Apparent Molar Heat Capacities of Aqueous -Alanine, -Alanine

J. Phys. Chem. B 2000, 104, 11781-11793

11781

Amino Acids under Hydrothermal Conditions: Apparent Molar Heat Capacities of Aqueous r-Alanine, β-Alanine, Glycine, and Proline at Temperatures from 298 to 500 K and Pressures up to 30.0 MPa Rodney G. Clarke,† Lubomı´r Hneˇ dkovsky´ ,‡ Peter R. Tremaine,*,† and Vladimı´r Majer§ Department of Chemistry, Memorial UniVersity of Newfoundland, St. John’s, NF, Canada A1C 3X7, Department of Physical Chemistry, Institute of Chemical Technology, 16628 Prague 6, Czech Republic, and Laboratoire de Thermodynamique des Solutions et des Polymeres, UniVersite´ Blaise Pascal/CNRS, 24 AVenue des Landais, 63177 Aubiere Cedex, France ReceiVed: July 12, 2000; In Final Form: September 21, 2000

The apparent molar heat capacities Cp° of aqueous R-alanine, β-alanine, glycine, and proline have been determined using a differential flow calorimeter and a Picker flow microcalorimeter at temperatures of 298 K e T e 500 K and at pressures from steam saturation to 30 MPa. Comprehensive equations to describe the standard-state properties over this range are reported. Values of the standard partial molar heat capacities Cp° for the aqueous amino acids increase with temperature and then deviate toward negative values at temperatures above about 390 K, consistent with increasing the critical temperature in the solutions relative to water, i.e., negative Krichevskii parameters. This is opposite to the behavior predicted by correlations reported in the geochemical and chemical literature. The temperature dependence of Cp° predicted using the very recent functional group additivity model of Yezdimer et al. (Chem. Geol. 2000, 164, 259-280) is only in qualitative agreement with the experimental results. The results are consistent with a simple solvation model in which the zwitterions are represented by point dipoles.

1. Introduction The properties of amino acids in hydrothermal solutions are of intense interest for understanding metabolic processes in thermophilic bacteria and possible mechanisms for the origin of life at deep ocean vents. Because they are zwitterions, amino acids are useful probes to examine the effect of dipole solvation on partial molar properties at elevated temperatures and pressures. Only five amino acids have sufficiently long half-lives to be suitable for measurements by flow densitometry or calorimetry at high temperatures. These are R-alanine, phenylalanine, glutamic acid, proline, and glycine. Phenylalanine and glutamic acid are only sparingly soluble in water, leaving R-alanine, proline, and glycine as the “best” model systems for studying the properties of amino acids under hydrothermal conditions.1 The structures of R-alanine, β-alanine, glycine, and proline are illustrated in Figure 1. β-Alanine is included for comparison, to examine the effect of separating the amino and carboxylic groups. In the initial phase of this study,1 we examined the thermal stability of these candidate amino acids under hydrothermal conditions and determined the apparent molar volumes Vφ of R-alanine, β-alanine, and proline using the platinum vibrating tube densitometers at Memorial University of Newfoundland over the range 298 K e T e 523 K and psat e p e 20 MPa. These results, and the very recent measurements of Vφ for glycine by Hakin et al.,2 have shown that the values of the standard partial molar volumes V° for the aqueous amino acids increase with temperature and then deviate toward negative

Figure 1. Structure of R-alanine, β-alanine, glycine, and proline.

values at temperatures above 398 K. This is opposite to the behavior predicted by the correlations developed by Amend and Helgeson,3 but consistent with the solvation behavior expected for zwitterions.1 There are no experimental values for the standard molar heat capacities of aqueous amino acids above 328 K in the literature with which to confirm these observations. In this paper, we report new results for the apparent molar heat capacities Cp,φ of R-alanine, β-alanine, proline, and glycine at temperatures from 323 to 498 K and pressures from 0.1 to 30 MPa, determined with the high-temperature differential flow calorimeter at the Blaise Pascal University.4 The results have been used to test the validity of simple models based on zwitterionic solvation, and to develop comprehensive “equations of state” for predicting the thermodynamic properties of these amino acids at infinite dilution. 2. Experimental Section

†

Memorial University of Newfoundland. ‡ Institute of Chemical Technology. § Universite ´ Blaise Pascal/CNRS.

2.1. Apparent Molar Volumes. The high temperature density measurements reported by Clarke and Tremaine1 were made

10.1021/jp002473y CCC: $19.00 © 2000 American Chemical Society Published on Web 11/18/2000

11782 J. Phys. Chem. B, Vol. 104, No. 49, 2000

Clarke et al.

using a platinum vibrating-tube densitometer described in detail by Xiao et al.5 Apparent molar volumes, Vφ, were calculated from these densities according to the definition

Vφ )

(

) ()

1000(Fw - F) (mFFw)

+

M2 F

(1)

Here F and Fw are the densities (g‚cm-3) of the sample solution and water respectively; m is the molality (mol‚kg-1), and M2 is the molar mass of the solute (g‚mol-1). Additional high-pressure values at T ) 298.15 K were made as part of the present study, for the heat capacity calculations described below. Aqueous NaCl solutions and water were used to calibrate the densitometer at all temperatures and pressures using the literature values of Archer6 and Hill,7 respectively. Details are described in ref 1. 2.2. Apparent Molar Heat Capacities. The high-temperature apparent molar heat capacity measurements were made using a differential flow calorimeter capable of operating at temperatures and pressures as high as 700 K and 40 MPa. The design of this calorimeter and operating procedures have been described by Hneˇdkovsky´ et al.4 The calorimeter uses the usual sequential twin cell arrangement to determine the relative power required to impose the same temperature increment on a sample solution and a reference fluid flowing at a known volumetric flow rate through the working cell. The measurements yield a heat capacity density ratio:

(

)( )

cp ∆W Fw,Td ) 1+f cp,w W FTd

(2)

