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Thermodynamics of proton dissociations from aqueous threonine and isoleucine at temperatures from (278.15 to 393.15) K, molalities from (0.01 to 1.0) mol · kg−1, and at the pressure 0.35 MPa: Apparent molar heat capacities and apparent molar volumes of zwitterionic, protonated cationic, and deprotonated anionic forms
J. Chem. Thermodynamics 39 (2007) 67–87 www.elsevier.com/locate/jct
Thermodynamics of proton dissociations from aqueous threonine and isoleucine at temperatures from (278.15 to 393.15) K, molalities from (0.01 to 1.0) mol Æ kg1, and at the pressure 0.35 MPa: Apparent molar heat capacities and apparent molar volumes of zwitterionic, protonated cationic, and deprotonated anionic forms S.P. Ziemer, E.M. Woolley
*
Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602-5700, USA Received 1 April 2006; received in revised form 26 May 2006; accepted 30 May 2006 Available online 9 June 2006
Abstract We have measured the densities of aqueous solutions of isoleucine, threonine, and equimolal solutions of these two amino acids with HCl and with NaOH at temperatures 278.15 6 T/K 6 368.15, at molalities 0.01 6 m/mol Æ kg1 6 1.0, and at the pressure 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 each of the protonated aqueous cationic amino acids. We used Young’s Rule and integrated these results iteratively to account for the effects of equilibrium speciation and chemical relaxation on V/(T, m) and Cp,/(T, m). This procedure gave parameters for V/(T, m) and Cp,/(T, m) for threoninium and isoleucinium chloride and for sodium threoninate and isoleucinate which modeled our observed results within experimental uncertainties. We report values for DrCp,m, DrHm, pQa, DrSm, and DrVm for the first and second proton dissociations from protonated aqueous threonine and isoleucine as functions of T and m. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Apparent molar volume; Apparent molar heat capacity; Threonine; 2-Amino-3-hydroxybutanoic acid; Isoleucine; 2-Amino-3-methylpentanoic acid; Zwitterion; Threoninium chloride; Isoleucininium chloride; Sodium threoninate; Sodium isoleucinate; Proton dissociations; Acidity; Young’s Rule
1. Introduction Although there is an abundance of work reported in the literature on the properties of aqueous amino acids, the great majority of this work focuses on the unionized zwitterionic forms of the amino acids. The works that include information for the charged species often neglect or approximate the effects of incomplete ionization and equi*
Corresponding author. Tel.: +1 801 422 3669; fax: +1 801 422 0550. E-mail address: [email protected] (E.M. Woolley).
0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.05.013
librium concentrations, introducing significant uncertainties in the values of their thermodynamic properties. In our continuing efforts to enlarge the database of accurate thermodynamic properties of aqueous solutions of L-2-amino acids in their protonated, zwitterionic, and deprotonated forms, taking into account the actual species concentrations, we have studied aqueous threonine and isoleucine. Both are essential amino acids, meaning that they are not produced by humans and must be included in the diet. Threonine is required for the formation of collagen and elastin and is concentrated in the central nervous
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system. Isoleucine is found particularly in muscle tissue and is necessary for formation of hemoglobin. It contributes significantly to the tertiary structure of proteins. We recently reported our results for the apparent molar volumes V/ and apparent molar heat capacities Cp,/ of aqueous proline [1], valine [2], L-2-aminobutanoic acid [2], serine [3], alanine [4], and others. In this paper we report our measured densities and heat capacities of aqueous solutions of threonine and isoleucine in their zwitterionic forms HThr±(aq) and HIle±(aq) and with the addition of equimolal HCl {HThr±(aq) + HCl(aq)} and {HIle±(aq) + HCl(aq)}, and equimolal NaOH {HThr±(aq) + NaOH(aq)} and {HIle±(aq) + NaOH(aq)}. Our analysis applies Young’s Rule and a relaxation heat capacity term to account for the equilibrium molalities of the species H2Thr+Cl(aq), H2Ile+Cl(aq), HThr±(aq), HIle±(aq), Na+Thr(aq), and Na+Ile(aq) present in the solutions containing HCl(aq) and NaOH(aq). Our resulting values of V/(T, m) and Cp,/(T, m) for H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq) allow calculation of the thermodynamic quantities DrCp,m, DrHm, pQa, DrSm, and DrVm for the first and second proton dissociations from protonated aqueous threonine and isoleucine. We have compared all of our results to those found in the literature [5–45].
2. Experimental Crystalline L-threonine {HThr±(c), 2-amino-3-hydroxybutanoic acid, CH3CH(OH)CH(NH2)COOH, molar mass M2 = 119.1197 g Æ mol1, density qc = 1.5 g Æ cm3; Fluka 89179, lot 1132757, 0.995+ mass fraction} and L-isoleucine {HIle±(c), 2-amino-3-methylpentanoic acid, C2H5CH(CH3)CH(NH2)COOH, M2 = 131.1736 g Æ mol1, qc = 1.2 g Æ cm3; Fluka 58879, lot 413187/1, 0.995+ mass fraction} were used as received. The purity of each solute was confirmed by elemental analysis by MHW Laboratories. We prepared aqueous stock solutions of L-threonine and L-isoleucine by mass using distilled, deionized, autoclaved, degassed water. We prepared stock solutions of {HThr±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, ± {HIle (aq) + HCl(aq)}, and {HIle±(aq) + NaOH(aq)} in a similar fashion, using previously standardized stock solutions of HCl(aq) [46] and carbonate-free NaOH(aq) [47] to achieve the nearly equimolal ratios of amino acid + HCl or + NaOH as follows: {m(HThr±)/m(HCl)} = 0.9997, {m(HThr±)/m(NaOH)} = 0.9997, {m(HIle±)/m(HCl)} = 0.997 and {m(HIle±)/m(NaOH)} = 0.998. All other solutions were prepared by mass dilution of these stock solutions with water. Air buoyancy corrections (qair = 0.0010 g Æ cm3) were applied to all weighings.
TABLE 1A Observed densities qs and apparent molar volumes V/ for aqueous zwitterionic threonine at p = 0.35 MPa m
V/
qs 1
3
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
1
cm Æ mol
3
g Æ cm
cm3 Æ mol1
mol Æ kg
g Æ cm
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
T = 278.15 K 1.00036 102 ± 13 1.00146 73.7 ± 1.1 1.00202 80.6 ± 4.3 1.00454 74.80 ± 0.52 1.00862 75.7 ± 1.1 1.01693 75.29 ± 0.42 1.02745 75.24 ± 0.48
T = 283.15 K 1.00006 104 ± 13 1.00118 74.0 ± 1.4 1.00170 81.5 ± 4.0 1.00421 75.43 ± 0.58 1.00825 76.2 ± 1.1 1.01645 75.85 ± 0.42 1.02687 75.73 ± 0.47
T = 288.15 K 0.99945 105 ± 12 1.00055 74.81 ± 0.91 1.00105 82.4 ± 3.7 1.00355 76.02 ± 0.47 1.00754 76.7 ± 1.0 1.01561 76.45 ± 0.41 1.02598 76.20 ± 0.46
T = 298.15 K 0.99739 105 ± 13 0.99848 75.0 ± 1.8 0.99887 84.8 ± 4.0 1.00139 77.00 ± 0.66 1.00530 77.7 ± 1.1 1.01325 77.29 ± 0.42 1.02339 77.09 ± 0.46
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
T = 308.15 K 0.99438 104 ± 13 0.99541 76.9 ± 1.2 0.99580 86.0 ± 4.1 0.99829 77.86 ± 0.52 1.00215 78.5 ± 1.1 1.01005 77.88 ± 0.41 1.01998 77.82 ± 0.47
T = 318.15 K 0.99056 104 ± 12 0.99149 80.29 ± 0.64 0.99198 86.3 ± 3.9 0.99445 78.22 ± 0.42 0.99825 79.0 ± 1.1 1.00610 78.34 ± 0.40 1.01589 78.39 ± 0.47
T = 328.15 K 0.98606 103 ± 10 0.98695 81.22 ± 0.64 0.98747 86.3 ± 3.2 0.98992 78.55 ± 0.43 0.99370 79.40 ± 0.90 1.00149 78.75 ± 0.41 1.01123 78.80 ± 0.46
T = 338.15 K 0.98092 104 ± 10 0.98188 79.2 ± 0.6 0.98235 86.1 ± 3.2 0.98475 79.06 ± 0.42 0.98854 79.71 ± 0.90 0.99628 79.15 ± 0.41 1.00598 79.18 ± 0.46
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
T = 348.15 K 0.97523 103.8 ± 9.7 0.97617 79.82 ± 0.76 0.97666 86.3 ± 3.1 0.97904 79.42 ± 0.44 0.98279 80.21 ± 0.87 0.99053 79.50 ± 0.40 1.00021 79.51 ± 0.47
T = 358.15 K 0.96907 100.3 ± 8.0 0.96995 79.71 ± 0.54 0.97043 86.6 ± 2.5 0.97280 79.79 ± 0.42 0.97658 80.36 ± 0.76 0.98429 79.78 ± 0.41 0.99398 79.75 ± 0.46
T = 368.15 K 0.96239 98.4 ± 5.7 0.96324 79.90 ± 0.50 0.96373 86.7 ± 1.8 0.96609 79.99 ± 0.42 0.96988 80.51 ± 0.62 0.97759 79.98 ± 0.41 0.98723 80.09 ± 0.47
The ± values are from propagation of uncertainties as described in reference [48].
g Æ cm
V/
qs 3
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
69
TABLE 1B Observed densities ps and apparent molar volumes V/ for aqueous zwitterionic isoleucine at p = 0.35 MPa m
V/
qs 1
3
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
g Æ cm
cm3 Æ mol1
mol Æ kg
g Æ cm
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
T = 278.15 K 1.00038 102.9 ± 6.8 1.00077 97.9 ± 5.8 1.00121 103.3 ± 1.3 1.00199 107.2 ± 2.9 1.00448 103.30 ± 0.43 1.00541 105.6 ± 1.1
T = 283.15 K 1.00006 107.5 ± 5.4 1.00050 98.3 ± 5.6 1.00090 104.3 ± 1.2 1.00164 108.3 ± 3.0 1.00411 103.98 ± 0.41 1.00496 106.5 ± 1.2
T = 288.15 K 0.99945 108.5 ± 3.5 0.99991 97.4 ± 5.5 1.00030 104.32 ± 0.81 1.00102 108.6 ± 3.3 1.00345 104.39 ± 0.33 1.00421 107.2 ± 1.3
T = 298.15 K 0.99737 109.6 ± 2.2 0.99785 97.4 ± 5.8 0.99820 105.26 ± 0.86 0.99888 109.6 ± 3.2 1.00124 105.45 ± 0.33 1.00191 108.5 ± 1.2
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
T = 308.15 K 0.99435 110.5 ± 1.6 0.99480 98.9 ± 7.8 0.99515 106.20 ± 0.70 0.99589 109.5 ± 3.4 0.99812 106.32 ± 0.30 0.99869 109.8 ± 1.3
T = 318.15 K 0.99051 111.9 ± 1.2 0.99093 101.5 ± 8.4 0.99131 107.06 ± 0.27 0.99212 109.2 ± 3.4 0.99420 107.25 ± 0.25 0.99476 110.6 ± 1.3
T = 328.15 K 0.98599 113.3 ± 1.9 0.98641 102.2 ± 8.2 0.98678 107.66 ± 0.28 0.98763 109.3 ± 3.4 0.98964 107.97 ± 0.25 0.99022 111.2 ± 1.3
T = 338.15 K 0.98086 113.2 ± 2.1 0.98124 104.4 ± 6.1 0.98165 108.11 ± 0.44 0.98254 109.1 ± 2.9 0.98444 108.77 ± 0.26 0.98505 111.7 ± 1.1
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
T = 348.15 K 0.97514 115.4 ± 2.3 0.97549 107.3 ± 7.3 0.97592 109.20 ± 0.66 0.97683 109.7 ± 2.9 0.97870 109.53 ± 0.29 0.97940 112.0 ± 1.1
T = 358.15 K 0.96897 111.0 ± 2.4 0.96926 108.1 ± 5.5 0.96970 109.83 ± 0.76 0.97067 109.4 ± 2.9 0.97246 110.20 ± 0.31 0.97324 112.3 ± 1.1
T = 368.15 K 0.96220 116.6 ± 4.3 0.96255 108.3 ± 7.0 0.96298 110.35 ± 0.76 0.96402 109.0 ± 3.0 0.96573 110.89 ± 0.31 0.96655 112.8 ± 1.2
The ± values are from propagation of uncertainties as described in reference [48].
TABLE 2A Observed densities qs and apparent molar volumes V/ for aqueous (threonine + HC1) at p = 0.35 MPa ma
qs
V/
qs
V/
qs
V/
qs
V/
mol Æ kg1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
1.00107 1.00155 1.00295 1.00567 1.01351 1.02619 1.04699
T = 278.15 K 91.7 ± 3.4 105.8 ± 8.1 98.22 ± 0.12 99.16 ± 0.11 100.6 ± 1.2 100.67 ± 0.10 101.75 ± 0.33
1.00078 1.00123 1.00265 1.00528 1.01310 1.02555 1.04627
T = 283.15 K 92.8 ± 3.2 107.6 ± 8.4 98.87 ± 0.71 100.41 ± 0.36 101.2 ± 1.1 101.43 ± 0.11 102.26 ± 0.32
1.00019 1.00059 1.00200 1.00463 1.01235 1.02466 1.04521
T = 288.15 K 92.2 ± 2.0 108.8 ± 9.0 99.68 ± 0.86 100.92 ± 0.44 101.8 ± 1.1 102.05 ± 0.13 102.79 ± 0.32
0.99811 0.99842 0.99987 1.00248 1.01013 1.02215 1.04239
T = 298.15 K 93.1 ± 2.2 112.6 ± 8.9 101.1 ± 1.2 101.82 ± 0.62 102.52 ± 0.99 103.08 ± 0.15 103.73 ± 0.29
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
0.99506 0.99534 0.99678 0.99944 1.00698 1.01884 1.03875
T = 308.15 K 95.3 ± 1.7 114.9 ± 9.3 102.68 ± 0.59 102.22 ± 0.30 103.20 ± 0.94 103.827 ± 0.089 104.58 ± 0.28
0.99119 0.99149 0.99293 0.99557 1.00304 1.01479 1.03442
T = 318.15 K 98.03 ± 0.26 116.1 ± 9.3 103.37 ± 0.12 102.861 ± 0.081 103.86 ± 0.82 104.507 ± 0.058 105.36 ± 0.25
0.98666 0.98700 0.98848 0.99101 0.99849 1.01016 1.02958
T = 328.15 K 99.18 ± 0.36 115.6 ± 9.3 102.41 ± 0.11 103.552 ± 0.079 104.26 ± 0.87 105.008 ± 0.062 105.99 ± 0.27
0.98153 0.98191 0.98335 0.98586 0.99325 1.00496 1.02425
T = 338.15 K 99.38 ± 0.95 114.3 ± 8.1 102.42 ± 0.19 103.91 ± 0.11 104.98 ± 0.82 105.411 ± 0.061 106.50 ± 0.25
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
0.97582 0.97625 0.97764 0.98018 0.98754 0.99920 1.01854
T = 348.15 K 100.1 ± 1.6 113.2 ± 8.0 102.83 ± 0.31 104.00 ± 0.17 105.31 ± 0.85 105.862 ± 0.063 106.84 ± 0.26
0.96960 0.97007 0.97143 0.97397 0.98132 0.99303 1.01233
T = 358.15 K 99.9 ± 1.9 111.9 ± 8.0 103.00 ± 0.32 104.20 ± 0.17 105.63 ± 0.87 106.069 ± 0.062 107.18 ± 0.27
0.96290 0.96345 0.96475 0.96732 0.97473 0.98640 1.00573
T = 368.15 K 99.1 ± 1.9 109.0 ± 8.4 102.52 ± 0.49 103.76 ± 0.25 105.41 ± 0.64 106.255 ± 0.076 107.44 ± 0.21
The ± values are from propagation of uncertainties as described in reference [48]. a Molality of theronine, with stoichiometric molality {m(HThr)/m(HCl)} = 0.9997.
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We measured densities qs of each solution 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 ðM 2 =qs Þ ðqs qw Þ=ðqs qw mÞ;
(aq) + NaOH(aq)}, and {HIle±(aq) + NaOH(aq)} at 0.01 6 m/mol Æ kg16 1.0 and 278.15 6 T/K 6 368.15 are given in tables 1 to 3 equation (3) was fit by regression to these results: V / ðT ; mÞ ¼ w3=2 AV ðm Þ1=2 þ m0 þ m1 m þ
ð1Þ
where qw [1] is the density of water as described previously [1–4]. Solution heat capacities 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 previously [1,2,48]. We used values of the heat capacity of water cp,w [1] and our cp,s with equation (2) to calculate Cp,/(T, m): C p;/ ¼ ðM 2 cp;s Þ þ ðcp;s cp;w Þ=m:
ð2Þ
3. Results and discussion Values of V/,obs(T, m) for HThr±(aq), HIle±(aq), {HThr±(aq) + HCl(aq)}, {HIle±(aq) + HCl(aq)}, {HThr±-
2
2
m2 ðm Þ þ m3 m T þ m4 ðm Þ T þ 2
m5 lnðT Þ þ m6 T þ m7 ðT Þ :
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 [49] as given by Sorenson, et al. [1], w = 0 for HThr±(aq) and for HIle±(aq), and w = 1 for {HThr±(aq) + HCl(aq)}, H2Thr+Cl(aq), {HIle±(aq) + HCl(aq)}, H2Ile+Cl(aq), {HThr±(aq) + NaOH(aq)}, Na+Thr(aq), {HIle±(aq) + NaOH(aq)}, and for Na+Ile(aq). The squares of the reciprocals of the uncertainties in tables 1 to 3 were used as weighting factors in the regressions. The uncertainties reported in this work were calculated by standard error propagation statistics as described previously [48].
TABLE 2B Observed densities qs and apparent molar volumes V/ for aqueous (isoleucine + HCl) at p = 0.35 MPa ma
qs
V/
qs
V/
qs
V/
qs
V/
mol Æ kg1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
0.0151 0.0301 0.0502 0.1003 0.1003 0.2500 0.5012 0.5012 0.9531
1.00077 1.00120 1.00235 1.00374 1.00403 1.00949 1.01763 1.01770 1.03172
T = 278.15 K 122.6 ± 6.2 130.8 ± 1.2 122.37 ± 0.95 130.76 ± 0.36 127.82 ± 0.74 128.83 ± 0.20 130.344 ± 0.094 130.20 ± 0.16 130.32 ± 0.15
1.00045 1.00090 1.00203 1.00352 1.00368 1.00902 1.01694 1.01708 1.03074
T = 283.15 K 125.9 ± 5.7 131.67 ± 0.97 123.58 ± 0.52 130.31 ± 0.30 128.69 ± 0.68 129.66 ± 0.13 131.250 ± 0.098 130.97 ± 0.13 131.16 ± 0.15
0.99981 1.00028 1.00138 1.00282 1.00300 1.00825 1.01599 1.01617 1.02951
T = 288.15 K 128.4 ± 4.3 132.5 ± 1.3 124.49 ± 0.53 131.31 ± 0.39 129.56 ± 0.46 130.42 ± 0.13 132.04 ± 0.11 131.666 ± 0.095 131.93 ± 0.15
0.99771 0.99811 0.99926 1.00057 1.00076 1.00593 1.01327 1.01354 1.02639
T = 298.15 K 130.6 ± 2.2 135.9 ± 2.5 125.7 ± 1.7 133.36 ± 0.77 131.45 ± 0.32 131.64 ± 0.35 133.61 ± 0.17 133.037 ± 0.068 133.35 ± 0.15
0.0151 0.0301 0.0502 0.1003 0.1003 0.2500 0.5012 0.5012 0.9531
0.99467 0.99502 0.99619 0.99741 0.99765 1.00282 1.00977 1.01012 1.02262
T = 308.15 K 132.8 ± 1.0 138.8 ± 4.6 127.0 ± 3.1 135.1 ± 1.4 132.65 ± 0.22 132.32 ± 0.64 134.93 ± 0.30 134.193 ± 0.055 134.53 ± 0.20
0.99083 0.99113 0.99235 0.99349 0.99375 0.99886 1.00561 1.00599 1.01819
T = 318.15 K 134.23 ± 0.81 141.6 ± 5.9 127.7 ± 3.9 136.5 ± 1.8 133.89 ± 0.17 133.28 ± 0.81 136.05 ± 0.38 135.233 ± 0.045 135.64 ± 0.21
0.98632 0.98662 0.98776 0.98898 0.98919 0.99418 1.00091 1.00125 1.01320
T = 328.15 K 133.9 ± 1.9 141.8 ± 6.0 129.6 ± 3.5 136.9 ± 1.8 134.71 ± 0.16 134.39 ± 0.72 136.93 ± 0.39 136.191 ± 0.057 136.67 ± 0.21
0.98118 0.98149 0.98260 0.98388 0.98401 0.98892 0.99562 0.99593 1.00771
T = 338.15 K 134.9 ± 1.9 142.2 ± 4.6 130.6 ± 2.1 137.1 ± 1.4 135.69 ± 0.17 135.46 ± 0.44 137.79 ± 0.30 137.125 ± 0.057 137.63 ± 0.17
0.0151 0.0301 0.0502 0.1003 0.1003 0.2500 0.5012 0.5012 0.9531
0.97546 0.97581 0.97689 0.97816 0.97827 0.98309 0.98982 0.99011 1.00175
T = 348.15 K 136.5 ± 2.1 142.1 ± 5.5 131.2 ± 2.4 137.9 ± 1.7 136.75 ± 0.18 136.58 ± 0.51 138.63 ± 0.36 137.986 ± 0.060 138.56 ± 0.19
0.96925 0.96960 0.97068 0.97192 0.97205 0.97686 0.98359 0.98384 0.99534
T = 358.15 K 136.5 ± 2.3 142.3 ± 3.8 131.6 ± 1.2 138.8 ± 1.1 137.37 ± 0.23 137.26 ± 0.26 139.31 ± 0.25 138.767 ± 0.061 139.47 ± 0.15
0.96255 0.96288 0.96396 0.96522 0.96539 0.97018 0.97683 0.97713 0.98860
T = 368.15 K 136.4 ± 4.8 143.3 ± 5.8 132.2 ± 3.3 139.3 ± 1.7 137.43 ± 0.49 137.82 ± 0.68 140.15 ± 0.37 139.480 ± 0.098 140.25 ± 0.18
The ± values are from propagation of uncertainties as described in reference [48]. a Molality of theronine, with stoichiometric molality ratio {m(HIle)/m(HCl)} = 0.997.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
The resultant values of mi for the regressions with equation (3) are given in tables 4A and 4B. Figure 1 shows our V/,obs(T, m) results for HThr±(aq) and HIle±(aq) along with the regression surfaces and values from the literature [5–20]. The differences between V/(T, m) values on our regression surface and all literature values for HThr±(aq) are in the range D = (19.9 [5] to 6.0 [6]) cm3 Æ mol1, with an average difference D = 0.1 cm3 Æ mol1 whereas the same comparison for HIle±(aq) gives values in the range D = (2.1 [18] to 0.4 [19]) cm3 Æ mol1, with an average difference D = 0.2 cm3 Æ mol1. Tables 5 to 7 give our values of Cp,/,obs(T,m) for HThr±(aq), HIle±(aq), {HThr±(aq) + HCl(aq)}, {HIle±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, and {HIle±(aq) + NaOH(aq)}. Equation (4) was fit by regression to these results using the squares of the reciprocals of the uncertainties given in the tables as weighting factors: 1=2
C p;/ ðT ; mÞ ¼ w3=2 AC ðm Þ
2
þ c0 þ c1 m þ c2 ðm Þ þ 2
c3 m lnðT Þ þ c4 m T þ c5 m ðT Þ þ 2
71
Figure 2 shows our Cp,/,obs(T, m) for HThr±(aq) and HIle±(aq) from tables 5A and 5B and the regression surfaces, along with values from the literature [12,13,20–23]. The differences between Cp,/(T, m) values on our regression surface and all the values from the literature are in the range D = (23.1 [12] to 74.8 [21]) J Æ K1 Æ mol1 with an average difference D = 4.5 J Æ K1 Æ mol1 for aqueous threonine, and are in the range D = (39.3 [21] to 20.5 [21]) J Æ K1 Æ mol1 with an average difference D = 2.8 J Æ K1 Æ mol1 for aqueous isoleucine. In order to calculate apparent molar properties Cp,/(i) and V/(i) of the individual species H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq), we must account for chemical equilibria in our solutions of {HThr±(aq) + HCl(aq)}, {HIle±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, and {HIle±(aq) + NaOH(aq)}, respectively. Aqueous amino acids can undergo reactions (5) to (8), where A signifies the amino acid moiety: H2 Aþ ðaqÞ ¼ HA ðaqÞ þ Hþ ðaqÞ
ð5Þ
þ
HA ðaqÞ ¼ A ðaqÞ þ H ðaqÞ
3
c6 lnðT Þ þ c7 T þ c8 ðT Þ þ c9 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 [49] as given by Sorenson, et al. [1]. Tables 8A and 8B give the regression parameters (ci).
ð6Þ
þ
HA ðaqÞ þ H2 O ¼ H2 A ðaqÞ þ OH ðaqÞ
ð7Þ
A ðaqÞ þ H2 O ¼ HA ðaqÞ þ OH ðaqÞ
ð8Þ
Reactions (6) and (7) do not occur to an appreciable extent at the m, T, and p of our experiments for solutions of HThr±(aq) or HIle±(aq). Thus, we treat solutions of the zwitterionic amino acids as containing only the species
TABLE 3A Observed densities qs and apparent molar volumes V/ for aqueous (threonine + NaOH) at p = 0.35 MPa ma
qs
V/
qs
V/
qs
V/
qs
V/
mol Æ kg1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
1.00124 1.00223 1.00368 1.00713 1.01705 1.03285 1.06081
T = 278.15 K 75 ± 17 69.5 ± 1.3 72.0 ± 6.3 70.47 ± 0.45 72.1 ± 1.3 73.21 ± 0.68 75.54 ± 0.13
1.00101 1.00190 1.00340 1.00671 1.01649 1.03210 1.05980
T = 283.15 K 73 ± 15 71.4 ± 2.2 72.3 ± 6.4 71.95 ± 0.68 73.2 ± 1.3 74.18 ± 0.69 76.30 ± 0.11
1.00040 1.00123 1.00276 1.00598 1.01562 1.03103 1.05849
T = 288.15 K 74 ± 15 73.8 ± 1.6 73.0 ± 6.5 73.22 ± 0.50 74.3 ± 1.4 75.13 ± 0.70 77.04 ± 0.11
0.99834 0.99911 1.00064 1.00371 1.01313 1.02819 1.05516
T = 298.15 K 73 ± 14 75.5 ± 2.1 74.0 ± 6.6 75.25 ± 0.64 76.0 ± 1.4 76.71, ± 0.71 78.37 ± 0.11
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
0.99535 0.99610 0.99755 1.00056 1.00980 1.02458 1.05111
T = 308.15 K 71.4 ± 13.1 75.14 ± 0.97 75.3 ± 6.5 76.67 ± 0.33 77.4 ± 1.4 77.96 ± 0.71 79.481 ± 0.086
0.99152 0.99226 0.99371 0.99668 1.00571 1.02033 1.04645
T = 318.15 K 72 ± 11 75.99 ± 0.34 75.7 ± 6.0 77.21 ± 0.19 78.5 ± 1.3 78.90 ± 0.65 80.438 ± 0.071
0.98702 0.98773 0.98920 0.99211 1.00108 1.01553 1.04143
T = 328.15 K 71 ± 12 76.31 ± 0.21 75.7 ± 5.5 77.89 ± 0.17 79.0 ± 1.2 79.57 ± 0.61 81.065 ± 0.075
0.98179 0.98258 0.98402 0.98693 0.99577 1.01015 1.03588
T = 338.15 K 77 ± 11 77.02 ± 0.34 76.6 ± 5.1 78.37 ± 0.19 79.8 ± 1.1 80.18 ± 0.57 81.625 ± 0.071
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
0.97606 0.97685 0.97832 0.98120 0.99001 1.00434 1.02985
T = 348.15 K 79 ± 12 77.83 ± 0.47 76.6 ± 4.8 78.81 ± 0.21 80.2 ± 1.0 80.50 ± 0.53 82.110 ± 0.069
0.96981 0.97063 0.97213 0.97496 0.98377 0.99801 1.02344
T = 358.15 K 80 ± 12 77.93 ± 0.45 76.1 ± 4.6 79.01 ± 0.21 80.35 ± 0.97 80.84 ± 0.51 82.459 ± 0.064
0.96309 0.96389 0.96538 0.96823 0.97696 0.99123 1.01664
T = 368.15 K 80.2 ± 8.8 78.84 ± 0.34 76.8 ± 3.7 79.20 ± 0.19 80.89 ± 0.80 81.12 ± 0.43 82.708 ± 0.067
The ± values are from propagation of uncertainties as described in reference [48]. a Molality of threonine, with stoichiometric molality ratio {m(HThr)/m(NaOH)} = 0.9997.
