Thermodynamics of proton dissociations from aqueous alanine at temperatures from (278.15 to 393.15) K, molalities from (0.0075 to 1.0) mol · kg−1, and at the pressure 0.35 MPa: Apparent molar heat capacities and apparent molar volumes of alanine, alaninium chloride, and sodium alaninate

J. Chem. Thermodynamics 38 (2006) 939–951 www.elsevier.com/locate/jct

Thermodynamics of proton dissociations from aqueous alanine at temperatures from (278.15 to 393.15) K, molalities from (0.0075 to 1.0) mol Æ kg1, and at the pressure 0.35 MPa: Apparent molar heat capacities and apparent molar volumes of alanine, alaninium chloride, and sodium alaninate S.P. Ziemer, T.L. Niederhauser, J.L. Price, E.M. Woolley

*

Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602-5700, USA Received 31 August 2005; received in revised form 7 October 2005; accepted 11 October 2005 Available online 22 November 2005

Abstract We have measured the densities of aqueous solutions of alanine, alanine plus equimolal HCl, and alanine plus equimolal NaOH at temperatures 278.15 6 T/K 6 368.15, at molalities 0.0075 6 m/mol Æ kg1 6 1.0, and at the pressure p = 0.35 MPa using a vibrating tube densimeter. We have also measured the heat capacities of these solutions at 278.15 6 T/K 6 393.15 and at the same m and p using a twin fixed-cell differential temperature-scanning calorimeter. We used the densities to calculate apparent molar volumes V/ and the heat capacities to calculate apparent molar heat capacities Cp,/ for these solutions. We used our results and values from the literature for V/(T, m) and Cp,/(T, m) for HCl(aq), NaOH(aq), and NaCl(aq) and the molar heat capacity change DrCp,m(T, m) for ionization of water to calculate parameters for DrCp,m(T, m) for the two proton dissociations from protonated aqueous cationic alanine. We integrated these results in an iterative algorithm using Youngs Rule to account for the effects of speciation and chemical relaxation on V/(T, m) and Cp,/(T, m). This procedure yielded parameters for V/(T, m) and Cp,/(T, m) for alaninium chloride {H2Ala+Cl(aq)} and for sodium alaninate {Na+Ala(aq)} which successfully modeled our observed results. Values are given for DrCp,m, DrHm, pQa, DrSm, and DrVm for the first and second proton dissociations from protonated aqueous alanine as functions of T and m. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Apparent molar volume; Apparent molar heat capacity; Alanine; 2-Aminopropanoic acid; Zwitterion; Alaninium chloride; Sodium alaninate; Proton dissociations; Acidity; Youngs Rule

1. Introduction In our continuing efforts to enlarge the database of thermodynamic properties of aqueous solutions of L-2-amino acids in their protonated, zwitterionic, and deprotonated forms, we have studied aqueous alanine. Alanine is a major component of silks, and it is the simplest amino acid following glycine. It is a non-essential amino acid, which plays

*

Corresponding author. Tel.: +1 801 378 2674; fax: +1 801 378 2575. E-mail address: [email protected] (E.M. Woolley).

0021-9614/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2005.10.007

a role in human metabolism as a transamination product of pyruvate. We have reported recently analogous results for the apparent molar volumes V/ and apparent molar heat capacities Cp,/ of aqueous histidine [1,2], proline [3], valine [4], L-2-aminobutanoic acid [4], glycine [5], and serine [6]. In this paper, we report our measured densities and heat capacities of aqueous solutions of zwitterionic alanine {HAla±(aq)}, alanine plus equimolal HCl {HAla±(aq) + HCl(aq)}, and alanine plus equimolal NaOH {HAla±(aq) + NaOH(aq)}. Our analysis applies Youngs Rule and a relaxation heat capacity term to account for the equilibrium molalities of

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the species {H2Ala+Cl(aq)}, HAla±(aq), and {Na+Ala(aq)} present in the solutions containing HCl(aq) and NaOH(aq). Our resulting values of V/ and Cp,/ for {H2Ala+Cl(aq)} and for {Na+Ala (aq)} allow calculation of the thermodynamic quantities DrCp,m, DrHm, pQa, DrSm, and DrVm for the first and second proton dissociations from protonated aqueous alanine. 2. Experimental Crystalline L-alanine (HAla±, 2-aminopropanoic acid, CH3CH(NH2)COOH, molar mass M2 = 89.0935 g Æ mol1; Fluka, lot 397418/1, 0.998 mass fraction) was used as received. Purity of the solute was verified by elemental analysis to be 0.998 mass fraction alanine. We prepared aqueous stock solutions of L-alanine by mass using distilled, deionized, autoclaved, degassed water. We prepared stock solutions of {HAla±(aq) + HCl(aq)} and {HAla±(aq) + NaOH(aq)} in a similar fashion, combining mass dilutions of the HAla±(aq) solution with previously standardized stock solutions of HCl(aq) [7] and carbonate-free NaOH(aq) [8] to achieve nearly 1:1 equimolal ratios of L-alanine + HCl {m(HAla±)/m(HCl) = 0.998}

and L-alanine + NaOH {m(HAla±)/m(NaOH) = 1.010}. Subsequent solutions were prepared by mass dilution of these stock solutions. Air buoyancy corrections were applied to all weighings. We measured solution densities qs at regular temperature intervals in the range 278.15 6 T/K 6 368.15 with an Anton PAAR (Graz, Austria) Model 512 vibrating-tube densimeter and calculated V/(T, m) with the following equation: V / ¼ M 2 =qs  ðqs  qw Þ=ðqs  qw  mÞ;

ð1Þ

where qw [3] is the density of water. Detailed discussions of the procedures used to obtain qs from our experiments have been published previously [3–5,9]. Heat capacities of solutions cp,s were determined with a Calorimetry Sciences Corp. (Lindon, UT, USA) Model 6100 Nano-DSC twin fixed-cell, differential-output, power-compensation, temperature-scanning calorimeter at 278.15 6 T/K 6 393.15 as described recently [3–5,9]. We used values of the heat capacity of water cp,w [3] and our cp,s with the following equation to calculate Cp,/: C p;/ ¼ M 2  cp;s þ ðcp;s  cp;w Þ=m.

ð2Þ

TABLE 1 Observed apparent molar volumes V/ for aqueous zwitterionic alanine at p = 0.35 MPaa m/(mol Æ kg1)

0.0152 0.0299 0.0500 0.0800 0.1247 0.2493 0.5149 1.0019

0.0152 0.0299 0.0500 0.0800 0.1247 0.2493 0.5149 1.0019

0.0152 0.0299 0.0500 0.0800 0.1247 0.2493 0.5149 1.0019

V//(cm3 Æ mol1) T = 278.15 K

T = 283.15 K

T = 288.15 K

T = 298.15 K

44.3 ± 7.7 63.5 ± 3.9 62.94 ± 0.22 56.34 ± 0.15 60.08 ± 0.67 60.25 ± 0.34 59.76 ± 0.17 59.59 ± 0.10

46.3 ± 6.3 64.2 ± 3.2 62.47 ± 0.19 57.27 ± 0.13 60.34 ± 0.68 60.58 ± 0.34 60.31 ± 0.17 60.03 ± 0.10

48.8 ± 5.2 66.2 ± 2.6 62.46 ± 0.39 57.93 ± 0.24 60.66 ± 0.52 60.87 ± 0.26 60.71 ± 0.13 60.40 ± 0.07

51.0 ± 4.0 65.4 ± 2.0 62.70 ± 0.43 58.79 ± 0.27 61.11 ± 0.45 61.39 ± 0.23 61.38 ± 0.12 61.01 ± 0.07

T = 308.15 K

T = 318.15 K

T = 328.15 K

T = 338.15 K

53.2 ± 3.4 65.6 ± 1.7 63.23 ± 0.35 59.22 ± 0.22 61.68 ± 0.28 61.76 ± 0.15 61.91 ± 0.08 61.52 ± 0.05

53.0 ± 2.3 66.7 ± 1.2 63.19 ± 0.25 59.92 ± 0.16 62.18 ± 0.34 62.08 ± 0.17 62.39 ± 0.09 61.92 ± 0.05

55.9 ± 2.8 67.0 ± 1.4 59.35 ± 0.27 60.73 ± 0.17 62.39 ± 0.23 62.26 ± 0.12 62.61 ± 0.06 62.18 ± 0.04

62.4 ± 4.1 67.2 ± 2.1 63.5 ± 1.1 61.00 ± 0.67 61.87 ± 0.60 62.10 ± 0.30 62.88 ± 0.15 62.29 ± 0.08

T = 348.15 K

T = 358.15 K

T = 368.15 K

59.60 ± 0.74 68.95 ± 0.38 63.21 ± 0.38 61.23 ± 0.24 62.44 ± 0.12 62.49 ± 0.06 63.02 ± 0.04 62.57 ± 0.03

59.27 ± 0.08 69.01 ± 0.04 62.87 ± 0.75 61.33 ± 0.47 62.47 ± 0.09 62.52 ± 0.05 63.14 ± 0.03 62.67 ± 0.03

58.95 ± 0.41 71.06 ± 0.21 62.83 ± 0.61 61.47 ± 0.38 62.53 ± 0.03 62.71 ± 0.03 63.21 ± 0.03 62.69 ± 0.03

The ± values are from propagation of uncertainties as described in reference [9]. a Experimental values of qs can be obtained by equation (1) with m, qw from reference [3], and M2 = 75.0672 g Æ mol1.