Here cp and cp,w are the massic heat capacities (J‚K-1‚g-1) of the sample solution and water, respectively; f is a heat-loss correction factor; W is the power input to the working cell when water is present; ∆W is the difference in the power input between solution and water in the working cell; FTd and Fw,Td are the densities of the sample solution and water at the temperature Td of the delay line that separates the two cells (Td ) 298.15 K in our work). Apparent molar heat capacities Cp,φ were calculated according to the equation

Cp,φ ) M2cp +

(

)

1000(cp - cp,w) m

(3)

Water was used as the reference fluid at all temperatures and pressures using the literature values from the current IAPWS formulation.8 An absolute calibration was used to determine the heat-loss correction factor f at each temperature and pressure.9 This calibration simulates changes in the heat capacity of the fluid in the working cell by varying the mass flow rate of water supplied by the high-precision pump according to the expression

f)

W∆Fm Fm∆W

(4)

Here Fm is the mass flow rate at which the measurements were made and ∆Fm is the change in the mass flow rate from Fm. The heat leak correction factor typically fell in the range f ) 1.008 ( 0.005. A Beckman 121MB amino acid analyzer was used to measure the degree of amino acid decomposition in the densitometer measurements described in ref 1. No decomposition products were detected in the R-alanine or proline effluent that had passed through the densitometer at any of the temperatures or pressures of this study. While no decomposition products were detected in the β-alanine effluent solution at T e 423 K, approximately

Figure 2. Apparent molar heat capacities Cp,φ of R-alanine for 323.2 e T e 473.8 K at steam saturation plotted against molality. Symbols are experimental results: O, 323.17 K, 0.10 MPa; 0, 373.56 K, 2.08 MPa; 4, 423.77 K, 2.01 MPa; 3, 447.75 K, 10.30 MPa; ], 473.80 K, 5.62 MPa. Lines are the isothermal fits to the experimental data.

26% of the β-alanine was converted to ammonia at 473 K. Although the calorimeter was not configured for sampling the effluent solutions, decomposition could readily be observed as a very large positive deviation in Cp,φ at low molalities. Typically, decomposition took place at temperatures about 2550 K below those required to initiate decomposition in the densitometer. Specific heat capacity measurements at 298.10 K and 0.10 MPa were made with a Sodev Picker flow microcalorimeter and vibrating tube densimeter equipped with platinum cells,10,11 using methods described by Xie and Tremaine.12 2.3. Materials. DL-R-Alanine was obtained from BDH (reagent grade, assay 98.5%-100.5%), while β-alanine, glycine, and L-proline were obtained from Aldrich (assay 99+%). Before use, each compound was recrystallized using variations of the method of Perrin and Armarego,13 as described in ref 1. NaCl (Fisher Scientific, Certified A.C.S. Crystal) used to prepare the standard solutions for calibrating the instruments was dried at 473 K for 20 h prior to use. All solutions were prepared by mass from degassed Nanopure water (resistivity > 8 MΩ‚cm). 3. Results 3.1. Apparent Molar Heat Capacities. The experimental values of (f∆W/W) and of the apparent molar heat capacities for aqueous R-alanine, β-alanine, glycine, and proline are listed in Tables 1-4. The experimental scatter of duplicate data determinations was usually within (2 J‚K-1‚mol-1, the range expected for commercial Picker microcalorimeters near room temperature.2,10 Simple polynomial expressions were used to fit the molality dependence of the apparent molar heat capacity data for each amino acid. Following Xiao and Tremaine,14 the experimental values of Cp,φ were assigned weighting factors proportional to their molality in the least-squares fit. A quadratic function was required for glycine and proline:

Cp,φ ) C°p + bm + cm2

(5)

Here Cp,φ is the apparent molar heat capacity, Cp° is the standard partial molar heat capacity, m is the molality of the

Amino Acids Under Hydrothermal Conditions

J. Phys. Chem. B, Vol. 104, No. 49, 2000 11783

TABLE 1: Apparent Molar Heat Capacities Cp,O of Aqueous r-Alanine as a Function of Molality m, mol‚kg-1

(f∆W/W) × 103

Cp,φ, J‚mol-1‚K-1

0.102 03 0.311 34 0.405 62 0.522 69

-2.75 -8.08 -10.37 -13.11

Taverage ) 298.10 ( 0.01 K; paverage ) 0.10 ( 0.01 MPa 142.38 0.631 54 142.63 0.835 74 144.28 0.952 58 146.31

-15.68 -20.28 -22.87

146.43 148.01 148.48

0.080 118 0.080 118 0.148 99 0.148 99 0.287 86

-1.58 -1.60 -2.97 -2.96 -5.59

Taverage ) 323.173 ( 0.001 K; paverage ) 0.10 ( 0.01 MPa 169.06 (3.60) 0.287 86 168.41 (3.67) 0.591 73 168.22 (1.93) 0.591 73 168.52 (2.33) 1.214 77 169.97 (0.95) 1.214 77

-5.64 -11.34 -11.35 -22.02 -22.05

169.14 (1.09) 170.29 (0.57) 170.24 (0.58) 173.79 (0.41) 173.67 (0.42)

0.080 118 0.080 118 0.148 99 0.148 99 0.287 86 0.287 86

-1.32 -1.41 -2.60 -2.53 -4.82 -4.71

Taverage ) 373.563 ( 0.001 K; paverage ) 2.08 ( 0.02 MPa 184.34 (7.36) 0.591 73 179.70 (6.30) 0.591 73 180.24 (3.71) 0.591 73 182.43 (3.31) 1.214 77 183.03 (2.20) 1.214 77 184.70 (2.65)

-9.66 -9.73 -9.61 -18.69 -18.97

184.39 (1.11) 183.83 (0.92) 184.72 (1.18) 187.86 (0.52) 186.80 (0.47)