72
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
TABLE 3B Observed densities qs and apparent molar volumes V/ for aqueous (isoleucine + NaOH) at p = 0.35 MPa ma
V/
qs 1
3
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
cm3 Æ mol1
mol Æ kg
g Æ cm
g Æ cm
0.0151 0.0151 0.0313 0.0501 0.1000 0.2576 0.2576 0.4998 0.9940
T = 278.15 K 1.00098 94.6 ± 6.1 1.00095 96.5 ± 1.7 1.00124 96.2 ± 3.0 1.00223 98.0 ± 1.9 1.00368 96.31 ± 0.40 1.00713 101.08 ± 0.17 1.01705 101.03 ± 0.19 1.03285 100.35 ± 0.13 1.06081 101.56 ± 0.10
T = 283.15 K 1.00067 97.2 ± 6.3 1.00067 97.2 ± 2.8 1.00101 98.1 ± 2.8 1.00190 98.0 ± 1.7 1.00340 97.95 ± 0.35 1.00671 102.31 ± 0.21 1.01649 102.13 ± 0.19 1.03210 101.49 ± 0.14 1.05980 102.64 ± 0.11
T = 288.15 K 1.00004 98.8 ± 5.0 1.00005 98.1 ± 3.1 1.00040 99.7 ± 2.1 1.00123 100.0 ± 1.3 1.00276 99.04 ± 0.27 1.00598 103.35 ± 0.22 1.01562 103.14 ± 0.16 1.03103 102.47 ± 0.13 1.05849 103.65 ± 0.11
T = 298.15 K 0.99793 102.3 ± 3.6 0.99796 100.1 ± 3.3 0.99834 102.0 ± 1.1 0.99911 101.92 ± 0.67 1.00064 101.04 ± 0.54 1.00371 105.16 ± 0.23 1.01313 104.90 ± 0.25 1.02819 104.29 ± 0.16 1.05516 105.42 ± 0.13
0.0151 0.0151 0.0313 0.0501 0.1000 0.2576 0.2576 0.4998 0.9940
T = 308.15 K 0.99487 105.0 ± 4.2 0.99493 101.0 ± 1.1 0.99535 103.61 ± 0.51 0.99610 103.36 ± 0.34 0.99755 102.77 ± 0.79 1.00056 106.56 ± 0.13 1.00980 106.42 ± 0.34 1.02458 105.83 ± 0.20 1.05111 106.94 ± 0.20
T = 318.15 K 0.99102 107.1 ± 4.6 0.99107 103.61 ± 0.93 0.99152 105.44 ± 0.41 0.99226 105.16 ± 0.28 0.99371 103.75 ± 0.96 0.99668 107.88 ± 0.12 1.00571 107.59 ± 0.40 1.02033 107.07 ± 0.23 1.04645 108.28 ± 0.24
T = 328.15 K 0.98647 109.7 ± 5.1 0.98655 103.7 ± 1.6 0.98702 106.53 ± 0.92 0.98773 106.26 ± 0.59 0.98920 104.93 ± 0.83 0.99211 109.01 ± 0.14 1.00108 108.72 ± 0.35 1.01553 108.20 ± 0.22 1.04143 109.50 ± 0.22
T = 338.15 K 0.98132 110.9 ± 4.4 0.98141 104.74 ± 0.67 0.98179 107.54 ± 0.92 0.98258 105.81 ± 0.58 0.98402 105.81 ± 0.57 0.98693 110.00 ± 0.11 0.99577 109.58 ± 0.26 1.01015 109.27 ± 0.17 1.03588 110.57 ± 0.16
0.0151 0.0151 0.0313 0.0501 0.1000 0.2576 0.2576 0.4998 0.9940
T = 348.15 K 0.97560 112.5 ± 3.9 0.97569 106.03 ± 0.79 0.97606 108.2 ± 1.0 0.97685 108.06 ± 0.64 0.97832 106.62 ± 0.51 0.98120 110.88 ± 0.11 0.99001 110.59 ± 0.24 1.00434 110.22 ± 0.16 1.02985 111.63 ± 0.17
T = 358.15 K 0.96937 113.4 ± 2.4 0.96947 106.1 ± 1.9 0.96981 108.2 ± 1.1 0.97063 108.30 ± 0.71 0.97213 107.83 ± 0.29 0.97496 111.66 ± 0.15 0.98377 111.40 ± 0.17 0.99801 111.16 ± 0.14 1.02344 112.56 ± 0.13
T = 368.15 K 0.96268 112.2 ± 4.5 0.96275 107.0 ± 1.6 0.96309 107.3 ± 2.3 0.96389 108.8 ± 1.5 0.96538 108.47 ± 0.56 0.96823 112.27 ± 0.14 0.97696 112.29 ± 0.25 0.99123 112.03 ± 0.17 1.01664 113.50 ± 0.21
The ± values are from propagation of uncertainties as described in reference [48]. a Molality of isoleucine, with stoichiometric molality ratio {m(Hlle)/m(NaOH)} = 0.998.
HA±(aq). Alternately, aqueous solutions of {HA±(aq) + HCl(aq)} and of {HA±(aq) + NaOH(aq)}, undergo reactions (5) and (8), respectively, extensively, though not to completion. For this reason {HA±(aq) + HCl(aq)} solu-
tions are equilibrium mixtures of H2A+Cl(aq), HA±(aq), and H+Cl(aq), whereas {HA±(aq) + NaOH(aq)} solutions are equilibrium mixtures of Na+A(aq), HA±(aq), and Na+OH(aq).
TABLE 4A Regression parameters of equation (3) for apparent molar volumes V/(T, m) of {HThr±(aq)}, {HThr±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, {H2Thr+Cl(aq)}, and {Na+Thr(aq)} mi m0 m1 m2 103 Æ m3 103 Æ m4 m5 103 Æ m6 106 Æ m7 Da Highest m
HThr±(aq) observed, w = 0 (Table 1A)
{HThr±(aq) + HCl(aq)} observed, w = 1 (Table 2A)
{HThr±(aq) + NaOH(aq)} observed, w = 1 (Table 3A)
2.98 ± 0.01
3.96 ± 0.01 7.27 ± 0.01 2.29 ± 0.01 10.86 ± 0.01
52.51 ± 0.01 13.26 ± 0.01 1.95 ± 0.01 27.8 ± 0.1
415.85 ± 0.01 561.14 ± 0.04 ± 0.89 0.65
559.03 ± 0.01 792.5 ± 0.1 ± 0.46 1.0
716.0 ± 0.1 984.37 ± 0.03 ± 0.18 1.0
H2Thr+Cl(aq) iteration, w = 1 (see text)
Na+Thr(aq) iteration, w = 1 (see text)
642.23 ± 0.01 4.13 ± 0.01 3.25 ± 0.01
990.98 ± 0.01 0.86 ± 0.01
153.938 ± 0.001 439.85 ± 0.01
219.829 ± 0.001 626.54 ± 0.01
± 0.063 1.0
± 0.17 1.0
The ± values are chosen to reproduce the generated V/ alues to within ± 0.01 cm3 Æ mol1 at 278.15 6 T/K 6 393.15 and at m 6 0.65 mol Æ kg1 for the zwitterion and m 6 1.0 mol Æ kg1 for the cationic and anionic forms. a Standard deviation of the regressions.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
73
TABLE 4B Regression parameters of equation (3) for apparent molar volumes V/(T, m) of{HIle±(aq)}, {HIle±(aq) + HCl(aq)}, {HIle±(aq) + NaOH(aq)}, {H2Ile+Cl(aq)}, and {Na+Ile(aq)} HIle±(aq) observed, w = 0 (Table 1B)
mi
{HIle±(aq) + HCl(aq)} observed, w = 1 (Table 2B)
63.95 ± 0.01
m0 m1 m2 103 Æ m3 103 Æ m4 m5 103 Æ m6 106 Æ m7 Da Highest m
190.74 ± 0.01 171.56 ± 0.04 ± 0.86 0.21
{HIle±(aq) + NaOH(aq)} observed, w = 1 (Table 3B) 39.24 ± 0.01 8.07 ± 0.01 2.36 ± 0.01 15.9 ± 0.1
43.005 ± 0.004 8.25 ± 0.01 2.99 ± 0.01 13.98 ± 0.01
465.74 ± 0.01 579.34 ± 0.03 ± 0.40 1.0
782.32 ± 0.01 1029.5 ± 0.1 ± 0.80 1.0
{H2Ile+Cl(aq)} iteration, w = 1 (see text)
Na+Ile(aq) iteration, w = 1 (see text)
525.62 ± 0.01 2.825 ± 0.004
803.32 ± 0.01 4.696 ± 0.004 3.14 ± 0.01
10.54 ± 0.01 132.086 ± 0.001 318.0 ± 0.1
183.649 ± 0.001 464.5 ± 0.1
± 0.15 1.0
± 0.13 1.0
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 0.21 mol Æ kg1 for the zwitterion and m 6 1.0 mol Æ kg1 for the cationic and anionic forms. a Standard deviations of the regressions.
m(i) is the molality of species i, Y/(i) is the apparent molar property V/ or Cp,/ of species i, and mt is given by equation (10): X mt ¼ mðiÞ: ð10Þ
-1 3 Vφ / (cm .mol )
120 110
Equations (11) and (12) define V/,tot and Cp,/,tot: 100 90
ð11Þ
C p;/;tot ¼ ðM av cp;s Þ þ fðcp;s cp;w Þ=mt g;
ð12Þ
where the weighted average molar mass of solutes in solution Mav is given by the following equation: X M av ¼ fmðiÞ=mt g MðiÞ: ð13Þ
80 0.6
m/
V /;tot ¼ ðM av =qs Þ fðqs qw Þ=ðqs qw mt Þg;
380
0.4
(m ol·
360 340
0.2
kg - 1 )
320 0.0
300 280
T/
K
FIGURE 1. Apparent molar volume V/ of zwitterionic threonine HThr±(aq) (lower surface) and isoleucine HIle±(aq) (upper surface) plotted against temperature T and molality m. Surfaces generated from equation (3) with parameters in column 2 of tables 4A and 4B, respectively; (s), experimental values from table 1A; (h), experimental values from table 1B; (d), references [5–16]; (n), references [13–20].
Apparent molar properties of these mixtures can be represented approximately at m* > 0 by Young’s Rule equation (9): h nX oi. mðiÞ Y / ðiÞ mt ; ð9Þ Y /;tot ¼ m Y rel þ where Y/,tot is the apparent molar property of the mixture, Yrel results from shifts in the equilibrium position by reaction (5) or (8) from scanning 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{HA±(aq)} < m{HCl(aq)} for reaction (5) and m = m{HA±(aq)} < m{NaOH(aq)} for reaction (8)],
We used the procedure outlined in our recent work on other aqueous amino acids [1–4] to analyze our results with equations (9) to (13). Reference values used for integration constants in this report for threonine at T* = 298.15 are pQa = (2.26 ± 0.20) [26–29,36–41,43,44] and DrHm = (3.75 ± 2.0) kJ Æ mol1 [25–29] for reaction (5), and pQa = (9.16 ± 0.36) [26–29,35–41,43–45] and DrHm = (41.51 ± 0.49) kJ Æ mol1 [25–29,33–35] for reaction (6). Reference values used for isoleucine at T* = 298.15 are pQa = (2.345 ± 0.093) [29–32,36,37] and DrHm = (0.979 ± 0.51) kJ Æ mol1 [24,29–32] for reaction (5), and pQa = (9.702 ± 0.076) [29–31,36,37] and DrHm = (45.67 ± 0.63) kJ Æ mol1 [24,29–31,33] for reaction (6). These values are averages of the values at T* = 298.15 given in the cited references, and the ± values given are the standard deviations of these values. As indicated by the large standard deviations for the values for reaction (5) where A = threonine, there is disagreement among the reported literature values. All values for reaction (8) were calculated from those for reaction (6) using values of pQw and DrHm,w at T* = 298.15 from Patterson et al. [50] to give pQb = (4.833 ± 0.200 and DrHm = 14.30 ± 2.00 kJ Æ mol1) for aqueous threonine and pQb = (4.295 ± 0.093 and DrHm = 10.137 ± 0.510 kJ Æ mol1) for aqueous isoleucine.
74
TABLE 5A Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for zwitterionic aqueous threonine at p = 0.35 MPa m mol Æ kg
cp,s 1
Cp,/ 1
JÆK
1
Æg
JÆK
cp,s 1
1
Æ mol
JÆK
Cp,/ 1
1
Æg
JÆK
cp,s 1
Æ mol
1
JÆK
Cp,/ 1
Æg
1
cp,s 1
JÆK
1
Æ mol
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
1
Æ mol
Cp,/ 1
JÆK
1
Æg
J Æ K1 Æ mol1
4.1975 4.1929 4.1861 4.1676 4.1385 4.0759 4.0042
T = 278.15 K 160 ± 26 172 ± 27 167.5 ± 8.6 149.7 ± 7.7 170.6 ± 3.1 163.6 ± 3.0 173.5 ± 2.9
4.1881 4.1840 4.1774 4.1596 4.1322 4.0723 4.0052
T = 283.15 K 175 ± 24 198 ± 31 183.8 ± 7.8 163.7 ± 8.2 186.7 ± 2.8 177.9 ± 3.0 189.9 ± 2.2
4.1818 4.1782 4.1715 4.1543 4.1281 4.0705 4.0061
T = 288.15 K 196 ± 23 219 ± 34 194.8 ± 7.6 175.2 ± 8.6 198.3 ± 2.7 188.8 ± 3.0 201.2 ± 2.1
4.1776 4.1742 4.1676 4.1514 4.1258 4.0707 4.0078
T = 293.15 K 206 ± 23 231 ± 28 205.4 ± 7.4 189.6 ± 7.8 208.4 ± 2.7 201.2 ± 2.8 210.8 ± 2.0
4.1750 4.1715 4.1653 4.1501 4.1247 4.0720 4.0101
T = 298.15 K 215 ± 22 234 ± 25 214.0 ± 7.2 204.1 ± 7.1 216.8 ± 2.6 216.0 ± 2.6 218.8 ± 1.9
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
4.1733 4.1698 4.1639 4.1496 4.1244 4.0735 4.0126
T = 303.15 K 222 ± 21 238 ± 25 221.5 ± 7.0 216.9 ± 6.8 224.1 ± 2.5 222.4 ± 2.5 225.8 ± 1.9
4.1726 4.1691 4.1634 4.1498 4.1248 4.0753 4.0155
T = 308.15 K 228 ± 21 242 ± 26 228.0 ± 6.8 227.3 ± 6.5 230.4 ± 2.4 229.8 ± 2.4 231.7 ± 1.8
4.1726 4.1692 4.1636 4.1504 4.1258 4.0774 4.0185
T = 313.15 K 233 ± 20 248 ± 26 233.6 ± 6.6 234.5 ± 6.3 235.8 ± 2.4 235.9 ± 2.4 236.8 ± 1.8
4.1733 4.1701 4.1645 4.1516 4.1274 4.0800 4.0219
T = 318.15 K 239 ± 19 253 ± 27 238.6 ± 6.4 239.2 ± 6.3 240.6 ± 2.3 241.2 ± 2.4 241.3 ± 1.8
4.1746 4.1714 4.1659 4.1531 4.1293 4.0829 4.0254
T = 323.15 K 243 ± 19 258 ± 27 242.8 ± 6.2 242.6 ± 6.3 244.7 ± 2.3 245.9 ± 2.3 245.3 ± 1.8
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
4.1765 4.1733 4.1679 4.1552 4.1318 4.0861 4.0292
T = 328.15 K 246 ± 18 260 ± 28 246.5 ± 6.0 245.4 ± 6.4 248.3 ± 2.2 249.9 ± 2.3 248.7 ± 1.7
4.1787 4.1755 4.1702 4.1576 4.1346 4.0894 4.0331
T = 333.15 K 250 ± 18 263 ± 28 249.8 ± 5.8 248.0 ± 6.5 251.5 ± 2.2 253.1 ± 2.3 251.9 ± 1.7
4.1814 4.1783 4.1731 4.1605 4.1378 4.0931 4.0373
T = 338.15 K 253 ± 17 265 ± 28 252.8 ± 5.6 249.9 ± 6.6 254.4 ± 2.1 255.7 ± 2.3 254.6 ± 1.7
4.1847 4.1816 4.1764 4.1637 4.1414 4.0970 4.0417
T = 343.15 K 255 ± 17 269 ± 29 255.3 ± 5.5 250.9 ± 6.7 256.8 ± 2.1 257.7 ± 2.3 257.0 ± 1.7
4.1883 4.1853 4.1801 4.1674 4.1453 4.1013 4.0462
T = 348.15 K 258 ± 16 272 ± 29 257.5 ± 5.3 251.9 ± 6.9 258.9 ± 2.1 259.7 ± 2.4 259.0 ± 1.7
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
4.1923 4.1893 4.1841 4.1714 4.1496 4.1058 4.0510
T = 353.15 K 259 ± 15 275 ± 29 259.4 ± 5.1 252.7 ± 7.0 260.8 ± 2.0 261.3 ± 2.4 260.8 ± 1.6
4.1967 4.1938 4.1886 4.1758 4.1542 4.1105 4.0560
T = 358.15 K 261 ± 15 278 ± 30 261.0 ± 4.9 253.3 ± 7.2 262.3 ± 2.0 262.6 ± 2.4 262.3 ± 1.6
4.2015 4.1987 4.1934 4.1806 4.1591 4.1155 4.0613
T = 363.15 K 262 ± 14 280 ± 31 262.5 ± 4.7 253.6 ± 7.5 263.7 ± 2.0 263.6 ± 2.5 263.6 ± 1.6
4.2069 4.2040 4.1988 4.1858 4.1645 4.1209 4.0668
T = 368.15 K 263 ± 14 282 ± 32 263.5 ± 4.6 253.5 ± 7.7 264.6 ± 1.9 264.1 ± 2.5 264.6 ± 1.6
4.2126 4.2098 4.2045 4.1914 4.1702 4.1265 4.0726
T = 373.15 K 263 ± 13 285 ± 34 264.2 ± 4.4 253.4 ± 8.1 265.5 ± 1.9 264.4 ± 2.6 265.4 ± 1.6
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
4.2188 4.2161 4.2107 4.1976 4.1765 4.1326 4.0787
T = 378.15 K 263 ± 12 287 ± 36 264.7 ± 4.2 252.7 ± 8.5 266.0 ± 1.9 264.3 ± 2.7 265.9 ± 1.6
4.2255 4.2229 4.2174 4.2042 4.1830 4.1389 4.0852
T = 383.15 K 264 ± 12 289 ± 37 264.9 ± 4.0 252.4 ± 8.7 266.2 ± 1.9 264.0 ± 2.7 266.3 ± 1.6
4.2328 4.2303 4.2247 4.2113 4.1902 4.1457 4.0919
T = 388.15 K 263 ± 11 294 ± 39 264.8 ± 3.8 251.7 ± 8.8 266.0 ± 1.8 263.2 ± 2.8 266.3 ± 1.6
4.2407 4.2385 4.2325 4.2189 4.1977 4.1528 4.0988
T = 393.15 K 262 ± 11 304 ± 46 263.6 ± 3.7 249.7 ± 9.7 265.0 ± 1.8 261.1 ± 3.0 265.5 ± 1.6
The ± uncertainties are from propagation of uncertainties as described in reference [48].
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
TABLE 5B Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for zwitterionic aqueous isoleucine at p = 0.35 MPa cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
mol Æ kg1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.2004 4.1989 4.1952 4.1878 4.1726 4.1633
T = 278.15 K 328 ± 36 364 ± 13 364.5 ± 7.7 362.4 ± 4.8 357.2 ± 3.6 360.5 ± 3.0
4.1909 4.1895 4.1861 4.1791 4.1649 4.1563
T = 283.15 K 333 ± 38 372 ± 13 374.0 ± 7.5 373.6 ± 4.7 369.3 ± 3.6 372.1 ± 3.0
4.1844 4.1832 4.1799 4.1732 4.1597 4.1514
T = 288.15 K 333 ± 44 380 ± 13 381.1 ± 7.4 379.9 ± 4.6 377.3 ± 3.8 379.0 ± 2.9
4.1800 4.1789 4.1757 4.1693 4.1562 4.1483
T = 293.15 K 334 ± 50 386 ± 13 386.7 ± 7.4 385.6 ± 4.6 383.0 ± 3.9 384.8 ± 2.9
4.1774 4.1762 4.1731 4.1669 4.1542 4.1466
T = 298.15 K 345 ± 46 390 ± 13 391.0 ± 7.2 390.1 ± 4.5 387.3 ± 3.8 389.3 ± 2.9
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.1757 4.1745 4.1715 4.1654 4.1530 4.1456
T = 303.15 K 359 ± 37 394 ± 12 395.0 ± 7.2 393.8 ± 4.5 390.9 ± 3.6 393.1 ± 2.9
4.1751 4.1737 4.1708 4.1649 4.1526 4.1454
T = 308.15 K 375 ± 30 397 ± 12 398.2 ± 7.1 397.0 ± 4.4 394.0 ± 3.5 396.2 ± 2.8
4.1751 4.1737 4.1708 4.1650 4.1530 4.1459
T = 313.15 K 385 ± 25 400 ± 12 400.8 ± 7.0 399.5 ± 4.4 396.6 ± 3.5 398.7 ± 2.8
4.1759 4.1744 4.1716 4.1658 4.1540 4.1470
T = 318.15 K 395 ± 24 402 ± 12 403.1 ± 6.9 401.7 ± 4.3 398.5 ± 3.4 400.8 ± 2.8
4.1771 4.1757 4.1729 4.1672 4.1555 4.1485
T = 323.15 K 403 ± 25 404 ± 12 404.8 ± 6.9 403.6 ± 4.3 400.0 ± 3.4 402.5 ± 2.8
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.1790 4.1775 4.1747 4.1691 4.1574 4.1505
T = 328.15 K 411 ± 30 405 ± 12 406.3 ± 6.8 404.9 ± 4.3 400.8 ± 3.4 403.8 ± 2.8
4.1813 4.1797 4.1770 4.1713 4.1598 4.1529
T = 333.15 K 419 ± 37 407 ± 11 407.6 ± 6.8 406.0 ± 4.2 401.6 ± 3.4 404.8 ± 2.8
4.1840 4.1824 4.1797 4.1741 4.1626 4.1557
T = 338.15 K 424 ± 46 408 ± 11 408.5 ± 6.7 406.9 ± 4.2 402.3 ± 3.5 405.6 ± 2.8
4.1873 4.1856 4.1829 4.1773 4.1660 4.1589
T = 343.15 K 429 ± 58 408 ± 11 409.2 ± 6.6 407.5 ± 4.2 403.6 ± 3.7 406.1 ± 2.8
4.1910 4.1892 4.1865 4.1809 4.1697 4.1624
T = 348.15 K 438 ± 77 409 ± 11 409.5 ± 6.6 407.8 ± 4.2 404.8 ± 4.2 406.4 ± 2.7
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.1951 4.1932 4.1905 4.1848 4.1738 4.1663
T = 353.15 K 448 ± 101 409 ± 11 409.7 ± 6.5 408.1 ± 4.1 405.4 ± 4.9 406.5 ± 2.7
4.1996 4.1976 4.1949 4.1892 4.1782 4.1706
T = 358.15 K 457 ± 128 409 ± 11 409.8 ± 6.4 408.1 ± 4.1 405.6 ± 5.9 406.4 ± 2.7
4.2044 4.2024 4.1996 4.1939 4.1830 4.1752
T = 363.15 K 465 ± 148 409 ± 11 409.6 ± 6.4 407.9 ± 4.1 405.5 ± 6.7 406.2 ± 2.7
4.2097 4.2077 4.2049 4.1991 4.1881 4.1803
T = 368.15 K 466 ± 153 408 ± 11 409.2 ± 6.3 407.6 ± 4.1 405.0 ± 6.8 405.8 ± 2.7
4.2154 4.2133 4.2105 4.2047 4.1935 4.1857
T = 373.15 K 462 ± 138 408 ± 11 408.5 ± 6.3 407.1 ± 4.1 404.5 ± 6.3 405.2 ± 2.7
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.2215 4.2196 4.2168 4.2109 4.1995 4.1917
T = 378.15 K 447 ± 101 407 ± 10 407.9 ± 6.2 406.4 ± 4.1 403.9 ± 4.9 404.4 ± 2.7
4.2279 4.2263 4.2234 4.2175 4.2056 4.1980
T = 383.15 K 418 ± 38 406 ± 10 407.0 ± 6.2 405.5 ± 4.0 402.8 ± 3.2 403.5 ± 2.7
4.2348 4.2335 4.2306 4.2246 4.2121 4.2049
T = 388.15 K 376 ± 76 405 ± 10 405.7 ± 6.1 404.2 ± 4.0 401.0 ± 4.9 402.4 ± 2.7
4.2422 4.2413 4.2383 4.2322 4.2191 4.2120
T = 393.15 K 330 ± 191 402 ± 10 402.4 ± 6.1 401.2 ± 4.1 398.7 ± 9.5 399.6 ± 2.8
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
m
The ± uncertainties are from propagation of uncertainties as described in reference [48].