S.P. Ziemer et al. / J. Chem. Thermodynamics 38 (2006) 939–951

3. Results and discussion Values of V/,obs for HAla±(aq), {HAla±(aq) + HCl(aq)}, and {HAla±(aq) + NaOH(aq)} at 0.0075 6 m/ mol Æ kg1 6 1.0 and 278.15 6 T/K 6 368.15 are given in tables 1 to 3, respectively. The following equation was fit by regression to these results: 1=2

V / ¼ w3=2  AV  ðm Þ  2

þ m0 þ m1  m þ m2  ðm Þ  2

3=2

þ

 2

m3  ðm Þ  T  þ m4  ðm Þ  ðT Þ þ m5  T  þ m6 =ðT   200Þ þ m7  lnðT  Þ þ m8  ðT  Þ2 .

ð3Þ

In equation (3), mi are the parameters of the regression, T* = (T/T) with T = 1 K, m* = (m/m) with m = 1 mol Æ kg1, AV is the temperature-dependant Debye– Hu¨ckel coefficient for volumes from Archer and Wang [10] as given by Sorenson et al. [3], w = 0 for HAla±(aq), and w = 1 for {HAla±(aq) + HCl(aq)}, H2Ala+Cl(aq), {HAla±(aq) + NaOH(aq)}, and for Na+Ala(aq). The reciprocals of the uncertainties in tables 1 to 3 were used as weighting factors in the regressions. These and other uncertainties reported in this work were calculated by standard error propagation statistics as described previously [9].

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Regression values of mi for equation (3) are given in table 4. Figure 1 shows our V/,obs(T, m) results for HAla±(aq) along with the regression surface and values from the literature [11–32]. The differences DV = {V/(us)  V/(lit)} between V/ values on our regression surface and all the literature values for HAla±(aq) are in the range DV = (10.5 to 1.7) cm3 Æ mol1, with an average difference DV = 0.4 cm3 Æ mol1. Tables 5 to 7 give our values of Cp,/,obs(T, m) for HAla±(aq), {HAla±(aq) + HCl(aq)}, and {HAla±(aq) + NaOH(aq)}, respectively. The following equation was fit by regression to these results using as weighting factors the reciprocals of the uncertainties given in the tables: C p;/ ¼ w3=2  AC  ðm Þ1=2 þ c0 þ c1  m þ c2  ðm Þ3=2 þ c3  m  T  þ c4  ðm Þ2  T  þ c5 ðm Þ2  ðT  Þ2 þ 2

3

c6  T  þ c7  lnðT  Þ þ c8  ðT  Þ þ c9  ðT  Þ þ 4

c10  ðT  Þ .

ð4Þ

In equation (4), ci are the regression parameters, and AC is the temperature-dependant Debye–Hu¨ckel coefficient for heat capacities from Archer and Wang [10] as given by Sorenson et al. [3]. Table 8 gives the regression parameters.

TABLE 2 Observed apparent molar volumes V/ for aqueous alanine plus (nearly) equimolal HCl at p = 0.35 MPaa,b mb/(mol Æ kg1)

0.0150 0.0299 0.0499 0.0799 0.0983 0.1746 0.2991 0.4990

0.0150 0.0299 0.0499 0.0799 0.0983 0.1746 0.2991 0.4990

0.0150 0.0299 0.0499 0.0799 0.0983 0.1746 0.2991 0.4990

V//(cm3 Æ mol1) T = 278.15 K

T = 283.15 K

T = 288.15 K

T = 298.15 K

82.74 ± 0.18 80.71 ± 0.19 83.91 ± 0.14 82.66 ± 1.99 83.02 ± 1.14 84.04 ± 1.29 83.83 ± 0.57 84.25 ± 0.22

82.56 ± 0.47 82.07 ± 0.47 84.24 ± 0.29 83.33 ± 2.37 83.66 ± 1.36 84.68 ± 0.60 84.57 ± 0.62 84.99 ± 0.16

82.68 ± 0.82 82.83 ± 0.82 84.43 ± 0.51 84.13 ± 2.39 84.41 ± 1.37 85.17 ± 0.91 85.15 ± 0.61 85.58 ± 0.13

82.7 ± 1.9 83.72 ± 0.34 85.14 ± 0.21 85.14 ± 0.42 85.51 ± 0.34 86.03 ± 0.20 86.17 ± 0.12 86.57 ± 0.09

T = 308.15 K

T = 318.15 K

T = 328.15 K

T = 338.15 K

82.5 ± 1.7 84.23 ± 0.64 85.43 ± 0.39 85.95 ± 0.25 86.18 ± 0.20 86.66 ± 0.12 86.95 ± 0.11 87.39 ± 0.08

82.1 ± 1.5 84.81 ± 0.26 85.73 ± 0.16 86.55 ± 0.21 86.79 ± 0.18 87.12 ± 0.11 87.46 ± 0.09 87.97 ± 0.06

82.3 ± 1.2 84.88 ± 0.31 85.97 ± 0.19 86.93 ± 0.14 87.15 ± 0.11 87.50 ± 0.08 87.99 ± 0.07 88.49 ± 0.06

82.5 ± 1.1 84.97 ± 0.55 86.09 ± 0.33 87.13 ± 0.12 87.31 ± 0.10 87.81 ± 0.07 88.39 ± 0.05 88.87 ± 0.05

T = 348.15 K

T = 358.15 K

T = 368.15 K

80.9 ± 1.1 84.27 ± 0.65 85.81 ± 0.39 87.02 ± 0.11 87.30 ± 0.09 88.24 ± 0.06 88.75 ± 0.05 89.14 ± 0.04

82.1 ± 2.2 84.6 ± 1.3 85.72 ± 0.76 86.93 ± 0.18 87.56 ± 0.15 88.32 ± 0.09 88.97 ± 0.06 89.36 ± 0.05

81.4 ± 1.5 82.6 ± 1.2 85.20 ± 0.73 86.92 ± 0.19 87.58 ± 0.15 88.29 ± 0.09 89.12 ± 0.08 89.45 ± 0.06

The ± values are from propagation of uncertainties as described in reference [9]. a Experimental values of qs can be obtained by equation (1) with m, qw from reference [3], and M2 = 111.5278 g Æ mol1. b Molality of alanine, with stoichiometric molality ratio r = m(HAla)/m{HCl} = 0.998.

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TABLE 3 Observed apparent molar volumes V/ for aqueous alanine plus (nearly) equimolal NaOH at p = 0.35 MPaa,b mb/(mol Æ kg1)

V//(cm3 Æ mol1)

0.0075 0.0150 0.0301 0.0503 0.0851 0.1747 0.3494 0.6594

0.0075 0.0150 0.0301 0.0503 0.0851 0.1747 0.3494 0.6594

0.0075 0.0150 0.0301 0.0503 0.0851 0.1747 0.3494 0.6594

T = 278.15 K

T = 283.15 K

T = 288.15 K

T = 298.15 K

75 ± 24 34 ± 12 49.7 ± 6.1 58.5 ± 3.8 55.0 ± 2.3 58.1 ± 1.4 56.8 ± 0.7 59.0 ± 0.4

69 ± 28 36 ± 14 52.0 ± 7.0 61.1 ± 4.2 57.4 ± 2.5 59.5 ± 1.1 58.0 ± 0.6 60.0 ± 0.3

76 ± 24 44 ± 12 54.4 ± 6.0 61.0 ± 3.8 58.0 ± 2.2 59.4 ± 1.1 58.7 ± 0.6 60.5 ± 0.3

78 ± 22 48 ± 11 56.1 ± 5.5 61.9 ± 3.3 59.4 ± 1.9 60.4 ± 1.0 60.1 ± 0.5 61.7 ± 0.3

T = 308.15 K

T = 318.15 K

T = 328.15 K

T = 338.15 K

70 ± 16 47.5 ± 7.9 57.4 ± 3.9 62.1 ± 2.6 60.4 ± 1.5 61.2 ± 0.8 61.1 ± 0.4 62.6 ± 0.2

75 ± 16 51.9 ± 8.1 59.1 ± 4.0 62.7 ± 2.9 61.3 ± 1.7 61.7 ± 0.9 61.9 ± 0.5 63.3 ± 0.2

71 ± 14 54.4 ± 6.9 58.4 ± 3.5 62.5 ± 2.3 59.3 ± 1.4 62.1 ± 0.7 62.5 ± 0.4 63.8 ± 0.2

56 ± 19 46.8 ± 9.5 57.4 ± 4.8 61.1 ± 3.6 60.6 ± 2.1 62.6 ± 1.0 62.7 ± 0.5 64.0 ± 0.3

T = 348.15 K

T = 358.15 K

T = 368.15 K

69 ± 10 56.0 ± 5.2 60.3 ± 2.6 62.8 ± 1.8 61.7 ± 1.1 62.6 ± 0.5 63.1 ± 0.3 64.4 ± 0.2

64.6 ± 8.5 53.6 ± 4.3 60.0 ± 2.1 62.2 ± 1.6 62.1 ± 0.9 62.5 ± 0.5 63.2 ± 0.2 64.5 ± 0.1

63.0 ± 8.2 56.2 ± 4.1 59.7 ± 2.1 62.5 ± 1.3 61.7 ± 0.8 62.5 ± 0.4 64.4 ± 0.2 64.6 ± 0.1

The ± values are from propagation of uncertainties as described in reference [9]. a Experimental values of qs can be obtained by equation (1) with m, qw from reference [3], and M2 = 97.0487 g Æ mol1. b Molality of alanine, with stoichiometric molality ratio r = m(HAla)/m{NaOH} = 1.010.