0.080 118 0.080 118 0.148 99 0.148 99 0.287 86

-1.46 -1.47 -2.75 -2.67 -5.09


-5.18 -10.23 -10.19 -19.51 -19.39

181.54 (2.00) 184.08 (0.76) 184.39 (0.93) 188.84 (0.61) 189.27 (0.59)

0.080 118 0.080 118 0.148 99 0.148 99 0.287 86

-1.58 -1.60 -3.00 -2.97 -5.69


-5.72 -11.36 -11.29 -21.76 -21.81

176.89 (2.79) 179.18 (1.90) 179.70 (1.89) 183.98 (0.78) 183.78 (0.84)

0.080 118 0.080 118 0.148 99 0.148 99 0.287 86

-1.74 -1.78 -3.24 -3.26 -6.17

Taverage ) 473.799 (0.002 K; paverage ) 5.62 ( 0.03 MPa 173.18 (12.56) 0.287 86 171.19 (11.58) 0.591 73 173.15 (7.26) 0.591 73 172.52 (5.83) 1.214 77 174.06 (4.53) 1.214 77

-6.17 -12.33 -12.36 -23.29 -23.30

174.03 (3.44) 175.81 (2.16) 175.63 (1.91) 182.28 (1.13) 182.26 (1.01)

0.080 118 0.148 99 0.148 99 0.287 86 0.287 86

-1.55 -2.83 -2.85 -5.41 -5.51

Taverage ) 323.168 ( 0.001 K; paverage ) 29.77 ( 0.14 MPa 174.62 (4.17) 0.591 73 175.86 (1.98) 0.591 73 175.08 (2.38) 1.214 77 176.21 (1.42) 1.214 77 174.77 (0.98)

-10.91 -10.87 -21.29 -21.16

177.12 (0.58) 177.40 (0.78) 180.26 (0.48) 180.72 (0.44)

0.080 118 0.080 118 0.148 99 0.148 99 0.287 86

-1.33 -1.27 -2.44 -2.39 -4.61

Taverage ) 373.543 ( 0.001 K; paverage ) 30.03 ( 0.09 MPa 187.22 (5.93) 0.287 86 -4.62 190.76 (5.09) 0.591 73 -9.12 188.24 (2.62) 0.591 73 -9.27 189.61 (2.99) 1.214 77 -17.86 189.47 (1.66) 1.214 77 -17.77

189.37 (1.46) 191.72 (0.94) 190.66 (0.74) 194.42 (0.61) 194.76 (0.48)

0.080 118 0.080 118 0.148 99 0.287 86 0.287 86

-1.42 -1.39 -2.51 -4.80 -4.85

Taverage ) 423.769 ( 0.001 K; paverage ) 30.56 ( 0.05 MPa 185.97 (4.97) 0.591 73 -9.45 187.26 (6.10) 0.591 73 -9.36 189.47 (3.58) 1.214 77 -17.62 189.99 (1.65) 1.214 77 -17.61 189.27 (1.97)

0.080 118 0.080 118 0.148 99 0.148 99 0.287 86

-1.46 -1.46 -2.70 -2.70 -5.15


-5.13 -10.12 -10.16 -19.10 -19.08

187.48 (1.76) 190.00 (0.86) 189.71 (0.90) 195.61 (0.60) 195.66 (0.95)

0.080 118 0.080 118 0.080 118 0.080 118 0.148 99 0.148 99

-1.52 -1.49 -1.48 -1.46 -2.91 -2.87

Taverage ) 473.818 ( 0.001 K; paverage ) 30.19 ( 0.08 MPa 186.08 (7.01) 0.287 86 188.19 (9.85) 0.287 86 188.42 (7.47) 0.591 73 189.35 (7.01) 0.591 73 183.81 (7.16) 1.214 77 184.91 (9.34) 1.214 77

-5.50 -5.49 -10.81 -10.84 -20.36 -20.23

185.30 (2.57) 185.45 (2.15) 188.31 (0.77) 188.09 (1.07) 194.42 (0.57) 194.91 (0.64)

amino acid solution, and b and c are functions that depend on temperature and/or pressure. A linear function was adequate

m, mol‚kg-1

(f∆W/W) × 103


192.54 (0.92) 193.21 (1.08) 198.66 (0.62) 198.69 (0.49)

for R-alanine and β-alanine. As an example, the Cp,φ results for R-alanine are plotted in Figures 2 and 3. Values of Cp°, b, and


Clarke et al.

TABLE 2: Apparent Molar Heat Capacities Cp,O of Aqueous β-Alanine as a Function of Molality m, mol‚kg-1

(f∆W/W) × 103


0.081 666 0.081 666 0.150 25 0.150 25 0.305 85

-2.56 -2.58 -4.73 -4.72 -9.46


-9.45 -19.19 -19.22 -37.38 -37.37

113.08 (1.03) 116.80 (0.63) 116.56 (0.62) 123.12 (0.46) 123.16 (0.46)

0.081 666 0.081 666 0.150 25 0.305 85 0.305 85

-2.00 -2.11 -3.66 -7.54 -7.54

Taverage ) 373.554 ( 0.001 K; paverage ) 2.02 ( 0.03 MPa 142.28 (7.62) 0.644 58 136.62 (8.30) 0.644 58 142.87 (4.05) 1.339 41 141.07 (1.83) 1.339 41 141.05 (1.88)

-14.79 -14.94 -29.09 -29.43

147.88 (1.15) 146.87 (0.86) 152.52 (0.51) 151.39 (0.45)

0.081 666 0.081 666 0.150 25 0.150 25 0.305 85

-1.80 -1.77 -3.31 -3.29 -6.66


-6.70 -13.79 -13.30 -25.30 -25.24

156.30 (2.00) 157.99 (1.07) 161.40 (0.85) 169.03 (0.77) 169.24 (0.60)