75
76
TABLE 6A Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for aqueous (threonine + HCl) at p = 0.35 MPa ma mol Æ kg
cp,s 1
Cp,/ 1
JÆK
1
Æg
JÆK
cp,s 1
1
Æ mol
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
Æ mol
1
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
1
Æ mol
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
1
Æ mol
JÆK
Cp,/ 1
1
Æg
J Æ K1 Æ mol1
4.1944 4.1870 4.1768 4.1528 4.0835 3.9827 3.8143
T = 278.15 K 95 ± 24 118 ± 19 133.0 ± 7.6 146.6 ± 3.6 158.5 ± 1.8 180.3 ± 1.2 187.15 ± 0.97
4.1851 4.1781 4.1682 4.1452 4.0791 3.9814 3.8212
T = 283.15 K 111 ± 25 142 ± 18 151.5 ± 8.0 165.0 ± 3.5 178.9 ± 1.7 196.5 ± 1.2 205.54 ± 0.87
4.1788 4.1720 4.1625 4.1401 4.0761 3.9811 3.8257
T = 288.15 K 136 ± 28 154 ± 18 165.2 ± 8.7 178.6 ± 3.6 192.6 ± 1.6 208.8 ± 1.2 217.73 ± 0.19
4.1745 4.1680 4.1587 4.1369 4.0745 3.9818 3.8301
T = 293.15 K 145 ± 29 165 ± 17 177.1 ± 9.1 189.9 ± 3.8 203.5 ± 1.6 218.7 ± 1.2 227.64 ± 0.78
4.1718 4.1655 4.1563 4.1350 4.0738 3.9828 3.8339
T = 298.15 K 151 ± 28 174 ± 17 185.7 ± 8.8 198.5 ± 3.5 211.8 ± 1.5 226.1 ± 1.1 235.09 ± 0.78
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
4.1701 4.1639 4.1549 4.1338 4.0738 3.9841 3.8375
T = 303.15 K 155 ± 26 182 ± 17 192.0 ± 8.0 204.9 ± 3.5 218.7 ± 1.5 232.3 ± 1.1 241.28 ± 0.77
4.1693 4.1633 4.1543 4.1335 4.0743 3.9858 3.8408
T = 308.15 K 157 ± 23 188 ± 16 196.9 ± 7.4 210.1 ± 3.8 224.2 ± 1.5 237.2 ± 1.2 246.16 ± 0.77
4.1693 4.1633 4.1544 4.1339 4.0753 3.9877 3.8440
T = 313.15 K 161 ± 23 193 ± 16 200.9 ± 7.2 214.5 ± 3.8 228.5 ± 1.4 241.3 ± 1.2 250.10 ± 0.76
4.1700 4.1641 4.1553 4.1350 4.0768 3.9900 3.8473
T = 318.15 K 166 ± 22 197 ± 16 204.7 ± 7.0 218.5 ± 3.6 232.0 ± 1.4 244.7 ± 1.2 253.31 ± 0.75
4.1713 4.1654 4.1566 4.1364 4.0786 3.9925 3.8504
T = 323.15 K 170 ± 22 200 ± 16 207.6 ± 6.8 221.5 ± 3.6 234.6 ± 1.4 247.5 ± 1.2 255.81 ± 0.75
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
4.1731 4.1673 4.1585 4.1384 4.0808 3.9952 3.8536
T = 328.15 K 172 ± 21 202 ± 15 209.6 ± 6.7 223.5 ± 3.8 236.6 ± 1.4 249.7 ± 1.2 257.74 ± 0.74
4.1754 4.1695 4.1608 4.1408 4.0833 3.9980 3.8569
T = 333.15 K 176 ± 21 204 ± 15 211.5 ± 6.7 225.3 ± 3.9 238.2 ± 1.3 251.3 ± 1.2 259.37 ± 0.73
4.1781 4.1722 4.1636 4.1436 4.0862 4.0013 3.8603
T = 338.15 K 181 ± 23 205 ± 15 213.6 ± 7.1 226.9 ± 3.8 239.5 ± 1.3 252.9 ± 1.2 260.63 ± 0.73
4.1815 4.1754 4.1669 4.1468 4.0894 4.0047 3.8637
T = 343.15 K 191 ± 26 206 ± 15 216.4 ± 8.1 228.0 ± 3.5 240.1 ± 1.3 253.9 ± 1.1 261.37 ± 0.72
4.1852 4.1790 4.1706 4.1505 4.0930 4.0083 3.8672
T = 348.15 K 201 ± 32 206 ± 15 219 ± 26 228.8 ± 3.3 240.4 ± 1.2 254.7 ± 1.1 261.87 ± 0.71
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
4.1894 4.1830 4.1747 4.1544 4.0968 4.0122 3.8709
T = 353.15 K 210 ± 42 206 ± 15 221 ± 13 229.2 ± 3.1 240.3 ± 1.2 255.1 ± 1.1 262.08 ± 0.71
4.1939 4.1874 4.1791 4.1588 4.1010 4.0164 3.8748
T = 358.15 K 217 ± 54 206 ± 15 222 ± 17 229.1 ± 2.9 240.0 ± 1.2 255.3 ± 1.0 262.14 ± 0.70
4.1987 4.1921 4.1839 4.1635 4.1055 4.0208 3.8789
T = 363.15 K 222 ± 63 205 ± 15 223 ± 19 229.1 ± 2.8 239.6 ± 1.2 255.4 ± 1.0 262.05 ± 0.70
4.2040 4.1974 4.1891 4.1686 4.1103 4.0255 3.8830
T = 368.15 K 223 ± 64 204 ± 14 223 ± 20 228.2 ± 2.7 238.6 ± 1.1 254.88 ± 0.99 261.45 ± 0.69
4.2097 4.2030 4.1947 4.1741 4.1156 4.0306 3.8875
T = 373.15 K 221 ± 58 203 ± 14 221 ± 18 227.4 ± 2.6 237.6 ± 1.1 254.37 ± 0.96 260.87 ± 0.69
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
4.2159 4.2093 4.2008 4.1802 4.1213 4.0360 3.8923
T = 378.15 K 214 ± 41 201 ± 14 219 ± 13 225.9 ± 2.4 236.4 ± 1.1 253.50 ± 0.91 260.06 ± 0.69
4.2223 4.2159 4.2072 4.1866 4.1275 4.0417 3.8973
T = 383.15 K 198 ± 15 199 ± 14 213.5 ± 4.8 224.2 ± 2.3 235.0 ± 1.1 252.24 ± 0.87 259.13 ± 0.69
4.2292 4.2231 4.2141 4.1936 4.1342 4.0478 3.9027
T = 388.15 K 170 ± 42 197 ± 14 205 ± 13 222.2 ± 2.2 233.8 ± 1.1 250.94 ± 0.87 257.96 ± 0.73
4.2365 4.2309 4.2214 4.2011 4.1415 4.0545 3.9079
T = 393.15 K 134 ± 93 194 ± 15 196 ± 29 219.4 ± 2.4 232.4 ± 1.2 249.91 ± 0.92 255.90 ± 0.93
The ± uncertainties are from propagation of uncertainties as described in reference [48]. a Molality of threonine, with stoichiometric molality ratio {m(HThr)/m(HCl)} = 0.9997.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
TABLE 6B Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for aqueous (isoleucine + HCl) at p = 0.35 MPa cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
mol Æ kg1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.1966 4.1910 4.1832 4.1654 4.1133 4.0366 3.9000
T = 278.15 K 287 ± 10 313.8 ± 4.7 313.1 ± 3.1 326.5 ± 2.0 331.95 ± 0.97 346.55 ± 0.93 336.16 ± 0.66
4.1873 4.1820 4.1747 4.1574 4.1084 4.0336 3.9054
T = 283.15 K 303 ± 10 331.8 ± 5.0 332.7 ± 3.3 341.3 ± 2.0 350.10 ± 0.90 359.6 ± 1.0 352.85 ± 0.56
4.1810 4.1758 4.1687 4.1521 4.1047 4.0317 3.9075
T = 288.15 K 326 ± 11 341.3 ± 5.2 343.0 ± 3.4 351.6 ± 1.9 360.38 ± 0.88 368.4 ± 1.1 362.16 ± 0.48
4.1767 4.1717 4.1647 4.1485 4.1023 4.0307 3.9094
T = 293.15 K 335 ± 11 349.5 ± 5.5 350.6 ± 3.5 359.2 ± 2.0 368.14 ± 0.90 375.0 ± 1.2 369.09 ± 0.49
4.1740 4.1691 4.1623 4.1463 4.1009 4.0302 3.9107
T = 298.15 K 342 ± 12 355.4 ± 5.8 356.5 ± 3.6 364.7 ± 2.1 373.39 ± 0.93 379.3 ± 1.1 373.67 ± 0.50
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.1723 4.1674 4.1607 4.1449 4.1001 4.0301 3.9119
T = 303.15 K 347 ± 12 360.5 ± 6.0 361.2 ± 3.8 368.8 ± 2.4 377.50 ± 0.97 382.43 ± 0.98 377.01 ± 0.51
4.1716 4.1667 4.1601 4.1444 4.1000 4.0305 3.9130
T = 308.15 K 351 ± 13 364.1 ± 6.3 364.7 ± 3.9 371.7 ± 3.4 380.3 ± 1.0 384.55 ± 0.90 379.20 ± 0.52
4.1715 4.1667 4.1601 4.1446 4.1004 4.0311 3.9140
T = 313.15 K 354 ± 13 366.3 ± 6.6 366.9 ± 4.1 374.3 ± 3.5 382.0 ± 1.0 385.96 ± 0.88 380.55 ± 0.53
4.1722 4.1675 4.1609 4.1454 4.1013 4.0321 3.9153
T = 318.15 K 356 ± 14 368.1 ± 6.9 368.5 ± 4.2 376.2 ± 3.7 383.1 ± 1.1 386.81 ± 0.89 381.33 ± 0.54
4.1734 4.1687 4.1621 4.1467 4.1026 4.0334 3.9164
T = 323.15 K 357 ± 14 368.9 ± 7.2 369.2 ± 4.4 377.4 ± 4.0 383.6 ± 1.1 387.20 ± 0.93 381.47 ± 0.55
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.1752 4.1705 4.1639 4.1486 4.1043 4.0350 3.9177
T = 328.15 K 357 ± 15 369.3 ± 7.5 369.3 ± 4.6 378.5 ± 3.7 383.5 ± 1.1 387.1 ± 1.0 381.16 ± 0.56
4.1774 4.1727 4.1661 4.1508 4.1063 4.0368 3.9192
T = 333.15 K 358 ± 15 369.2 ± 7.7 369.1 ± 4.7 379.1 ± 4.0 383.1 ± 1.2 386.7 ± 1.1 380.67 ± 0.57
4.1801 4.1753 4.1687 4.1535 4.1087 4.0389 3.9210
T = 338.15 K 357 ± 16 368.6 ± 8.0 368.6 ± 4.9 379.2 ± 5.0 382.3 ± 1.2 385.7 ± 1.3 379.99 ± 0.58
4.1833 4.1785 4.1718 4.1566 4.1114 4.0413 3.9228
T = 343.15 K 356 ± 17 367.6 ± 8.3 367.4 ± 5.1 378.3 ± 6.1 381.0 ± 1.2 384.3 ± 1.5 378.84 ± 0.59
4.1869 4.1820 4.1753 4.1600 4.1145 4.0440 3.9249
T = 348.15 K 355 ± 17 366.2 ± 8.7 366.0 ± 5.3 377.0 ± 7.8 379.4 ± 1.3 382.7 ± 1.8 377.60 ± 0.60
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.1908 4.1860 4.1792 4.1638 4.1179 4.0470 3.9272
T = 353.15 K 354 ± 18 364.4 ± 9.0 364.2 ± 5.5 376 ± 10 377.6 ± 1.3 381.0 ± 2.3 376.19 ± 0.61
4.1952 4.1903 4.1835 4.1680 4.1217 4.0504 3.9298
T = 358.15 K 352 ± 18 362.6 ± 9.3 362.3 ± 5.7 375 ± 13 375.7 ± 1.4 379.3 ± 2.9 374.72 ± 0.62
4.2000 4.1950 4.1881 4.1726 4.1258 4.0541 3.9327
T = 363.15 K 350 ± 19 360.4 ± 9.6 360.1 ± 5.9 373 ± 15 373.6 ± 1.4 377.5 ± 3.3 373.25 ± 0.64
4.2052 4.2002 4.1932 4.1775 4.1303 4.0580 3.9357
T = 368.15 K 347 ± 20 357.8 ± 9.9 357.4 ± 6.1 370 ± 15 371.0 ± 1.4 375.3 ± 3.4 371.38 ± 0.65
4.2109 4.2058 4.1988 4.1827 4.1351 4.0622 3.9392
T = 373.15 K 344 ± 21 355 ± 10 354.6 ± 6.3 366 ± 14 368.5 ± 1.5 373.1 ± 3.1 369.65 ± 0.66
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.2171 4.2120 4.2049 4.1884 4.1405 4.0668 3.9431
T = 378.15 K 342 ± 21 352 ± 11 351.6 ± 6.5 362 ± 10 365.9 ± 1.5 370.7 ± 2.4 367.68 ± 0.68
4.2237 4.2185 4.2113 4.1944 4.1463 4.0716 3.9472
T = 383.15 K 339 ± 22 349 ± 11 348.5 ± 6.7 355.3 ± 4.6 363.1 ± 1.6 368.0 ± 1.2 365.71 ± 0.71
4.2310 4.2257 4.2184 4.2009 4.1527 4.0767 3.9518
T = 388.15 K 335 ± 23 346 ± 11 345.2 ± 7.0 348.1 ± 8.1 360.5 ± 1.6 365.2 ± 1.9 363.68 ± 0.78
4.2388 4.2334 4.2260 4.2079 4.1595 4.0825 3.9560
T = 393.15 K 329 ± 24 341 ± 12 340.7 ± 7.3 341 ± 19 357.2 ± 1.8 362.9 ± 4.2 360.4 ± 1.1 77
The ± uncertainties are from propagation of uncertainties as described in reference [48]. a Molality of isoleucine, with stoichiometric molality ratio {m(HIle)/m(HCl)} = 0.997.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
ma
78
TABLE 7A Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for aqueous (threonine + NaOH) at p = 0.35 MPa cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
mol Æ kg1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.1943 4.1878 4.1777 4.1546 4.0915 3.9987 3.8491
T = 278.15 K 111 ± 40 90 ± 23 111 ± 14 107 ± 10 132.8 ± 2.8 147.5 ± 1.4 188.0 ± 1.1
4.1852 4.1792 4.1696 4.1484 4.0884 4.0005 3.8578
T = 283.15 K 138 ± 39 125 ± 23 138 ± 13 140 ± 11 158.4 ± 2.7 171.4 ± 1.3 207.6 ± 1.2
4.1791 4.1736 4.1642 4.1447 4.0869 4.0028 3.8660
T = 288.15 K 159 ± 37 153 ± 22 159 ± 13 167 ± 12 178.2 ± 2.6 189.0 ± 1.3 223.6 ± 1.2
4.1750 4.1698 4.1608 4.1423 4.0868 4.0059 3.8741
T = 293.15 K 177 ± 36 173 ± 22 177 ± 12 186.3 ± 9.8 195.4 ± 2.5 205.1 ± 1.2 237.2 ± 1.0
4.1725 4.1675 4.1589 4.1410 4.0875 4.0092 3.8818
T = 298.15 K 193 ± 35 189 ± 21 193 ± 12 201.7 ± 9.0 209.5 ± 2.4 218.4 ± 1.2 248.91 ± 0.91
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.1709 4.1661 4.1577 4.1406 4.0887 4.0126 3.8890
T = 303.15 K 205 ± 34 202 ± 21 206 ± 12 214.9 ± 9.0 221.6 ± 2.4 229.8 ± 1.2 258.91 ± 0.92
4.1703 4.1656 4.1575 4.1409 4.0904 4.0162 3.8957
T = 308.15 K 216 ± 33 214 ± 21 217 ± 11 226.1 ± 9.1 231.8 ± 2.3 239.6 ± 1.1 267.38 ± 0.94
4.1704 4.1659 4.1579 4.1418 4.0924 4.0199 3.9019
T = 313.15 K 226 ± 33 225 ± 21 227 ± 11 236.1 ± 9.2 240.6 ± 2.2 248.0 ± 1.1 274.58 ± 0.94
4.1712 4.1668 4.1590 4.1433 4.0949 4.0238 3.9079
T = 318.15 K 234 ± 32 234 ± 20 235 ± 11 244.7 ± 9.3 248.1 ± 2.2 255.4 ± 1.1 280.82 ± 0.96
4.1725 4.1683 4.1606 4.1452 4.0977 4.0277 3.9137
T = 323.15 K 240 ± 31 242 ± 19 241 ± 10 252.0 ± 9.3 254.6 ± 2.1 261.7 ± 1.0 286.19 ± 0.96
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.1744 4.1702 4.1627 4.1475 4.1007 4.0318 3.9192
T = 328.15 K 246 ± 30 248 ± 19 247.3 ± 9.9 2.57.7 ± 9.4 260.1 ± 2.0 267.18 ± 0.99 290.71 ± 0.97
4.1767 4.1726 4.1651 4.1502 4.1040 4.0359 3.9245
T = 333.15 K 250 ± 29 253 ± 19 252.3 ± 9.6 262.6 ± 9.4 264.9 ± 2.0 272.00 ± 0.95 294.51 ± 0.97
4.1794 4.1754 4.1680 4.1533 4.1076 4.0402 3.9297
T = 338.15 K 254 ± 28 257 ± 19 256.5 ± 9.3 266.8 ± 9.4 269.0 ± 1.9 276.14 ± 0.92 297.84 ± 0.98
4.1827 4.1787 4.1714 4.1568 4.1115 4.0447 3.9350
T = 343.15 K 257 ± 27 262 ± 18 259.8 ± 9.0 270.4 ± 9.4 272.4 ± 1.8 279.62 ± 0.89 300.66 ± 0.98
4.1863 4.1824 4.1751 4.1606 4.1157 4.0493 3.9402
T = 348.15 K 260 ± 26 265 ± 17 262.5 ± 8.6 273.3 ± 9.5 275.1 ± 1.8 282.52 ± 0.86 302.98 ± 0.99
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.1903 4.1864 4.1792 4.1648 4.1201 4.0540 3.9452
T = 353.15 K 261 ± 25 267 ± 16 264.6 ± 8.3 275.4 ± 9.6 277.4 ± 1.7 284.88 ± 0.83 304.8 ± 1.0
4.1947 4.1908 4.1836 4.1693 4.1247 4.0589 3.9503
T = 358.15 K 262 ± 24 268 ± 15 266.0 ± 8.0 277.1 ± 9.7 279.0 ± 1.6 286.77 ± 0.79 306.1 ± 1.0
4.1995 4.1956 4.1884 4.1741 4.1296 4.0640 3.9552
T = 363.15 K 262 ± 23 269 ± 15 266.8 ± 7.7 278.4 ± 9.9 280.2 ± 1.6 288.22 ± 0.76 307.0 ± 1.0
4.2048 4.2009 4.1937 4.1794 4.1349 4.0692 3.9602
T = 368.15 K 262 ± 22 269 ± 14 267.1 ± 7.4 279 ± 10 280.9 ± 1.5 289.16 ± 0.73 307.3 ± 1.1
4.2105 4.2066 4.1993 4.1851 4.1405 4.0747 3.9652
T = 373.15 K 261 ± 21 268 ± 13 267.0 ± 7.1 279 ± 11 281.1 ± 1.4 289.72 ± 0.70 307.3 ± 1.1
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.2167 4.2128 4.2056 4.1912 4.1465 4.0805 3.9703
T = 378.15 K 260 ± 20 267 ± 13 266.3 ± 6.7 278 ± 11 280.7 ± 1.4 289.81 ± 0.67 306.9 ± 1.2
4.2234 4.2194 4.2121 4.1977 4.1528 4.0865 3.9756
T = 383.15 K 259 ± 19 264 ± 12 265.1 ± 6.4 277 ± 12 279.9 ± 1.3 289.51 ± 0.65 306.2 ± 1.2
4.2306 4.2266 4.2193 4.2048 4.1595 4.0928 3.9812
T = 588.15 K 257 ± 18 262 ± 12 263.4 ± 6.1 276 ± 12 278.5 ± 1.3 288.85 ± 0.62 305.3 ± 1.3
4.2385 4.2344 4.2270 4.2125 4.1664 4.0990 3.9872
T = 393.15 K 256 ± 17 260 ± 12 261.2 ± 5.8 276 ± 14 275.7 ± 1.2 287.81 ± 0.61 304.3 ± 1.5
The ± uncertainties are from propagation of uncertainties as described in reference [48]. a Molality of isoleucine, with stoichiometric molality ratio {m(HThr)/m(NaOH)} = 0.9997.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
ma
TABLE 7B Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for aqueous (isoleucine + Na) at p = 0.35 MPa ma mol Æ kg
cp,s 1
JÆK
Cp,/ 1
1
Æg
cp,s 1
JÆK
1
Æ mol
JÆK
Cp,/ 1
1
Æg
JÆK
cp,s 1
1
Æ mol
Cp,/ 1
JÆK
1
Æg
JÆK
cp,s 1
Æ mol
1
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
Æ mol
1
Cp,/ 1
JÆK
1
Æg
J Æ K1 Æ mol1
4.1975 4.1919 4.1857 4.1680 4.1225 4.0556 3.9550
T = 278.15 K 304.5 ± 7.9 296.4 ± 4.9 302.1 ± 2.5 291.2 ± 1.8 320.18 ± 0.89 321.41 ± 0.86 356.49 ± 0.51
4.1882 4.1831 4.1774 4.1613 4.1188 4.0576 3.9632
T = 283.15 K 326.6 ± 7.0 320.6 ± 4.6 325.7 ± 2.3 319.2 ± 1.7 342.48 ± 0.83 346.45 ± 0.92 375.68 ± 0.50
4.1820 4.1771 4.1718 4.1570 4.1166 4.0601 3.9704
T = 288.15 K 339.7 ± 6.7 337.5 ± 4.1 343.1 ± 2.3 340.7 ± 1.6 358.93 ± 0.80 365.59 ± 0.99 390.58 ± 0.47
4.1779 4.1733 4.1681 4.1543 4.1158 4.0627 3.9768
T = 293.15 K 354.8 ± 6.5 353.1 ± 5.8 358.1 ± 2.2 357.5 ± 2.0 372.80 ± 0.78 380.9 ± 1.1 402.38 ± 0.46
4.1753 4.1709 4.1660 4.1529 4.1159 4.0655 3.9822
T = 298.15 K 367.5 ± 6.3 367.6 ± 7.3 370.0 ± 2.2 371.4 ± 2.4 384.03 ± 0.76 392.98 ± 0.91 411.55 ± 0.46
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
4.1736 4.1695 4.1647 4.1525 4.1165 4.0682 3.9868
T = 303.15 K 377.9 ± 6.4 381 ± 10 380.4 ± 2.2 384.8 ± 3.4 393.42 ± 0.76 402.74 ± 0.88 418.60 ± 0.47
4.1730 4.1691 4.1643 4.1528 4.1177 4.0709 3.9907
T = 308.15 K 386.6 ± 6.3 392 ± 13 388.6 ± 2.2 396.3 ± 4.2 401.08 ± 0.75 410.6 ± 1.1 424.02 ± 0.53
4.1730 4.1693 4.1645 4.1536 4.1191 4.0736 3.9943
T = 313.15 K 393.6 ± 6.2 402 ± 13 395.4 ± 2.1 404.9 ± 4.1 407.38 ± 0.74 416.9 ± 1.1 428.28 ± 0.54
4.1738 4.1702 4.1655 4.1548 4.1211 4.0765 3.9977
T = 318.15 K 399.4 ± 6.2 407 ± 13 400.9 ± 2.1 410.4 ± 4.2 412.62 ± 0.74 422.0 ± 1.1 431.53 ± 0.55
4.1750 4.1714 4.1669 4.1563 4.1233 4.0793 4.0008
T = 323.15 K 404.1 ± 6.1 410 ± 14 405.4 ± 2.1 413.9 ± 4.4 416.85 ± 0.73 425.9 ± 1.1 433.86 ± 0.57
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
4.1769 4.1734 4.1689 4.1584 4.1259 4.0822 4.0039
T = 328.15 K 407.5 ± 6.1 413.8 ± 9.9 409.0 ± 2.1 417.2 ± 3.2 420.24 ± 0.73 428.83 ± 0.94 435.61 ± 0.54
4.1791 4.1756 4.1712 4.1608 4.1286 4.0852 4.0066
T = 333.15 K 410.8 ± 6.1 416.2 ± 8.6 411.7 ± 2.1 419.4 ± 2.8 422.88 ± 0.73 430.88 ± 0.81 436.55 ± 0.56
4.1818 4.1783 4.1740 4.1636 4.1317 4.0883 4.0092
T = 338.15 K 412.5 ± 6.0 417.1 ± 9.5 413.7 ± 2.1 421.0 ± 3.1 424.81 ± 0.72 432.26 ± 0.71 436.86 ± 0.65
4.1851 4.1815 4.1772 4.1669 4.1351 4.0915 4.0118
T = 343.15 K 413.5 ± 6.0 417 ± 11 414.9 ± 2.1 421.9 ± 3.6 426.05 ± 0.72 432.93 ± 0.64 436.64 ± 0.75
4.1887 4.1851 4.1808 4.1704 4.1387 4.0949 4.0143
T = 348.15 K 413.7 ± 5.9 417 ± 14 415.4 ± 2.1 422.1 ± 4.5 426.72 ± 0.72 432.98 ± 0.60 435.97 ± 0.92
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
4.1926 4.1891 4.1848 4.1744 4.1426 4.0983 4.0169
T = 353.15 K 413.4 ± 6.0 417 ± 18 415.4 ± 2.1 422.1 ± 5.8 426.89 ± 0.72 432.48 ± 0.58 434.9 ± 1.2
4.1970 4.1934 4.1891 4.1787 4.1468 4.1019 4.0195
T = 358.15 K 412.5 ± 5.9 417 ± 23 414.9 ± 2.0 421.7 ± 7.3 426.58 ± 0.72 431.50 ± 0.57 433.5 ± 1.4
4.2018 4.1982 4.1938 4.1833 4.1512 4.1057 4.0222
T = 363.15 K 410.9 ± 5.9 416 ± 27 413.9 ± 2.0 420.8 ± 8.4 425.78 ± 0.72 430.12 ± 0.57 431.8 ± 1.6
4.2070 4.2034 4.1990 4.1883 4.1560 4.1097 4.0250
T = 368.15 K 408.5 ± 6.0 413 ± 27 412.3 ± 2.0 418.5 ± 8.6 424.43 ± 0.72 428.22 ± 0.57 429.7 ± 1.7
4.2127 4.2089 4.2046 4.1936 4.1610 4.1139 4.0278
T = 373.15 K 406.1 ± 6.0 408 ± 25 410.4 ± 2.1 415.2 ± 7.8 422.70 ± 0.72 425.86 ± 0.58 427.3 ± 1.5
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
4.2189 4.2150 4.2107 4.1993 4.1665 4.1185 4.0309
T = 378.15 K 403.4 ± 6.0 401 ± 17 407.8 ± 2.1 410.6 ± 5.5 420.53 ± 0.73 423.05 ± 0.57 424.5 ± 1.2
4.2256 4.2213 4.2172 4.2054 4.1723 4.1233 4.0340
T = 383.15 K 400.2 ± 6.0 392.0 ± 5.8 404.9 ± 2.1 404.9 ± 2.0 417.90 ± 0.73 419.83 ± 0.57 421.36 ± 0.57
4.2328 4.2282 4.2243 4.2118 4.1786 4.1284 4.0373
T = 388.15 K 397.0 ± 6.1 380 ± 15 401.4 ± 2.1 397.4 ± 4.7 414.78 ± 0.74 416.14 ± 0.61 417.87 ± 0.93
4.2406 4.2357 4.2319 4.2188 4.1850 4.1341 4.0409
T = 393.15 K 394.2 ± 6.5 367 ± 37 396.7 ± 2.1 389 ± 12 410.09 ± 0.76 412.51 ± 0.60 414.1 ± 2.1
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
The ± uncertainties are from propagation of uncertainties as described in reference [48]. a Molality of isoleucine, with stoichiometric molality ratio {m(Hlle)/m(NaOH)} = 0.998. 79
80
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
TABLE 8A Regression parameters of equation (4) for apparent molar heat capacities Cp,/(T, m) of {HThr±(aq)}, {HThr±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, {H2Thr+Cl (aq)}, and {Na+Thr(aq)} ci
HThr±(aq) observed, w = 0 (Table 5A)
{HThr±(aq) + HCl(aq)} observed, w = 1 (Table 6A)
{HThr±(aq) + NaOH(aq)} observed, w = 1 (Table 7A)
H2Thr+Cl(aq) iteration, w = 1 (see text)
Na+Thr(aq)iteration, w = 1 (see text)
103 Æ c0 103 Æ c1 c2 103 Æ c3 c4 103 Æ c5 103 Æ c6 c7 103 Æ c8 106 Æ c9 Da Highest m
1.2481 ± 0.0001 74.8176 ± 0.0001
2.15884 ± 0.00004 53.7880 ± 0.0001 26.2 ± 0.1 12.61910 ± 0.00002 78.5542 ± 0.0001 59.8207 ± 0.0002
282.26625 ± 0.00004 0.65054 ± 0.00004 33.8 ± 0.1 0.10727 ± 0.00001
201.75770 ± 0.00004 1.04318 ± 0.00004
17.43383 ± 0.00001 105.959 ± 0.001 79.7715 ± 0.0004
1.2458 ± 0.0001 48.84194 ± 0.00004 46.2 ± 0.1 11.39916 ± 0.00001 69.1885 ± 0.0001 51.6897 ± 0.0002
8.1802 ± 0.0001 11.0436 ± 0.0002
8.3149 ± 0.0001 11.889 ± 0.001
13.3127 ± 0.0001 18.298 ± 0.001
69.92825 ± 0.00001 592.1496 ± 0.0001 841.1296 ± 0.0002 534.787 ± 0.001 ± 0.93 1.0
49.51713 ± 0.00001 406.1359 ± 0.0001 567.1334 ± 0.0002 358.862 ± 0.001 ± 0.59 1.0
± 2.8 0.65
± 2.1 1.0
± 1.8 1.0
0.17811 ± 0.00001
The ± values are chosen to reproduce the generated Cp,/ values to within ±0.1 J Æ K1 Æ mol1 at 278.15 < T/K < 393.15 and at m < 0.65 mol Æ kg1 for the zwitterion and w < 1.0 mol Æ kg1 for the cationic and anionic forms. a Standard deviations of the regressions.
TABLE 8B Regression parameters of equation (4) for apparent molar heat capacities Cp,/(T, m) of {HIle±(aq)}, {HIle±(aq) + HCl(aq)}, {HIle±(aq) + NaOH(aq)}, {H2Ile+Cl (aq)}, and {Na+Ile(aq)} ci
HIle±(aq) observed, w = 0 (Table 5B)
{HIle±(aq) + HCl(aq)} observed, w = 1 (Table 6B)
{HIle±(aq) + NaOH(aq)} observed, w = 1 (Table 7B)
H2Ile+Cl(aq)iteration, w = 1 (see text)
Na+Ile(aq)iteration, w = 1 (see text)
103 Æ c0 103 Æ c1 c2 103 Æ c3 c4 103 Æ c5 103 Æ c6 c7 103 Æ c8 106 Æ c9 Da Highest m
0.46953 ± 0.00006
1.0411 ± 0.0001 51.41595 ± 0.00004 41.04 ± 0.04 12.07547 ± 0.00001 75.5692 ± 0.0001 58.258 ± 0.001
2.06545 ± 0.00004 78.9648 ± 0.0001 1.66 ± 0.04 18.53567 ± 0.00001 115.6438 ± 0.0001 88.431 ± 0.001
315.46322 ± 0.00003
289.19595 ± 0.00003 1.3601 ± 0.0001
8.4728 ± 0.0001 12.795 ± 0.001
14.1226 ± 0.0001 20.1286 ± 0.0002
4.9460 ± 0.0001 6.9632 ± 0.0004 ± 2.9 0.21
± 2.4 1.0
± 2.9 1.0
0.23640 ± 0.00002 0.1305 ± 0.0001 78.53056 ± 0.00001 674.9853 ± 0.0001 968.5031 ± 0.0002 620.123 ± 0.001 ± 1.2 1.0
71.35138 ± 0.00001 594.4049 ± 0.0001 835.2597 ± 0.0002 528.156 ± 0.001 ± 0.86 1.0
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 0.21 mol Æ kg1 for the zwitterion and w 6 1.0 mol Æ kg1 for the cationic and anionic forms. a Standard deviations of the regressions.
We fit by regression equation (4) to our derived Cp,/(T, m) results for H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq) using the squares of the reciprocals of the uncertainties in Cp,/,obs from tables 6 and 7 as weighting factors. The regression parameters ci are given in columns 5 and 6 of tables 8A and 8B. Figures 3 and 4 show our Cp,/(T, m) results for these species, surfaces calculated from the regression parameters in columns 5 and 6 of tables 8A and 8B, and ‘‘ideal’’ surfaces obtained by simple addition of the surfaces for each of the reactant components. We know of no results in the literature that give Cp,/ for any of these species. We have also calculated V/(T, m) for H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq) and then fit equation (3) by regression to these results to give the parameters in columns 5 and 6 in tables 4A and 4B. The results of these calculations are the solid surfaces shown in figures 5 and 6. The points calculated using Young’s
Rule as well as the ‘‘ideal’’ surfaces are also shown in figures 5 and 6. We are unaware of results from the literature for V/ of any of these species. Our iterative Young’s Rule results allow us to calculate values of DrCp,m, DrHm, pQa, DrSm, and DrVm for reactions (5) and (6) analogous to what was done in our previous reports [1–4]. Figure 7 shows DrCp,m(T, m) for reactions (5) and (6) for both threonine and isoleucine, together with values from the literature [24]. The difference between our value of Dr C p;m for reaction (5) for isoleucine at T* = 298.15 and m* = 0 and the value from reference [24] is D = 41.0 J Æ K1 Æ mol1. The comparable difference for reaction (6) for isoleucine is D = 58.9 J Æ K1 Æ mol1. We found no results in the literature for DrCp,m for reaction (5) or (6) for threonine. Figure 8 shows DrHm(T, m) for reactions (5) and (6) together with values from the literature [24–35]. The differences between our values of DrHm(T, m) for reaction (5)
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
81
450 -1 -1 Cp,φ / (J·K ·mol )
-1 -1 Cp,φ / (J·K mol )
550 400 350 300 250 200
450 350 250 150 50 1.00
0.6
m/
(m ol·
0.75
380
0.4
360 340
0.2
kg - 1 )
m/
320 0.0
300
T
280
/K
FIGURE 2. Apparent molar heat capacity Cp,/ of zwitterionic threonine HThr±(aq) (lower surface) and isoleucine HIle±(aq) (upper surface) plotted against temperature T and molality m. Surfaces generated from equation (4) with parameters in column 2 of tables 8A and 8B, respectively; (s), experimental values from table 5A; (h), experimental values from table 5B; (d), references [12,13,21–23]; (n), references [13,20,21].
360
0.50
(m ol·
380
340 320
0.25
kg - 1 )
0.00
300 280
T/
K
FIGURE 4. Apparent molar heat capacities Cp,/ of sodium threoninate Na+Thr(aq) (lower solid surface and ), [Cp,/{HThr±(aq)} + Cp,/{NaOH(aq)}] (lower wire frame), sodium isoleucinate {Na+Thr(aq) + 200 J Æ K1 Æ mol1} (upper solid surface and d), and of [Cp,/{HIle±(aq)} + Cp,/{NaOH(aq)} + 200 J Æ K1 Æ mol1] (upper 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 tables 8A and 8B, respectively; (s), experimental values from table 7A; (d), experimental values from table 7B; wire frames generated by adding Cp,/(T, m) for Na+(aq) [1] to Cp,/(T, m) for threonine(aq) or isoleucine(aq).