TABLE 4 Regression parameters of equation (3) for apparent molar volumes V/ of {HAla±(aq)}, {HAla±(aq) + HCl(aq)}, {HAla±(aq) + NaOH(aq)}, {H2Ala+Cl(aq)}, and {Na+Ala(aq)} mi

HAla±(aq) observed, w = 0 (table 1)

{HAla±(aq) + HCl(aq)} observed, w = 1 (table 2)

m0 m1 m2 m3 106 Æ m4 103 Æ m5 103 Æ m6 m7 106 Æ m8 Da Maximum m

389.74 ± 0.01 4.97 ± 0.01 4.465 ± 0.004

174.81 ± 0.01 49.99 ± 0.01 125.14 ± 0.01 0.53708 ± 0.00002 832.2 ± 0.1

254.0 ± 0.1 92.308 ± 0.001

1.1184 ± 0.0007 14.112 ± 0.001

±0.06 1.0

{HAla±(aq) + NaOH(aq)} observed, w = 1 (table 3) 90.76 ± 0.01 6.06 ± 0.01

43.9 ± 0.1 58.86 ± 0.01 1.504 ± 0.001

±0.17 0.5

±0.44 0.7

H2Ala+Cl(aq) iteration, w = 1 (see text) 101.100 ± 0.003 34.98 ± 0.01 103.35 ± 0.01 0.50401 ± 0.00002 798.1 ± 0.1 1.048 ± 0.001 55.85 ± 0.02 ±0.05 0.5

Na+Ala(aq) iteration, w = 1 (see text) 68.08 ± 0.01

0.08690 ± 0.00003 256.7 ± 0.1 0.965 ± 0.001

±0.28 0.7

The ± values are chosen to reproduce the generated V/ values to within ±0.01 cm3 Æ mol1 at 278.15 6 T/K 6 393.15 and at m 6 the maximum. a Standard deviations of the regressions.

Figure 2 shows our Cp,/,obs(T, m) for HAla±(aq) from table 5 and the regression surface, along with values from the literature [28–36]. The differences DC = {Cp,/(us)  Cp,/(lit)} between Cp,/ values on our regression surface and all the values from the literature are in the range

DC = (44.9 to 70.8) J Æ K1 Æ mol1, with an average difference DC = 1.3 J Æ K1 Æ mol1. The two largest values of DC both correspond to values from reference [36]. In order to calculate apparent molar properties Cp,/(i) and V/(i) of the individual species H2Ala+Cl(aq)

S.P. Ziemer et al. / J. Chem. Thermodynamics 38 (2006) 939–951

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tion (5) or reaction (8) from perturbation of T or p during the measurement (or calculation) of the property Y/,tot, m is the stoichiometric molality of the limiting reagent in the solution [m = m{HAla±(aq)} < m{HCl(aq)} for reaction (5) and m = m{NaOH(aq)} < m{HAla±(aq)} for reaction (8)], m(i) is the molality of species i, Y/(i) is the apparent molar property of species i, and mt is given by the following equation: X mðiÞ. ð10Þ mt ¼ The following equations define V/,tot and Cp,/,tot: V /;tot ¼ M av =qs  fðqs  qw Þ=ðqs  qw  mt Þg; C p;/;tot ¼ M av  cp;s þ fðcp;s  cp;w Þ=mt g;

ð11Þ ð12Þ

where the weighted average molar mass of solutes in solution Mav is given by the following equation: X fmðiÞ=mt g  MðiÞ. ð13Þ M av ¼ FIGURE 1. Apparent molar volume V/ of zwitterionic alanine HAla±(aq) plotted against temperature T and molality m. Surface generated from equation (3) with parameters in column 2 of table 4; s, experimental values from table 1; d, T = 298.15 K, m = 0 mol Æ kg1, references [11,12,32]; j, T = 298.15 K, 0 6 m/mol Æ kg1 6 1.0, references [13–17,27,29–31]; m, 273.15 6 T/K 6 328.15, m = 0 mol Æ kg1, references [18–21]; r, 278.15 6 T/K 6 375.02, 0 6 m/mol Æ kg1 6 0.5991, references [22–26,28].

and Na+Ala(aq), we must account for chemical equilibria in our solutions of {HAla±(aq) + HCl(aq)} and {HAla±(aq) + NaOH(aq)}, respectively. Aqueous alanine can undergo the following reactions: H2 Alaþ ðaqÞ ¼ HAla ðaqÞ þ Hþ ðaqÞ 



ð5Þ

þ

HAla ðaqÞ ¼ Ala ðaqÞ þ H ðaqÞ 

ð6Þ

þ



HAla ðaqÞ þ H2 O ¼ H2 Ala ðaqÞ þ OH ðaqÞ 





Ala ðaqÞ þ H2 O ¼ HAla ðaqÞ þ OH ðaqÞ

ð7Þ ð8Þ

Reactions (6) and (7) do not occur to an appreciable extent at the m, T, and p of our experiments for solutions of HAla±(aq). Therefore, HAla±(aq) solutions are treated as consisting of the single solute species HAla±(aq). However, in aqueous solutions of {HAla±(aq) + HCl(aq)} and of {HAla±(aq) + NaOH(aq)}, reactions (5) and (8), respectively, proceed to a significant degree, but not to completion. Thus, {HAla±(aq) + HCl(aq)} solutions are equilibrium mixtures of H2Ala+Cl(aq), HAla±(aq), and H+Cl(aq), whereas {HAla±(aq) + NaOH(aq)} solutions are equilibrium mixtures of Na+Ala(aq), HAla±(aq), and Na+OH(aq). Apparent molar properties of these two mixtures can be represented approximately at m* > 0 by Youngs Rule equation (9) h nX oi. Y /;tot ¼ m  Y rel þ mðiÞ  Y / ðiÞ mt ; ð9Þ where Y/,tot is the apparent molar property of the mixture, Yrel results from shifts in the equilibrium position by reac-

The procedure to analyze our results with equations (9) to (13) follows that outlined recently in Ziemer et al. [5]. Reference values used for integration constants in this report are pQa = (2.3354 ± 0.0043) and DrHm = (2.91 ± 0.29) kJ Æ mol1 for reaction (5), and pQa = (9.862 ± 0.013) and DrHm = (45.65 ± 0.46) kJ Æ mol1 for reaction (6). These values were the averages of eight values from seven sources [37–43], nine values from eight sources [37,38,41– 46], nine values from six sources [39–43,47], and seven values from five sources [41–44,47] in the literature, respectively, with standard deviations as given above. Values for reaction (8) were calculated from those for reaction (6) using values of pQw and DrHm,w from Patterson et al. [48], giving pQb = 4.1344 and DrHm = 10.163 kJ Æ mol1 for reaction (8). We then fit by regression equation (4) to our derived Cp,/(i)(T, m) results for i = {H2Ala+Cl(aq)} and i = {Na+Ala(aq)} using the reciprocals of the uncertainties in Cp,/,obs from tables 6 and 7, respectively, as weighting factors. The regression parameters ci are given in columns 5 and 6 of table 8. Figures 3 and 4 show our Cp,/(i)(T, m) results for the species i = {H2Ala+Cl(aq)} and i = {Na+Ala(aq)}, respectively, along with surfaces calculated from the regression parameters in columns 5 and 6 of table 8. We know of no results in the literature that give Cp,/(i) for these two species. We have also calculated V/(i)(T, m) for i = {H2Ala+Cl(aq)} and i = {Na+Ala(aq)}, and then fit equation (3) by regression to these results to give the parameters in columns 5 and 6 in table 4 and the surfaces shown in figures 5 and 6. The differences between our regressed values for V/(i) for H2Ala+Cl(aq) and those in references [27,39] are in the range DV = (1.1 to 0.7) cm3 Æ mol1, with an average difference DV = 0.3 cm3 Æ mol1. The differences between our regressed values for V/(i) for Na+Ala(aq) and those in references [27,39] are in the range DV = (0.1 to 1.2) cm3 Æ mol1, with an average difference DV = 0.7 cm3 Æ mol1.