0.081 666 0.081 666 0.150 25 0.150 25 0.305 85

-2.48 -2.48 -4.49 -4.55 -9.04


-9.19 -18.46 -18.46 -36.06 -36.01

120.98 (0.96) 125.82 (0.65) 125.81 (0.61) 131.46 (0.46) 131.62 (0.46)

0.081 666 0.081 666 0.150 25 0.150 25 0.305 85

-1.95 -1.95 -3.53 -3.55 -7.15


-7.19 -14.70 -14.56 -28.28 -28.28

149.78 (1.41) 152.14 (0.85) 153.08 (0.72) 158.70 (0.49) 158.67 (0.48)

0.081 666 0.081 666 0.150 25 0.150 25 0.305 85

-1.71 -1.72 -3.20 -3.15 -6.22


-6.30 -12.54 -12.50 -23.77 -23.74

164.85 (2.81) 169.42 (1.37) 169.68 (1.43) 176.79 (0.94) 176.88 (0.54)

Figure 3. Apparent molar heat capacities Cp,φ of R-alanine for 323.2 e T e 473.8 K at 30.15 MPa plotted against molality. Symbols are experimental results: O, 323.19 K; 0, 373.54 K; 4, 423.77 K; 3, 447.86 K; ], 473.82 K. Lines are the isothermal fits to the experimental data.

c determined by least-squares fits to the isothermal data are listed in Table 5. These are the first experimental values of Cp,φ reported for any aqueous amino acid above 328 K. The temperature and pressure dependence of the standard partial molar heat capacities for R-alanine, β-alanine, glycine,

m, mol‚kg-1

(f∆W/W) × 103


Figure 4. Standard partial molar heat capacities Cp° of R-alanine from 0.1 to 30.15 MPa from fitted isotherms obtained using eq 5: 4, p ) 30.15 MPa; 0, p ) steam saturation pressure; ], p ) 0.1 MPa; ∇, p ) 0.1 MPa from Hakin et al.15 Lines are fitted values obtained using the extended density model.

and proline are shown in Figures 4-7. These values for Cp° are consistent with the results obtained by other authors near room temperature,15-17 within the combined experimental uncertainties. We have confirmed the literature values of Hakin



TABLE 3: Apparent Molar Heat Capacities Cp,O of Aqueous Glycine as a Function of Molality m, mol‚kg-1

(f∆W/W) × 103


0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.58 -2.55 -6.56 -6.55 -13.06


-13.08 -25.56 -25.56 -47.73 -47.73

74.72 (0.70) 80.04 (0.49) 80.01 (0.51) 90.19 (0.38) 90.17 (0.38)

0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.24 -1.97 -5.49 -5.34 -10.90


-10.67 -21.17 -20.86 -39.65 -39.91

95.48 (0.96) 98.79 (0.65) 100.06 (0.63) 107.63 (0.40) 107.09 (0.42)

0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.18 -2.23 -5.65 -5.84 -11.65


-11.44 -21.22 -21.59 -39.86 -39.63

91.08 (1.19) 100.74 (0.69) 99.18 (0.73) 109.53 (0.44) 110.02 (0.44)

0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.65 -2.65 -6.73 -6.72 -13.14


-13.14 -24.89 -24.85 -44.64 -44.68

80.26 (1.46) 89.35 (0.72) 89.54 (0.91) 104.07 (0.53) 104.00 (0.57)

0.096 677 0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.84 -2.88 -2.90 -7.33 -7.35 -14.42


-14.40 -26.89 -26.90 -46.55 -46.53

71.50 (1.39) 83.48 (1.07) 83.45 (0.80) 103.38 (0.54) 103.43 (0.53)

0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.37 -2.36 -6.15 -6.10 -12.20


-12.24 -24.07 -24.07 -45.15 -45.19

84.25 (0.88) 88.72 (0.58) 88.73 (0.59) 98.06 (0.38) 97.99 (0.39)

0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.03 -2.01 -5.16 -5.18 -10.41


-10.64 -20.10 -20.53 -38.57 -38.66

98.04 (1.01) 105.44 (0.57) 103.73 (0.53) 112.21 (0.44) 112.03 (0.38)

0.096 677 0.096 677 0.096 677 0.096 677 0.253 94 0.253 94

-2.25 -2.32 -2.16 -2.28 -5.39 -5.44

Taverage ) 423.761 ( 0.003 K; paverage ) 30.34 ( 0.09 MPa 88.32 (4.79) 0.519 60 85.39 (4.36) 0.519 60 92.53 (8.60) 1.079 65 87. 27 (12.88) 1.079 65 96.99 (3.31) 2.268 47 96.13 (1.61) 2.268 47

-10.47 -10.36 -19.99 -19.87 -36.88 -36.77

101.13 (1.03) 102.12 (1.02) 107.69 (0.61) 108.19 (0.59) 117.60 (0.49) 117.83 (0.44)

0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.21 -2.22 -5.49 -5.49 -10.86


-10.79 -20.58 -20.60 -36.30 -36.64

99.77 (1.17) 106.67 (0.58) 106.56 (0.58) 120.32 (0.39) 119.62 (0.43)

0.096 677 0.096 677 0.253 94 0.253 94 0.253 94 0.253 94 0.519 60

-2.22 -2.18 -5.72 -5.72 -5.77 -5.77 -11.20

Taverage ) 473.438 ( 0.620 K; paverage ) 30.20 ( 0.24 MPa 92.72 (6.88) 0.519 60 94.72 (5.80) 1.079 65 94.37 (2.82) 1.079 65 94.33 (2.54) 2.268 47 93.35 (2.49) 2.268 47 93.43 (1.76) 2.268 47 98.16 (1.29) 2.268 47

-11.24 -21.48 -21.42 -38.74 -38.74 -38.91 -38.93

97.79 (1.24) 104.84 (0.69) 105.11 (1.09) 117.41 (0.43) 117.42 (0.42) 116.93 (0.39) 116.89 (0.42)

0.096 677 0.096 677 0.096 677 0.253 94 0.253 94 0.519 60

-2.23 -2.17 -2.19 -5.99 -5.98 -11.70


-11.64 -22.00 -21.98 -38.26 -38.28

96.66 (0.77) 105.15 (0.51) 105.24 (0.52) 121.31 (0.47) 121.27 (0.48)

m, mol‚kg-1

(f∆W/W) × 103



Clarke et al.