450 350 160
250 1
150
3 Vφ / (cm ·mol )
-1 -1 Cp,φ / (J·K mol )
550
50 1.00 0.75
m/
360
0.50
(m ol·
kg - 1 0.25 )
380
340 320 0.00
300 280
T/
K
FIGURE 3. Apparent molar heat capacities Cp,/ of threoninium hydrochloride H2Thr+Cl(aq) (lower solid surface and s), [Cp,/{HThr±(aq)} + Cp,/{HCl(aq)}] (lower wire frame), isoleucininium hydrochloride {H2Ile+Cl(aq) + 200 J Æ K1 Æ mol1} (upper solid surface and d), and of [Cp,/{HIle±(aq)} + Cp,/{HCl(aq)} + 200 J Æ K1 Æ mol1] (upper wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surfaces generated from equation (4) with regression parameters from column 5 of tables 8A and 8B, respectively; (s), experimental values from table 6A; (d), experimental values from table 6B; wire frames generated by adding Cp,/(T, m) for HCl(aq) [1] to Cp,/(T, m) for threonine (aq) or isoleucine (aq).
and those from the literature are in the range D = (2.20 [25,29] to 1.94 [27]) kJ Æ mol1 with an average difference D = 0.25 kJ Æ mol1 for aqueous threonine, and those differences are D = (1.81 [31] to 0.52 [31]) kJ Æ mol1 with
140
120
100 1.00 0.75
m/
380 360
0.50
(m ol·
340 320
0.25
kg - 1 )
0.00
300 280
T/
K
FIGURE 5. Apparent molar volume V/(i) of threoninium hydrochloride H2Thr+Cl(aq) (lower solid surface and ), [Cp,/{HThr±(aq)} + Cp,/{HCl(aq)}] (lower wire frame), isoleucininium hydrochloride {H2Ile+Cl(aq) + 25 cm3 Æ mol1} (upper solid surface and d), and of [Cp,/{HIle±(aq)} + Cp,/{HCl(aq)} + 25 cm3 Æ mol1] (upper wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surfaces generated from equation (3) with regression parameters from column 5 of tables 4A and 4B, respectively; (s), experimental values from table 2A; (d), experimental values from table 2B; wire frames generated by adding V/(T, m) for HCl(aq) [52] to V/(T, m) for threonine(aq) or isoleucine(aq).
82
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
1
3 Vφ / (cm ·mol )
140
120
100
80 1.00 0.75
m/
380 360
0.50
(m ol·
340 320
0.25
kg - 1 )
0.00
300 280
T/
K
FIGURE 6. Apparent molar volume V/(i) of sodium threoninate Na+Thr(aq) (lower solid surface and ), [Cp,/{HThr±(aq)} + Cp,/{NaOH(aq)}] (lower wire frame), sodium isoleucinate {Na+Thr(aq) + 25 cm3 Æ mol1} (upper solid surface and d), and of [Cp,/{HIle±(aq)} + Cp,/{NaOH(aq)} + 25 cm3 Æ mol1] (upper wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surfaces generated from equation (3) with regression parameters from column 6 of tables 4A and 4B, respectively; (s), experimental values from table 3A; (d), experimental values from table 3B; wire frames generated by adding V/(T, m) for Na+(aq) [1] to V/(T, m) for threonine(aq) or isoleucine(aq).
an average difference D = 0.16 kJ Æ mol1 for aqueous isoleucine. The differences between our DrHm(T, m) for reaction (6) and values from the literature are in the range D = (0.92 [26] to 0.73 [34]) kJ Æ mol1 with an average difference D = 0.15 kJ Æ mol1 for aqueous threonine,
and those differences are D = (2.03 [31] to 0.69 [29,33]) kJ Æ mol1 with an average difference D = 0.49 kJ Æ mol1 for aqueous isoleucine. Figure 9 shows pQa(T, m) for reactions (5) and (6) and values from the literature [26–32,35–45]. Our values of pQa(T, m) for reaction (5) differ from the literature values by D = (0.20 [26] to 0.45 [37]) with an average difference D = 0.052 for aqueous threonine, and those differences are D = (0.17 [30,32] to 0.13 [32]) with an average difference D = 0.013 for aqueous isoleucine. Our values of pQa(T, m) for reaction (6) differ from the literature values by D = (0.67 [42] to 1.27 [36]) with an average difference D = 0.18 for aqueous threonine, and D = (0.57 [30] to 0.37 [29]) with an average difference D = 0.014 for aqueous isoleucine. Figure 10 shows DrSm(T, m) for reactions (5) and (6) together with values from the literature [24–27,29–35]. The differences between our values of DrSm(T, m) for reaction (5) and those from the literature are in the range D = (4.2 [25,29] to 9.8 [27]) J Æ K1 Æ mol1 with an average difference D = 3.6 J Æ K1 Æ mol1 for aqueous threonine, and those differences are D = (5.39 [31] to 2.25 [31]) J Æ K1 Æ mol1 with an average difference D = 0.46 J Æ K1 Æ mol1 for aqueous isoleucine. The differences between our DrSm(T, m) results for reaction (6) and those from the literature are in the range D = (2.2 [26] to 10.9 [34]) J Æ K1 Æ mol1 with an average difference D = 1.7 J Æ K1 Æ mol1 for aqueous threonine, and those differences are D = (8.0 [31] to 0.046 [29,33]) J Æ K1 Æ mol1 with an average difference D = 2.7 J Æ K1 Æ mol1 for aqueous isoleucine.
45 -1 Δ rH m / (kJ·mol )
-1 -1 Δ rCp,m / (J·K mol )
0
-50
-100
35 25 15 5 -5 1.00
-150 1.00
0.75 0.75
m/
380 360
0.50
(m ol·
340 0.25
kg -1 )
320 0.00
300 280
T/
m/
380 360
0.50 0.25 (m ol· kg - 1 0.00 )
340 320 300 280
T/
K
K
FIGURE 7. Heat capacity change DrCp,m for reactions (5) and (6) of threonine and isoleucine, plotted against temperature T and molality m. (m) surface, DrCp,m for reaction (5) of threonine; (.) surface, DrCp,m for reaction (5) of isoleucine; (n), DrCp,m,1 of isoleucine, reference [24]; (n) surface, DrCp,m for reaction (6) of threonine; (,) surface, DrCp,m for reaction (6) of isoleucine; (h), DrCp,m,2 of isoleucine, reference [24].
FIGURE 8. Enthalpy change DrHm for reactions (5) and (6) of threonine and isoleucine plotted against temperature T and molality m. (m) surface, DrHm for reaction (5) of threonine; (d), DrHm,1 of threonine, references [25–29]; (.) surface, DrHm for reaction (5) of isoleucine; (n), DrHm,1 of isoleucine, references [24,29–32]; (n) surface, DrHmfor reaction (6) of threonine; (s), DrHm,2 of threonine, references [25–29,33–35]; (,) surface, DrHm for reaction (6) of isoleucine; (h), DrHm,2 of isoleucine, references [24,29–31,33].
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
10
pQa
8
6 4 1.00 0.75
m/
380 360
0.50
(m ol·
340 0.25
kg - 1 )
320 0.00
300 280
T/
K
FIGURE 9. Equilibrium molality quotient pQa for reactions (5) and (6) of threonine and isoleucine plotted against temperature T and molality m. (m) surface, pQa for reaction (5) of threonine; (d), pQa,1 of threonine, references [26,36–44]; (.) surface, pQa for reaction (5) of isoleucine; (n), pQa,1 of isoleucine, references [29–32,36,37]; (n) surface, pQa for reaction (6) of threonine; (s), pQa,2 of threonine, references [26–29,35–45]; (,) surface, pQa for reaction (6) of isoleucine; (h), pQa,2 of isoleucine, references [29–31,36,37].
We have also calculated values of DrVm(T, m) for reactions (5) and (6) using our values of V/ for HThr±(aq), HIle±(aq), H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq), values of V/ for HCl(aq) from Sharygin
83
and Wood [51], and values of V/ for NaCl(aq) and NaOH(aq) from Sorenson et al. [1]. These results are shown in figure 11. We know of no previously reported values of DrVm for reaction (5) or (6) at any T or m for aqueous solutions of either threonine or isoleucine. 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 pKa at 278.15 6 T* 6 393.15 for reactions (5) and (6) that are given in tables 9 and 10, respectively. We suggest that our values of DrVm, DrCp,m, DrHm, DrSm, and pQa are to be preferred at (0 6 m* 6 1) from (278.15 6 T* 6 393.15) over those currently extant in the literature. The greatest source of uncertainties in our reported values arise from the integration constants pQa and DrHm obtained from the literature. Uncertainties in our recommended values are limited to the uncertainties in these reference values. Interesting comparisons are possible between the properties V/(T, m) and Cp,/(T, m) for aqueous zwitterionic, cationic, and anionic species of threonine, isoleucine, valine, L-2-aminobutanoic acid, and serine. We calculate the average differences DV/(x y) at (278.15 6 T* 6 368.15) and DCp,/(x y) at (278.15 6 T* 6 393.15) at (0.0 6 m* 6 0.5) for the species of the amino acids x and y. Table 11 gives the results of these calculations. Table 12 gives our average values of the differences for these group substitutions over the temperature ranges of our experiments. These values are the averages of the values calculated using the individual values of the cationic, zwitterionic, and anionic forms. The values for replacing a proton with a methyl group are the averages for all three calculations reported in table 11.
-40 0 -1 3 Δ rVm / (cm mol )
-1 -1 Δ rSm / (J·K .mol )
-20
-60 -80 -100 1.00 0.75
m/
380
-6 -9 -12
360
0.50
(m ol·
-3
340 0.25
kg - 1 )
320 0.00
300 280
K T/
FIGURE 10. Entropy changes DrSm for reactions (5) and (6) of threonine and isoleucine plotted against temperature T and molality m. (m) surface, DrSm for reaction (5) of threonine; (d), DrSm,1 of threonine, references [25–27,29]; (.) surface, DrSm for reaction (5) of isoleucine; (n), DrSm,1 of isoleucine, references [25–27,29,33–35]; (n) surface, DrSmfor reaction (6) of threonine; (s), DrSm,2 of threonine, references [24,29–32]; (,) surface, DrSm for reaction (6) of isoleucine; (h), DrSm,2 of isoleucine, references [24,29–31,33].
1.00 0.75
m/
360
0.50 0.25 (m ol· kg - 1 0.00 )
380
340 320 300 280
T/
K
FIGURE 11. Volume changes DrVm for reactions (5) and (6) of threonine and isoleucine plotted against temperature T and molality m. (m) surface, DrVm for reaction (5) of threonine; (.) surface, DrVm for reaction (5) of isoleucine; (n) surface, DrVm for reaction (6) of threonine; (,) surface, DrVm for reaction (6) of isoleucine.
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TABLE 9A ‘‘Best’’ standard thermodynamic values for the first proton dissociation of aqueous threonine, reaction (5), H2A+(aq) = HA±(aq) + H+(aq), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K
Dr V m =ðcm3 mol1 Þ
Dr C p;m =ðJ K1 mol1 Þ
Dr H m =ðkJ mol1 Þ
Dr S m =ðJ K1 mol1 Þ
pK
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
9.77 ± 0.83 9.46 ± 0.83 9.20 ± 0.83 8.98 ± 0.84 8.81 ± 0.84 8.67 ± 0.84 8.56 ± 0.84 8.49 ± 0.84 8.44 ± 0.84 8.42 ± 0.84 8.44 ± 0.84 8.47 ± 0.84 8.54 ± 0.84 8.63 ± 0.84 8.76 ± 0.84 8.91 ± 0.84 9.09 ± 0.84 9.31 ± 0.84 9.56 ± 0.84 9.84 ± 0.83 10.17 ± 0.83 10.54 ± 0.83 10.96 ± 0.83 11.42 ± 0.82
143.5 ± 8.9 137.0 ± 8.8 130.6 ± 8.6 124.4 ± 8.4 118.4 ± 8.3 112.7 ± 8.1 107.3 ± 8.0 102.3 ± 7.8 97.7 ± 7.7 93.6 ± 7.6 90.0 ± 7.5 86.9 ± 7.4 84.4 ± 7.3 82.4 ± 7.2 81.0 ± 7.2 80.1 ± 7.1 79.7 ± 7.1 80.0 ± 7.0 80.7 ± 7.0 82.0 ± 7.0 83.7 ± 7.0 85.9 ± 7.0 88.4 ± 7.0 91.4 ± 7.1
6.4 ± 2.0 5.7 ± 2.0 5.0 ± 2.0 4.4 ± 2.0 3.7 ± 2.0 3.2 ± 2.0 2.6 ± 2.0 2.1 ± 2.0 1.6 ± 2.1 1.1 ± 2.1 0.7 ± 2.1 0.2 ± 2.1 0.2 ± 2.1 0.6 ± 2.1 1.0 ± 2.1 1.4 ± 2.1 1.8 ± 2.1 2.2 ± 2.1 2.6 ± 2.1 3.0 ± 2.1 3.5 ± 2.1 3.9 ± 2.1 4.3 ± 2.1 4.8 ± 2.1
21.7 ± 7.9 24.2 ± 7.9 26.5 ± 7.9 28.7 ± 7.8 30.7 ± 7.8 32.7 ± 7.8 34.5 ± 7.7 36.2 ± 7.7 37.7 ± 7.7 39.2 ± 7.6 40.6 ± 7.6 42.0 ± 7.5 43.3 ± 7.5 44.5 ± 7.5 45.7 ± 7.4 46.8 ± 7.4 47.9 ± 7.3 49.0 ± 7.3 50.1 ± 7.2 51.2 ± 7.2 52.3 ± 7.2 53.4 ± 7.1 54.6 ± 7.1 55.7 ± 7.0
2.33 ± 0.20 2.31 ± 0.20 2.29 ± 0.20 2.27 ± 0.20 2.26 ± 0.20 2.25 ± 0.20 2.24 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.24 ± 0.20 2.24 ± 0.20 2.24 ± 0.20 2.25 ± 0.21 2.26 ± 0.21 2.26 ± 0.21 2.27 ± 0.21 2.28 ± 0.21
a
The ± values are propagated uncertainties.
Much has been said concerning the validity of group contribution calculations and rationalizations. There have also been discrepancies reported in the literature as to the
best standard group contribution values to invoke. We have used V/(H)/cm3 Æ mol1 = Cp,/(H)/J Æ K1mol1 = 0. The interested reader can recalculate any of the values
TABLE 9B ‘‘Best’’ standard thermodynamic values for the first proton dissociation of aqueous isoleucine, reaction (5), H2A+(aq) = HA±(aq) + H+(aq), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K
Dr V m =ðcm3 mol1 Þ
Dr C p;m =ðJ K1 mol1 Þ
Dr H m =ðkJ mol1 Þ
Dr S m =ðJ K1 mol1 Þ
pK
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
8.8 ± 1.1 8.7 ± 1.1 8.7 ± 1.1 8.7 ± 1.1 8.8 ± 1.1 8.8 ± 1.1 8.9 ± 1.1 9.0 ± 1.1 9.1 ± 1.1 9.2 ± 1.1 9.4 ± 1.1 9.5 ± 1.1 9.7 ± 1.1 9.9 ± 1.1 10.1 ± 1.1 10.3 ± 1.1 10.5 ± 1.1 10.8 ± 1.1 11.0 ± 1.1 11.3 ± 1.1 11.6 ± 1.1 11.9 ± 1.1 12.3 ± 1.0 12.7 ± 1.0
144.5 ± 3.6 138.5 ± 3.6 132.4 ± 3.6 126.4 ± 3.6 120.5 ± 3.6 114.8 ± 3.6 109.4 ± 3.6 104.4 ± 3.6 99.7 ± 3.6 95.4 ± 3.6 91.7 ± 3.6 88.4 ± 3.6 85.6 ± 3.6 83.3 ± 3.6 81.5 ± 3.5 80.2 ± 3.5 79.4 ± 3.5 79.1 ± 3.5 79.1 ± 3.5 79.5 ± 3.5 80.3 ± 3.5 81.3 ± 3.5 82.5 ± 3.5 83.8 ± 3.5
3.63 ± 0.63 2.92 ± 0.63 2.24 ± 0.63 1.60 ± 0.63 0.98 ± 0.63 0.39 ± 0.63 0.17 ± 0.63 0.70 ± 0.63 1.21 ± 0.63 1.70 ± 0.63 2.17 ± 0.63 2.62 ± 0.63 3.05 ± 0.64 3.48 ± 0.64 3.89 ± 0.64 4.29 ± 0.64 4.69 ± 0.65 5.09 ± 0.65 5.48 ± 0.66 5.88 ± 0.66 6.28 ± 0.67 6.68 ± 0.67 7.09 ± 0.68 7.51 ± 0.69
32.4 ± 2.8 34.9 ± 2.8 37.3 ± 2.8 39.5 ± 2.8 41.6 ± 2.8 43.6 ± 2.7 45.4 ± 2.7 47.1 ± 2.7 48.7 ± 2.7 50.3 ± 2.7 51.7 ± 2.7 53.1 ± 2.7 54.4 ± 2.7 55.6 ± 2.7 56.8 ± 2.7 57.9 ± 2.7 59.1 ± 2.7 60.2 ± 2.7 61.2 ± 2.7 62.3 ± 2.7 63.4 ± 2.7 64.4 ± 2.7 65.5 ± 2.7 66.6 ± 2.7
2.374 ± 0.093 2.363 ± 0.093 2.355 ± 0.093 2.349 ± 0.093 2.345 ± 0.093 2.343 ± 0.093 2.343 ± 0.093 2.344 ± 0.093 2.346 ± 0.093 2.350 ± 0.093 2.355 ± 0.093 2.360 ± 0.093 2.367 ± 0.093 2.374 ± 0.093 2.382 ± 0.093 2.391 ± 0.093 2.400 ± 0.093 2.410 ± 0.093 2.420 ± 0.094 2.431 ± 0.094 2.443 ± 0.094 2.454 ± 0.094 2.466 ± 0.094 2.479 ± 0.094
a
The ± values are propagated uncertainties.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
85
TABLE 10A ‘‘Best’’ standard thermodynamic values for the second proton dissociation of aqueous threonine, reaction (6), HA±(aq) = A(aq) + H+(aq), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K
Dr V m =ðcm3 mol1 Þ
Dr C p;m =ðJ K1 mol1 Þ
Dr H m =ðkJ mol1 Þ
Dr S m =ðJ K1 mol1 Þ
pK
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
0.41 ± 0.36 0.76 ± 0.36 0.92 ± 0.36 1.04 ± 0.36 1.16 ± 0.35 1.30 ± 0.35 1.45 ± 0.35 1.61 ± 0.35 1.80 ± 0.35 1.99 ± 0.35 2.20 ± 0.35 2.42 ± 0.34 2.64 ± 0.34 2.88 ± 0.34 3.12 ± 0.34 3.36 ± 0.34 3.62 ± 0.34 3.88 ± 0.34 4.15 ± 0.34 4.42 ± 0.35 4.71 ± 0.35 5.01 ± 0.35 5.32 ± 0.35 5.65 ± 0.35
56.5 ± 3.0 59.8 ± 2.9 60.7 ± 2.7 61.2 ± 2.6 61.8 ± 2.5 62.5 ± 2.5 63.3 ± 2.5 64.1 ± 2.4 65.0 ± 2.4 65.7 ± 2.4 66.3 ± 2.4 66.9 ± 2.4 67.2 ± 2.4 67.4 ± 2.4 67.5 ± 2.4 67.5 ± 2.4 67.3 ± 2.4 67.0 ± 2.4 66.7 ± 2.4 66.3 ± 2.4 66.0 ± 2.4 65.6 ± 2.5 65.2 ± 2.5 64.9 ± 2.5
42.71 ± 0.50 42.42 ± 0.50 42.12 ± 0.49 41.82 ± 0.49 41.51 ± 0.49 41.20 ± 0.49 40.88 ± 0.49 40.56 ± 0.49 40.24 ± 0.49 39.92 ± 0.50 39.58 ± 0.50 39.25 ± 0.50 38.92 ± 0.50 38.58 ± 0.50 38.24 ± 0.51 37.90 ± 0.51 37.57 ± 0.51 37.23 ± 0.52 36.90 ± 0.52 36.57 ± 0.52 36.23 ± 0.53 35.91 ± 0.53 35.58 ± 0.54 35.25 ± 0.54
32.1 ± 7.0 33.1 ± 7.0 34.2 ± 7.0 35.2 ± 7.0 36.2 ± 7.0 37.3 ± 7.0 38.3 ± 7.0 39.3 ± 7.0 40.4 ± 7.0 41.4 ± 7.0 42.4 ± 7.0 43.4 ± 7.0 44.4 ± 7.0 45.4 ± 7.0 46.4 ± 7.0 47.3 ± 7.0 48.3 ± 7.0 49.2 ± 7.0 50.1 ± 7.0 51.0 ± 6.9 51.9 ± 6.9 52.8 ± 6.9 53.6 ± 6.9 54.4 ± 6.9
9.69 ± 0.36 9.55 ± 0.36 9.42 ± 0.36 9.29 ± 0.36 9.16 ± 0.36 9.04 ± 0.36 8.93 ± 0.36 8.82 ± 0.36 8.71 ± 0.36 8.61 ± 0.36 8.51 ± 0.36 8.42 ± 0.36 8.33 ± 0.36 8.24 ± 0.36 8.16 ± 0.36 8.08 ± 0.36 8.00 ± 0.36 7.92 ± 0.36 7.85 ± 0.36 7.78 ± 0.36 7.71 ± 0.36 7.65 ± 0.36 7.59 ± 0.36 7.53 ± 0.36
a
The ± values are propagated uncertainties.
using the parameters and equations we report in tables 4 and 8 with any specified standard state. The values calculated for these group contributions using different methods
agree within experimental uncertainties, and we suggest that they can be useful in predicting values for related compounds.
TABLE 10B ‘‘Best’’ standard thermodynamic values for the second proton dissociation of aqueous threonine, reaction (6), HA±(aq) = A(aq) + H+(aq), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K
Dr V m =ðcm3 mol1 Þ
Dr C p;m =ðJ K1 mol1 Þ
Dr H m =ðkJ mol1 Þ
Dr S m =ðJ K1 mol1 Þ
pK
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
0.19 ± 0.93 0.03 ± 0.93 0.06 ± 0.92 0.12 ± 0.92 0.17 ± 0.92 0.20 ± 0.92 0.21 ± 0.92 0.18 ± 0.92 0.13 ± 0.92 0.06 ± 0.92 0.04 ± 0.92 0.15 ± 0.92 0.29 ± 0.92 0.45 ± 0.92 0.62 ± 0.92 0.81 ± 0.92 1.03 ± 0.92 1.26 ± 0.92 1.51 ± 0.92 1.78 ± 0.92 2.08 ± 0.92 2.40 ± 0.92 2.75 ± 0.92 3.13 ± 0.92
68.7 ± 3.6 67.1 ± 3.5 63.9 ± 3.4 61.1 ± 3.4 58.9 ± 3.3 57.3 ± 3.3 56.3 ± 3.2 55.7 ± 3.2 55.4 ± 3.2 55.2 ± 3.2 55.2 ± 3.2 55.3 ± 3.2 55.4 ± 3.2 55.6 ± 3.2 55.7 ± 3.2 55.8 ± 3.2 56.0 ± 3.2 56.2 ± 3.2 56.5 ± 3.2 57.0 ± 3.2 57.6 ± 3.2 58.4 ± 3.2 59.6 ± 3.2 61.0 ± 3.2
46.95 ± 0.64 46.61 ± 0.63 46.28 ± 0.63 45.97 ± 0.63 45.67 ± 0.63 45.38 ± 0.63 45.10 ± 0.63 44.82 ± 0.63 44.54 ± 0.63 44.26 ± 0.63 43.99 ± 0.63 43.71 ± 0.64 43.44 ± 0.64 43.16 ± 0.64 42.88 ± 0.65 42.60 ± 0.65 42.32 ± 0.65 42.04 ± 0.66 41.76 ± 0.66 41.48 ± 0.67 41.19 ± 0.68 40.90 ± 0.68 40.60 ± 0.69 40.30 ± 0.70
28.1 ± 2.6 29.4 ± 2.6 30.5 ± 2.6 31.6 ± 2.6 32.6 ± 2.6 33.6 ± 2.6 34.5 ± 2.6 35.4 ± 2.6 36.3 ± 2.6 37.1 ± 2.6 38.0 ± 2.6 38.8 ± 2.6 39.6 ± 2.6 40.4 ± 2.6 41.2 ± 2.6 42.0 ± 2.6 42.8 ± 2.6 43.6 ± 2.6 44.4 ± 2.6 45.1 ± 2.6 45.9 ± 2.6 46.7 ± 2.6 47.4 ± 2.7 48.2 ± 2.7
10.285 ± 0.076 10.130 ± 0.076 9.981 ± 0.076 9.839 ± 0.076 9.702 ± 0.076 9.570 ± 0.076 9.444 ± 0.076 9.322 ± 0.076 9.205 ± 0.076 9.092 ± 0.076 8.984 ± 0.077 8.879 ± 0.077 8.778 ± 0.077 8.680 ± 0.077 8.586 ± 0.078 8.496 ± 0.078 8.408 ± 0.078 8.323 ± 0.078 8.241 ± 0.079 8.162 ± 0.079 8.086 ± 0.079 8.012 ± 0.080 7.940 ± 0.080 7.871 ± 0.080
a
The ± values are propagated uncertainties.
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TABLE 11 Temperature dependence of group contribution for replacing a hydrogen atom on carbon with a methyl or hydroxyl group at p = 0.35 MPa and (0 6 m/ mol Æ kg1 6 0.5)a Amino acids
Form
Substitution
DV//(cm3 Æ mol1)
DCp,//(J Æ K1 Æ mol1)
x
y
Threonine
Serine
HA± H2A+ A
H–CH3 H–CH3 H–CH3
16.18 ± 0.39 16.58 ± 0.54 15.21 ± 0.20
87.9 ± 6.0 79.7 ± 4.8 84.1 ± 7.1
Isoleucine
Valine
HA± H2A+ A
H–CH3 H–CH3 H–CH3
15.08 ± 0.57 16.0 ± 1.3 15.2 ± 1.1
72.6 ± 5.1 66.6 ± 6.6 76.5 ± 9.7
Valine
L-2-Aminobutanoic
acid
HA± H2A+ A
H–CH3 H–CH3 H–CH3
15.55 ± 0.28 16.05 ± 0.51 15.37 ± 0.96
76.5 ± 2.2 69.2 ± 3.1 70.6 ± 5.9
Threonine
L-2-Aminobutanoic
acid
HA± H2A+ A
H–OH H–OH H–OH
1.414 ± 0.047 1.10 ± 0.79 0.59 ± 0.31
7.8 ± 9.9 7 ± 14 12 ± 11
a
The ± values are the standard deviations.
TABLE 12 Temperature dependance of group contribution for replacing a hydrogen atom on carbon with a methyl or hydroxyl group at p = 0.35 MPa and (0 6 m/ mol Æ kg1 6 0.5)a,b 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 b
V//(cm3 Æ mol1)
Cp,//(J Æ K1 Æ mol1)
H–CH3
H–OH
H–CH3
H–OH
15.31 ± 0.19 15.26 ± 0.19 15.23 ± 0.18 15.22 ± 0.18 15.24 ± 0.18 15.27 ± 0.17 15.32 ± 0.17 15.38 ± 0.16 15.45 ± 0.16 15.53 ± 0.16 15.63 ± 0.15 15.73 ± 0.15 15.84 ± 0.14 15.96 ± 0.14 16.08 ± 0.14 16.21 ± 0.13 16.36 ± 0.13 16.50 ± 0.12 16.66 ± 0.12
1.31 ± 0.18 1.22 ± 0.18 1.14 ± 0.18 1.07 ± 0.18 1.01 ± 0.18 0.97 ± 0.18 0.93 ± 0.18 0.90 ± 0.18 0.88 ± 0.18 0.88 ± 0.18 0.88 ± 0.18 0.90 ± 0.18 0.92 ± 0.18 0.96 ± 0.18 1.01 ± 0.18 1.06 ± 0.18 1.13 ± 0.18 1.22 ± 0.18 1.31 ± 0.18
87.4 ± 1.2 84.4 ± 1.0 82.10 ± 0.89 80.35 ± 0.81 78.98 ± 0.75 77.90 ± 0.73 77.06 ± 0.71 76.40 ± 0.71 75.88 ± 0.71 75.48 ± 0.71 75.16 ± 0.71 74.90 ± 0.71 74.69 ± 0.72 74.50 ± 0.73 74.31 ± 0.75 74.12 ± 0.77 73.91 ± 0.79 73.65 ± 0.81 73.34 ± 0.84 72.95 ± 0.86 72.48 ± 0.89 71.90 ± 0.90 71.20 ± 0.91 70.36 ± 0.92
22.5 ± 5.6 22.7 ± 5.7 22.4 ± 5.6 21.5 ± 5.6 20.4 ± 5.4 19.0 ± 5.3 17.5 ± 5.1 15.8 ± 4.9 14.1 ± 4.7 12.4 ± 4.4 10.6 ± 4.2 8.9 ± 3.9 7.2 ± 3.7 5.5 ± 3.5 3.9 ± 3.3 2.4 ± 3.2 1.0 ± 3.0 0.3 ± 2.9 1.4 ± 2.8 2.4 ± 2.8 3.2 ± 2.8 3.8 ± 2.8 4.1 ± 2.8 4.2 ± 2.9
Values for ‘‘H–CH3’’ are calculated as the average of those for Thr-Ser, Ile-Val, and Val-Aba. The ± value are the standard deviations.