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TABLE 5 Observed apparent molar heat capacities Cp,/ for zwitterionic aqueous alanine at p = 0.35 MPaa m/(mol Æ kg1)

0.0152 0.0299 0.0500 0.0800 0.1247 0.2493 0.5149 1.0019

0.0152 0.0299 0.0500 0.0800 0.1247 0.2493 0.5149 1.0019

0.0152 0.0299 0.0500 0.0800 0.1247 0.2493 0.5149 1.0019

0.0152 0.0299 0.0500 0.0800 0.1247 0.2493 0.5149 1.0019

0.0152 0.0299 0.0500 0.0800 0.1247 0.2493 0.5149 1.0019

Cp,//(J Æ K1 Æ mol1) T = 278.15 K

T = 283.15 K

T = 288.15 K

T = 293.15 K

T = 298.15 K

107 ± 34 137 ± 17 101.3 ± 6.1 106.0 ± 3.8 107.0 ± 3.6 113.3 ± 1.8 122.6 ± 0.9 118.5 ± 0.5

119 ± 34 148 ± 17 113.2 ± 5.8 117.9 ± 3.6 118.8 ± 3.4 124.8 ± 1.7 133.2 ± 0.9 128.7 ± 0.5

131 ± 35 156 ± 18 123.3 ± 5.5 127.8 ± 3.5 128.9 ± 3.1 134.4 ± 1.6 142.0 ± 0.8 137.2 ± 0.5

143 ± 34 163 ± 17 131.5 ± 5.2 136.0 ± 3.3 137.4 ± 2.8 142.4 ± 1.4 149.5 ± 0.7 144.3 ± 0.4

152 ± 33 170 ± 17 138.2 ± 4.9 142.8 ± 3.1 144.2 ± 2.7 149.1 ± 1.4 155.6 ± 0.7 150.2 ± 0.4

T = 303.15 K

T = 308.15 K

T = 313.15 K

T = 318.15 K

T = 323.15 K

158 ± 32 174 ± 17 143.9 ± 4.8 148.7 ± 3.0 150.3 ± 2.6 154.9 ± 1.3 160.8 ± 0.7 155.5 ± 0.4

163 ± 32 178 ± 16 148.9 ± 4.6 153.7 ± 2.9 155.4 ± 2.4 159.8 ± 1.2 165.3 ± 0.6 159.8 ± 0.4

169 ± 32 182 ± 16 153.6 ± 4.4 158.0 ± 2.8 159.9 ± 2.3 164.1 ± 1.2 169.3 ± 0.6 163.8 ± 0.4

172 ± 31 185 ± 16 157.3 ± 4.3 161.6 ± 2.7 163.9 ± 2.0 167.7 ± 1.0 172.6 ± 0.5 167.1 ± 0.3

175 ± 30 188 ± 15 160.9 ± 4.2 164.9 ± 2.6 167.3 ± 1.8 170.9 ± 0.9 175.5 ± 0.5 170.0 ± 0.3

T = 328.15 K

T = 333.15 K

T = 338.15 K

T = 343.15 K

T = 348.15 K

178 ± 30 190 ± 15 163.7 ± 4.0 167.7 ± 2.5 170.3 ± 1.5 173.6 ± 0.8 178.0 ± 0.4 172.5 ± 0.3

181 ± 29 192 ± 15 166.4 ± 3.8 170.2 ± 2.4 173.0 ± 1.3 176.1 ± 0.7 180.3 ± 0.4 174.8 ± 0.3

184 ± 29 194 ± 15 168.8 ± 3.6 172.4 ± 2.3 175.4 ± 1.0 178.3 ± 0.5 182.3 ± 0.3 176.9 ± 0.2

187 ± 28 196 ± 14 170.7 ± 3.3 174.2 ± 2.1 177.3 ± 0.8 180.1 ± 0.4 183.9 ± 0.3 178.6 ± 0.2

188 ± 28 197 ± 14 172.4 ± 3.3 175.9 ± 2.1 178.9 ± 0.7 181.7 ± 0.4 185.3 ± 0.2 180.1 ± 0.2

T = 353.15 K

T = 358.15 K

T = 363.15 K

T = 368.15 K

T = 373.15 K

190 ± 27 198 ± 14 174.0 ± 3.3 177.4 ± 2.0 180.5 ± 0.6 183.1 ± 0.3 186.6 ± 0.2 181.4 ± 0.2

191 ± 28 199 ± 14 175.2 ± 3.3 178.5 ± 2.1 181.6 ± 0.5 184.3 ± 0.3 187.6 ± 0.2 182.5 ± 0.2

192 ± 28 199 ± 14 176.1 ± 3.2 179.4 ± 2.0 182.5 ± 0.4 185.1 ± 0.3 188.4 ± 0.2 183.5 ± 0.2

192 ± 28 200 ± 14 176.6 ± 2.9 180.1 ± 1.8 183.3 ± 0.3 185.8 ± 0.2 189.0 ± 0.2 184.2 ± 0.2

192 ± 27 200 ± 14 177.1 ± 2.6 180.5 ± 1.6 183.7 ± 0.2 186.2 ± 0.2 189.4 ± 0.2 184.8 ± 0.2

T = 378.15 K

T = 383.15 K

T = 388.15 K

T = 393.15 K

192 ± 26 200 ± 13 177.2 ± 2.3 180.6 ± 1.4 183.8 ± 0.2 186.4 ± 0.2 189.5 ± 0.2 185.1 ± 0.2

192 ± 26 200 ± 13 177.1 ± 2.1 180.7 ± 1.3 183.9 ± 0.3 186.4 ± 0.2 189.6 ± 0.2 185.4 ± 0.2

192 ± 27 199 ± 14 176.8 ± 2.1 180.3 ± 1.3 183.6 ± 0.4 186.2 ± 0.2 189.4 ± 0.1 185.5 ± 0.1

190 ± 27 200 ± 14 176.6 ± 2.0 179.8 ± 1.2 183.1 ± 0.7 185.8 ± 0.4 189.2 ± 0.2 185.5 ± 0.1

The ± uncertainties are from propagation of uncertainties as described in reference [9]. a Average experimental values of cp,s can be obtained by equation (2) with m, cp,w from reference [3], and M2 = 75.0672 g Æ mol1.

Our iterative Youngs Rule results lead to calculated values of DrCp,m, DrHm, pQa, DrSm, and DrVm for reactions (5) and (6) as described by Ziemer et al. [5]. Figure 7 shows DrCp,m(T, m) for reactions (5) and (6), respectively, together with values from the literature [46,47]. The difference between our value of DrCp,m for reaction (5) at T = 298.1 K and m* = 0 and the value from reference [46] is

DC = 2.9 J Æ K1 Æ mol1. The differences between our values of DrCp,m for reaction (6) and those given in references [46,47] are in the range DC = (30.9 to 0.5) J Æ K1 Æ mol1, with an average difference DC = 15.5 J Æ K1 Æ mol1. Figure 8 shows DrHm(T, m) for reactions (5) and (6) together with values from the literature [37,38,41–47].

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945

TABLE 6 Observed apparent molar heat capacities Cp,/ for aqueous alanine plus (nearly) equimolal HCl at p = 0.35 MPaa,b m/(mol Æ kg1)b

0.0150 0.0299 0.0499 0.0799 0.0983 0.1746 0.2991 0.4990

0.0150 0.0299 0.0499 0.0799 0.0983 0.1746 0.2991 0.4990

0.0150 0.0299 0.0499 0.0799 0.0983 0.1746 0.2991 0.4990

0.0150 0.0299 0.0499 0.0799 0.0983 0.1746 0.2991 0.4990

0.0150 0.0299 0.0499 0.0799 0.0983 0.1746 0.2991 0.4990

Cp,//(J Æ K1 Æ mol1) T = 278.15 K

T = 283.15 K

T = 288.15 K

T = 293.15 K

T = 298.15 K

61.1 ± 4.6 69.4 ± 2.3 79.6 ± 1.4 87.69 ± 0.97 90.86 ± 0.81 100.27 ± 0.53 108.61 ± 0.35 114.83 ± 0.32

76.9 ± 4.0 85.5 ± 2.0 95.5 ± 1.3 103.30 ± 0.81 106.41 ± 0.68 115.14 ± 0.47 123.23 ± 0.35 128.44 ± 0.32

86.6 ± 4.3 97.3 ± 2.2 106.8 ± 1.3 114.56 ± 0.77 117.79 ± 0.65 126.10 ± 0.44 133.52 ± 0.33 138.69 ± 0.30

95.7 ± 4.9 105.6 ± 2.5 114.8 ± 1.5 122.77 ± 0.87 126.08 ± 0.73 134.28 ± 0.48 141.13 ± 0.34 146.49 ± 0.30

103.3 ± 5.9 112.5 ± 3.0 121.0 ± 1.8 128.7 ± 1.1 132.15 ± 0.93 140.12 ± 0.58 146.57 ± 0.35 152.10 ± 0.30

T = 303.15 K

T = 308.15 K

T = 313.15 K

T = 318.15 K

T = 323.15 K

108.2 ± 5.8 118.7 ± 2.9 126.7 ± 1.8 133.7 ± 1.0 137.04 ± 0.84 144.79 ± 0.53 150.92 ± 0.35 156.72 ± 0.30

112.8 ± 6.2 122.8 ± 3.1 130.8 ± 1.9 137.6 ± 1.0 140.88 ± 0.87 148.47 ± 0.55 154.41 ± 0.37 160.33 ± 0.31

115.7 ± 6.3 126.5 ± 3.2 134.4 ± 1.9 140.6 ± 1.1 144.02 ± 0.90 151.46 ± 0.56 157.34 ± 0.38 163.37 ± 0.31

118 ± 6 129.3 ± 3.1 136.4 ± 1.9 142.7 ± 1.1 146.01 ± 0.93 153.46 ± 0.57 159.14 ± 0.39 165.47 ± 0.32

120.5 ± 6.5 131.5 ± 3.3 138.5 ± 2.0 144.5 ± 1.2 147.9 ± 1.0 155.16 ± 0.62 160.55 ± 0.42 167.22 ± 0.34

T = 328.15 K

T = 333.15 K

T = 338.15 K

T = 343.15 K

T = 348.15 K

122.7 ± 6.5 132.1 ± 3.3 139.2 ± 2.0 145.6 ± 1.3 149.0 ± 1.1 156.35 ± 0.66 161.77 ± 0.43 168.45 ± 0.34