TABLE 4: Apparent Molar Heat Capacities Cp,O of Aqueous Proline as a Function of Molality m, mol‚kg-1

(f∆W/W) × 103


0.097 407 0.097 407 0.253 41 0.253 41 0.521 71

-3.07 -3.06 -7.93 -7.92 -15.93


-15.92 -34.59 -34.60 -49.28 -49.27

212.60 (0.73) 213.68 (0.50) 213.64 (0.47) 215.17 (0.45) 215.22 (0.54)

0.097 407 0.097 407 0.253 41 0.253 41 0.521 71

-2.67 -2.58 -6.33 -6.61 -13.16


-13.06 -28.59 -28.60 -39.32 -39.96

238.64 (1.08) 238.87 (0.63) 238.83 (0.62) 244.10 (0.55) 242.37 (0.51)

0.097 407 0.097 407 0.253 41 0.253 41 0.521 71

-2.46 -2.43 -6.26 -6.27 -12.60


-12.50 -26.90 -26.93 -37.87 -37.94

248.67 (1.19) 250.72 (0.69) 250.60 (0.64) 253.43 (0.55) 253.23 (0.52)

0.097 407 0.097 407 0.097 407 0.097 407 0.253 41 0.253 41

-2.85 -2.88 -2.83 -2.85 -7.37 -7.47

Taverage ) 473.795 ( 0.001 K; paverage ) 5.60 ( 0.05 MPa 239.23 (9.71) 0.521 71 237.90 (10.27) 0.521 71 240.17 (7.15) 1.199 12 239.47 (5.87) 1.199 12 238.39 (4.35) 1.789 92 236.68 (4.25) 1.789 92

-14.94 -14.91 -31.35 -31.35 -43.45 -43.43

237.64 (2.00) 237.94 (2.26) 233.36 (0.92) 233.38 (0.95) 238.42 (0.63) 238.50 (0.73)

0.097 407 0.097 407 0.253 41 0.253 41 0.521 71

-3.27 -3.24 -8.44 -8.47 -17.30


-17.23 -36.03 -36.03 -49.41 -49.37

224.72 (1.59) 231.94 (0.75) 231.92 (0.86) 239.33 (0.68) 239.45 (0.68)

0.097 407 0.097 407 0.253 41 0.253 41 0.521 71

-3.02 -2.99 -7.79 -7.80 -15.64


-15.70 -34.03 -33.98 -48.31 -48.31

217.65 (0.71) 219.10 (0.49) 219.26 (0.47) 221.11 (0.50) 221.11 (0.45)

0.097 407 0.097 407 0.253 41 0.253 41 0.521 71

-2.45 -2.52 -6.59 -6.19 -12.94


-12.93 -27.85 -27.90 -39.87 -39.90

242.56 (0.76) 244.56 (0.57) 244.37 (0.61) 245.61 (0.49) 245.52 (0.56)

0.097 407 0.097 407 0.253 41 0.253 41 0.521 71

-2.40 -2.40 -6.10 -6.08 -12.20


-12.13 -26.06 -26.09 -36.64 -36.59

253.40 (1.21) 255.64 (0.75) 255.52 (0.91) 258.50 (0.59) 258.64 (0.49)

0.097 407 0.097 407 0.253 41 0.253 41 0.521 71

-2.49 -2.45 -6.23 -6.31 -12.56


-12.65 -26.90 -26.66 -37.63 -37.67

252.19 (1.17) 255.67 (0.69) 256.63 (0.99) 259.14 (0.51) 259.03 (0.60)

0.097 407 0.097 407 0.253 41 0.253 41 0.253 41 0.253 41 0.521 71

-2.57 -2.58 -6.67 -6.62 -6.76 -6.71 -13.42

Taverage ) 473.438 ( 0.619 K; paverage ) 30.39 ( 0.16 MPa 251.22 (4.91) 0.521 71 250.65 (4.21) 1.199 12 250.05 (1.63) 1.199 12 250.82 (1.84) 1.789 92 248.19 (1.58) 1.789 92 249.12 (1.81) 1.789 92 250.23 (1.36) 1.789 92

-13.45 -28.34 -28.23 -39.36 -39.45 -39.86 -39.83

249.98 (0.92) 254.74 (0.63) 255.18 (0.58) 259.18 (0.50) 258.93 (0.49) 257.49 (0.57) 257.56 (0.50)

0.253 41 0.253 41 0.521 71 0.521 71

-7.10 -7.12 -14.54 -14.56

Taverage ) 499.098 ( 0.001 K; paverage ) 30.61 ( 0.02 MPa 248.41 (1.62) 1.199 12 247.97 (1.56) 1.199 12 246.32 (0.76) 1.789 92 246.13 (0.86) 1.789 92

-30.88 -30.89 -42.95 -43.25

250.45 (0.63) 250.42 (0.52) 255.12 (0.45) 254.27 (0.46)

m, mol‚kg-1

(f∆W/W) × 103




TABLE 5: Values of Cp°, b, and c for r-Alanine, β-Alanine, Glycine, and Proline Obtained from Fitting Eq 5 to Each Set of Isothermal Data T, K

p, MPa

298.10 323.173 373.563 423.772 447.746 473.799 323.168 373.543 423.769 447.857 473.818