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JCT 06-79
Thermodynamics of proton dissociations from aqueous threonine and isoleucine at temperatures from (278.15 to 393.15) K, molalities from (0.01 to 1.0) mol Æ kg1, and at the pressure 0.35 MPa: Apparent molar heat capacities and apparent molar volumes of zwitterionic, protonated cationic, and deprotonated anionic forms S.P. Ziemer, E.M. Woolley
*
Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602-5700, USA Received 1 April 2006; received in revised form 26 May 2006; accepted 30 May 2006 Available online 9 June 2006
Abstract We have measured the densities of aqueous solutions of isoleucine, threonine, and equimolal solutions of these two amino acids with HCl and with NaOH at temperatures 278.15 6 T/K 6 368.15, at molalities 0.01 6 m/mol Æ kg1 6 1.0, and at the pressure 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 each of the protonated aqueous cationic amino acids. We used Young’s Rule and integrated these results iteratively to account for the effects of equilibrium speciation and chemical relaxation on V/(T, m) and Cp,/(T, m). This procedure gave parameters for V/(T, m) and Cp,/(T, m) for threoninium and isoleucinium chloride and for sodium threoninate and isoleucinate which modeled our observed results within experimental uncertainties. We report values for DrCp,m, DrHm, pQa, DrSm, and DrVm for the first and second proton dissociations from protonated aqueous threonine and isoleucine as functions of T and m. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Apparent molar volume; Apparent molar heat capacity; Threonine; 2-Amino-3-hydroxybutanoic acid; Isoleucine; 2-Amino-3-methylpentanoic acid; Zwitterion; Threoninium chloride; Isoleucininium chloride; Sodium threoninate; Sodium isoleucinate; Proton dissociations; Acidity; Young’s Rule
1. Introduction Although there is an abundance of work reported in the literature on the properties of aqueous amino acids, the great majority of this work focuses on the unionized zwitterionic forms of the amino acids. The works that include information for the charged species often neglect or approximate the effects of incomplete ionization and equi*
Corresponding author. Tel.: +1 801 422 3669; fax: +1 801 422 0550. E-mail address: [email protected] (E.M. Woolley).
0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.05.013
librium concentrations, introducing significant uncertainties in the values of their thermodynamic properties. In our continuing efforts to enlarge the database of accurate thermodynamic properties of aqueous solutions of L-2-amino acids in their protonated, zwitterionic, and deprotonated forms, taking into account the actual species concentrations, we have studied aqueous threonine and isoleucine. Both are essential amino acids, meaning that they are not produced by humans and must be included in the diet. Threonine is required for the formation of collagen and elastin and is concentrated in the central nervous
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system. Isoleucine is found particularly in muscle tissue and is necessary for formation of hemoglobin. It contributes significantly to the tertiary structure of proteins. We recently reported our results for the apparent molar volumes V/ and apparent molar heat capacities Cp,/ of aqueous proline [1], valine [2], L-2-aminobutanoic acid [2], serine [3], alanine [4], and others. In this paper we report our measured densities and heat capacities of aqueous solutions of threonine and isoleucine in their zwitterionic forms HThr±(aq) and HIle±(aq) and with the addition of equimolal HCl {HThr±(aq) + HCl(aq)} and {HIle±(aq) + HCl(aq)}, and equimolal NaOH {HThr±(aq) + NaOH(aq)} and {HIle±(aq) + NaOH(aq)}. Our analysis applies Young’s Rule and a relaxation heat capacity term to account for the equilibrium molalities of the species H2Thr+Cl(aq), H2Ile+Cl(aq), HThr±(aq), HIle±(aq), Na+Thr(aq), and Na+Ile(aq) present in the solutions containing HCl(aq) and NaOH(aq). Our resulting values of V/(T, m) and Cp,/(T, m) for H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq) allow calculation of the thermodynamic quantities DrCp,m, DrHm, pQa, DrSm, and DrVm for the first and second proton dissociations from protonated aqueous threonine and isoleucine. We have compared all of our results to those found in the literature [5–45].
2. Experimental Crystalline L-threonine {HThr±(c), 2-amino-3-hydroxybutanoic acid, CH3CH(OH)CH(NH2)COOH, molar mass M2 = 119.1197 g Æ mol1, density qc = 1.5 g Æ cm3; Fluka 89179, lot 1132757, 0.995+ mass fraction} and L-isoleucine {HIle±(c), 2-amino-3-methylpentanoic acid, C2H5CH(CH3)CH(NH2)COOH, M2 = 131.1736 g Æ mol1, qc = 1.2 g Æ cm3; Fluka 58879, lot 413187/1, 0.995+ mass fraction} were used as received. The purity of each solute was confirmed by elemental analysis by MHW Laboratories. We prepared aqueous stock solutions of L-threonine and L-isoleucine by mass using distilled, deionized, autoclaved, degassed water. We prepared stock solutions of {HThr±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, ± {HIle (aq) + HCl(aq)}, and {HIle±(aq) + NaOH(aq)} in a similar fashion, using previously standardized stock solutions of HCl(aq) [46] and carbonate-free NaOH(aq) [47] to achieve the nearly equimolal ratios of amino acid + HCl or + NaOH as follows: {m(HThr±)/m(HCl)} = 0.9997, {m(HThr±)/m(NaOH)} = 0.9997, {m(HIle±)/m(HCl)} = 0.997 and {m(HIle±)/m(NaOH)} = 0.998. All other solutions were prepared by mass dilution of these stock solutions with water. Air buoyancy corrections (qair = 0.0010 g Æ cm3) were applied to all weighings.
TABLE 1A Observed densities qs and apparent molar volumes V/ for aqueous zwitterionic threonine at p = 0.35 MPa m
V/
qs 1
3
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
1
cm Æ mol
3
g Æ cm
cm3 Æ mol1
mol Æ kg
g Æ cm
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
T = 278.15 K 1.00036 102 ± 13 1.00146 73.7 ± 1.1 1.00202 80.6 ± 4.3 1.00454 74.80 ± 0.52 1.00862 75.7 ± 1.1 1.01693 75.29 ± 0.42 1.02745 75.24 ± 0.48
T = 283.15 K 1.00006 104 ± 13 1.00118 74.0 ± 1.4 1.00170 81.5 ± 4.0 1.00421 75.43 ± 0.58 1.00825 76.2 ± 1.1 1.01645 75.85 ± 0.42 1.02687 75.73 ± 0.47
T = 288.15 K 0.99945 105 ± 12 1.00055 74.81 ± 0.91 1.00105 82.4 ± 3.7 1.00355 76.02 ± 0.47 1.00754 76.7 ± 1.0 1.01561 76.45 ± 0.41 1.02598 76.20 ± 0.46
T = 298.15 K 0.99739 105 ± 13 0.99848 75.0 ± 1.8 0.99887 84.8 ± 4.0 1.00139 77.00 ± 0.66 1.00530 77.7 ± 1.1 1.01325 77.29 ± 0.42 1.02339 77.09 ± 0.46
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
T = 308.15 K 0.99438 104 ± 13 0.99541 76.9 ± 1.2 0.99580 86.0 ± 4.1 0.99829 77.86 ± 0.52 1.00215 78.5 ± 1.1 1.01005 77.88 ± 0.41 1.01998 77.82 ± 0.47
T = 318.15 K 0.99056 104 ± 12 0.99149 80.29 ± 0.64 0.99198 86.3 ± 3.9 0.99445 78.22 ± 0.42 0.99825 79.0 ± 1.1 1.00610 78.34 ± 0.40 1.01589 78.39 ± 0.47
T = 328.15 K 0.98606 103 ± 10 0.98695 81.22 ± 0.64 0.98747 86.3 ± 3.2 0.98992 78.55 ± 0.43 0.99370 79.40 ± 0.90 1.00149 78.75 ± 0.41 1.01123 78.80 ± 0.46
T = 338.15 K 0.98092 104 ± 10 0.98188 79.2 ± 0.6 0.98235 86.1 ± 3.2 0.98475 79.06 ± 0.42 0.98854 79.71 ± 0.90 0.99628 79.15 ± 0.41 1.00598 79.18 ± 0.46
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
T = 348.15 K 0.97523 103.8 ± 9.7 0.97617 79.82 ± 0.76 0.97666 86.3 ± 3.1 0.97904 79.42 ± 0.44 0.98279 80.21 ± 0.87 0.99053 79.50 ± 0.40 1.00021 79.51 ± 0.47
T = 358.15 K 0.96907 100.3 ± 8.0 0.96995 79.71 ± 0.54 0.97043 86.6 ± 2.5 0.97280 79.79 ± 0.42 0.97658 80.36 ± 0.76 0.98429 79.78 ± 0.41 0.99398 79.75 ± 0.46
T = 368.15 K 0.96239 98.4 ± 5.7 0.96324 79.90 ± 0.50 0.96373 86.7 ± 1.8 0.96609 79.99 ± 0.42 0.96988 80.51 ± 0.62 0.97759 79.98 ± 0.41 0.98723 80.09 ± 0.47
The ± values are from propagation of uncertainties as described in reference [48].
g Æ cm
V/
qs 3
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
69
TABLE 1B Observed densities ps and apparent molar volumes V/ for aqueous zwitterionic isoleucine at p = 0.35 MPa m
V/
qs 1
3
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
g Æ cm
cm3 Æ mol1
mol Æ kg
g Æ cm
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
T = 278.15 K 1.00038 102.9 ± 6.8 1.00077 97.9 ± 5.8 1.00121 103.3 ± 1.3 1.00199 107.2 ± 2.9 1.00448 103.30 ± 0.43 1.00541 105.6 ± 1.1
T = 283.15 K 1.00006 107.5 ± 5.4 1.00050 98.3 ± 5.6 1.00090 104.3 ± 1.2 1.00164 108.3 ± 3.0 1.00411 103.98 ± 0.41 1.00496 106.5 ± 1.2
T = 288.15 K 0.99945 108.5 ± 3.5 0.99991 97.4 ± 5.5 1.00030 104.32 ± 0.81 1.00102 108.6 ± 3.3 1.00345 104.39 ± 0.33 1.00421 107.2 ± 1.3
T = 298.15 K 0.99737 109.6 ± 2.2 0.99785 97.4 ± 5.8 0.99820 105.26 ± 0.86 0.99888 109.6 ± 3.2 1.00124 105.45 ± 0.33 1.00191 108.5 ± 1.2
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
T = 308.15 K 0.99435 110.5 ± 1.6 0.99480 98.9 ± 7.8 0.99515 106.20 ± 0.70 0.99589 109.5 ± 3.4 0.99812 106.32 ± 0.30 0.99869 109.8 ± 1.3
T = 318.15 K 0.99051 111.9 ± 1.2 0.99093 101.5 ± 8.4 0.99131 107.06 ± 0.27 0.99212 109.2 ± 3.4 0.99420 107.25 ± 0.25 0.99476 110.6 ± 1.3
T = 328.15 K 0.98599 113.3 ± 1.9 0.98641 102.2 ± 8.2 0.98678 107.66 ± 0.28 0.98763 109.3 ± 3.4 0.98964 107.97 ± 0.25 0.99022 111.2 ± 1.3
T = 338.15 K 0.98086 113.2 ± 2.1 0.98124 104.4 ± 6.1 0.98165 108.11 ± 0.44 0.98254 109.1 ± 2.9 0.98444 108.77 ± 0.26 0.98505 111.7 ± 1.1
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
T = 348.15 K 0.97514 115.4 ± 2.3 0.97549 107.3 ± 7.3 0.97592 109.20 ± 0.66 0.97683 109.7 ± 2.9 0.97870 109.53 ± 0.29 0.97940 112.0 ± 1.1
T = 358.15 K 0.96897 111.0 ± 2.4 0.96926 108.1 ± 5.5 0.96970 109.83 ± 0.76 0.97067 109.4 ± 2.9 0.97246 110.20 ± 0.31 0.97324 112.3 ± 1.1
T = 368.15 K 0.96220 116.6 ± 4.3 0.96255 108.3 ± 7.0 0.96298 110.35 ± 0.76 0.96402 109.0 ± 3.0 0.96573 110.89 ± 0.31 0.96655 112.8 ± 1.2
The ± values are from propagation of uncertainties as described in reference [48].
TABLE 2A Observed densities qs and apparent molar volumes V/ for aqueous (threonine + HC1) at p = 0.35 MPa ma
qs
V/
qs
V/
qs
V/
qs
V/
mol Æ kg1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
1.00107 1.00155 1.00295 1.00567 1.01351 1.02619 1.04699
T = 278.15 K 91.7 ± 3.4 105.8 ± 8.1 98.22 ± 0.12 99.16 ± 0.11 100.6 ± 1.2 100.67 ± 0.10 101.75 ± 0.33
1.00078 1.00123 1.00265 1.00528 1.01310 1.02555 1.04627
T = 283.15 K 92.8 ± 3.2 107.6 ± 8.4 98.87 ± 0.71 100.41 ± 0.36 101.2 ± 1.1 101.43 ± 0.11 102.26 ± 0.32
1.00019 1.00059 1.00200 1.00463 1.01235 1.02466 1.04521
T = 288.15 K 92.2 ± 2.0 108.8 ± 9.0 99.68 ± 0.86 100.92 ± 0.44 101.8 ± 1.1 102.05 ± 0.13 102.79 ± 0.32
0.99811 0.99842 0.99987 1.00248 1.01013 1.02215 1.04239
T = 298.15 K 93.1 ± 2.2 112.6 ± 8.9 101.1 ± 1.2 101.82 ± 0.62 102.52 ± 0.99 103.08 ± 0.15 103.73 ± 0.29
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
0.99506 0.99534 0.99678 0.99944 1.00698 1.01884 1.03875
T = 308.15 K 95.3 ± 1.7 114.9 ± 9.3 102.68 ± 0.59 102.22 ± 0.30 103.20 ± 0.94 103.827 ± 0.089 104.58 ± 0.28
0.99119 0.99149 0.99293 0.99557 1.00304 1.01479 1.03442
T = 318.15 K 98.03 ± 0.26 116.1 ± 9.3 103.37 ± 0.12 102.861 ± 0.081 103.86 ± 0.82 104.507 ± 0.058 105.36 ± 0.25
0.98666 0.98700 0.98848 0.99101 0.99849 1.01016 1.02958
T = 328.15 K 99.18 ± 0.36 115.6 ± 9.3 102.41 ± 0.11 103.552 ± 0.079 104.26 ± 0.87 105.008 ± 0.062 105.99 ± 0.27
0.98153 0.98191 0.98335 0.98586 0.99325 1.00496 1.02425
T = 338.15 K 99.38 ± 0.95 114.3 ± 8.1 102.42 ± 0.19 103.91 ± 0.11 104.98 ± 0.82 105.411 ± 0.061 106.50 ± 0.25
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
0.97582 0.97625 0.97764 0.98018 0.98754 0.99920 1.01854
T = 348.15 K 100.1 ± 1.6 113.2 ± 8.0 102.83 ± 0.31 104.00 ± 0.17 105.31 ± 0.85 105.862 ± 0.063 106.84 ± 0.26
0.96960 0.97007 0.97143 0.97397 0.98132 0.99303 1.01233
T = 358.15 K 99.9 ± 1.9 111.9 ± 8.0 103.00 ± 0.32 104.20 ± 0.17 105.63 ± 0.87 106.069 ± 0.062 107.18 ± 0.27
0.96290 0.96345 0.96475 0.96732 0.97473 0.98640 1.00573
T = 368.15 K 99.1 ± 1.9 109.0 ± 8.4 102.52 ± 0.49 103.76 ± 0.25 105.41 ± 0.64 106.255 ± 0.076 107.44 ± 0.21
The ± values are from propagation of uncertainties as described in reference [48]. a Molality of theronine, with stoichiometric molality {m(HThr)/m(HCl)} = 0.9997.
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We measured densities qs of each solution 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 ðM 2 =qs Þ ðqs qw Þ=ðqs qw mÞ;
(aq) + NaOH(aq)}, and {HIle±(aq) + NaOH(aq)} at 0.01 6 m/mol Æ kg16 1.0 and 278.15 6 T/K 6 368.15 are given in tables 1 to 3 equation (3) was fit by regression to these results: V / ðT ; mÞ ¼ w3=2 AV ðm Þ1=2 þ m0 þ m1 m þ
ð1Þ
where qw [1] is the density of water as described previously [1–4]. Solution heat capacities 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 previously [1,2,48]. We used values of the heat capacity of water cp,w [1] and our cp,s with equation (2) to calculate Cp,/(T, m): C p;/ ¼ ðM 2 cp;s Þ þ ðcp;s cp;w Þ=m:
ð2Þ
3. Results and discussion Values of V/,obs(T, m) for HThr±(aq), HIle±(aq), {HThr±(aq) + HCl(aq)}, {HIle±(aq) + HCl(aq)}, {HThr±-
2
2
m2 ðm Þ þ m3 m T þ m4 ðm Þ T þ 2
m5 lnðT Þ þ m6 T þ m7 ðT Þ :
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 [49] as given by Sorenson, et al. [1], w = 0 for HThr±(aq) and for HIle±(aq), and w = 1 for {HThr±(aq) + HCl(aq)}, H2Thr+Cl(aq), {HIle±(aq) + HCl(aq)}, H2Ile+Cl(aq), {HThr±(aq) + NaOH(aq)}, Na+Thr(aq), {HIle±(aq) + NaOH(aq)}, and for Na+Ile(aq). The squares of the reciprocals of the uncertainties in tables 1 to 3 were used as weighting factors in the regressions. The uncertainties reported in this work were calculated by standard error propagation statistics as described previously [48].
TABLE 2B Observed densities qs and apparent molar volumes V/ for aqueous (isoleucine + HCl) at p = 0.35 MPa ma
qs
V/
qs
V/
qs
V/
qs
V/
mol Æ kg1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
0.0151 0.0301 0.0502 0.1003 0.1003 0.2500 0.5012 0.5012 0.9531
1.00077 1.00120 1.00235 1.00374 1.00403 1.00949 1.01763 1.01770 1.03172
T = 278.15 K 122.6 ± 6.2 130.8 ± 1.2 122.37 ± 0.95 130.76 ± 0.36 127.82 ± 0.74 128.83 ± 0.20 130.344 ± 0.094 130.20 ± 0.16 130.32 ± 0.15
1.00045 1.00090 1.00203 1.00352 1.00368 1.00902 1.01694 1.01708 1.03074
T = 283.15 K 125.9 ± 5.7 131.67 ± 0.97 123.58 ± 0.52 130.31 ± 0.30 128.69 ± 0.68 129.66 ± 0.13 131.250 ± 0.098 130.97 ± 0.13 131.16 ± 0.15
0.99981 1.00028 1.00138 1.00282 1.00300 1.00825 1.01599 1.01617 1.02951
T = 288.15 K 128.4 ± 4.3 132.5 ± 1.3 124.49 ± 0.53 131.31 ± 0.39 129.56 ± 0.46 130.42 ± 0.13 132.04 ± 0.11 131.666 ± 0.095 131.93 ± 0.15
0.99771 0.99811 0.99926 1.00057 1.00076 1.00593 1.01327 1.01354 1.02639
T = 298.15 K 130.6 ± 2.2 135.9 ± 2.5 125.7 ± 1.7 133.36 ± 0.77 131.45 ± 0.32 131.64 ± 0.35 133.61 ± 0.17 133.037 ± 0.068 133.35 ± 0.15
0.0151 0.0301 0.0502 0.1003 0.1003 0.2500 0.5012 0.5012 0.9531
0.99467 0.99502 0.99619 0.99741 0.99765 1.00282 1.00977 1.01012 1.02262
T = 308.15 K 132.8 ± 1.0 138.8 ± 4.6 127.0 ± 3.1 135.1 ± 1.4 132.65 ± 0.22 132.32 ± 0.64 134.93 ± 0.30 134.193 ± 0.055 134.53 ± 0.20
0.99083 0.99113 0.99235 0.99349 0.99375 0.99886 1.00561 1.00599 1.01819
T = 318.15 K 134.23 ± 0.81 141.6 ± 5.9 127.7 ± 3.9 136.5 ± 1.8 133.89 ± 0.17 133.28 ± 0.81 136.05 ± 0.38 135.233 ± 0.045 135.64 ± 0.21
0.98632 0.98662 0.98776 0.98898 0.98919 0.99418 1.00091 1.00125 1.01320
T = 328.15 K 133.9 ± 1.9 141.8 ± 6.0 129.6 ± 3.5 136.9 ± 1.8 134.71 ± 0.16 134.39 ± 0.72 136.93 ± 0.39 136.191 ± 0.057 136.67 ± 0.21
0.98118 0.98149 0.98260 0.98388 0.98401 0.98892 0.99562 0.99593 1.00771
T = 338.15 K 134.9 ± 1.9 142.2 ± 4.6 130.6 ± 2.1 137.1 ± 1.4 135.69 ± 0.17 135.46 ± 0.44 137.79 ± 0.30 137.125 ± 0.057 137.63 ± 0.17
0.0151 0.0301 0.0502 0.1003 0.1003 0.2500 0.5012 0.5012 0.9531
0.97546 0.97581 0.97689 0.97816 0.97827 0.98309 0.98982 0.99011 1.00175
T = 348.15 K 136.5 ± 2.1 142.1 ± 5.5 131.2 ± 2.4 137.9 ± 1.7 136.75 ± 0.18 136.58 ± 0.51 138.63 ± 0.36 137.986 ± 0.060 138.56 ± 0.19
0.96925 0.96960 0.97068 0.97192 0.97205 0.97686 0.98359 0.98384 0.99534
T = 358.15 K 136.5 ± 2.3 142.3 ± 3.8 131.6 ± 1.2 138.8 ± 1.1 137.37 ± 0.23 137.26 ± 0.26 139.31 ± 0.25 138.767 ± 0.061 139.47 ± 0.15
0.96255 0.96288 0.96396 0.96522 0.96539 0.97018 0.97683 0.97713 0.98860
T = 368.15 K 136.4 ± 4.8 143.3 ± 5.8 132.2 ± 3.3 139.3 ± 1.7 137.43 ± 0.49 137.82 ± 0.68 140.15 ± 0.37 139.480 ± 0.098 140.25 ± 0.18
The ± values are from propagation of uncertainties as described in reference [48]. a Molality of theronine, with stoichiometric molality ratio {m(HIle)/m(HCl)} = 0.997.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
The resultant values of mi for the regressions with equation (3) are given in tables 4A and 4B. Figure 1 shows our V/,obs(T, m) results for HThr±(aq) and HIle±(aq) along with the regression surfaces and values from the literature [5–20]. The differences between V/(T, m) values on our regression surface and all literature values for HThr±(aq) are in the range D = (19.9 [5] to 6.0 [6]) cm3 Æ mol1, with an average difference D = 0.1 cm3 Æ mol1 whereas the same comparison for HIle±(aq) gives values in the range D = (2.1 [18] to 0.4 [19]) cm3 Æ mol1, with an average difference D = 0.2 cm3 Æ mol1. Tables 5 to 7 give our values of Cp,/,obs(T,m) for HThr±(aq), HIle±(aq), {HThr±(aq) + HCl(aq)}, {HIle±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, and {HIle±(aq) + NaOH(aq)}. Equation (4) was fit by regression to these results using the squares of the reciprocals of the uncertainties given in the tables as weighting factors: 1=2
C p;/ ðT ; mÞ ¼ w3=2 AC ðm Þ
2
þ c0 þ c1 m þ c2 ðm Þ þ 2
c3 m lnðT Þ þ c4 m T þ c5 m ðT Þ þ 2
71
Figure 2 shows our Cp,/,obs(T, m) for HThr±(aq) and HIle±(aq) from tables 5A and 5B and the regression surfaces, along with values from the literature [12,13,20–23]. The differences between Cp,/(T, m) values on our regression surface and all the values from the literature are in the range D = (23.1 [12] to 74.8 [21]) J Æ K1 Æ mol1 with an average difference D = 4.5 J Æ K1 Æ mol1 for aqueous threonine, and are in the range D = (39.3 [21] to 20.5 [21]) J Æ K1 Æ mol1 with an average difference D = 2.8 J Æ K1 Æ mol1 for aqueous isoleucine. In order to calculate apparent molar properties Cp,/(i) and V/(i) of the individual species H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq), we must account for chemical equilibria in our solutions of {HThr±(aq) + HCl(aq)}, {HIle±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, and {HIle±(aq) + NaOH(aq)}, respectively. Aqueous amino acids can undergo reactions (5) to (8), where A signifies the amino acid moiety: H2 Aþ ðaqÞ ¼ HA ðaqÞ þ Hþ ðaqÞ
ð5Þ
þ
HA ðaqÞ ¼ A ðaqÞ þ H ðaqÞ
3
c6 lnðT Þ þ c7 T þ c8 ðT Þ þ c9 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 [49] as given by Sorenson, et al. [1]. Tables 8A and 8B give the regression parameters (ci).
ð6Þ
þ
HA ðaqÞ þ H2 O ¼ H2 A ðaqÞ þ OH ðaqÞ
ð7Þ
A ðaqÞ þ H2 O ¼ HA ðaqÞ þ OH ðaqÞ
ð8Þ
Reactions (6) and (7) do not occur to an appreciable extent at the m, T, and p of our experiments for solutions of HThr±(aq) or HIle±(aq). Thus, we treat solutions of the zwitterionic amino acids as containing only the species
TABLE 3A Observed densities qs and apparent molar volumes V/ for aqueous (threonine + NaOH) at p = 0.35 MPa ma
qs
V/
qs
V/
qs
V/
qs
V/
mol Æ kg1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
g Æ cm3
cm3 Æ mol1
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
1.00124 1.00223 1.00368 1.00713 1.01705 1.03285 1.06081
T = 278.15 K 75 ± 17 69.5 ± 1.3 72.0 ± 6.3 70.47 ± 0.45 72.1 ± 1.3 73.21 ± 0.68 75.54 ± 0.13
1.00101 1.00190 1.00340 1.00671 1.01649 1.03210 1.05980
T = 283.15 K 73 ± 15 71.4 ± 2.2 72.3 ± 6.4 71.95 ± 0.68 73.2 ± 1.3 74.18 ± 0.69 76.30 ± 0.11
1.00040 1.00123 1.00276 1.00598 1.01562 1.03103 1.05849
T = 288.15 K 74 ± 15 73.8 ± 1.6 73.0 ± 6.5 73.22 ± 0.50 74.3 ± 1.4 75.13 ± 0.70 77.04 ± 0.11
0.99834 0.99911 1.00064 1.00371 1.01313 1.02819 1.05516
T = 298.15 K 73 ± 14 75.5 ± 2.1 74.0 ± 6.6 75.25 ± 0.64 76.0 ± 1.4 76.71, ± 0.71 78.37 ± 0.11
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
0.99535 0.99610 0.99755 1.00056 1.00980 1.02458 1.05111
T = 308.15 K 71.4 ± 13.1 75.14 ± 0.97 75.3 ± 6.5 76.67 ± 0.33 77.4 ± 1.4 77.96 ± 0.71 79.481 ± 0.086
0.99152 0.99226 0.99371 0.99668 1.00571 1.02033 1.04645
T = 318.15 K 72 ± 11 75.99 ± 0.34 75.7 ± 6.0 77.21 ± 0.19 78.5 ± 1.3 78.90 ± 0.65 80.438 ± 0.071
0.98702 0.98773 0.98920 0.99211 1.00108 1.01553 1.04143
T = 328.15 K 71 ± 12 76.31 ± 0.21 75.7 ± 5.5 77.89 ± 0.17 79.0 ± 1.2 79.57 ± 0.61 81.065 ± 0.075
0.98179 0.98258 0.98402 0.98693 0.99577 1.01015 1.03588
T = 338.15 K 77 ± 11 77.02 ± 0.34 76.6 ± 5.1 78.37 ± 0.19 79.8 ± 1.1 80.18 ± 0.57 81.625 ± 0.071
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
0.97606 0.97685 0.97832 0.98120 0.99001 1.00434 1.02985
T = 348.15 K 79 ± 12 77.83 ± 0.47 76.6 ± 4.8 78.81 ± 0.21 80.2 ± 1.0 80.50 ± 0.53 82.110 ± 0.069
0.96981 0.97063 0.97213 0.97496 0.98377 0.99801 1.02344
T = 358.15 K 80 ± 12 77.93 ± 0.45 76.1 ± 4.6 79.01 ± 0.21 80.35 ± 0.97 80.84 ± 0.51 82.459 ± 0.064
0.96309 0.96389 0.96538 0.96823 0.97696 0.99123 1.01664
T = 368.15 K 80.2 ± 8.8 78.84 ± 0.34 76.8 ± 3.7 79.20 ± 0.19 80.89 ± 0.80 81.12 ± 0.43 82.708 ± 0.067
The ± values are from propagation of uncertainties as described in reference [48]. a Molality of threonine, with stoichiometric molality ratio {m(HThr)/m(NaOH)} = 0.9997.