125.1 ± 6.8 133.8 ± 3.4 140.8 ± 2.1 146.8 ± 1.4 150.1 ± 1.1 157.37 ± 0.69 162.71 ± 0.46 169.55 ± 0.37

127.2 ± 6.8 134.8 ± 3.4 141.8 ± 2.1 147.6 ± 1.4 150.8 ± 1.2 158.02 ± 0.72 163.29 ± 0.45 170.31 ± 0.35

128.9 ± 7.1 135.1 ± 3.6 142.1 ± 2.2 147.9 ± 1.4 151.0 ± 1.2 158.21 ± 0.72 163.49 ± 0.47 170.73 ± 0.37

129.4 ± 7.4 134.8 ± 3.7 142.0 ± 2.3 148.0 ± 1.5 151.0 ± 1.2 158.21 ± 0.75 163.54 ± 0.48 170.79 ± 0.37

T = 353.15 K

T = 358.15 K

T = 363.15 K

T = 368.15 K

T = 373.15 K

128.7 ± 7.7 134.5 ± 3.9 142.0 ± 2.4 147.9 ± 1.6 150.9 ± 1.3 158.07 ± 0.78 163.40 ± 0.51 170.75 ± 0.40

130.3 ± 8.0 135.1 ± 4.0 142.1 ± 2.5 147.8 ± 1.6 150.6 ± 1.3 157.87 ± 0.80 163.41 ± 0.54 170.66 ± 0.42

131.1 ± 8.5 134.7 ± 4.3 141.8 ± 2.6 147.5 ± 1.7 150.3 ± 1.4 157.62 ± 0.83 163.22 ± 0.56 170.50 ± 0.44

131.3 ± 9.0 133.7 ± 4.5 140.8 ± 2.7 146.7 ± 1.7 149.4 ± 1.4 156.75 ± 0.88 162.52 ± 0.58 169.86 ± 0.45

131.0 ± 9.1 133.3 ± 4.6 140.0 ± 2.8 146.0 ± 1.8 148.8 ± 1.5 156.08 ± 0.88 161.79 ± 0.59 169.18 ± 0.45

T = 378.15 K

T = 383.15 K

T = 388.15 K

T = 393.15 K

128.3 ± 9.5 132.2 ± 4.8 139.1 ± 2.9 144.7 ± 1.8 147.7 ± 1.5 155.03 ± 0.91 160.79 ± 0.58 168.22 ± 0.43

125.7 ± 9.9 131.6 ± 5.0 138.0 ± 3.0 143.2 ± 2.0 146.7 ± 1.6 154.05 ± 0.95 159.80 ± 0.60 167.14 ± 0.44

122 ± 11 130.9 ± 5.5 137.0 ± 3.3 141.4 ± 2.1 145.5 ± 1.7 152.76 ± 1.02 158.43 ± 0.64 165.69 ± 0.45

117 ± 13 129.4 ± 6.5 135.5 ± 3.9 139.1 ± 2.3 143.8 ± 1.9 151.17 ± 1.09 156.74 ± 0.67 164.02 ± 0.46

The ± uncertainties are from propagation of uncertainties as described in reference [9]. a Average experimental values of cp,s can be obtained by equation (2) with m, cp,w from reference [3], and M2 = 111.5278 g Æ mol1. b Molality of alanine, with stoichiometric molality ratio r = m(HAla)/m{HCl} = 0.998.

The differences DH = {DrHm(us)  DrHm(lit)} between our values of DrHm for reaction (5) and those from the literature are in the range DH = (0.4 to 0.9) kJ Æ mol1, with an average difference DH = 0.5 kJ Æ mol1. The differences between our DrHm for reaction (6) and values from the

literature are in the range DH = (2.6 to 10.1) kJ Æ mol1, with an average difference DH = 0.2 kJ Æ mol1. Figure 9 shows pQa(T, m) for reactions (5) and (6) and values from the literature [37–43,47,49]. Our values of pQa for reaction (5) differ from the literature

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TABLE 7 Observed apparent molar heat capacities Cp,/ for aqueous alanine plus (nearly) equimolal NaOH at p = 0.35 MPaa,b m/(mol Æ kg1)b

0.0075 0.0150 0.0301 0.0503 0.0851 0.1747 0.3494 0.6594

0.0075 0.0150 0.0301 0.0503 0.0851 0.1747 0.3494 0.6594

0.0075 0.0150 0.0301 0.0503 0.0851 0.1747 0.3494 0.6594

0.0075 0.0150 0.0301 0.0503 0.0851 0.1747 0.3494 0.6594

0.0075 0.0150 0.0301 0.0503 0.0851 0.1747 0.3494 0.6594

Cp,//(J Æ K1 Æ mol1) T = 278.15 K

T = 283.15 K

T = 288.15 K

T = 293.15 K

T = 298.15 K

1 ± 87 52 ± 44 55 ± 22 56 ± 13 52.6 ± 7.4 60.9 ± 3.7 75.7 ± 1.9 102.1 ± 1.1

29 ± 83 81 ± 42 81 ± 21 82 ± 13 78.2 ± 7.1 86.4 ± 3.5 99.5 ± 1.8 122.3 ± 1.0

56 ± 78 102 ± 39 102 ± 20 103 ± 12 99.5 ± 6.7 107.1 ± 3.3 118.6 ± 1.7 138.6 ± 1.0

79 ± 73 119 ± 37 118 ± 18 120 ± 11 116.8 ± 6.4 123.7 ± 3.2 134.2 ± 1.6 152.1 ± 0.9

98 ± 68 133 ± 34 132 ± 17 133 ± 10 130.9 ± 6.1 137.2 ± 3.0 147.0 ± 1.6 163.3 ± 0.9

T = 303.15 K

T = 308.15 K

T = 313.15 K

T = 318.15 K

T = 323.15 K

112 ± 64 144 ± 33 142 ± 16 144.1 ± 9.8 142.3 ± 5.9 148.4 ± 2.9 157.8 ± 1.5 172.7 ± 0.9

128 ± 60 155 ± 31 152 ± 15 153.1 ± 9.3 151.6 ± 5.7 157.6 ± 2.8 166.6 ± 1.5 180.6 ± 0.8

140 ± 57 162 ± 29 160 ± 15 161.2 ± 8.8 159.8 ± 5.4 165.7 ± 2.7 174.2 ± 1.4 187.4 ± 0.8

151 ± 54 169 ± 28 166 ± 14 167.7 ± 8.3 166.6 ± 5.2 172.2 ± 2.6 180.5 ± 1.4 193.1 ± 0.8

162 ± 51 174 ± 26 171 ± 13 173.1 ± 7.9 172.4 ± 5.0 177.7 ± 2.5 185.7 ± 1.3 198.0 ± 0.8

T = 328.15 K

T = 333.15 K

T = 338.15 K

T = 343.15 K

T = 348.15 K

169 ± 48 178 ± 25 175 ± 12 178.0 ± 7.4 177.1 ± 4.7 182.4 ± 2.4 190.2 ± 1.2 202.1 ± 0.7

179 ± 46 182 ± 23 179 ± 12 181.8 ± 6.9 181.2 ± 4.5 186.3 ± 2.2 194.0 ± 1.2 205.7 ± 0.7

185 ± 43 184 ± 21 183 ± 11 185.2 ± 6.5 184.5 ± 4.2 189.7 ± 2.1 197.1 ± 1.1 208.7 ± 0.7

187 ± 40 186 ± 20 185 ± 10 187.8 ± 6.1 187.0 ± 3.9 192.2 ± 2.0 199.6 ± 1.1 211.0 ± 0.6

190 ± 37 187 ± 19 186.3 ± 9.4 189.2 ± 5.7 188.9 ± 3.7 194.3 ± 1.9 201.5 ± 1.0 213.0 ± 0.6

T = 353.15 K

T = 358.15 K

T = 363.15 K

T = 368.15 K

T = 373.15 K

188 ± 34 188 ± 17 187.2 ± 8.7 190.7 ± 5.3 190.3 ± 3.5 195.8 ± 1.7 203.1 ± 0.9 214.5 ± 0.6

188 ± 31 188 ± 16 187.7 ± 8.0 191.0 ± 4.9 191.0 ± 3.2 196.9 ± 1.6 204.2 ± 0.9 215.7 ± 0.5

186 ± 28 187 ± 15 187.6 ± 7.5 191.0 ± 4.5 191.3 ± 3.0 197.5 ± 1.5 204.9 ± 0.8 216.4 ± 0.5

183 ± 25 186 ± 14 186.6 ± 7.0 190.7 ± 4.2 191.1 ± 2.7 197.6 ± 1.4 205.2 ± 0.8 216.8 ± 0.5

182 ± 23 184 ± 13 185.6 ± 6.3 189.3 ± 3.8 190.4 ± 2.5 197.3 ± 1.3 205.0 ± 0.7 216.9 ± 0.4

T = 378.15 K

T = 383.15 K

T = 388.15 K

T = 393.15 K

180 ± 20 182 ± 12 183.7 ± 6.0 188.1 ± 3.6 189.2 ± 2.4 196.4 ± 1.2 204.6 ± 0.7 216.6 ± 0.4

182 ± 18 181 ± 11 181.7 ± 5.6 185.7 ± 3.4 187.7 ± 2.1 195.3 ± 1.1 204.0 ± 0.6 216.1 ± 0.4

181 ± 16 178 ± 11 179.1 ± 5.4 183.2 ± 3.3 186.0 ± 1.9 193.8 ± 1.0 203.0 ± 0.6 215.3 ± 0.4

185 ± 20 175 ± 13 175.5 ± 6.7 180.5 ± 4.0 183.9 ± 1.7 192.2 ± 0.9 201.5 ± 0.5 214.5 ± 0.4

The ± uncertainties are from propagation of uncertainties as described in reference [9]. a Average experimental values of cp,s can be obtained by equation (2) with m, cp,w from reference [3], and M2 = 97.0487 g Æ mol1. b Molality of alanine, with stoichiometric molality ratio r = m(HAla)/m{NaOH} = 1.010.

values by DpQ = {pQa(us)  pQa(lit)} = (0.19 to 0.01), with an average difference DpQ = 0.02. Our values of pQa for reaction (6) differ from the literature values by DpQ = (0.92 to 0.45), with an average difference DpQ = 0.08.