0.10 0.10 2.08 2.01 10.30 5.62 29.77 30.03 30.56 30.22 30.19

323.172 373.554 423.778 323.169 373.557 423.765

0.10 2.02 2.02 29.77 30.23 30.34

323.17 373.56 423.78 473.81 499.10 323.17 373.54 423.76 447.84 473.44 499.10

0.10 2.09 2.03 5.56 5.55 30.12 30.11 30.34 30.09 30.20 30.58

323.17 373.57 423.77 473.80 499.10 323.17 373.56 423.77 447.85 473.82 499.10

0.10 2.10 2.00 5.60 5.57 29.83 30.35 30.48 30.18 30.39 30.61

Cp°, J‚mol-1‚K-1

b, J‚kg‚mol-2‚K-1

R-Alanine 140.52 ( 0.49 167.76 ( 0.25 181.67 ( 0.59 180.01 ( 0.35 175.50 ( 0.31 170.94 ( 0.37 174.25 ( 0.31 188.04 ( 0.38 187.00 ( 0.35 184.79 ( 0.15 182.47 ( 0.27 β-Alanine 110.34 ( 0.16 140.20 ( 1.12 153.16 ( 0.95 119.94 ( 0.38 147.76 ( 0.34 162.11 ( 0.33 Glycine 69.88 ( 0.27 89.89 ( 1.74 83.93 ( 1.80 70.35 ( 0.14 60.74 ( 0.51 80.61 ( 0.21 95.75 ( 1.18 92.75 ( 0.79 91.92 ( 0.76 90.68 ( 0.50 87.52 ( 0.21 Proline 212.44 ( 0.22 238.37 ( 1.90 247.05 ( 0.35 237.35 ( 0.82 225.54 ( 1.53 217.95 ( 0.40 242.25 ( 1.50 251.30 ( 0.28 250.80 ( 0.67 248.37 ( 1.05 246.87 ( 1.41

Figure 5. Standard partial molar heat capacities Cp° of β-alanine from 0.1 to 30.11 MPa from fitted isotherms obtained using eq 5: 4, p ) 30.11 MPa; 0, p ) steam saturation pressure; 3, p ) 0.1 MPa from Gucker and Allen.16 Lines are fitted values obtained using the extended density model.

c, J‚kg2‚mol-3‚K-1

9.01 ( 0.93 4.86 ( 0.26 4.65 ( 0.66 7.42 ( 0.37 6.86 ( 0.33 9.22 ( 0.39 5.13 ( 0.33 5.38 ( 0.41 9.64 ( 0.36 8.89 ( 0.16 10.00 ( 0.28 9.58 ( 0.16 8.95 ( 1.07 11.76 ( 0.92 8.69 ( 0.37 8.10 ( 0.32 11.04 ( 0.32 9.81 ( 0.49 9.77 ( 3.17 17.03 ( 3.27 20.27 ( 0.25 22.77 ( 0.94 7.35 ( 0.39 8.60 ( 2.16 17.18 ( 1.42 14.90 ( 1.38 14.59 ( 0.97 17.73 ( 0.37

-0.38 ( 0.17 -0.91 ( 1.11 -2.48 ( 1.15 -2.39 ( 0.09 -1.74 ( 0.35 0.15 ( 0.14 -0.61 ( 0.76 -2.72 ( 0.49 -1.12 ( 0.49 -1.29 ( 0.35 -1.25 ( 0.13

-0.14 ( 0.46 -3.36 ( 4.00 1.92 ( 0.75 1.48 ( 1.80 -1.25 ( 3.21 -0.64 ( 0.84 1.38 ( 3.15 2.76 ( 0.59 3.87 ( 1.41 4.61 ( 2.34 -0.65 ( 2.83

0.94 ( 0.20 3.37 ( 1.79 0.89 ( 0.33 2.67 ( 0.83 5.07 ( 1.44 1.35 ( 0.38 0.28 ( 1.41 0.72 ( 0.26 0.43 ( 0.63 0.53 ( 1.06 2.82 ( 1.23

Figure 6. Standard partial molar heat capacities Cp° of glycine from 0.1 to 30.24 MPa from fitted isotherms obtained using eq 5: 4, p ) 30.24 MPa; 0, p ) steam saturation pressure; 3, p ) 0.1 MPa from Hakin et al.15 Lines are fitted values obtained using the extended density model.


Clarke et al.

et al.,15 Spink and Wadso¨,18 and Gucker and Allen 16 for Cp° of R-alanine at 298.10 K and 0.10 MPa with our own experimental value, Cp° ) 140.52 ( 0.49 J‚K-1‚mol-1. 3.2. “Equations of State” for Aqueous R-Alanine, β-Alanine, Glycine, and Proline. In our earlier study,1 we successfully used the “density” model of Mesmer et al.19 to describe the temperature and pressure dependence of V° for these amino acids under hydrothermal conditions. An extended version of this density model is required to represent the temperature and pressure dependencies of the apparent molar heat capacity data reported in this paper. The model is based on the following function for Gibbs energy, from which expressions were derived for Cp°, V°, and the standard partial molar isothermal compressibility κT° by the usual thermodynamic identities:20

∆G° ) p(Ao + A1Tr) + 2.303R

) ]

A6Tr2 log Fw

[(

A2 2

+

TABLE 6: Literature Data Sources Used in Fitting Parameters for the Extended Density Model Eqs 6-9 data

R-alanine

Cp° Hakin et al.15 V° Hakin et al.15 κT° Kikuchi et al.21 Kharakoz22

β-alanine

glycine

Gucker and Allen16 Hakin et al.15 Chalikian et al.23 Hakin et al.15 Hakin et al.2 Chalikian et al.23 Kikuchi et al.21 Kharakoz22

proline Hakin et al.17 Hakin et al.17 Kikuchi et al.21 Kharakoz22

A3 + A 4 + A 5T r + Tr

Tr A8 A9 A10 + 2.303R 4 + 3 + 2 + + A11 + Tr Tr Tr Tr

(

A7

)