72
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
TABLE 3B Observed densities qs and apparent molar volumes V/ for aqueous (isoleucine + NaOH) at p = 0.35 MPa ma
V/
qs 1
3
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
g Æ cm
V/
qs 3
1
cm Æ mol
3
cm3 Æ mol1
mol Æ kg
g Æ cm
g Æ cm
0.0151 0.0151 0.0313 0.0501 0.1000 0.2576 0.2576 0.4998 0.9940
T = 278.15 K 1.00098 94.6 ± 6.1 1.00095 96.5 ± 1.7 1.00124 96.2 ± 3.0 1.00223 98.0 ± 1.9 1.00368 96.31 ± 0.40 1.00713 101.08 ± 0.17 1.01705 101.03 ± 0.19 1.03285 100.35 ± 0.13 1.06081 101.56 ± 0.10
T = 283.15 K 1.00067 97.2 ± 6.3 1.00067 97.2 ± 2.8 1.00101 98.1 ± 2.8 1.00190 98.0 ± 1.7 1.00340 97.95 ± 0.35 1.00671 102.31 ± 0.21 1.01649 102.13 ± 0.19 1.03210 101.49 ± 0.14 1.05980 102.64 ± 0.11
T = 288.15 K 1.00004 98.8 ± 5.0 1.00005 98.1 ± 3.1 1.00040 99.7 ± 2.1 1.00123 100.0 ± 1.3 1.00276 99.04 ± 0.27 1.00598 103.35 ± 0.22 1.01562 103.14 ± 0.16 1.03103 102.47 ± 0.13 1.05849 103.65 ± 0.11
T = 298.15 K 0.99793 102.3 ± 3.6 0.99796 100.1 ± 3.3 0.99834 102.0 ± 1.1 0.99911 101.92 ± 0.67 1.00064 101.04 ± 0.54 1.00371 105.16 ± 0.23 1.01313 104.90 ± 0.25 1.02819 104.29 ± 0.16 1.05516 105.42 ± 0.13
0.0151 0.0151 0.0313 0.0501 0.1000 0.2576 0.2576 0.4998 0.9940
T = 308.15 K 0.99487 105.0 ± 4.2 0.99493 101.0 ± 1.1 0.99535 103.61 ± 0.51 0.99610 103.36 ± 0.34 0.99755 102.77 ± 0.79 1.00056 106.56 ± 0.13 1.00980 106.42 ± 0.34 1.02458 105.83 ± 0.20 1.05111 106.94 ± 0.20
T = 318.15 K 0.99102 107.1 ± 4.6 0.99107 103.61 ± 0.93 0.99152 105.44 ± 0.41 0.99226 105.16 ± 0.28 0.99371 103.75 ± 0.96 0.99668 107.88 ± 0.12 1.00571 107.59 ± 0.40 1.02033 107.07 ± 0.23 1.04645 108.28 ± 0.24
T = 328.15 K 0.98647 109.7 ± 5.1 0.98655 103.7 ± 1.6 0.98702 106.53 ± 0.92 0.98773 106.26 ± 0.59 0.98920 104.93 ± 0.83 0.99211 109.01 ± 0.14 1.00108 108.72 ± 0.35 1.01553 108.20 ± 0.22 1.04143 109.50 ± 0.22
T = 338.15 K 0.98132 110.9 ± 4.4 0.98141 104.74 ± 0.67 0.98179 107.54 ± 0.92 0.98258 105.81 ± 0.58 0.98402 105.81 ± 0.57 0.98693 110.00 ± 0.11 0.99577 109.58 ± 0.26 1.01015 109.27 ± 0.17 1.03588 110.57 ± 0.16
0.0151 0.0151 0.0313 0.0501 0.1000 0.2576 0.2576 0.4998 0.9940
T = 348.15 K 0.97560 112.5 ± 3.9 0.97569 106.03 ± 0.79 0.97606 108.2 ± 1.0 0.97685 108.06 ± 0.64 0.97832 106.62 ± 0.51 0.98120 110.88 ± 0.11 0.99001 110.59 ± 0.24 1.00434 110.22 ± 0.16 1.02985 111.63 ± 0.17
T = 358.15 K 0.96937 113.4 ± 2.4 0.96947 106.1 ± 1.9 0.96981 108.2 ± 1.1 0.97063 108.30 ± 0.71 0.97213 107.83 ± 0.29 0.97496 111.66 ± 0.15 0.98377 111.40 ± 0.17 0.99801 111.16 ± 0.14 1.02344 112.56 ± 0.13
T = 368.15 K 0.96268 112.2 ± 4.5 0.96275 107.0 ± 1.6 0.96309 107.3 ± 2.3 0.96389 108.8 ± 1.5 0.96538 108.47 ± 0.56 0.96823 112.27 ± 0.14 0.97696 112.29 ± 0.25 0.99123 112.03 ± 0.17 1.01664 113.50 ± 0.21
The ± values are from propagation of uncertainties as described in reference [48]. a Molality of isoleucine, with stoichiometric molality ratio {m(Hlle)/m(NaOH)} = 0.998.
HA±(aq). Alternately, aqueous solutions of {HA±(aq) + HCl(aq)} and of {HA±(aq) + NaOH(aq)}, undergo reactions (5) and (8), respectively, extensively, though not to completion. For this reason {HA±(aq) + HCl(aq)} solu-
tions are equilibrium mixtures of H2A+Cl(aq), HA±(aq), and H+Cl(aq), whereas {HA±(aq) + NaOH(aq)} solutions are equilibrium mixtures of Na+A(aq), HA±(aq), and Na+OH(aq).
TABLE 4A Regression parameters of equation (3) for apparent molar volumes V/(T, m) of {HThr±(aq)}, {HThr±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, {H2Thr+Cl(aq)}, and {Na+Thr(aq)} mi m0 m1 m2 103 Æ m3 103 Æ m4 m5 103 Æ m6 106 Æ m7 Da Highest m
HThr±(aq) observed, w = 0 (Table 1A)
{HThr±(aq) + HCl(aq)} observed, w = 1 (Table 2A)
{HThr±(aq) + NaOH(aq)} observed, w = 1 (Table 3A)
2.98 ± 0.01
3.96 ± 0.01 7.27 ± 0.01 2.29 ± 0.01 10.86 ± 0.01
52.51 ± 0.01 13.26 ± 0.01 1.95 ± 0.01 27.8 ± 0.1
415.85 ± 0.01 561.14 ± 0.04 ± 0.89 0.65
559.03 ± 0.01 792.5 ± 0.1 ± 0.46 1.0
716.0 ± 0.1 984.37 ± 0.03 ± 0.18 1.0
H2Thr+Cl(aq) iteration, w = 1 (see text)
Na+Thr(aq) iteration, w = 1 (see text)
642.23 ± 0.01 4.13 ± 0.01 3.25 ± 0.01
990.98 ± 0.01 0.86 ± 0.01
153.938 ± 0.001 439.85 ± 0.01
219.829 ± 0.001 626.54 ± 0.01
± 0.063 1.0
± 0.17 1.0
The ± values are chosen to reproduce the generated V/ alues to within ± 0.01 cm3 Æ mol1 at 278.15 6 T/K 6 393.15 and at m 6 0.65 mol Æ kg1 for the zwitterion and m 6 1.0 mol Æ kg1 for the cationic and anionic forms. a Standard deviation of the regressions.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
73
TABLE 4B Regression parameters of equation (3) for apparent molar volumes V/(T, m) of{HIle±(aq)}, {HIle±(aq) + HCl(aq)}, {HIle±(aq) + NaOH(aq)}, {H2Ile+Cl(aq)}, and {Na+Ile(aq)} HIle±(aq) observed, w = 0 (Table 1B)
mi
{HIle±(aq) + HCl(aq)} observed, w = 1 (Table 2B)
63.95 ± 0.01
m0 m1 m2 103 Æ m3 103 Æ m4 m5 103 Æ m6 106 Æ m7 Da Highest m
190.74 ± 0.01 171.56 ± 0.04 ± 0.86 0.21
{HIle±(aq) + NaOH(aq)} observed, w = 1 (Table 3B) 39.24 ± 0.01 8.07 ± 0.01 2.36 ± 0.01 15.9 ± 0.1
43.005 ± 0.004 8.25 ± 0.01 2.99 ± 0.01 13.98 ± 0.01
465.74 ± 0.01 579.34 ± 0.03 ± 0.40 1.0
782.32 ± 0.01 1029.5 ± 0.1 ± 0.80 1.0
{H2Ile+Cl(aq)} iteration, w = 1 (see text)
Na+Ile(aq) iteration, w = 1 (see text)
525.62 ± 0.01 2.825 ± 0.004
803.32 ± 0.01 4.696 ± 0.004 3.14 ± 0.01
10.54 ± 0.01 132.086 ± 0.001 318.0 ± 0.1
183.649 ± 0.001 464.5 ± 0.1
± 0.15 1.0
± 0.13 1.0
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 0.21 mol Æ kg1 for the zwitterion and m 6 1.0 mol Æ kg1 for the cationic and anionic forms. a Standard deviations of the regressions.
m(i) is the molality of species i, Y/(i) is the apparent molar property V/ or Cp,/ of species i, and mt is given by equation (10): X mt ¼ mðiÞ: ð10Þ
-1 3 Vφ / (cm .mol )
120 110
Equations (11) and (12) define V/,tot and Cp,/,tot: 100 90
ð11Þ
C p;/;tot ¼ ðM av cp;s Þ þ fðcp;s cp;w Þ=mt g;
ð12Þ
where the weighted average molar mass of solutes in solution Mav is given by the following equation: X M av ¼ fmðiÞ=mt g MðiÞ: ð13Þ
80 0.6
m/
V /;tot ¼ ðM av =qs Þ fðqs qw Þ=ðqs qw mt Þg;
380
0.4
(m ol·
360 340
0.2
kg - 1 )
320 0.0
300 280
T/
K
FIGURE 1. Apparent molar volume V/ of zwitterionic threonine HThr±(aq) (lower surface) and isoleucine HIle±(aq) (upper surface) plotted against temperature T and molality m. Surfaces generated from equation (3) with parameters in column 2 of tables 4A and 4B, respectively; (s), experimental values from table 1A; (h), experimental values from table 1B; (d), references [5–16]; (n), references [13–20].
Apparent molar properties of these mixtures can be represented approximately at m* > 0 by Young’s Rule equation (9): h nX oi. mðiÞ Y / ðiÞ mt ; ð9Þ Y /;tot ¼ m Y rel þ where Y/,tot is the apparent molar property of the mixture, Yrel results from shifts in the equilibrium position by reaction (5) or (8) from scanning 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{HA±(aq)} < m{HCl(aq)} for reaction (5) and m = m{HA±(aq)} < m{NaOH(aq)} for reaction (8)],
We used the procedure outlined in our recent work on other aqueous amino acids [1–4] to analyze our results with equations (9) to (13). Reference values used for integration constants in this report for threonine at T* = 298.15 are pQa = (2.26 ± 0.20) [26–29,36–41,43,44] and DrHm = (3.75 ± 2.0) kJ Æ mol1 [25–29] for reaction (5), and pQa = (9.16 ± 0.36) [26–29,35–41,43–45] and DrHm = (41.51 ± 0.49) kJ Æ mol1 [25–29,33–35] for reaction (6). Reference values used for isoleucine at T* = 298.15 are pQa = (2.345 ± 0.093) [29–32,36,37] and DrHm = (0.979 ± 0.51) kJ Æ mol1 [24,29–32] for reaction (5), and pQa = (9.702 ± 0.076) [29–31,36,37] and DrHm = (45.67 ± 0.63) kJ Æ mol1 [24,29–31,33] for reaction (6). These values are averages of the values at T* = 298.15 given in the cited references, and the ± values given are the standard deviations of these values. As indicated by the large standard deviations for the values for reaction (5) where A = threonine, there is disagreement among the reported literature values. All values for reaction (8) were calculated from those for reaction (6) using values of pQw and DrHm,w at T* = 298.15 from Patterson et al. [50] to give pQb = (4.833 ± 0.200 and DrHm = 14.30 ± 2.00 kJ Æ mol1) for aqueous threonine and pQb = (4.295 ± 0.093 and DrHm = 10.137 ± 0.510 kJ Æ mol1) for aqueous isoleucine.
74
TABLE 5A Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for zwitterionic aqueous threonine at p = 0.35 MPa m mol Æ kg
cp,s 1
Cp,/ 1
JÆK
1
Æg
JÆK
cp,s 1
1
Æ mol
JÆK
Cp,/ 1
1
Æg
JÆK
cp,s 1
Æ mol
1
JÆK
Cp,/ 1
Æg
1
cp,s 1
JÆK
1
Æ mol
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
1
Æ mol
Cp,/ 1
JÆK
1
Æg
J Æ K1 Æ mol1
4.1975 4.1929 4.1861 4.1676 4.1385 4.0759 4.0042
T = 278.15 K 160 ± 26 172 ± 27 167.5 ± 8.6 149.7 ± 7.7 170.6 ± 3.1 163.6 ± 3.0 173.5 ± 2.9
4.1881 4.1840 4.1774 4.1596 4.1322 4.0723 4.0052
T = 283.15 K 175 ± 24 198 ± 31 183.8 ± 7.8 163.7 ± 8.2 186.7 ± 2.8 177.9 ± 3.0 189.9 ± 2.2
4.1818 4.1782 4.1715 4.1543 4.1281 4.0705 4.0061
T = 288.15 K 196 ± 23 219 ± 34 194.8 ± 7.6 175.2 ± 8.6 198.3 ± 2.7 188.8 ± 3.0 201.2 ± 2.1
4.1776 4.1742 4.1676 4.1514 4.1258 4.0707 4.0078
T = 293.15 K 206 ± 23 231 ± 28 205.4 ± 7.4 189.6 ± 7.8 208.4 ± 2.7 201.2 ± 2.8 210.8 ± 2.0
4.1750 4.1715 4.1653 4.1501 4.1247 4.0720 4.0101
T = 298.15 K 215 ± 22 234 ± 25 214.0 ± 7.2 204.1 ± 7.1 216.8 ± 2.6 216.0 ± 2.6 218.8 ± 1.9
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
4.1733 4.1698 4.1639 4.1496 4.1244 4.0735 4.0126
T = 303.15 K 222 ± 21 238 ± 25 221.5 ± 7.0 216.9 ± 6.8 224.1 ± 2.5 222.4 ± 2.5 225.8 ± 1.9
4.1726 4.1691 4.1634 4.1498 4.1248 4.0753 4.0155
T = 308.15 K 228 ± 21 242 ± 26 228.0 ± 6.8 227.3 ± 6.5 230.4 ± 2.4 229.8 ± 2.4 231.7 ± 1.8
4.1726 4.1692 4.1636 4.1504 4.1258 4.0774 4.0185
T = 313.15 K 233 ± 20 248 ± 26 233.6 ± 6.6 234.5 ± 6.3 235.8 ± 2.4 235.9 ± 2.4 236.8 ± 1.8
4.1733 4.1701 4.1645 4.1516 4.1274 4.0800 4.0219
T = 318.15 K 239 ± 19 253 ± 27 238.6 ± 6.4 239.2 ± 6.3 240.6 ± 2.3 241.2 ± 2.4 241.3 ± 1.8
4.1746 4.1714 4.1659 4.1531 4.1293 4.0829 4.0254
T = 323.15 K 243 ± 19 258 ± 27 242.8 ± 6.2 242.6 ± 6.3 244.7 ± 2.3 245.9 ± 2.3 245.3 ± 1.8
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
4.1765 4.1733 4.1679 4.1552 4.1318 4.0861 4.0292
T = 328.15 K 246 ± 18 260 ± 28 246.5 ± 6.0 245.4 ± 6.4 248.3 ± 2.2 249.9 ± 2.3 248.7 ± 1.7
4.1787 4.1755 4.1702 4.1576 4.1346 4.0894 4.0331
T = 333.15 K 250 ± 18 263 ± 28 249.8 ± 5.8 248.0 ± 6.5 251.5 ± 2.2 253.1 ± 2.3 251.9 ± 1.7
4.1814 4.1783 4.1731 4.1605 4.1378 4.0931 4.0373
T = 338.15 K 253 ± 17 265 ± 28 252.8 ± 5.6 249.9 ± 6.6 254.4 ± 2.1 255.7 ± 2.3 254.6 ± 1.7
4.1847 4.1816 4.1764 4.1637 4.1414 4.0970 4.0417
T = 343.15 K 255 ± 17 269 ± 29 255.3 ± 5.5 250.9 ± 6.7 256.8 ± 2.1 257.7 ± 2.3 257.0 ± 1.7
4.1883 4.1853 4.1801 4.1674 4.1453 4.1013 4.0462
T = 348.15 K 258 ± 16 272 ± 29 257.5 ± 5.3 251.9 ± 6.9 258.9 ± 2.1 259.7 ± 2.4 259.0 ± 1.7
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
4.1923 4.1893 4.1841 4.1714 4.1496 4.1058 4.0510
T = 353.15 K 259 ± 15 275 ± 29 259.4 ± 5.1 252.7 ± 7.0 260.8 ± 2.0 261.3 ± 2.4 260.8 ± 1.6
4.1967 4.1938 4.1886 4.1758 4.1542 4.1105 4.0560
T = 358.15 K 261 ± 15 278 ± 30 261.0 ± 4.9 253.3 ± 7.2 262.3 ± 2.0 262.6 ± 2.4 262.3 ± 1.6
4.2015 4.1987 4.1934 4.1806 4.1591 4.1155 4.0613
T = 363.15 K 262 ± 14 280 ± 31 262.5 ± 4.7 253.6 ± 7.5 263.7 ± 2.0 263.6 ± 2.5 263.6 ± 1.6
4.2069 4.2040 4.1988 4.1858 4.1645 4.1209 4.0668
T = 368.15 K 263 ± 14 282 ± 32 263.5 ± 4.6 253.5 ± 7.7 264.6 ± 1.9 264.1 ± 2.5 264.6 ± 1.6
4.2126 4.2098 4.2045 4.1914 4.1702 4.1265 4.0726
T = 373.15 K 263 ± 13 285 ± 34 264.2 ± 4.4 253.4 ± 8.1 265.5 ± 1.9 264.4 ± 2.6 265.4 ± 1.6
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
4.2188 4.2161 4.2107 4.1976 4.1765 4.1326 4.0787
T = 378.15 K 263 ± 12 287 ± 36 264.7 ± 4.2 252.7 ± 8.5 266.0 ± 1.9 264.3 ± 2.7 265.9 ± 1.6
4.2255 4.2229 4.2174 4.2042 4.1830 4.1389 4.0852
T = 383.15 K 264 ± 12 289 ± 37 264.9 ± 4.0 252.4 ± 8.7 266.2 ± 1.9 264.0 ± 2.7 266.3 ± 1.6
4.2328 4.2303 4.2247 4.2113 4.1902 4.1457 4.0919
T = 388.15 K 263 ± 11 294 ± 39 264.8 ± 3.8 251.7 ± 8.8 266.0 ± 1.8 263.2 ± 2.8 266.3 ± 1.6
4.2407 4.2385 4.2325 4.2189 4.1977 4.1528 4.0988
T = 393.15 K 262 ± 11 304 ± 46 263.6 ± 3.7 249.7 ± 9.7 265.0 ± 1.8 261.1 ± 3.0 265.5 ± 1.6
The ± uncertainties are from propagation of uncertainties as described in reference [48].
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
0.0157 0.0301 0.0501 0.1011 0.1993 0.3956 0.6542
TABLE 5B Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for zwitterionic aqueous isoleucine at p = 0.35 MPa cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
mol Æ kg1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.2004 4.1989 4.1952 4.1878 4.1726 4.1633
T = 278.15 K 328 ± 36 364 ± 13 364.5 ± 7.7 362.4 ± 4.8 357.2 ± 3.6 360.5 ± 3.0
4.1909 4.1895 4.1861 4.1791 4.1649 4.1563
T = 283.15 K 333 ± 38 372 ± 13 374.0 ± 7.5 373.6 ± 4.7 369.3 ± 3.6 372.1 ± 3.0
4.1844 4.1832 4.1799 4.1732 4.1597 4.1514
T = 288.15 K 333 ± 44 380 ± 13 381.1 ± 7.4 379.9 ± 4.6 377.3 ± 3.8 379.0 ± 2.9
4.1800 4.1789 4.1757 4.1693 4.1562 4.1483
T = 293.15 K 334 ± 50 386 ± 13 386.7 ± 7.4 385.6 ± 4.6 383.0 ± 3.9 384.8 ± 2.9
4.1774 4.1762 4.1731 4.1669 4.1542 4.1466
T = 298.15 K 345 ± 46 390 ± 13 391.0 ± 7.2 390.1 ± 4.5 387.3 ± 3.8 389.3 ± 2.9
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.1757 4.1745 4.1715 4.1654 4.1530 4.1456
T = 303.15 K 359 ± 37 394 ± 12 395.0 ± 7.2 393.8 ± 4.5 390.9 ± 3.6 393.1 ± 2.9
4.1751 4.1737 4.1708 4.1649 4.1526 4.1454
T = 308.15 K 375 ± 30 397 ± 12 398.2 ± 7.1 397.0 ± 4.4 394.0 ± 3.5 396.2 ± 2.8
4.1751 4.1737 4.1708 4.1650 4.1530 4.1459
T = 313.15 K 385 ± 25 400 ± 12 400.8 ± 7.0 399.5 ± 4.4 396.6 ± 3.5 398.7 ± 2.8
4.1759 4.1744 4.1716 4.1658 4.1540 4.1470
T = 318.15 K 395 ± 24 402 ± 12 403.1 ± 6.9 401.7 ± 4.3 398.5 ± 3.4 400.8 ± 2.8
4.1771 4.1757 4.1729 4.1672 4.1555 4.1485
T = 323.15 K 403 ± 25 404 ± 12 404.8 ± 6.9 403.6 ± 4.3 400.0 ± 3.4 402.5 ± 2.8
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.1790 4.1775 4.1747 4.1691 4.1574 4.1505
T = 328.15 K 411 ± 30 405 ± 12 406.3 ± 6.8 404.9 ± 4.3 400.8 ± 3.4 403.8 ± 2.8
4.1813 4.1797 4.1770 4.1713 4.1598 4.1529
T = 333.15 K 419 ± 37 407 ± 11 407.6 ± 6.8 406.0 ± 4.2 401.6 ± 3.4 404.8 ± 2.8
4.1840 4.1824 4.1797 4.1741 4.1626 4.1557
T = 338.15 K 424 ± 46 408 ± 11 408.5 ± 6.7 406.9 ± 4.2 402.3 ± 3.5 405.6 ± 2.8
4.1873 4.1856 4.1829 4.1773 4.1660 4.1589
T = 343.15 K 429 ± 58 408 ± 11 409.2 ± 6.6 407.5 ± 4.2 403.6 ± 3.7 406.1 ± 2.8
4.1910 4.1892 4.1865 4.1809 4.1697 4.1624
T = 348.15 K 438 ± 77 409 ± 11 409.5 ± 6.6 407.8 ± 4.2 404.8 ± 4.2 406.4 ± 2.7
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.1951 4.1932 4.1905 4.1848 4.1738 4.1663
T = 353.15 K 448 ± 101 409 ± 11 409.7 ± 6.5 408.1 ± 4.1 405.4 ± 4.9 406.5 ± 2.7
4.1996 4.1976 4.1949 4.1892 4.1782 4.1706
T = 358.15 K 457 ± 128 409 ± 11 409.8 ± 6.4 408.1 ± 4.1 405.6 ± 5.9 406.4 ± 2.7
4.2044 4.2024 4.1996 4.1939 4.1830 4.1752
T = 363.15 K 465 ± 148 409 ± 11 409.6 ± 6.4 407.9 ± 4.1 405.5 ± 6.7 406.2 ± 2.7
4.2097 4.2077 4.2049 4.1991 4.1881 4.1803
T = 368.15 K 466 ± 153 408 ± 11 409.2 ± 6.3 407.6 ± 4.1 405.0 ± 6.8 405.8 ± 2.7
4.2154 4.2133 4.2105 4.2047 4.1935 4.1857
T = 373.15 K 462 ± 138 408 ± 11 408.5 ± 6.3 407.1 ± 4.1 404.5 ± 6.3 405.2 ± 2.7
0.0101 0.0204 0.0402 0.0799 0.1601 0.2125
4.2215 4.2196 4.2168 4.2109 4.1995 4.1917
T = 378.15 K 447 ± 101 407 ± 10 407.9 ± 6.2 406.4 ± 4.1 403.9 ± 4.9 404.4 ± 2.7
4.2279 4.2263 4.2234 4.2175 4.2056 4.1980
T = 383.15 K 418 ± 38 406 ± 10 407.0 ± 6.2 405.5 ± 4.0 402.8 ± 3.2 403.5 ± 2.7
4.2348 4.2335 4.2306 4.2246 4.2121 4.2049
T = 388.15 K 376 ± 76 405 ± 10 405.7 ± 6.1 404.2 ± 4.0 401.0 ± 4.9 402.4 ± 2.7
4.2422 4.2413 4.2383 4.2322 4.2191 4.2120
T = 393.15 K 330 ± 191 402 ± 10 402.4 ± 6.1 401.2 ± 4.1 398.7 ± 9.5 399.6 ± 2.8
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
m
The ± uncertainties are from propagation of uncertainties as described in reference [48].