Figure 10 shows DrSm(T, m) for reactions (5) and (6) together with values from the literature [38,41,44–47]. The differences DS = {DrSm(us)  DrSm(lit)} between our values of DrSm for reaction (5) and those from the literature are in the range DS = (1.1 to 3.3) J Æ K1 Æ mol1, with an

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947

TABLE 8 Regression parameters of equation (4) for apparent molar heat capacities Cp,/ of {HAla±(aq)}, {HAla±(aq) + HCl(aq)}, {HAla±(aq) + NaOH(aq)}, {H2Ala+Cl(aq)}, and {Na+Ala(aq)} ci

HAla±(aq) observed, w = 0 (table 5)

{HAla±(aq) + HCl(aq)} observed, w = 1 (table 6)

{HAla±(aq) + NaOH(aq)} observed, w = 1 (table 7)

H2Ala+Cl(aq) iteration, w = 1 (see text)

Na+Ala(aq) iteration, w = 1 (see text)

103 Æ c0 c1 c2 103 Æ c3 c4 103 Æ c5 c6 103 Æ c7 c8 103 Æ c9 106 Æ c10 Da Maximum m

120.39824 ± 0.00003 123.25 ± 0.03

1254.0291 ± 0.0001 800.1 ± 0.1 931.2 ± 0.1 1215.2 ± 0.2 2.341 ± 0.001 1.571 ± 0.001 3775.0347 ± 0.0001 331.81555 ± 0.00001 8.0559678 ± 0.0000002 10.181575 ± 0.000001 5.420285 ± 0.000001 ±1.3 0.5

224.7715 ± 0.0001 173.5 ± 0.1

238.5921 ± 0.0001

255.14325 ± 0.00003 420.4 ± 0.1

530.0 ± 0.1

51.6 ± 0.1

239.4 ± 0.1 0.3756 ± 0.0001 0.8011 ± 0.0002 241.7326 ± 0.0001 29.55879 ± 0.00001 0.3340304 ± 0.0000002 0.207418 ± 0.000001 ±0.4 1.0

0.140 ± 0.001 451.5829 ± 0.0001 55.16335 ± 0.00001 0.6251736 ± 0.0000002 0.390141 ± 0.000001

505.5137 ± 0.0001 59.22882 ± 0.00001 0.7228415 ± 0.0000003 0.462561 ± 0.000001

±1.1 0.7

1295.4 ± 0.1 0.7004 ± 0.0002 2.2530 ± 0.0004 518.7067 ± 0.0001 62.75584 ± 0.00001 0.7249008 ± 0.0000002 0.455970 ± 0.000001

±0.9 0.5

±0.8 0.7

The ± values are chosen to reproduce the generated Cp,/ values to within ±0.1 J Æ K1 Æ mol1 at 278.15 6 T/K 6 393.15 and at m 6 the maximum. a Standard deviations of the regressions.

FIGURE 2. Apparent molar heat capacity Cp,/ of zwitterionic alanine HAla±(aq) plotted against temperature T and molality m. Surface generated from equation (4) with parameters in column 2 of table 8; s, experimental values from table 5; d, T = 298.15 K, m = 0 mol Æ kg1, reference [32]; j, T = 298.15 K, 0 6 m/mol Æ kg1 6 1.0, references [29– 31,33]; m, 278.15 6 T/K 6 373.15, m = 0 mol Æ kg1, references [35,36]; r, 288.15 6 T/K 6 373, 0.08 6 m/mol Æ kg1 6 0.95, references [28,34].

FIGURE 3. Apparent molar heat capacities Cp,/ of alaninium hydrochloride H2Ala+Cl(aq) (solid surface and s) and of [Cp,/{HAla±(aq)} + Cp,/{HCl(aq)}] (wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surface generated from equation (4) with regression parameters from column 5 of table 8; s, calculated Youngs rule values; wire frame generated by adding Cp,/(T, m) for HCl(aq) [3] to Cp,/(T, m) for alanine (aq).

average difference DS = 1.7 J Æ K1 Æ mol1. The differences between our DrSm results for reaction (6) and those from the literature are in the range DS = (6.9 to 10.7) J Æ K1 Æ mol1, with an average difference DS = 1.1 J Æ K1 Æ mol1. We have also calculated values of DrVm(T, m) for reactions (5) and (6) using our values of V/(i) for HAla±(aq), H2Ala+Cl(aq), and Na+Ala(aq), values of V/ for HCl(aq) from Sharygin and Wood [50], and values of V/

for NaCl(aq) and NaOH(aq) from Sorenson et al. [3]. These results are shown in figure 11. We know of no previously reported values of DrVm for reaction (5) or (6) in the ranges of T and m of our results. By extrapolation of our results for DrVm, DrCp,m, DrHm, DrSm, and pQa to m* = 0, we obtain the standard state values Dr V m ; Dr C p;m ; Dr H m ; Dr S m ; and pK a for reactions (5) and (6) given in tables 9 and 10, respectively. We suggest that, since our experiments generally cover broader ranges

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S.P. Ziemer et al. / J. Chem. Thermodynamics 38 (2006) 939–951

FIGURE 4. Apparent molar heat capacities Cp,/ of sodium alaninate Na+Ala(aq) (solid surface and s) and of [Cp,/{HAla±(aq)} + Cp,/ {NaOH(aq)}] (wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surface generated from equation (4) with regression parameters from column 6 of table 8; s, calculated Youngs rule values; wire frame generated by adding Cp,/(T, m) for Na+(aq) [3] to Cp,/(T, m) for alanine(aq).

FIGURE 5. Apparent molar volume V/(i) of alaninium hydrochloride H2Ala+Cl(aq) (solid surface and s) and of [Cp,/{HAla±(aq)} + Cp,/{HCl(aq)}] (wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surface generated from equation (3) with regression parameters from column 5 of table 4; s, calculated Youngs rule values; wire frame generated by adding V/(T, m) for HCl(aq) [50] to V/(T, m) for alanine(aq); d, T = 298.15 K, 0.01 6 m/mol Æ kg1 6 0.5, reference [38].

of T and m than those from the literature, and since our analysis of results include Youngs Rule estimates of species contributions to the observed V/ and Cp,/, our values

FIGURE 6. Apparent molar volume V/(i) of sodium alaninate Na+Ala(aq) (solid surface and s) and of [Cp,/{HAla±(aq)} + Cp,/{NaCl(aq)}] (wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surface generated from equation (3) with regression parameters from column 6 of table 4; s, calculated Youngs rule values; wire frame generated by adding Cp,/(T, m) for Na+(aq) [3] to Cp,/(T, m) for alanine(aq); d, T = 298.15 K, 0.01 6 m/mol Æ kg1 6 0.5, reference [39].

FIGURE 7. Heat capacity change DrCp,m for reactions (5) and (6), respectively, plotted against temperature T and molality m. Lower surface DrCp,m for reaction (5), this work; d, T = 298.1 K, m = 0 mol Æ kg1, reference [46]. Upper surface DrCp,m for reaction (6), this work; s, 298.15 6 T/K 6 348.15, m = 0 mol Æ kg1, references [46,47].

of DrVm, DrCp,m, DrHm, DrSm, and pQa are to be preferred at all m from (0 to 1) mol Æ kg1 and T from (278.15 to 393.15) K. Interesting comparisons are possible between the properties V/ and Cp,/ for the aqueous zwitterionic, cationic,

S.P. Ziemer et al. / J. Chem. Thermodynamics 38 (2006) 939–951

FIGURE 8. Enthalpy change DrHm for reactions (5) and (6), respectively, plotted against temperature T and molality m. Lower surface, DrHm for reaction (5), this work; d, T = 298.15 K, m = 0 mol Æ kg1, references [37,42,44–46]; m, 283.15 6 T/K 6 323.15, m = 0 mol Æ kg1, references [38,41,43]. Upper surface DrHm for reaction (6), this work; s, T = 298.15 K, m = 0 mol Æ kg1, references [42,44]; n, 285.65 6 T/K 6 348.15, m = 0 mol Æ kg1, references [41,43,47].

949

FIGURE 10. Entropy changes DrSm for reactions (5) and (6), respectively, plotted against temperature T and molality m. Upper surface, DrSm for reaction (5), this work; d, T = 298.15 K, m = 0 mol Æ kg1, references [44–46]; m, 283.15 6 T/K 6 323.15, m = 0 mol Æ kg1, references [38,41]. Lower surface (DrSm 40 J Æ K1 Æ mol1) for reaction (6), this work; s, (DrSm 40 J Æ K1 Æ mol1), T = 298.15 K, m = 0 mol Æ kg1 references [44–46]; n, (DrSm 40 J Æ K1 Æ mol1), 274.15 6 T/K 6 348.15, m = 0 mol Æ kg1, references [41,47].

