant 8.31451 J K 1 mol 1 JK 1 mol 1 T temperature K Tr reference temperature usually 298.15 K K z charge number dimensionless activity coefficient b dimensionless ratio of activity coefficients dimensionless density kg dm 3 a 3 The symbol M has been used as an abbreviation for mol dm . b When needed, a subscipt c or m has been added to these quantities to designate, respectively, a concentration, or molality basis. 1. Introduction Thermodynamic data on the ionization reactions of acids and bases are needed to predict the extent of these reactions and the position of equilibrium for processes in which these reactions occur. Acid-base chemistry is a particularly large area of chemical research and extensive tabulations 1,2 of thermodynamic data primarily pKs currently exist for a very large number of acids and bases. Of the many thousands of acid and base reactions which have been studied, the ionization reactions of those substances that are used as buffers in aqueous solutions assumes a particular significance in that a knowledge of these ionization constants plays an important role in the establishment and use of the pH scale. 3 Also, in order to maintain the pH at a constant value, biochemical reactions are generally studied in buffered solutions. Thus, one needs the values for the pertinent ionization constants to properly analyze the results of any equilibrium measurements which have been performed. Additionally, calorimetric J. Phys. Chem. Ref. Data, Vol. 31, No. 2, 2002 measurements on biochemical reactions require a knowledge of the molar enthalpy changes for the ionization reactions. Corrections for the enthalpy of buffer protonation can be quite significant in the treatment of calorimetric data for biochemical reactions. 4 The aim of this study is to survey the available literature that leads to values of the equilibrium constants, standard molar enthalpies, and standard molar heat-capacity changes for the ionization reactions of a variety of commonly used buffers at the temperature T298.15 K. This is the data that is needed to predict the value of the ionization constant over the temperature range that is generally encountered in the vast majority of biochemical studies. The selection of buffers was done by first constructing a list of those buffers identified in previous reviews 5–10 to have been used in thermodynamic studies on enzyme-catalyzed reactions. To this list we have added the commonly used buffers of the type suggested by Good et al. 11–13 as well as several other buffers that have often been used in much of general chemistry.
2. Thermodynamic Background Of primary interest to this review is the thermodynamic equilibrium constant K a,maH aq•aA aq/aHAaq 1 for the ionization reaction HAaqHaqAaq). 2 The above equilibrium constant has been defined in terms of activity and has been denoted as such by affixing a subscript a to the equilibrium constant. It is also necessary to specify the standard state. In this review the principal standard state used for the solute is the hypothetical ideal solution at the standard molality (m°1 mol kg1 ). The standard state for the solvent is the pure solvent. This choice of a molality standard state has been indicated by attaching a subscript m to the equilibrium constant. Eq. 1 can also be written in terms of the molalities and activity coefficients molality basis m of the solute species: Ka,mmH aq•mA aq/mHAaq•m°]) • mH aq• mA aq/ mHAaq). 3 The standard molality m° has been used in Eq. 3 to keep the equilibrium constant dimensionless. An alternative way of writing Eq. 3 is Ka,mK m• m , 4 where and K mmH aq•mA aq/mHAaq•m°], 5 m mH aq• mA aq/ mHAaq. 6 Here Km is the equilibrium constant molality basis that pertains to an actual real solution as distinct from the equilibrium constant activity basis that relates to a hypothetical standard state that is approached by real solutions as the sum of the molalities of all solute species approaches zero. One can also formulate equilibrium constants in terms of concentrations c: Ka,cK c• c , 7 where and K ccH aq•cA aq/cHAaq•c°], 8 c cH aq• cA aq/ cHAaq. 9 Here, c° is the standard concentration 1 mol dm 3 and c is the activity coefficient on a concentration basis. The density of the pure solvent is needed to calculate values of K a,m from K a,c and vice versa: K a,c•K a,m . 10 On a logarithmic scale the difference between K a,c and K a,m in water at T298.15 K is very small (pK a,cpK a,m IONIZATION REACTIONS OF BUFFERS 0.001 27) and can be neglected except for the most accurate work. While values of the standard molar enthalpy of reaction rH° are identical for different standard states, values of rH° are often determined by use of the van’t Hoff equation rH°RT 2 ln K/T p . 