75
76
TABLE 6A Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for aqueous (threonine + HCl) at p = 0.35 MPa ma mol Æ kg
cp,s 1
Cp,/ 1
JÆK
1
Æg
JÆK
cp,s 1
1
Æ mol
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
Æ mol
1
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
1
Æ mol
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
1
Æ mol
JÆK
Cp,/ 1
1
Æg
J Æ K1 Æ mol1
4.1944 4.1870 4.1768 4.1528 4.0835 3.9827 3.8143
T = 278.15 K 95 ± 24 118 ± 19 133.0 ± 7.6 146.6 ± 3.6 158.5 ± 1.8 180.3 ± 1.2 187.15 ± 0.97
4.1851 4.1781 4.1682 4.1452 4.0791 3.9814 3.8212
T = 283.15 K 111 ± 25 142 ± 18 151.5 ± 8.0 165.0 ± 3.5 178.9 ± 1.7 196.5 ± 1.2 205.54 ± 0.87
4.1788 4.1720 4.1625 4.1401 4.0761 3.9811 3.8257
T = 288.15 K 136 ± 28 154 ± 18 165.2 ± 8.7 178.6 ± 3.6 192.6 ± 1.6 208.8 ± 1.2 217.73 ± 0.19
4.1745 4.1680 4.1587 4.1369 4.0745 3.9818 3.8301
T = 293.15 K 145 ± 29 165 ± 17 177.1 ± 9.1 189.9 ± 3.8 203.5 ± 1.6 218.7 ± 1.2 227.64 ± 0.78
4.1718 4.1655 4.1563 4.1350 4.0738 3.9828 3.8339
T = 298.15 K 151 ± 28 174 ± 17 185.7 ± 8.8 198.5 ± 3.5 211.8 ± 1.5 226.1 ± 1.1 235.09 ± 0.78
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
4.1701 4.1639 4.1549 4.1338 4.0738 3.9841 3.8375
T = 303.15 K 155 ± 26 182 ± 17 192.0 ± 8.0 204.9 ± 3.5 218.7 ± 1.5 232.3 ± 1.1 241.28 ± 0.77
4.1693 4.1633 4.1543 4.1335 4.0743 3.9858 3.8408
T = 308.15 K 157 ± 23 188 ± 16 196.9 ± 7.4 210.1 ± 3.8 224.2 ± 1.5 237.2 ± 1.2 246.16 ± 0.77
4.1693 4.1633 4.1544 4.1339 4.0753 3.9877 3.8440
T = 313.15 K 161 ± 23 193 ± 16 200.9 ± 7.2 214.5 ± 3.8 228.5 ± 1.4 241.3 ± 1.2 250.10 ± 0.76
4.1700 4.1641 4.1553 4.1350 4.0768 3.9900 3.8473
T = 318.15 K 166 ± 22 197 ± 16 204.7 ± 7.0 218.5 ± 3.6 232.0 ± 1.4 244.7 ± 1.2 253.31 ± 0.75
4.1713 4.1654 4.1566 4.1364 4.0786 3.9925 3.8504
T = 323.15 K 170 ± 22 200 ± 16 207.6 ± 6.8 221.5 ± 3.6 234.6 ± 1.4 247.5 ± 1.2 255.81 ± 0.75
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
4.1731 4.1673 4.1585 4.1384 4.0808 3.9952 3.8536
T = 328.15 K 172 ± 21 202 ± 15 209.6 ± 6.7 223.5 ± 3.8 236.6 ± 1.4 249.7 ± 1.2 257.74 ± 0.74
4.1754 4.1695 4.1608 4.1408 4.0833 3.9980 3.8569
T = 333.15 K 176 ± 21 204 ± 15 211.5 ± 6.7 225.3 ± 3.9 238.2 ± 1.3 251.3 ± 1.2 259.37 ± 0.73
4.1781 4.1722 4.1636 4.1436 4.0862 4.0013 3.8603
T = 338.15 K 181 ± 23 205 ± 15 213.6 ± 7.1 226.9 ± 3.8 239.5 ± 1.3 252.9 ± 1.2 260.63 ± 0.73
4.1815 4.1754 4.1669 4.1468 4.0894 4.0047 3.8637
T = 343.15 K 191 ± 26 206 ± 15 216.4 ± 8.1 228.0 ± 3.5 240.1 ± 1.3 253.9 ± 1.1 261.37 ± 0.72
4.1852 4.1790 4.1706 4.1505 4.0930 4.0083 3.8672
T = 348.15 K 201 ± 32 206 ± 15 219 ± 26 228.8 ± 3.3 240.4 ± 1.2 254.7 ± 1.1 261.87 ± 0.71
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
4.1894 4.1830 4.1747 4.1544 4.0968 4.0122 3.8709
T = 353.15 K 210 ± 42 206 ± 15 221 ± 13 229.2 ± 3.1 240.3 ± 1.2 255.1 ± 1.1 262.08 ± 0.71
4.1939 4.1874 4.1791 4.1588 4.1010 4.0164 3.8748
T = 358.15 K 217 ± 54 206 ± 15 222 ± 17 229.1 ± 2.9 240.0 ± 1.2 255.3 ± 1.0 262.14 ± 0.70
4.1987 4.1921 4.1839 4.1635 4.1055 4.0208 3.8789
T = 363.15 K 222 ± 63 205 ± 15 223 ± 19 229.1 ± 2.8 239.6 ± 1.2 255.4 ± 1.0 262.05 ± 0.70
4.2040 4.1974 4.1891 4.1686 4.1103 4.0255 3.8830
T = 368.15 K 223 ± 64 204 ± 14 223 ± 20 228.2 ± 2.7 238.6 ± 1.1 254.88 ± 0.99 261.45 ± 0.69
4.2097 4.2030 4.1947 4.1741 4.1156 4.0306 3.8875
T = 373.15 K 221 ± 58 203 ± 14 221 ± 18 227.4 ± 2.6 237.6 ± 1.1 254.37 ± 0.96 260.87 ± 0.69
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
4.2159 4.2093 4.2008 4.1802 4.1213 4.0360 3.8923
T = 378.15 K 214 ± 41 201 ± 14 219 ± 13 225.9 ± 2.4 236.4 ± 1.1 253.50 ± 0.91 260.06 ± 0.69
4.2223 4.2159 4.2072 4.1866 4.1275 4.0417 3.8973
T = 383.15 K 198 ± 15 199 ± 14 213.5 ± 4.8 224.2 ± 2.3 235.0 ± 1.1 252.24 ± 0.87 259.13 ± 0.69
4.2292 4.2231 4.2141 4.1936 4.1342 4.0478 3.9027
T = 388.15 K 170 ± 42 197 ± 14 205 ± 13 222.2 ± 2.2 233.8 ± 1.1 250.94 ± 0.87 257.96 ± 0.73
4.2365 4.2309 4.2214 4.2011 4.1415 4.0545 3.9079
T = 393.15 K 134 ± 93 194 ± 15 196 ± 29 219.4 ± 2.4 232.4 ± 1.2 249.91 ± 0.92 255.90 ± 0.93
The ± uncertainties are from propagation of uncertainties as described in reference [48]. a Molality of threonine, with stoichiometric molality ratio {m(HThr)/m(HCl)} = 0.9997.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
0.0152 0.0294 0.0500 0.0999 0.2501 0.4991 0.9561
TABLE 6B Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for aqueous (isoleucine + HCl) at p = 0.35 MPa cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
mol Æ kg1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.1966 4.1910 4.1832 4.1654 4.1133 4.0366 3.9000
T = 278.15 K 287 ± 10 313.8 ± 4.7 313.1 ± 3.1 326.5 ± 2.0 331.95 ± 0.97 346.55 ± 0.93 336.16 ± 0.66
4.1873 4.1820 4.1747 4.1574 4.1084 4.0336 3.9054
T = 283.15 K 303 ± 10 331.8 ± 5.0 332.7 ± 3.3 341.3 ± 2.0 350.10 ± 0.90 359.6 ± 1.0 352.85 ± 0.56
4.1810 4.1758 4.1687 4.1521 4.1047 4.0317 3.9075
T = 288.15 K 326 ± 11 341.3 ± 5.2 343.0 ± 3.4 351.6 ± 1.9 360.38 ± 0.88 368.4 ± 1.1 362.16 ± 0.48
4.1767 4.1717 4.1647 4.1485 4.1023 4.0307 3.9094
T = 293.15 K 335 ± 11 349.5 ± 5.5 350.6 ± 3.5 359.2 ± 2.0 368.14 ± 0.90 375.0 ± 1.2 369.09 ± 0.49
4.1740 4.1691 4.1623 4.1463 4.1009 4.0302 3.9107
T = 298.15 K 342 ± 12 355.4 ± 5.8 356.5 ± 3.6 364.7 ± 2.1 373.39 ± 0.93 379.3 ± 1.1 373.67 ± 0.50
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.1723 4.1674 4.1607 4.1449 4.1001 4.0301 3.9119
T = 303.15 K 347 ± 12 360.5 ± 6.0 361.2 ± 3.8 368.8 ± 2.4 377.50 ± 0.97 382.43 ± 0.98 377.01 ± 0.51
4.1716 4.1667 4.1601 4.1444 4.1000 4.0305 3.9130
T = 308.15 K 351 ± 13 364.1 ± 6.3 364.7 ± 3.9 371.7 ± 3.4 380.3 ± 1.0 384.55 ± 0.90 379.20 ± 0.52
4.1715 4.1667 4.1601 4.1446 4.1004 4.0311 3.9140
T = 313.15 K 354 ± 13 366.3 ± 6.6 366.9 ± 4.1 374.3 ± 3.5 382.0 ± 1.0 385.96 ± 0.88 380.55 ± 0.53
4.1722 4.1675 4.1609 4.1454 4.1013 4.0321 3.9153
T = 318.15 K 356 ± 14 368.1 ± 6.9 368.5 ± 4.2 376.2 ± 3.7 383.1 ± 1.1 386.81 ± 0.89 381.33 ± 0.54
4.1734 4.1687 4.1621 4.1467 4.1026 4.0334 3.9164
T = 323.15 K 357 ± 14 368.9 ± 7.2 369.2 ± 4.4 377.4 ± 4.0 383.6 ± 1.1 387.20 ± 0.93 381.47 ± 0.55
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.1752 4.1705 4.1639 4.1486 4.1043 4.0350 3.9177
T = 328.15 K 357 ± 15 369.3 ± 7.5 369.3 ± 4.6 378.5 ± 3.7 383.5 ± 1.1 387.1 ± 1.0 381.16 ± 0.56
4.1774 4.1727 4.1661 4.1508 4.1063 4.0368 3.9192
T = 333.15 K 358 ± 15 369.2 ± 7.7 369.1 ± 4.7 379.1 ± 4.0 383.1 ± 1.2 386.7 ± 1.1 380.67 ± 0.57
4.1801 4.1753 4.1687 4.1535 4.1087 4.0389 3.9210
T = 338.15 K 357 ± 16 368.6 ± 8.0 368.6 ± 4.9 379.2 ± 5.0 382.3 ± 1.2 385.7 ± 1.3 379.99 ± 0.58
4.1833 4.1785 4.1718 4.1566 4.1114 4.0413 3.9228
T = 343.15 K 356 ± 17 367.6 ± 8.3 367.4 ± 5.1 378.3 ± 6.1 381.0 ± 1.2 384.3 ± 1.5 378.84 ± 0.59
4.1869 4.1820 4.1753 4.1600 4.1145 4.0440 3.9249
T = 348.15 K 355 ± 17 366.2 ± 8.7 366.0 ± 5.3 377.0 ± 7.8 379.4 ± 1.3 382.7 ± 1.8 377.60 ± 0.60
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.1908 4.1860 4.1792 4.1638 4.1179 4.0470 3.9272
T = 353.15 K 354 ± 18 364.4 ± 9.0 364.2 ± 5.5 376 ± 10 377.6 ± 1.3 381.0 ± 2.3 376.19 ± 0.61
4.1952 4.1903 4.1835 4.1680 4.1217 4.0504 3.9298
T = 358.15 K 352 ± 18 362.6 ± 9.3 362.3 ± 5.7 375 ± 13 375.7 ± 1.4 379.3 ± 2.9 374.72 ± 0.62
4.2000 4.1950 4.1881 4.1726 4.1258 4.0541 3.9327
T = 363.15 K 350 ± 19 360.4 ± 9.6 360.1 ± 5.9 373 ± 15 373.6 ± 1.4 377.5 ± 3.3 373.25 ± 0.64
4.2052 4.2002 4.1932 4.1775 4.1303 4.0580 3.9357
T = 368.15 K 347 ± 20 357.8 ± 9.9 357.4 ± 6.1 370 ± 15 371.0 ± 1.4 375.3 ± 3.4 371.38 ± 0.65
4.2109 4.2058 4.1988 4.1827 4.1351 4.0622 3.9392
T = 373.15 K 344 ± 21 355 ± 10 354.6 ± 6.3 366 ± 14 368.5 ± 1.5 373.1 ± 3.1 369.65 ± 0.66
0.0151 0.0301 0.0502 0.1003 0.2500 0.5012 0.9531
4.2171 4.2120 4.2049 4.1884 4.1405 4.0668 3.9431
T = 378.15 K 342 ± 21 352 ± 11 351.6 ± 6.5 362 ± 10 365.9 ± 1.5 370.7 ± 2.4 367.68 ± 0.68
4.2237 4.2185 4.2113 4.1944 4.1463 4.0716 3.9472
T = 383.15 K 339 ± 22 349 ± 11 348.5 ± 6.7 355.3 ± 4.6 363.1 ± 1.6 368.0 ± 1.2 365.71 ± 0.71
4.2310 4.2257 4.2184 4.2009 4.1527 4.0767 3.9518
T = 388.15 K 335 ± 23 346 ± 11 345.2 ± 7.0 348.1 ± 8.1 360.5 ± 1.6 365.2 ± 1.9 363.68 ± 0.78
4.2388 4.2334 4.2260 4.2079 4.1595 4.0825 3.9560
T = 393.15 K 329 ± 24 341 ± 12 340.7 ± 7.3 341 ± 19 357.2 ± 1.8 362.9 ± 4.2 360.4 ± 1.1 77
The ± uncertainties are from propagation of uncertainties as described in reference [48]. a Molality of isoleucine, with stoichiometric molality ratio {m(HIle)/m(HCl)} = 0.997.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
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78
TABLE 7A Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for aqueous (threonine + NaOH) at p = 0.35 MPa cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
cp,s
Cp,/
mol Æ kg1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
J Æ K1 Æ g1
J Æ K1 Æ mol1
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.1943 4.1878 4.1777 4.1546 4.0915 3.9987 3.8491
T = 278.15 K 111 ± 40 90 ± 23 111 ± 14 107 ± 10 132.8 ± 2.8 147.5 ± 1.4 188.0 ± 1.1
4.1852 4.1792 4.1696 4.1484 4.0884 4.0005 3.8578
T = 283.15 K 138 ± 39 125 ± 23 138 ± 13 140 ± 11 158.4 ± 2.7 171.4 ± 1.3 207.6 ± 1.2
4.1791 4.1736 4.1642 4.1447 4.0869 4.0028 3.8660
T = 288.15 K 159 ± 37 153 ± 22 159 ± 13 167 ± 12 178.2 ± 2.6 189.0 ± 1.3 223.6 ± 1.2
4.1750 4.1698 4.1608 4.1423 4.0868 4.0059 3.8741
T = 293.15 K 177 ± 36 173 ± 22 177 ± 12 186.3 ± 9.8 195.4 ± 2.5 205.1 ± 1.2 237.2 ± 1.0
4.1725 4.1675 4.1589 4.1410 4.0875 4.0092 3.8818
T = 298.15 K 193 ± 35 189 ± 21 193 ± 12 201.7 ± 9.0 209.5 ± 2.4 218.4 ± 1.2 248.91 ± 0.91
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.1709 4.1661 4.1577 4.1406 4.0887 4.0126 3.8890
T = 303.15 K 205 ± 34 202 ± 21 206 ± 12 214.9 ± 9.0 221.6 ± 2.4 229.8 ± 1.2 258.91 ± 0.92
4.1703 4.1656 4.1575 4.1409 4.0904 4.0162 3.8957
T = 308.15 K 216 ± 33 214 ± 21 217 ± 11 226.1 ± 9.1 231.8 ± 2.3 239.6 ± 1.1 267.38 ± 0.94
4.1704 4.1659 4.1579 4.1418 4.0924 4.0199 3.9019
T = 313.15 K 226 ± 33 225 ± 21 227 ± 11 236.1 ± 9.2 240.6 ± 2.2 248.0 ± 1.1 274.58 ± 0.94
4.1712 4.1668 4.1590 4.1433 4.0949 4.0238 3.9079
T = 318.15 K 234 ± 32 234 ± 20 235 ± 11 244.7 ± 9.3 248.1 ± 2.2 255.4 ± 1.1 280.82 ± 0.96
4.1725 4.1683 4.1606 4.1452 4.0977 4.0277 3.9137
T = 323.15 K 240 ± 31 242 ± 19 241 ± 10 252.0 ± 9.3 254.6 ± 2.1 261.7 ± 1.0 286.19 ± 0.96
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.1744 4.1702 4.1627 4.1475 4.1007 4.0318 3.9192
T = 328.15 K 246 ± 30 248 ± 19 247.3 ± 9.9 2.57.7 ± 9.4 260.1 ± 2.0 267.18 ± 0.99 290.71 ± 0.97
4.1767 4.1726 4.1651 4.1502 4.1040 4.0359 3.9245
T = 333.15 K 250 ± 29 253 ± 19 252.3 ± 9.6 262.6 ± 9.4 264.9 ± 2.0 272.00 ± 0.95 294.51 ± 0.97
4.1794 4.1754 4.1680 4.1533 4.1076 4.0402 3.9297
T = 338.15 K 254 ± 28 257 ± 19 256.5 ± 9.3 266.8 ± 9.4 269.0 ± 1.9 276.14 ± 0.92 297.84 ± 0.98
4.1827 4.1787 4.1714 4.1568 4.1115 4.0447 3.9350
T = 343.15 K 257 ± 27 262 ± 18 259.8 ± 9.0 270.4 ± 9.4 272.4 ± 1.8 279.62 ± 0.89 300.66 ± 0.98
4.1863 4.1824 4.1751 4.1606 4.1157 4.0493 3.9402
T = 348.15 K 260 ± 26 265 ± 17 262.5 ± 8.6 273.3 ± 9.5 275.1 ± 1.8 282.52 ± 0.86 302.98 ± 0.99
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.1903 4.1864 4.1792 4.1648 4.1201 4.0540 3.9452
T = 353.15 K 261 ± 25 267 ± 16 264.6 ± 8.3 275.4 ± 9.6 277.4 ± 1.7 284.88 ± 0.83 304.8 ± 1.0
4.1947 4.1908 4.1836 4.1693 4.1247 4.0589 3.9503
T = 358.15 K 262 ± 24 268 ± 15 266.0 ± 8.0 277.1 ± 9.7 279.0 ± 1.6 286.77 ± 0.79 306.1 ± 1.0
4.1995 4.1956 4.1884 4.1741 4.1296 4.0640 3.9552
T = 363.15 K 262 ± 23 269 ± 15 266.8 ± 7.7 278.4 ± 9.9 280.2 ± 1.6 288.22 ± 0.76 307.0 ± 1.0
4.2048 4.2009 4.1937 4.1794 4.1349 4.0692 3.9602
T = 368.15 K 262 ± 22 269 ± 14 267.1 ± 7.4 279 ± 10 280.9 ± 1.5 289.16 ± 0.73 307.3 ± 1.1
4.2105 4.2066 4.1993 4.1851 4.1405 4.0747 3.9652
T = 373.15 K 261 ± 21 268 ± 13 267.0 ± 7.1 279 ± 11 281.1 ± 1.4 289.72 ± 0.70 307.3 ± 1.1
0.0175 0.0299 0.0521 0.1003 0.2501 0.5002 0.9958
4.2167 4.2128 4.2056 4.1912 4.1465 4.0805 3.9703
T = 378.15 K 260 ± 20 267 ± 13 266.3 ± 6.7 278 ± 11 280.7 ± 1.4 289.81 ± 0.67 306.9 ± 1.2
4.2234 4.2194 4.2121 4.1977 4.1528 4.0865 3.9756
T = 383.15 K 259 ± 19 264 ± 12 265.1 ± 6.4 277 ± 12 279.9 ± 1.3 289.51 ± 0.65 306.2 ± 1.2
4.2306 4.2266 4.2193 4.2048 4.1595 4.0928 3.9812
T = 588.15 K 257 ± 18 262 ± 12 263.4 ± 6.1 276 ± 12 278.5 ± 1.3 288.85 ± 0.62 305.3 ± 1.3
4.2385 4.2344 4.2270 4.2125 4.1664 4.0990 3.9872
T = 393.15 K 256 ± 17 260 ± 12 261.2 ± 5.8 276 ± 14 275.7 ± 1.2 287.81 ± 0.61 304.3 ± 1.5
The ± uncertainties are from propagation of uncertainties as described in reference [48]. a Molality of isoleucine, with stoichiometric molality ratio {m(HThr)/m(NaOH)} = 0.9997.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
ma
TABLE 7B Observed massic heat capacities cp,s and apparent molar heat capacities Cp,/ for aqueous (isoleucine + Na) at p = 0.35 MPa ma mol Æ kg
cp,s 1
JÆK
Cp,/ 1
1
Æg
cp,s 1
JÆK
1
Æ mol
JÆK
Cp,/ 1
1
Æg
JÆK
cp,s 1
1
Æ mol
Cp,/ 1
JÆK
1
Æg
JÆK
cp,s 1
Æ mol
1
Cp,/ 1
JÆK
1
Æg
cp,s 1
JÆK
Æ mol
1
Cp,/ 1
JÆK
1
Æg
J Æ K1 Æ mol1
4.1975 4.1919 4.1857 4.1680 4.1225 4.0556 3.9550
T = 278.15 K 304.5 ± 7.9 296.4 ± 4.9 302.1 ± 2.5 291.2 ± 1.8 320.18 ± 0.89 321.41 ± 0.86 356.49 ± 0.51
4.1882 4.1831 4.1774 4.1613 4.1188 4.0576 3.9632
T = 283.15 K 326.6 ± 7.0 320.6 ± 4.6 325.7 ± 2.3 319.2 ± 1.7 342.48 ± 0.83 346.45 ± 0.92 375.68 ± 0.50
4.1820 4.1771 4.1718 4.1570 4.1166 4.0601 3.9704
T = 288.15 K 339.7 ± 6.7 337.5 ± 4.1 343.1 ± 2.3 340.7 ± 1.6 358.93 ± 0.80 365.59 ± 0.99 390.58 ± 0.47
4.1779 4.1733 4.1681 4.1543 4.1158 4.0627 3.9768
T = 293.15 K 354.8 ± 6.5 353.1 ± 5.8 358.1 ± 2.2 357.5 ± 2.0 372.80 ± 0.78 380.9 ± 1.1 402.38 ± 0.46
4.1753 4.1709 4.1660 4.1529 4.1159 4.0655 3.9822
T = 298.15 K 367.5 ± 6.3 367.6 ± 7.3 370.0 ± 2.2 371.4 ± 2.4 384.03 ± 0.76 392.98 ± 0.91 411.55 ± 0.46
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
4.1736 4.1695 4.1647 4.1525 4.1165 4.0682 3.9868
T = 303.15 K 377.9 ± 6.4 381 ± 10 380.4 ± 2.2 384.8 ± 3.4 393.42 ± 0.76 402.74 ± 0.88 418.60 ± 0.47
4.1730 4.1691 4.1643 4.1528 4.1177 4.0709 3.9907
T = 308.15 K 386.6 ± 6.3 392 ± 13 388.6 ± 2.2 396.3 ± 4.2 401.08 ± 0.75 410.6 ± 1.1 424.02 ± 0.53
4.1730 4.1693 4.1645 4.1536 4.1191 4.0736 3.9943
T = 313.15 K 393.6 ± 6.2 402 ± 13 395.4 ± 2.1 404.9 ± 4.1 407.38 ± 0.74 416.9 ± 1.1 428.28 ± 0.54
4.1738 4.1702 4.1655 4.1548 4.1211 4.0765 3.9977
T = 318.15 K 399.4 ± 6.2 407 ± 13 400.9 ± 2.1 410.4 ± 4.2 412.62 ± 0.74 422.0 ± 1.1 431.53 ± 0.55
4.1750 4.1714 4.1669 4.1563 4.1233 4.0793 4.0008
T = 323.15 K 404.1 ± 6.1 410 ± 14 405.4 ± 2.1 413.9 ± 4.4 416.85 ± 0.73 425.9 ± 1.1 433.86 ± 0.57
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
4.1769 4.1734 4.1689 4.1584 4.1259 4.0822 4.0039
T = 328.15 K 407.5 ± 6.1 413.8 ± 9.9 409.0 ± 2.1 417.2 ± 3.2 420.24 ± 0.73 428.83 ± 0.94 435.61 ± 0.54
4.1791 4.1756 4.1712 4.1608 4.1286 4.0852 4.0066
T = 333.15 K 410.8 ± 6.1 416.2 ± 8.6 411.7 ± 2.1 419.4 ± 2.8 422.88 ± 0.73 430.88 ± 0.81 436.55 ± 0.56
4.1818 4.1783 4.1740 4.1636 4.1317 4.0883 4.0092
T = 338.15 K 412.5 ± 6.0 417.1 ± 9.5 413.7 ± 2.1 421.0 ± 3.1 424.81 ± 0.72 432.26 ± 0.71 436.86 ± 0.65
4.1851 4.1815 4.1772 4.1669 4.1351 4.0915 4.0118
T = 343.15 K 413.5 ± 6.0 417 ± 11 414.9 ± 2.1 421.9 ± 3.6 426.05 ± 0.72 432.93 ± 0.64 436.64 ± 0.75
4.1887 4.1851 4.1808 4.1704 4.1387 4.0949 4.0143
T = 348.15 K 413.7 ± 5.9 417 ± 14 415.4 ± 2.1 422.1 ± 4.5 426.72 ± 0.72 432.98 ± 0.60 435.97 ± 0.92
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
4.1926 4.1891 4.1848 4.1744 4.1426 4.0983 4.0169
T = 353.15 K 413.4 ± 6.0 417 ± 18 415.4 ± 2.1 422.1 ± 5.8 426.89 ± 0.72 432.48 ± 0.58 434.9 ± 1.2
4.1970 4.1934 4.1891 4.1787 4.1468 4.1019 4.0195
T = 358.15 K 412.5 ± 5.9 417 ± 23 414.9 ± 2.0 421.7 ± 7.3 426.58 ± 0.72 431.50 ± 0.57 433.5 ± 1.4
4.2018 4.1982 4.1938 4.1833 4.1512 4.1057 4.0222
T = 363.15 K 410.9 ± 5.9 416 ± 27 413.9 ± 2.0 420.8 ± 8.4 425.78 ± 0.72 430.12 ± 0.57 431.8 ± 1.6
4.2070 4.2034 4.1990 4.1883 4.1560 4.1097 4.0250
T = 368.15 K 408.5 ± 6.0 413 ± 27 412.3 ± 2.0 418.5 ± 8.6 424.43 ± 0.72 428.22 ± 0.57 429.7 ± 1.7
4.2127 4.2089 4.2046 4.1936 4.1610 4.1139 4.0278
T = 373.15 K 406.1 ± 6.0 408 ± 25 410.4 ± 2.1 415.2 ± 7.8 422.70 ± 0.72 425.86 ± 0.58 427.3 ± 1.5
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
4.2189 4.2150 4.2107 4.1993 4.1665 4.1185 4.0309
T = 378.15 K 403.4 ± 6.0 401 ± 17 407.8 ± 2.1 410.6 ± 5.5 420.53 ± 0.73 423.05 ± 0.57 424.5 ± 1.2
4.2256 4.2213 4.2172 4.2054 4.1723 4.1233 4.0340
T = 383.15 K 400.2 ± 6.0 392.0 ± 5.8 404.9 ± 2.1 404.9 ± 2.0 417.90 ± 0.73 419.83 ± 0.57 421.36 ± 0.57
4.2328 4.2282 4.2243 4.2118 4.1786 4.1284 4.0373
T = 388.15 K 397.0 ± 6.1 380 ± 15 401.4 ± 2.1 397.4 ± 4.7 414.78 ± 0.74 416.14 ± 0.61 417.87 ± 0.93
4.2406 4.2357 4.2319 4.2188 4.1850 4.1341 4.0409
T = 393.15 K 394.2 ± 6.5 367 ± 37 396.7 ± 2.1 389 ± 12 410.09 ± 0.76 412.51 ± 0.60 414.1 ± 2.1
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
0.0151 0.0313 0.0501 0.1000 0.2576 0.4998 0.9940
The ± uncertainties are from propagation of uncertainties as described in reference [48]. a Molality of isoleucine, with stoichiometric molality ratio {m(Hlle)/m(NaOH)} = 0.998. 79
80
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
TABLE 8A Regression parameters of equation (4) for apparent molar heat capacities Cp,/(T, m) of {HThr±(aq)}, {HThr±(aq) + HCl(aq)}, {HThr±(aq) + NaOH(aq)}, {H2Thr+Cl (aq)}, and {Na+Thr(aq)} ci
HThr±(aq) observed, w = 0 (Table 5A)
{HThr±(aq) + HCl(aq)} observed, w = 1 (Table 6A)
{HThr±(aq) + NaOH(aq)} observed, w = 1 (Table 7A)
H2Thr+Cl(aq) iteration, w = 1 (see text)
Na+Thr(aq)iteration, w = 1 (see text)
103 Æ c0 103 Æ c1 c2 103 Æ c3 c4 103 Æ c5 103 Æ c6 c7 103 Æ c8 106 Æ c9 Da Highest m
1.2481 ± 0.0001 74.8176 ± 0.0001
2.15884 ± 0.00004 53.7880 ± 0.0001 26.2 ± 0.1 12.61910 ± 0.00002 78.5542 ± 0.0001 59.8207 ± 0.0002
282.26625 ± 0.00004 0.65054 ± 0.00004 33.8 ± 0.1 0.10727 ± 0.00001
201.75770 ± 0.00004 1.04318 ± 0.00004
17.43383 ± 0.00001 105.959 ± 0.001 79.7715 ± 0.0004
1.2458 ± 0.0001 48.84194 ± 0.00004 46.2 ± 0.1 11.39916 ± 0.00001 69.1885 ± 0.0001 51.6897 ± 0.0002
8.1802 ± 0.0001 11.0436 ± 0.0002
8.3149 ± 0.0001 11.889 ± 0.001
13.3127 ± 0.0001 18.298 ± 0.001
69.92825 ± 0.00001 592.1496 ± 0.0001 841.1296 ± 0.0002 534.787 ± 0.001 ± 0.93 1.0
49.51713 ± 0.00001 406.1359 ± 0.0001 567.1334 ± 0.0002 358.862 ± 0.001 ± 0.59 1.0
± 2.8 0.65
± 2.1 1.0
± 1.8 1.0
0.17811 ± 0.00001
The ± values are chosen to reproduce the generated Cp,/ values to within ±0.1 J Æ K1 Æ mol1 at 278.15 < T/K < 393.15 and at m < 0.65 mol Æ kg1 for the zwitterion and w < 1.0 mol Æ kg1 for the cationic and anionic forms. a Standard deviations of the regressions.
TABLE 8B Regression parameters of equation (4) for apparent molar heat capacities Cp,/(T, m) of {HIle±(aq)}, {HIle±(aq) + HCl(aq)}, {HIle±(aq) + NaOH(aq)}, {H2Ile+Cl (aq)}, and {Na+Ile(aq)} ci
HIle±(aq) observed, w = 0 (Table 5B)
{HIle±(aq) + HCl(aq)} observed, w = 1 (Table 6B)
{HIle±(aq) + NaOH(aq)} observed, w = 1 (Table 7B)
H2Ile+Cl(aq)iteration, w = 1 (see text)
Na+Ile(aq)iteration, w = 1 (see text)
103 Æ c0 103 Æ c1 c2 103 Æ c3 c4 103 Æ c5 103 Æ c6 c7 103 Æ c8 106 Æ c9 Da Highest m
0.46953 ± 0.00006
1.0411 ± 0.0001 51.41595 ± 0.00004 41.04 ± 0.04 12.07547 ± 0.00001 75.5692 ± 0.0001 58.258 ± 0.001
2.06545 ± 0.00004 78.9648 ± 0.0001 1.66 ± 0.04 18.53567 ± 0.00001 115.6438 ± 0.0001 88.431 ± 0.001
315.46322 ± 0.00003
289.19595 ± 0.00003 1.3601 ± 0.0001
8.4728 ± 0.0001 12.795 ± 0.001
14.1226 ± 0.0001 20.1286 ± 0.0002
4.9460 ± 0.0001 6.9632 ± 0.0004 ± 2.9 0.21
± 2.4 1.0
± 2.9 1.0
0.23640 ± 0.00002 0.1305 ± 0.0001 78.53056 ± 0.00001 674.9853 ± 0.0001 968.5031 ± 0.0002 620.123 ± 0.001 ± 1.2 1.0
71.35138 ± 0.00001 594.4049 ± 0.0001 835.2597 ± 0.0002 528.156 ± 0.001 ± 0.86 1.0
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 0.21 mol Æ kg1 for the zwitterion and w 6 1.0 mol Æ kg1 for the cationic and anionic forms. a Standard deviations of the regressions.
We fit by regression equation (4) to our derived Cp,/(T, m) results for H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq) using the squares of the reciprocals of the uncertainties in Cp,/,obs from tables 6 and 7 as weighting factors. The regression parameters ci are given in columns 5 and 6 of tables 8A and 8B. Figures 3 and 4 show our Cp,/(T, m) results for these species, surfaces calculated from the regression parameters in columns 5 and 6 of tables 8A and 8B, and ‘‘ideal’’ surfaces obtained by simple addition of the surfaces for each of the reactant components. We know of no results in the literature that give Cp,/ for any of these species. We have also calculated V/(T, m) for H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq) and then fit equation (3) by regression to these results to give the parameters in columns 5 and 6 in tables 4A and 4B. The results of these calculations are the solid surfaces shown in figures 5 and 6. The points calculated using Young’s
Rule as well as the ‘‘ideal’’ surfaces are also shown in figures 5 and 6. We are unaware of results from the literature for V/ of any of these species. Our iterative Young’s Rule results allow us to calculate values of DrCp,m, DrHm, pQa, DrSm, and DrVm for reactions (5) and (6) analogous to what was done in our previous reports [1–4]. Figure 7 shows DrCp,m(T, m) for reactions (5) and (6) for both threonine and isoleucine, together with values from the literature [24]. The difference between our value of Dr C p;m for reaction (5) for isoleucine at T* = 298.15 and m* = 0 and the value from reference [24] is D = 41.0 J Æ K1 Æ mol1. The comparable difference for reaction (6) for isoleucine is D = 58.9 J Æ K1 Æ mol1. We found no results in the literature for DrCp,m for reaction (5) or (6) for threonine. Figure 8 shows DrHm(T, m) for reactions (5) and (6) together with values from the literature [24–35]. The differences between our values of DrHm(T, m) for reaction (5)
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
81
450 -1 -1 Cp,φ / (J·K ·mol )
-1 -1 Cp,φ / (J·K mol )
550 400 350 300 250 200
450 350 250 150 50 1.00
0.6
m/
(m ol·
0.75
380
0.4
360 340
0.2
kg - 1 )
m/
320 0.0
300
T
280
/K
FIGURE 2. Apparent molar heat capacity Cp,/ of zwitterionic threonine HThr±(aq) (lower surface) and isoleucine HIle±(aq) (upper surface) plotted against temperature T and molality m. Surfaces generated from equation (4) with parameters in column 2 of tables 8A and 8B, respectively; (s), experimental values from table 5A; (h), experimental values from table 5B; (d), references [12,13,21–23]; (n), references [13,20,21].
360
0.50
(m ol·
380
340 320
0.25
kg - 1 )
0.00
300 280
T/
K
FIGURE 4. Apparent molar heat capacities Cp,/ of sodium threoninate Na+Thr(aq) (lower solid surface and ), [Cp,/{HThr±(aq)} + Cp,/{NaOH(aq)}] (lower wire frame), sodium isoleucinate {Na+Thr(aq) + 200 J Æ K1 Æ mol1} (upper solid surface and d), and of [Cp,/{HIle±(aq)} + Cp,/{NaOH(aq)} + 200 J Æ K1 Æ mol1] (upper 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 tables 8A and 8B, respectively; (s), experimental values from table 7A; (d), experimental values from table 7B; wire frames generated by adding Cp,/(T, m) for Na+(aq) [1] to Cp,/(T, m) for threonine(aq) or isoleucine(aq).