FIGURE 11. Volume changes DrVm for reactions (5) and (6), respectively, plotted against temperature T and molality m. Lower surface, DrVm for reaction (5), this work. Upper surface, DrVm for reaction (6), this work. FIGURE 9. Equilibrium molality quotient pQa for reactions (5) and (6), respectively, plotted against temperature T and molality m. Lower surface, pQa for reaction (5), this work; d, T = 298.15 K, m = 0 mol Æ kg1, references [37,39,40]; m, 273.15 6 T/K 6 323.15, m = 0 mol Æ kg1, references [38,41,43,49]; r, 293.15 6 T/K 6 298.15, 0.0 6 m/mol Æ kg1 6 0.5, reference [42]. Upper surface pQa for reaction (6), this work; s, T = 298.15 K, m = 0 mol Æ kg1, references [39,40]; n, 273.15 6 T/ K 6 348.15, m = 0 mol Æ kg1, references [41,43,47,49]; r, 293.15 6 T/ K 6 298.15, 0.0 6 m/mol Æ kg1 6 0.5, reference [42].

and anionic species of alanine, glycine and serine. The differences DY(a-g,species) = {Y/(ala)  Y/(gly)} are as follows: DV(a-g,zwitterion) = (17.5 ± 0.4) cm3 Æ mol1, DV(a-g, cation) = (19.2 ± 1.1) cm3 Æ mol1, and DV(a-g, anion) = (15.5 ± 1.7) cm3 Æ mol1; DC(a-g,zwitterion) = (99 ± 7) J Æ K1 Æ mol1, DC(a-g,cation) = (93 ± 6) J Æ K1 Æ mol1, and DC(a-g,anion) = (87 ± 5) J Æ K1 Æ mol1. These differences

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S.P. Ziemer et al. / J. Chem. Thermodynamics 38 (2006) 939–951

TABLE 9 ‘‘Best’’ standard thermodynamic values for the first proton dissociation from aqueous protonated alanine, reaction (5), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K

3

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 388.15 393.15 a

Dr C p;m

Dr V m 1

1

Dr S m

Dr H m 1

cm Æ mol

JÆK

Æ mol

7.41 ± 0.27 7.34 ± 0.27 7.27 ± 0.28 7.21 ± 0.28 7.17 ± 0.29 7.14 ± 0.29 7.14 ± 0.29 7.16 ± 0.29 7.21 ± 0.29 7.29 ± 0.29 7.39 ± 0.29 7.52 ± 0.29 7.68 ± 0.29 7.87 ± 0.28 8.09 ± 0.28 8.35 ± 0.28 8.64 ± 0.28 8.97 ± 0.27 9.34 ± 0.27 9.74 ± 0.26 10.19 ± 0.26 10.69 ± 0.26 11.23 ± 0.25 11.83 ± 0.25

167.9 ± 1.2 156.8 ± 1.2 147.2 ± 1.2 138.7 ± 1.2 131.4 ± 1.2 124.9 ± 1.2 119.3 ± 1.2 114.5 ± 1.2 110.3 ± 1.2 106.7 ± 1.2 103.6 ± 1.2 101.0 ± 1.2 98.8 ± 1.2 96.9 ± 1.2 95.4 ± 1.2 94.2 ± 1.2 93.2 ± 1.2 92.5 ± 1.2 92.1 ± 1.2 91.8 ± 1.2 91.7 ± 1.2 91.8 ± 1.2 92.1 ± 1.2 92.5 ± 1.3

1

kJ Æ mol

J Æ K1 Æ mol1

5.87 ± 0.29 5.06 ± 0.29 4.30 ± 0.29 3.59 ± 0.29 2.91 ± 0.29 2.27 ± 0.29 1.66 ± 0.29 1.08 ± 0.29 0.51 ± 0.29 0.03 ± 0.29 0.55 ± 0.29 1.07 ± 0.29 1.56 ± 0.29 2.05 ± 0.29 2.53 ± 0.29 3.01 ± 0.29 3.48 ± 0.29 3.94 ± 0.29 4.40 ± 0.29 4.86 ± 0.29 5.32 ± 0.29 5.78 ± 0.29 6.24 ± 0.29 6.70 ± 0.29

24.67 ± 0.96 27.56 ± 0.97 30.22 ± 0.97 32.68 ± 0.97 34.96 ± 0.97 37.09 ± 0.97 39.09 ± 0.97 40.97 ± 0.97 42.75 ± 0.97 44.44 ± 0.97 46.05 ± 0.97 47.60 ± 0.97 49.08 ± 0.97 50.52 ± 0.97 51.91 ± 0.97 53.26 ± 0.97 54.58 ± 0.97 55.87 ± 0.97 57.13 ± 0.97 58.37 ± 0.98 59.59 ± 0.98 60.80 ± 0.98 61.99 ± 0.98 63.17 ± 0.98

pKa 2.3904 ± 0.0056 2.3723 ± 0.0051 2.3573 ± 0.0047 2.3451 ± 0.0044 2.3354 ± 0.0043 2.3279 ± 0.0044 2.3224 ± 0.0046 2.3187 ± 0.0050 2.3166 ± 0.0054 2.3160 ± 0.0058 2.3167 ± 0.0063 2.3187 ± 0.0068 2.3217 ± 0.0074 2.3258 ± 0.0079 2.3308 ± 0.0084 2.3367 ± 0.0090 2.3434 ± 0.0095 2.351 ± 0.010 2.359 ± 0.011 2.368 ± 0.011 2.377 ± 0.011 2.387 ± 0.012 2.398 ± 0.012 2.409 ± 0.013

The ± values are propagated uncertainties.

TABLE 10 ‘‘Best’’ standard thermodynamic values for the second proton dissociation from aqueous zwitterionic alanine, reaction (6), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K

278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 388.15 393.15 a

Dr V m

Dr C p;m

Dr H m

Dr S m

cm3 Æ mol1

J Æ K1 Æ mol1

kJ Æ mol1

J Æ K1 Æ mol1

0.55 ± 0.10 0.81 ± 0.10 0.90 ± 0.10 0.95 ± 0.10 1.00 ± 0.10 1.06 ± 0.10 1.11 ± 0.10 1.17 ± 0.10 1.23 ± 0.11 1.27 ± 0.11 1.31 ± 0.11 1.34 ± 0.11 1.36 ± 0.11 1.36 ± 0.11 1.34 ± 0.11 1.31 ± 0.11 1.27 ± 0.11 1.22 ± 0.11 1.15 ± 0.11 1.07 ± 0.11 0.98 ± 0.11 0.88 ± 0.11 0.79 ± 0.11 0.69 ± 0.11

59.8 ± 2.5 62.5 ± 2.4 62.4 ± 2.4 61.6 ± 2.4 60.6 ± 2.4 59.6 ± 2.5 58.6 ± 2.5 57.6 ± 2.5 56.6 ± 2.6 55.6 ± 2.6 54.6 ± 2.7 53.6 ± 2.7 52.6 ± 2.7 51.8 ± 2.7 50.9 ± 2.7 50.2 ± 2.7 49.7 ± 2.7 49.3 ± 2.7 49.0 ± 2.7 49.1 ± 2.7 49.3 ± 2.8 49.8 ± 2.8 50.6 ± 2.8 51.6 ± 2.9

46.88 ± 0.47 46.57 ± 0.47 46.26 ± 0.46 45.95 ± 0.46 45.65 ± 0.46 45.35 ± 0.46 45.05 ± 0.46 44.76 ± 0.46 44.48 ± 0.46 44.19 ± 0.46 43.92 ± 0.47 43.65 ± 0.47 43.38 ± 0.47 43.12 ± 0.48 42.87 ± 0.48 42.61 ± 0.49 42.36 ± 0.49 42.12 ± 0.50 41.87 ± 0.51 41.63 ± 0.52 41.38 ± 0.52 41.13 ± 0.53 40.88 ± 0.54 40.63 ± 0.55

31.5 ± 2.2 32.5 ± 2.2 33.6 ± 2.2 34.7 ± 2.2 35.7 ± 2.2 36.7 ± 2.2 37.7 ± 2.2 38.6 ± 2.2 39.5 ± 2.2 40.4 ± 2.2 41.3 ± 2.2 42.1 ± 2.2 42.9 ± 2.2 43.6 ± 2.2 44.4 ± 2.2 45.1 ± 2.2 45.8 ± 2.2 46.5 ± 2.2 47.2 ± 2.2 47.8 ± 2.2 48.5 ± 2.2 49.1 ± 2.2 49.8 ± 2.2 50.4 ± 2.2

The ± values are propagated uncertainties.

pKa 10.445 ± 0.080 10.290 ± 0.080 10.142 ± 0.080 9.999 ± 0.080 9.862 ± 0.080 9.731 ± 0.080 9.604 ± 0.080 9.483 ± 0.080 9.366 ± 0.080 9.253 ± 0.080 9.145 ± 0.080 9.040 ± 0.080 8.939 ± 0.080 8.842 ± 0.080 8.748 ± 0.081 8.657 ± 0.081 8.569 ± 0.081 8.484 ± 0.081 8.402 ± 0.081 8.323 ± 0.081 8.246 ± 0.081 8.172 ± 0.081 8.100 ± 0.082 8.030 ± 0.082