11 Equation 11 is exact for equilibrium constants that have been determined by using a molality standard state. However, if Eq. 11 is used with values of K a,c , one has introduced an additional term RT 2 ( ln /T) p0.187 kJ mol 1 at T298.15 K for studies done with water as the solvent. We have applied this correction term to the values of rH° only when it was very clear that the measured equilibrium constants were based on the concentration scale. Since, in such cases, rH° is calculated as a derivative of equilibrium constants measured at several temperatures, temperature dependent errors in the values of K c are amplified. Thus, in the vast majority of cases, this correction term is significantly less than the overall uncertainty in the value of rH°. In this paper, we have used the equation of Clarke and Glew 14 to represent the temperature dependence of equilibrium constants: R ln K rG°/T r rH°1/T r1/T rC p Tr /T1 lnT/T rT r/2 rC p /TpT/T r 233 T r /T2 lnT/T r. 12 Here, T r is a reference temperature typically 298.15 K and R is the gas constant 8.31451 J K 1 mol 1 ; 15 rG°, rH°, and rC p are, respectively, the standard molar Gibbs energy, enthalpy, and heat-capacity changes for a reaction occurring at the selected reference temperature T r . A significant advantage to using Eq. 12 is that the parameters that predict the temperature dependence of the equilibrium constant are the standard thermodynamic quantities that can be obtained from additional types of measurements—calorimetry being the most important. Additional terms that involve higher order derivatives of ( rC p /T) p can be added to the right-hand side of Eq. 12. However, the values of these higher order derivatives are not known for most ionization reactions. In fact, since the quantity ( rC p /T) p involves the third derivative of ln K versus T data, it is exceedingly difficult to obtain an accurate value of ( rC p /T) p from measurements involving the temperature dependence of ionization constants. Errors in ( rC p /T) p can also be substantive when this quantity is obtained from the temperature dependence of rH°. Thus, the direct measurement of heat capacities is the favored method for obtaining information on the temperature dependence of rH° and rC p . Many values of the ionization constants are reported under conditions of ionic strength and solution composition where the values of the activity coefficients are not known. Yet, it is useful to make some attempt to adjust these pK values to I 0 for purposes of comparison with other results. In the J. Phys. Chem. Ref. Data, Vol. 31, No. 2, 2002
Page 1: Thermodynamic Quantities for the Io
Page 5 and 6: cal cells both with and without liq
Page 7 and 8: 7. Tables of Thermodynamic Quantiti
Page 9 and 10: IONIZATION REACTIONS OF BUFFERS Val
Page 11 and 12: TABLE 7.3. ADA Other names N-2-acet
Page 13 and 14: TABLE 7.4. 2-Amino-2-methyl-1,3-pro
Page 15 and 16: Values adjusted to TÄ298.15 K and
Page 19 and 20: Values from literature pK rH°/(kJ
Page 21 and 22: TABLE 7.10. Barbital Other names ba
Page 31 and 32: TABLE 7.17. Cacodylate Other names
Page 33 and 34: Values from literature—Continued
Page 45 and 46: TABLE 7.26. 3,3-Dimethylglutarate O
Page 47 and 48: TABLE 7.28. Ethanolamine Other name
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Values from literature—Continued
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IONIZATION REACTIONS OF BUFFERS Val
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TABLE 7.33. Glycylglycine Other nam
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Values adjusted to TÄ298.15 K and
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TABLE 7.38. HEPPSO Other names N-2-
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TABLE 7.42. Maleate Other names mal
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TABLE 7.44. MES Other names 2-N-mor
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TABLE 7.49. MOPSO Other names 3-N-m
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TABLE 7.51. Phosphate Other names p
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Values from literature pK rH°/(kJ
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TABLE 7.55. POPSO Other names piper
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TABLE 7.60. TABS Other names N-tris
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TABLE 7.68. Tris Other names 2-amin
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IONIZATION REACTIONS OF BUFFERS 8.
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IONIZATION REACTIONS OF BUFFERS 27C
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IONIZATION REACTIONS OF BUFFERS 57N
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IONIZATION REACTIONS OF BUFFERS 68V
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IONIZATION REACTIONS OF BUFFERS 76W
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IONIZATION REACTIONS OF BUFFERS 90D
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Thermodynamic Quantities for the Ionization Reactions of Buffers

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