A12Tr + A13Tr2 + A14Tr3 (6) ∆Cp° ) -2.303R

2.303R

(

[(

6A2

) ] )

2A3

+ 2A6Tr log Fw + Tr2 -4A2 -2A3 + + 2A5Tr + 4A6Tr2 RRw 2 T T r

(

20A7 Tr

5

+

3

Tr

r

+

12A8 4

+

6A9

+

3

2A10 2

Tr Tr Tr A2 ∂Rw + A3 + A4Tr + A5Tr2+ A6Tr3 R Tr ∂T

(

∆V° ) (Ao + A1Tr) + Rβw

(

∆κT° ) -R

A2

Tr

2

+

(

A2

Tr

2

+

)

+ 2A13Tr + 6A14Tr2 +

)( )

(7)

p

A3 + A4 + A5Tr + A6Tr2 Tr

)( )

A3 ∂βw + A4 + A5Tr + A6Tr2 Tr ∂p

)

(8) (9)

T

Here, we have used the relative absolute temperature Tr ) T/(373.15 K) to improve the convergence of our least-squares fit; Rw is the expansivity coefficient of water, Rw ) -(1/Fw)‚ (∂Fw/∂T)p; βw is the compressibility of water; βw ) (1/Fw)(∂Fw/ ∂p)T; and the Aj terms are adjustable fitting parameters. Not all parameters were required for each amino acid. The additional terms, absent in the original model, increase the flexibility of the fitting functions thereby improving its ability to reproduce the temperature and pressure dependence of the experimental data. To increase the temperature range and accuracy of the fitting parameters obtained from this model, a number of complementary data sets were included, along with the values of Cp° and V° from this work and our earlier paper.1 The literature sources used for complementary data are listed in Table 6. The fitting parameters obtained for the extended density model are tabulated in Table 7, along with their standard deviations. The standard partial molar heat capacities obtained using this model are plotted in Figures 4-7, where they are compared to those obtained from fitting eq 5 to each set of isothermal data. The standard partial molar volumes V° and

Figure 7. Standard partial molar heat capacities Cp° of proline from 0.1 to 30.31 MPa from fitted isotherms obtained using eq 5: 4, p ) 30.31 MPa; 0, p ) steam saturation pressure; 3, p ) 0.1 MPa from Hakin et al.17 Lines are fitted values obtained using the extended density model.

isothermal compressibilities κT° obtained for R-alanine are plotted in Figures 8 and 9. Figures 4 and 8 illustrate the difference in temperature dependence exhibited by Cp° and V°, respectively. The values of Cp° tend to increase sharply until they reach their maximum value and then reach a slowly declining plateau in the range 150-250 °C before the steep descent toward very negative values as Tc is approached. The values of V° tend to increase slowly until they reach their maximum value at T ) 125 °C and then decrease sharply as Tc is approached. As is true for treatments of this type on amines and carboxylic acids,1,24,25 it was difficult to reproduce the temperature dependence of κT° below 25 °C. Figure 9 includes a comparison with experimental values for κT° obtained by Kikuchi et al.21 and Kharakoz.22 The plots of V° and κT° for β-alanine, glycine, and proline are similar to those obtained for R-alanine. 3.3. Comparison with HKF Model Predictions. Amend and Helgeson3 have used the revised Helgeson-Kirkham-Flowers (HKF) model, with correlations derived for neutral organic species, to predict the standard partial molar heat capacities Cp° of aqueous R-alanine, glycine, and proline as a function of temperature. The predicted values of Cp° for R-alanine at 30.15 MPa are compared to the experimentally determined Cp° data in Figure 10. Glycine and proline show similar behavior. Unlike the experimental values of Cp° which deviate toward negative values at temperatures above 373 K, the values predicted by the HKF model continue to become more positive and approach +∞ at the critical point of water. The partial molar volumes show a similar discrepancy.1 Although quantitative errors are known to arise from the very limited high-temperature database on which the extension of the revised HKF model to organic



TABLE 7: Fitting Parameters for the Extended Density Model, Eqs 6-9 R-alanine A0, cm3‚mol-1 A1, cm3‚K‚mol-1 A2, K3 A3, K2 A4, K A5 A6, K-1 A7, K5 A8, K4 A9, K3 A10, K2 A13, K-1 A14, K-2 σa a

β-alanine

glycine

proline

61.89 (1.98) 6.97 (3.12)

56.216 (0.913) 14.25 (1.20)

30.77 (1.94) 21.92 (2.89)

71.98 (2.96) 18.48 (4.47) -117.1 (39.7) 467 (152) -1376 (407)

-42.34 (3.70) -1763 (293) -18.8 (12.8)

-33.486 (0.826) -1652 (337) -990 (187)

-27.37 (3.26) 1904 (612) -4034 (287)

2.0820 (0.0937) -8.691 (0.439) -2.987 (0.203)

1.2190 (0.0540) -3.828 (0.253) -4.398 (0.140)

1.28

0.18

5.322 (0.230) -24.03 (1.18) 15.17 (1.22) -3.737 (0.259) 0.94

-118.9 (27.8) -1.959 (0.783) 8.49 (3.04) -58.9 (18.3) 57.2 (18.0) -12.08 (3.36) 1.77

σ is the overall standard deviation for each fit. The standard deviation for each parameter is given in parentheses.