450 350 160
250 1
150
3 Vφ / (cm ·mol )
-1 -1 Cp,φ / (J·K mol )
550
50 1.00 0.75
m/
360
0.50
(m ol·
kg - 1 0.25 )
380
340 320 0.00
300 280
T/
K
FIGURE 3. Apparent molar heat capacities Cp,/ of threoninium hydrochloride H2Thr+Cl(aq) (lower solid surface and s), [Cp,/{HThr±(aq)} + Cp,/{HCl(aq)}] (lower wire frame), isoleucininium hydrochloride {H2Ile+Cl(aq) + 200 J Æ K1 Æ mol1} (upper solid surface and d), and of [Cp,/{HIle±(aq)} + Cp,/{HCl(aq)} + 200 J Æ K1 Æ mol1] (upper wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surfaces generated from equation (4) with regression parameters from column 5 of tables 8A and 8B, respectively; (s), experimental values from table 6A; (d), experimental values from table 6B; wire frames generated by adding Cp,/(T, m) for HCl(aq) [1] to Cp,/(T, m) for threonine (aq) or isoleucine (aq).
and those from the literature are in the range D = (2.20 [25,29] to 1.94 [27]) kJ Æ mol1 with an average difference D = 0.25 kJ Æ mol1 for aqueous threonine, and those differences are D = (1.81 [31] to 0.52 [31]) kJ Æ mol1 with
140
120
100 1.00 0.75
m/
380 360
0.50
(m ol·
340 320
0.25
kg - 1 )
0.00
300 280
T/
K
FIGURE 5. Apparent molar volume V/(i) of threoninium hydrochloride H2Thr+Cl(aq) (lower solid surface and ), [Cp,/{HThr±(aq)} + Cp,/{HCl(aq)}] (lower wire frame), isoleucininium hydrochloride {H2Ile+Cl(aq) + 25 cm3 Æ mol1} (upper solid surface and d), and of [Cp,/{HIle±(aq)} + Cp,/{HCl(aq)} + 25 cm3 Æ mol1] (upper wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surfaces generated from equation (3) with regression parameters from column 5 of tables 4A and 4B, respectively; (s), experimental values from table 2A; (d), experimental values from table 2B; wire frames generated by adding V/(T, m) for HCl(aq) [52] to V/(T, m) for threonine(aq) or isoleucine(aq).
82
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
1
3 Vφ / (cm ·mol )
140
120
100
80 1.00 0.75
m/
380 360
0.50
(m ol·
340 320
0.25
kg - 1 )
0.00
300 280
T/
K
FIGURE 6. Apparent molar volume V/(i) of sodium threoninate Na+Thr(aq) (lower solid surface and ), [Cp,/{HThr±(aq)} + Cp,/{NaOH(aq)}] (lower wire frame), sodium isoleucinate {Na+Thr(aq) + 25 cm3 Æ mol1} (upper solid surface and d), and of [Cp,/{HIle±(aq)} + Cp,/{NaOH(aq)} + 25 cm3 Æ mol1] (upper wire frame) plotted against temperature T and molality m at p = 0.35 MPa. Solid surfaces generated from equation (3) with regression parameters from column 6 of tables 4A and 4B, respectively; (s), experimental values from table 3A; (d), experimental values from table 3B; wire frames generated by adding V/(T, m) for Na+(aq) [1] to V/(T, m) for threonine(aq) or isoleucine(aq).
an average difference D = 0.16 kJ Æ mol1 for aqueous isoleucine. The differences between our DrHm(T, m) for reaction (6) and values from the literature are in the range D = (0.92 [26] to 0.73 [34]) kJ Æ mol1 with an average difference D = 0.15 kJ Æ mol1 for aqueous threonine,
and those differences are D = (2.03 [31] to 0.69 [29,33]) kJ Æ mol1 with an average difference D = 0.49 kJ Æ mol1 for aqueous isoleucine. Figure 9 shows pQa(T, m) for reactions (5) and (6) and values from the literature [26–32,35–45]. Our values of pQa(T, m) for reaction (5) differ from the literature values by D = (0.20 [26] to 0.45 [37]) with an average difference D = 0.052 for aqueous threonine, and those differences are D = (0.17 [30,32] to 0.13 [32]) with an average difference D = 0.013 for aqueous isoleucine. Our values of pQa(T, m) for reaction (6) differ from the literature values by D = (0.67 [42] to 1.27 [36]) with an average difference D = 0.18 for aqueous threonine, and D = (0.57 [30] to 0.37 [29]) with an average difference D = 0.014 for aqueous isoleucine. Figure 10 shows DrSm(T, m) for reactions (5) and (6) together with values from the literature [24–27,29–35]. The differences between our values of DrSm(T, m) for reaction (5) and those from the literature are in the range D = (4.2 [25,29] to 9.8 [27]) J Æ K1 Æ mol1 with an average difference D = 3.6 J Æ K1 Æ mol1 for aqueous threonine, and those differences are D = (5.39 [31] to 2.25 [31]) J Æ K1 Æ mol1 with an average difference D = 0.46 J Æ K1 Æ mol1 for aqueous isoleucine. The differences between our DrSm(T, m) results for reaction (6) and those from the literature are in the range D = (2.2 [26] to 10.9 [34]) J Æ K1 Æ mol1 with an average difference D = 1.7 J Æ K1 Æ mol1 for aqueous threonine, and those differences are D = (8.0 [31] to 0.046 [29,33]) J Æ K1 Æ mol1 with an average difference D = 2.7 J Æ K1 Æ mol1 for aqueous isoleucine.
45 -1 Δ rH m / (kJ·mol )
-1 -1 Δ rCp,m / (J·K mol )
0
-50
-100
35 25 15 5 -5 1.00
-150 1.00
0.75 0.75
m/
380 360
0.50
(m ol·
340 0.25
kg -1 )
320 0.00
300 280
T/
m/
380 360
0.50 0.25 (m ol· kg - 1 0.00 )
340 320 300 280
T/
K
K
FIGURE 7. Heat capacity change DrCp,m for reactions (5) and (6) of threonine and isoleucine, plotted against temperature T and molality m. (m) surface, DrCp,m for reaction (5) of threonine; (.) surface, DrCp,m for reaction (5) of isoleucine; (n), DrCp,m,1 of isoleucine, reference [24]; (n) surface, DrCp,m for reaction (6) of threonine; (,) surface, DrCp,m for reaction (6) of isoleucine; (h), DrCp,m,2 of isoleucine, reference [24].
FIGURE 8. Enthalpy change DrHm for reactions (5) and (6) of threonine and isoleucine plotted against temperature T and molality m. (m) surface, DrHm for reaction (5) of threonine; (d), DrHm,1 of threonine, references [25–29]; (.) surface, DrHm for reaction (5) of isoleucine; (n), DrHm,1 of isoleucine, references [24,29–32]; (n) surface, DrHmfor reaction (6) of threonine; (s), DrHm,2 of threonine, references [25–29,33–35]; (,) surface, DrHm for reaction (6) of isoleucine; (h), DrHm,2 of isoleucine, references [24,29–31,33].
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
10
pQa
8
6 4 1.00 0.75
m/
380 360
0.50
(m ol·
340 0.25
kg - 1 )
320 0.00
300 280
T/
K
FIGURE 9. Equilibrium molality quotient pQa for reactions (5) and (6) of threonine and isoleucine plotted against temperature T and molality m. (m) surface, pQa for reaction (5) of threonine; (d), pQa,1 of threonine, references [26,36–44]; (.) surface, pQa for reaction (5) of isoleucine; (n), pQa,1 of isoleucine, references [29–32,36,37]; (n) surface, pQa for reaction (6) of threonine; (s), pQa,2 of threonine, references [26–29,35–45]; (,) surface, pQa for reaction (6) of isoleucine; (h), pQa,2 of isoleucine, references [29–31,36,37].
We have also calculated values of DrVm(T, m) for reactions (5) and (6) using our values of V/ for HThr±(aq), HIle±(aq), H2Thr+Cl(aq), H2Ile+Cl(aq), Na+Thr(aq), and Na+Ile(aq), values of V/ for HCl(aq) from Sharygin
83
and Wood [51], and values of V/ for NaCl(aq) and NaOH(aq) from Sorenson et al. [1]. These results are shown in figure 11. We know of no previously reported values of DrVm for reaction (5) or (6) at any T or m for aqueous solutions of either threonine or isoleucine. 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 pKa at 278.15 6 T* 6 393.15 for reactions (5) and (6) that are given in tables 9 and 10, respectively. We suggest that our values of DrVm, DrCp,m, DrHm, DrSm, and pQa are to be preferred at (0 6 m* 6 1) from (278.15 6 T* 6 393.15) over those currently extant in the literature. The greatest source of uncertainties in our reported values arise from the integration constants pQa and DrHm obtained from the literature. Uncertainties in our recommended values are limited to the uncertainties in these reference values. Interesting comparisons are possible between the properties V/(T, m) and Cp,/(T, m) for aqueous zwitterionic, cationic, and anionic species of threonine, isoleucine, valine, L-2-aminobutanoic acid, and serine. We calculate the average differences DV/(x y) at (278.15 6 T* 6 368.15) and DCp,/(x y) at (278.15 6 T* 6 393.15) at (0.0 6 m* 6 0.5) for the species of the amino acids x and y. Table 11 gives the results of these calculations. Table 12 gives our average values of the differences for these group substitutions over the temperature ranges of our experiments. These values are the averages of the values calculated using the individual values of the cationic, zwitterionic, and anionic forms. The values for replacing a proton with a methyl group are the averages for all three calculations reported in table 11.
-40 0 -1 3 Δ rVm / (cm mol )
-1 -1 Δ rSm / (J·K .mol )
-20
-60 -80 -100 1.00 0.75
m/
380
-6 -9 -12
360
0.50
(m ol·
-3
340 0.25
kg - 1 )
320 0.00
300 280
K T/
FIGURE 10. Entropy changes DrSm for reactions (5) and (6) of threonine and isoleucine plotted against temperature T and molality m. (m) surface, DrSm for reaction (5) of threonine; (d), DrSm,1 of threonine, references [25–27,29]; (.) surface, DrSm for reaction (5) of isoleucine; (n), DrSm,1 of isoleucine, references [25–27,29,33–35]; (n) surface, DrSmfor reaction (6) of threonine; (s), DrSm,2 of threonine, references [24,29–32]; (,) surface, DrSm for reaction (6) of isoleucine; (h), DrSm,2 of isoleucine, references [24,29–31,33].
1.00 0.75
m/
360
0.50 0.25 (m ol· kg - 1 0.00 )
380
340 320 300 280
T/
K
FIGURE 11. Volume changes DrVm for reactions (5) and (6) of threonine and isoleucine plotted against temperature T and molality m. (m) surface, DrVm for reaction (5) of threonine; (.) surface, DrVm for reaction (5) of isoleucine; (n) surface, DrVm for reaction (6) of threonine; (,) surface, DrVm for reaction (6) of isoleucine.
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TABLE 9A ‘‘Best’’ standard thermodynamic values for the first proton dissociation of aqueous threonine, reaction (5), H2A+(aq) = HA±(aq) + H+(aq), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K
Dr V m =ðcm3 mol1 Þ
Dr C p;m =ðJ K1 mol1 Þ
Dr H m =ðkJ mol1 Þ
Dr S m =ðJ K1 mol1 Þ
pK
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
9.77 ± 0.83 9.46 ± 0.83 9.20 ± 0.83 8.98 ± 0.84 8.81 ± 0.84 8.67 ± 0.84 8.56 ± 0.84 8.49 ± 0.84 8.44 ± 0.84 8.42 ± 0.84 8.44 ± 0.84 8.47 ± 0.84 8.54 ± 0.84 8.63 ± 0.84 8.76 ± 0.84 8.91 ± 0.84 9.09 ± 0.84 9.31 ± 0.84 9.56 ± 0.84 9.84 ± 0.83 10.17 ± 0.83 10.54 ± 0.83 10.96 ± 0.83 11.42 ± 0.82
143.5 ± 8.9 137.0 ± 8.8 130.6 ± 8.6 124.4 ± 8.4 118.4 ± 8.3 112.7 ± 8.1 107.3 ± 8.0 102.3 ± 7.8 97.7 ± 7.7 93.6 ± 7.6 90.0 ± 7.5 86.9 ± 7.4 84.4 ± 7.3 82.4 ± 7.2 81.0 ± 7.2 80.1 ± 7.1 79.7 ± 7.1 80.0 ± 7.0 80.7 ± 7.0 82.0 ± 7.0 83.7 ± 7.0 85.9 ± 7.0 88.4 ± 7.0 91.4 ± 7.1
6.4 ± 2.0 5.7 ± 2.0 5.0 ± 2.0 4.4 ± 2.0 3.7 ± 2.0 3.2 ± 2.0 2.6 ± 2.0 2.1 ± 2.0 1.6 ± 2.1 1.1 ± 2.1 0.7 ± 2.1 0.2 ± 2.1 0.2 ± 2.1 0.6 ± 2.1 1.0 ± 2.1 1.4 ± 2.1 1.8 ± 2.1 2.2 ± 2.1 2.6 ± 2.1 3.0 ± 2.1 3.5 ± 2.1 3.9 ± 2.1 4.3 ± 2.1 4.8 ± 2.1
21.7 ± 7.9 24.2 ± 7.9 26.5 ± 7.9 28.7 ± 7.8 30.7 ± 7.8 32.7 ± 7.8 34.5 ± 7.7 36.2 ± 7.7 37.7 ± 7.7 39.2 ± 7.6 40.6 ± 7.6 42.0 ± 7.5 43.3 ± 7.5 44.5 ± 7.5 45.7 ± 7.4 46.8 ± 7.4 47.9 ± 7.3 49.0 ± 7.3 50.1 ± 7.2 51.2 ± 7.2 52.3 ± 7.2 53.4 ± 7.1 54.6 ± 7.1 55.7 ± 7.0
2.33 ± 0.20 2.31 ± 0.20 2.29 ± 0.20 2.27 ± 0.20 2.26 ± 0.20 2.25 ± 0.20 2.24 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.23 ± 0.20 2.24 ± 0.20 2.24 ± 0.20 2.24 ± 0.20 2.25 ± 0.21 2.26 ± 0.21 2.26 ± 0.21 2.27 ± 0.21 2.28 ± 0.21
a
The ± values are propagated uncertainties.
Much has been said concerning the validity of group contribution calculations and rationalizations. There have also been discrepancies reported in the literature as to the
best standard group contribution values to invoke. We have used V/(H)/cm3 Æ mol1 = Cp,/(H)/J Æ K1mol1 = 0. The interested reader can recalculate any of the values
TABLE 9B ‘‘Best’’ standard thermodynamic values for the first proton dissociation of aqueous isoleucine, reaction (5), H2A+(aq) = HA±(aq) + H+(aq), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K
Dr V m =ðcm3 mol1 Þ
Dr C p;m =ðJ K1 mol1 Þ
Dr H m =ðkJ mol1 Þ
Dr S m =ðJ K1 mol1 Þ
pK
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
8.8 ± 1.1 8.7 ± 1.1 8.7 ± 1.1 8.7 ± 1.1 8.8 ± 1.1 8.8 ± 1.1 8.9 ± 1.1 9.0 ± 1.1 9.1 ± 1.1 9.2 ± 1.1 9.4 ± 1.1 9.5 ± 1.1 9.7 ± 1.1 9.9 ± 1.1 10.1 ± 1.1 10.3 ± 1.1 10.5 ± 1.1 10.8 ± 1.1 11.0 ± 1.1 11.3 ± 1.1 11.6 ± 1.1 11.9 ± 1.1 12.3 ± 1.0 12.7 ± 1.0
144.5 ± 3.6 138.5 ± 3.6 132.4 ± 3.6 126.4 ± 3.6 120.5 ± 3.6 114.8 ± 3.6 109.4 ± 3.6 104.4 ± 3.6 99.7 ± 3.6 95.4 ± 3.6 91.7 ± 3.6 88.4 ± 3.6 85.6 ± 3.6 83.3 ± 3.6 81.5 ± 3.5 80.2 ± 3.5 79.4 ± 3.5 79.1 ± 3.5 79.1 ± 3.5 79.5 ± 3.5 80.3 ± 3.5 81.3 ± 3.5 82.5 ± 3.5 83.8 ± 3.5
3.63 ± 0.63 2.92 ± 0.63 2.24 ± 0.63 1.60 ± 0.63 0.98 ± 0.63 0.39 ± 0.63 0.17 ± 0.63 0.70 ± 0.63 1.21 ± 0.63 1.70 ± 0.63 2.17 ± 0.63 2.62 ± 0.63 3.05 ± 0.64 3.48 ± 0.64 3.89 ± 0.64 4.29 ± 0.64 4.69 ± 0.65 5.09 ± 0.65 5.48 ± 0.66 5.88 ± 0.66 6.28 ± 0.67 6.68 ± 0.67 7.09 ± 0.68 7.51 ± 0.69
32.4 ± 2.8 34.9 ± 2.8 37.3 ± 2.8 39.5 ± 2.8 41.6 ± 2.8 43.6 ± 2.7 45.4 ± 2.7 47.1 ± 2.7 48.7 ± 2.7 50.3 ± 2.7 51.7 ± 2.7 53.1 ± 2.7 54.4 ± 2.7 55.6 ± 2.7 56.8 ± 2.7 57.9 ± 2.7 59.1 ± 2.7 60.2 ± 2.7 61.2 ± 2.7 62.3 ± 2.7 63.4 ± 2.7 64.4 ± 2.7 65.5 ± 2.7 66.6 ± 2.7
2.374 ± 0.093 2.363 ± 0.093 2.355 ± 0.093 2.349 ± 0.093 2.345 ± 0.093 2.343 ± 0.093 2.343 ± 0.093 2.344 ± 0.093 2.346 ± 0.093 2.350 ± 0.093 2.355 ± 0.093 2.360 ± 0.093 2.367 ± 0.093 2.374 ± 0.093 2.382 ± 0.093 2.391 ± 0.093 2.400 ± 0.093 2.410 ± 0.093 2.420 ± 0.094 2.431 ± 0.094 2.443 ± 0.094 2.454 ± 0.094 2.466 ± 0.094 2.479 ± 0.094
a
The ± values are propagated uncertainties.
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
85
TABLE 10A ‘‘Best’’ standard thermodynamic values for the second proton dissociation of aqueous threonine, reaction (6), HA±(aq) = A(aq) + H+(aq), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K
Dr V m =ðcm3 mol1 Þ
Dr C p;m =ðJ K1 mol1 Þ
Dr H m =ðkJ mol1 Þ
Dr S m =ðJ K1 mol1 Þ
pK
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
0.41 ± 0.36 0.76 ± 0.36 0.92 ± 0.36 1.04 ± 0.36 1.16 ± 0.35 1.30 ± 0.35 1.45 ± 0.35 1.61 ± 0.35 1.80 ± 0.35 1.99 ± 0.35 2.20 ± 0.35 2.42 ± 0.34 2.64 ± 0.34 2.88 ± 0.34 3.12 ± 0.34 3.36 ± 0.34 3.62 ± 0.34 3.88 ± 0.34 4.15 ± 0.34 4.42 ± 0.35 4.71 ± 0.35 5.01 ± 0.35 5.32 ± 0.35 5.65 ± 0.35
56.5 ± 3.0 59.8 ± 2.9 60.7 ± 2.7 61.2 ± 2.6 61.8 ± 2.5 62.5 ± 2.5 63.3 ± 2.5 64.1 ± 2.4 65.0 ± 2.4 65.7 ± 2.4 66.3 ± 2.4 66.9 ± 2.4 67.2 ± 2.4 67.4 ± 2.4 67.5 ± 2.4 67.5 ± 2.4 67.3 ± 2.4 67.0 ± 2.4 66.7 ± 2.4 66.3 ± 2.4 66.0 ± 2.4 65.6 ± 2.5 65.2 ± 2.5 64.9 ± 2.5
42.71 ± 0.50 42.42 ± 0.50 42.12 ± 0.49 41.82 ± 0.49 41.51 ± 0.49 41.20 ± 0.49 40.88 ± 0.49 40.56 ± 0.49 40.24 ± 0.49 39.92 ± 0.50 39.58 ± 0.50 39.25 ± 0.50 38.92 ± 0.50 38.58 ± 0.50 38.24 ± 0.51 37.90 ± 0.51 37.57 ± 0.51 37.23 ± 0.52 36.90 ± 0.52 36.57 ± 0.52 36.23 ± 0.53 35.91 ± 0.53 35.58 ± 0.54 35.25 ± 0.54
32.1 ± 7.0 33.1 ± 7.0 34.2 ± 7.0 35.2 ± 7.0 36.2 ± 7.0 37.3 ± 7.0 38.3 ± 7.0 39.3 ± 7.0 40.4 ± 7.0 41.4 ± 7.0 42.4 ± 7.0 43.4 ± 7.0 44.4 ± 7.0 45.4 ± 7.0 46.4 ± 7.0 47.3 ± 7.0 48.3 ± 7.0 49.2 ± 7.0 50.1 ± 7.0 51.0 ± 6.9 51.9 ± 6.9 52.8 ± 6.9 53.6 ± 6.9 54.4 ± 6.9
9.69 ± 0.36 9.55 ± 0.36 9.42 ± 0.36 9.29 ± 0.36 9.16 ± 0.36 9.04 ± 0.36 8.93 ± 0.36 8.82 ± 0.36 8.71 ± 0.36 8.61 ± 0.36 8.51 ± 0.36 8.42 ± 0.36 8.33 ± 0.36 8.24 ± 0.36 8.16 ± 0.36 8.08 ± 0.36 8.00 ± 0.36 7.92 ± 0.36 7.85 ± 0.36 7.78 ± 0.36 7.71 ± 0.36 7.65 ± 0.36 7.59 ± 0.36 7.53 ± 0.36
a
The ± values are propagated uncertainties.
using the parameters and equations we report in tables 4 and 8 with any specified standard state. The values calculated for these group contributions using different methods
agree within experimental uncertainties, and we suggest that they can be useful in predicting values for related compounds.
TABLE 10B ‘‘Best’’ standard thermodynamic values for the second proton dissociation of aqueous threonine, reaction (6), HA±(aq) = A(aq) + H+(aq), at p = 0.35 MPa and m = 0 mol Æ kg1a T/K
Dr V m =ðcm3 mol1 Þ
Dr C p;m =ðJ K1 mol1 Þ
Dr H m =ðkJ mol1 Þ
Dr S m =ðJ K1 mol1 Þ
pK
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
0.19 ± 0.93 0.03 ± 0.93 0.06 ± 0.92 0.12 ± 0.92 0.17 ± 0.92 0.20 ± 0.92 0.21 ± 0.92 0.18 ± 0.92 0.13 ± 0.92 0.06 ± 0.92 0.04 ± 0.92 0.15 ± 0.92 0.29 ± 0.92 0.45 ± 0.92 0.62 ± 0.92 0.81 ± 0.92 1.03 ± 0.92 1.26 ± 0.92 1.51 ± 0.92 1.78 ± 0.92 2.08 ± 0.92 2.40 ± 0.92 2.75 ± 0.92 3.13 ± 0.92
68.7 ± 3.6 67.1 ± 3.5 63.9 ± 3.4 61.1 ± 3.4 58.9 ± 3.3 57.3 ± 3.3 56.3 ± 3.2 55.7 ± 3.2 55.4 ± 3.2 55.2 ± 3.2 55.2 ± 3.2 55.3 ± 3.2 55.4 ± 3.2 55.6 ± 3.2 55.7 ± 3.2 55.8 ± 3.2 56.0 ± 3.2 56.2 ± 3.2 56.5 ± 3.2 57.0 ± 3.2 57.6 ± 3.2 58.4 ± 3.2 59.6 ± 3.2 61.0 ± 3.2
46.95 ± 0.64 46.61 ± 0.63 46.28 ± 0.63 45.97 ± 0.63 45.67 ± 0.63 45.38 ± 0.63 45.10 ± 0.63 44.82 ± 0.63 44.54 ± 0.63 44.26 ± 0.63 43.99 ± 0.63 43.71 ± 0.64 43.44 ± 0.64 43.16 ± 0.64 42.88 ± 0.65 42.60 ± 0.65 42.32 ± 0.65 42.04 ± 0.66 41.76 ± 0.66 41.48 ± 0.67 41.19 ± 0.68 40.90 ± 0.68 40.60 ± 0.69 40.30 ± 0.70
28.1 ± 2.6 29.4 ± 2.6 30.5 ± 2.6 31.6 ± 2.6 32.6 ± 2.6 33.6 ± 2.6 34.5 ± 2.6 35.4 ± 2.6 36.3 ± 2.6 37.1 ± 2.6 38.0 ± 2.6 38.8 ± 2.6 39.6 ± 2.6 40.4 ± 2.6 41.2 ± 2.6 42.0 ± 2.6 42.8 ± 2.6 43.6 ± 2.6 44.4 ± 2.6 45.1 ± 2.6 45.9 ± 2.6 46.7 ± 2.6 47.4 ± 2.7 48.2 ± 2.7
10.285 ± 0.076 10.130 ± 0.076 9.981 ± 0.076 9.839 ± 0.076 9.702 ± 0.076 9.570 ± 0.076 9.444 ± 0.076 9.322 ± 0.076 9.205 ± 0.076 9.092 ± 0.076 8.984 ± 0.077 8.879 ± 0.077 8.778 ± 0.077 8.680 ± 0.077 8.586 ± 0.078 8.496 ± 0.078 8.408 ± 0.078 8.323 ± 0.078 8.241 ± 0.079 8.162 ± 0.079 8.086 ± 0.079 8.012 ± 0.080 7.940 ± 0.080 7.871 ± 0.080
a
The ± values are propagated uncertainties.
86
S.P. Ziemer, E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 67–87
TABLE 11 Temperature dependence of group contribution for replacing a hydrogen atom on carbon with a methyl or hydroxyl group at p = 0.35 MPa and (0 6 m/ mol Æ kg1 6 0.5)a Amino acids
Form
Substitution
DV//(cm3 Æ mol1)
DCp,//(J Æ K1 Æ mol1)
x
y
Threonine
Serine
HA± H2A+ A
H–CH3 H–CH3 H–CH3
16.18 ± 0.39 16.58 ± 0.54 15.21 ± 0.20
87.9 ± 6.0 79.7 ± 4.8 84.1 ± 7.1
Isoleucine
Valine
HA± H2A+ A
H–CH3 H–CH3 H–CH3
15.08 ± 0.57 16.0 ± 1.3 15.2 ± 1.1
72.6 ± 5.1 66.6 ± 6.6 76.5 ± 9.7
Valine
L-2-Aminobutanoic
acid
HA± H2A+ A
H–CH3 H–CH3 H–CH3
15.55 ± 0.28 16.05 ± 0.51 15.37 ± 0.96
76.5 ± 2.2 69.2 ± 3.1 70.6 ± 5.9
Threonine
L-2-Aminobutanoic
acid
HA± H2A+ A
H–OH H–OH H–OH
1.414 ± 0.047 1.10 ± 0.79 0.59 ± 0.31
7.8 ± 9.9 7 ± 14 12 ± 11
a
The ± values are the standard deviations.
TABLE 12 Temperature dependance of group contribution for replacing a hydrogen atom on carbon with a methyl or hydroxyl group at p = 0.35 MPa and (0 6 m/ mol Æ kg1 6 0.5)a,b 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 b
V//(cm3 Æ mol1)
Cp,//(J Æ K1 Æ mol1)
H–CH3
H–OH
H–CH3
H–OH
15.31 ± 0.19 15.26 ± 0.19 15.23 ± 0.18 15.22 ± 0.18 15.24 ± 0.18 15.27 ± 0.17 15.32 ± 0.17 15.38 ± 0.16 15.45 ± 0.16 15.53 ± 0.16 15.63 ± 0.15 15.73 ± 0.15 15.84 ± 0.14 15.96 ± 0.14 16.08 ± 0.14 16.21 ± 0.13 16.36 ± 0.13 16.50 ± 0.12 16.66 ± 0.12
1.31 ± 0.18 1.22 ± 0.18 1.14 ± 0.18 1.07 ± 0.18 1.01 ± 0.18 0.97 ± 0.18 0.93 ± 0.18 0.90 ± 0.18 0.88 ± 0.18 0.88 ± 0.18 0.88 ± 0.18 0.90 ± 0.18 0.92 ± 0.18 0.96 ± 0.18 1.01 ± 0.18 1.06 ± 0.18 1.13 ± 0.18 1.22 ± 0.18 1.31 ± 0.18
87.4 ± 1.2 84.4 ± 1.0 82.10 ± 0.89 80.35 ± 0.81 78.98 ± 0.75 77.90 ± 0.73 77.06 ± 0.71 76.40 ± 0.71 75.88 ± 0.71 75.48 ± 0.71 75.16 ± 0.71 74.90 ± 0.71 74.69 ± 0.72 74.50 ± 0.73 74.31 ± 0.75 74.12 ± 0.77 73.91 ± 0.79 73.65 ± 0.81 73.34 ± 0.84 72.95 ± 0.86 72.48 ± 0.89 71.90 ± 0.90 71.20 ± 0.91 70.36 ± 0.92
22.5 ± 5.6 22.7 ± 5.7 22.4 ± 5.6 21.5 ± 5.6 20.4 ± 5.4 19.0 ± 5.3 17.5 ± 5.1 15.8 ± 4.9 14.1 ± 4.7 12.4 ± 4.4 10.6 ± 4.2 8.9 ± 3.9 7.2 ± 3.7 5.5 ± 3.5 3.9 ± 3.3 2.4 ± 3.2 1.0 ± 3.0 0.3 ± 2.9 1.4 ± 2.8 2.4 ± 2.8 3.2 ± 2.8 3.8 ± 2.8 4.1 ± 2.8 4.2 ± 2.9
Values for ‘‘H–CH3’’ are calculated as the average of those for Thr-Ser, Ile-Val, and Val-Aba. The ± value are the standard deviations.
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JCT 06-79