S.P. Ziemer et al. / J. Chem. Thermodynamics 38 (2006) 939–951

are consistent with group contributions for replacing a hydrogen atom with a methyl group on an aqueous solute for the 1-alcohols [51,52]. These differences are relatively unaffected by temperature at 278.15 6 T/K 6 393.15. Similarly, we obtain DY(a-s,species) = {Y/(ala)  Y/(ser)} as follows: DV(a-s,zwitterion) = (0.6 ± 0.4) cm3 Æ mol1, DV(a-s,cation) = (0.1 ± 0.7) cm3 Æ mol1, and DV(a-s, anion) = (0.7 ± 1.0) cm3 Æ mol1; DC(a-s,zwitterion) = (13 ± 12) J Æ K1 Æ mol1,DC(a-s,cation) = (3 ± 13) J Æ K1 Æ mol1, and DC(a-s, anion) = (9 ± 10) J Æ K1 Æ mol1. The substitution of a hydroxyl group for a hydrogen atom is much more sensitive to temperature than the substitution of a methyl group for a hydrogen atom. This is undoubtedly the result of the effect of temperature on the hydrogen bonding structure of water and of the hydrogen bonding of water with the hydroxy group. Further investigation of this phenomenon is currently underway in our laboratory with other solutes. Similar comparisons of V/ and Cp,/ for the aqueous zwitterionic and anionic species of alanine with the structurally similar species 1-propanoic acid (Hp) and with 1-propanoate ion (p) [53] are also informative. The differences DY(a,species-Hp or p) = {Y/(ala)  Y/(Hp or p)} are as follows: DV(a,zwitterion-Hp) = (9.7 ± 2.8) cm3 Æ mol1, DV(a,zwitterion-p) = (15.7 ± 0.7) cm3 Æ mol1, DV(a,anionp) = (5.7 ± 0.7) cm3 Æ mol1;DC(a,zwitterion-Hp) = (91 ± 15) J Æ K1 Æ mol1, DC(a,zwitterion-p) = (26 ± 12) J Æ K1 Æ mol1, and DC(a,anion-p) = (15 ± 20). Again, these differences are consistent with group contributions for replacing a hydrogen atom with an amine group on an aqueous solute for alkyl amines [52]. As noted above, further investigation and discussion of this phenomenon is currently underway in our laboratory. References [1] J.J. Jardine, T.G. Call, B.A. Patterson, M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 1419–1440. [2] J.L. Price, J.J. Jardine, T.G. Call, B.A. Patterson, M.L. OrigliaLuster, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 195–198. [3] E.C. Sorenson, J.L. Price, B.R. McRae, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 529–553. [4] J.L Price, E.C. Sorenson, E.D. Merkley, B.R. McRae, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 1425–1467. [5] S.P. Ziemer, T.L. Niederhauser, E.D. Merkley, J.L. Price, E.C. Sorenson, B.R. McRae, M.L. Origlia-Luster, B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. (in press), doi:10.1016/j.jct.2005.06. 017. [6] S.P. Ziemer, T.L. Niederhauser, E.D. Merkley, J.L. Price, E.C. Sorenson, B.R. McRae, B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. (in press), doi:10.1016/j.jct.2005.07.019. [7] T.D. Ford, T.G. Call, M.L. Origlia, M.A. Stark, E.M. Woolley, J. Chem. Thermodyn. 32 (2000) 499–516. [8] T.D. Ford, T.G. Call, J.J. Jardine, M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 287–304. [9] T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 325–330. [10] D.G. Archer, P. Wang, J Phys. Chem. Ref. Data 19 (1990) 371–411. [11] T. Ogawa, K. Mizutani, M. Yasuda, Bull. Chem. Soc. Jpn. 57 (1984) 2064–2068.

951

[12] A.A. Zamyatnin, Prog. Biophys. Mol. Biol. 24 (1972) 109–123. [13] F.J. Millero, A. Lo Surdo, C. Shin, J. Phys. Chem. 82 (1978) 784–792. [14] Q. Liu, X. Hu, R. Lin, W. Sang, S. Li, J. Chem. Eng. Data 46 (2001) 522–525. [15] X. Ren, X. Hu, R. Lin, H. Zong, J. Chem. Eng. Data 43 (1998) 700– 702. [16] J. Daniel, E.J. Cohn, J. Am. Chem. Soc. 58 (1936) 415–423. [17] A.K. Mishra, J.C. Ahluwalia, J. Phys. Chem. 88 (1984) 86–92. [18] R.K. Wadi, R.K. Goyal, J. Solution Chem. 21 (1992) 163–170. [19] M. Iqbal, T. Ahmed, Indian J. Chem. A 32 (1993) 119–123. [20] T.V. Chalikian, A.P. Sarvazyan, T. Funck, C.A. Cain, K.J. Breslauer, J. Phys. Chem. 98 (1994) 321–328. [21] S. Cabani, G. Conti, E. Matteoli, M. Tine, J. Chem. Soc., Faraday Trans. 1 (77) (1981) 2385–2394. [22] D.P. Kharakoz, Biophys. Chem. 34 (1989) 115–125. [23] R.G. Clarke, P.R. Tremaine, J. Phys. Chem. B 103 (1999) 5131–5144. [24] M. Kikuchi, M. Sakurai, K. Nitta, J. Chem. Eng. Data 40 (1995) 935–942. [25] J.-L. Shen, Z.-F. Li, B.-H. Wang, Y.-M. Zhang, J. Chem. Thermodyn. 32 (2000) 805–819. [26] Z. Yan, J. Wang, W. Liu, J. Liu, Thermochim. Acta 334 (1999) 17–27. [27] E.F. Cohn, T.L. McMeekin, J.T. Edsall, M.H. Blanchard, J. Am. Chem. Soc. 56 (1934) 784–794. [28] A.W. Hakin, M.M. Duke, S.A. Klassen, R.M. McKay, K.E. Preuss, Can. J. Chem. 72 (1994) 362–368. [29] J.C. Ahluwalia, C. Ostiguy, G. Perron, J.E. Desnoyers, Can. J. Chem. 55 (1977) 3364–3367. [30] G. Dipaola, B. Belleau, Can. J. Chem. 56 (1978) 1827–1831. [31] C. Jolicoeur, J. Boileau, Can. J. Chem. 56 (1978) 2707–2713. [32] C. Jolicoeur, B. Riedl, D. Desrochers, L.L. Lemelin, R. Zamojska, O. Enea, J. Solution Chem. 15 (1986) 109–128. [33] J.T. Edsall, J. Am. Chem. Soc. 57 (1935) 1506–1507. [34] R.G. Clarke, L. Hnedkovsky´, P.R. Tremaine, V. Majer, J. Phys. Chem. B 104 (2000) 11781–11793. [35] K.P. Prasad, J.C. Ahluwalia, J. Solution Chem. 5 (1976) 491–507. [36] G.I. Makhatadze, P.L. Privalov, J. Mol. Biol. 213 (1990) 375–384. [37] J.J. Christensen, R.M. Izatt, L.D. Hansen, J. Am. Chem. Soc. 89 (1967) 213–222. [38] J.J. Christensen, J.L. Oscarson, R.M. Izatt, J. Am. Chem. Soc. 90 (1968) 5949–5953. [39] L. Lepori, V. Mollica, Z. Phys. Chem. Neue Fol. 123 (1980) 51–66. [40] W. Gerhartz, Exec. Ed. Ullmanns Encyclopedia of Industrial Chemistry, vol. A2, fifth ed., VCH, Verlagsgesellschaft mbH, Weinheim, Germany, 1985, pp. 62–63. [41] P.K. Smith, A.C. Taylor, E.R. Smith, J. Biol. Chem. 122 (1937) 109– 123. [42] A.E. Martell, R.M. SmithCritical Stability Constants, vol. 1, Plenum Press, New York, 1974, 1–5, 9, 10, 35, 36, 58, 69. [43] L.F. Nims, P.K. Smith, J. Biol. Chem. 101 (1933) 401–412. [44] F. Rodante, F. Fantauzzi, Thermochim. Acta 144 (1989) 75–81. [45] J.F. Coetzee, C.D. Ritchie (Eds.), Solute–Solvent Interactions, Marcel Dekker, New York, 1969, pp. 16–17. [46] D.H. Everett, W.F.K. Wynne-Jones, Trans. Faraday Soc. 35 (1939) 1380–1401. [47] S.E. Gillespie, J.L. Oscarson, R.M. Izatt, P. Wang, J.A.R. Renuncio, C. Pando, J. Solution Chem. 24 (1995) 1219–1247. [48] B.A. Patterson, T.G. Call, J.J. Jardine, M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 1237–1262. [49] H.S. Harned, B.B. Owen, Chem. Rev. 25 (1939) 31–65. [50] A.V. Sharygin, R.H. Wood, J. Chem. Thermodyn. 29 (1997) 125–148. [51] M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 1101–1108. [52] S. Cabani, P. Gianni, V. Mollica, L. Lepori, J. Solution Chem. 10 (1981) 563–595. [53] B.R. McRae, B.A. Patterson, L.A. Origlia-Luster, E.C. Sorenson, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 301–329.

JCT 05-225