Figure 8. Standard partial molar volumes V° of R-alanine from 0.1 to 30.77 MPa from fitted isotherms obtained using eq 5: 4, p ) 30.77 MPa; O, p ) 19.96 MPa; 0, p ) 10.05 MPa; ], p ) 0.1 MPa; 3, p ) 0.1 MPa from Hakin et al.15 Lines are fitted values obtained using the extended density model.

species was based,24,25 these differences are much more profound. In our previous work,1 we demonstrated that the discrepancy between the predicted and experimental behavior of V° and Cp° probably reflects the neglect of the zwitterionic nature of the aqueous amino acids. 3.4. Comparison with the Yezdimer-Sedlbauer-Wood Functional Group Additivity Model. Yezdimer et al.26 have used the equations of state developed by Sedlbauer et al.27 to develop a functional group additivity model for aqueous organic species. The model includes terms for the amino acid group derived from low-temperature V° and Cp° data. The values of Cp° and V° predicted for aqueous R-alanine are shown in Figure 11a and 11b, respectively. Glycine shows similar behavior. Although the predicted functions for Cp° and V° do deviate toward negative values above 398 K in a manner similar to the experimental results, the agreement is not quantitative. While some of this discrepancy arises from the very limited data set used to determine the parameters for the amino acid functional group, an attempt to recalculate the parameters for the amino acid functional group using the Cp° data obtained in this work and the V° data from Clarke and Tremaine1 and Hakin et al.2 did not improve the accuracy of the model. The recalculated parameters increased the accuracy of the temperature depen-

Figure 9. Standard partial molar isothermal compressibilities κT° of R-alanine at 0.1 MPa plotted against temperature. Symbols are the experimental values of: O, Kikuchi et al.;21 0, Kharakoz.22 The line represents the fitted values obtained using the extended density model.

dence of Cp° for both R-alanine and glycine. However, the new parameters also created an inversion in the pressure dependence predicted for V° at temperatures below 373 K. This behavior suggests that there is insufficient flexibility in the equations of state developed by Sedlbauer et al.,27 upon which Yezdimer et al.26 have developed their model. 4. Discussion 4.1. Speciation at Elevated Temperature and Pressure. The comparisons in the previous section are based on the assumption that the amino acids are entirely in the zwitterionic form under our experimental conditions. In aqueous solution, amino acids can exist as either the zwitterion HA(, the neutral undissociated molecule HA0, the deprotonated ion A-, or the protonated ion H2A+. The equilibria between the zwitterionic, neutral, and ionic forms can be summarized as follows: K1

HA( + H2O y\z H2A+ + OH K2

HA( y\z A- + H+ K3

HA( y\z HA0

(10) (11) (12)


Clarke et al.

Figure 10. Predicted and experimental standard partial molar heat capacities Cp° of R-alanine at 30.15 MPa.

Here K1, K2, and K3 are the equilibrium constants for each reaction. Equilibrium constants for the ionization reactions of the zwitterions at elevated temperatures were estimated in ref 1 by assuming that the heat capacities of the isocoulombic reactions corresponding to eqs 10-12 were independent of temperature. An alternative, probably better, estimate can now be made by using the functional group additivity model for aqueous organic species recently reported by Yezdimer et al.,26 which was discussed above in section 3. Although the model exhibits deviations from the experimental values of Cp° at elevated temperatures, it is sufficiently accurate to calculate K1 and K2. In both ref 1 and this work, K3 was taken to be equal to [K1K2/ Kw]. The degree of dissociation of R-alanine to form A-, H2A+, and HA0 is plotted in Figure 12, where it is compared with the estimates from the isocoulombic extrapolation reported in ref 1. Glycine gives a similar plot for the degree of dissociation as a function of temperature. Approximately 5% of the zwitterionic R-alanine is dissociated at 523 K according to this estimate, while the degree of dissociation at 523 K for glycine is approximately 4%. The Yezdimer model lacks data for the secondary amino functional groups >NH and >NH2+, required to estimate values for proline. In our earlier paper,1 the degree of dissociation at 523 K for both β-alanine and proline was estimated to be approximately 2%. Small errors in the calculated values of the equilibrium constants have little effect on the equilibrium concentrations of the ions since the aqueous amino acids studied form buffer solutions. The contribution of the undissociated neutral species HA0 under these conditions is negligible. Combining the predicted degree of dissociation with the predicted standard partial molar heat capacities and standard partial molar volumes for the ionic and neutral forms of each amino acid allowed us to estimate the zwitterionic contribution to the experimental Cp° and V°, according to the Yezdimer group additivity model.26 The results are plotted in Figure 13, along with error estimates calculated from the uncertainties cited for the functional group parameters in ref 26. The contribution of neutral and ionic species to the experimental values of Cp° and V° at temperatures above 373 K is estimated to be no more than -2 J‚K-1‚mol-1 and (0.2 cm3‚mol-1, respectively.

Figure 11. (a) Predicted and experimental standard partial molar heat capacities Cp° of R-alanine from 0.1 to 30.15 MPa. Lines are values obtained using the functional group additivity model of Yezdimer et al.26 Symbols are the fitted isotherms obtained using eq 5: 4, p ) 30.15 MPa; 0, p ) steam saturation pressure; ], p ) 0.1 MPa; 3, p ) 0.1 MPa from Hakin et al.15 (b) Predicted and experimental standard partial molar volumes V° of R-alanine from 0.1 to 30.77 MPa. Lines are values obtained using the functional group additivity model of Yezdimer et al.26 Symbols are the fitted isotherms obtained using eq 5: 4, p ) 30.77 MPa; O, p ) 19.96 MPa; 0, p ) 10.05 MPa; ], p ) 0.1 MPa; 3, p ) 0.1 MPa from Hakin et al.15

4.2. Dipole Solvation. The Gibbs free energy of solvation ∆solvG°, associated with transferring a species from an ideal gas into solution at infinite dilution, can be expressed as follows:

∆solvG° ) Gaq° - Gintr° - ∆solvGss°

(13)

where Gaq° is the Gibbs free energy of the aqueous species (hypothetical 1 molal standard state), Gintr° is the intrinsic gasphase Gibbs free energy of the species (100 kPa, ideal gas), and ∆solvGss° is the change in the Gibbs free energy arising from the difference in standard states between the gas phase



Figure 12. Sum of [H2A+], [A-], and [HA0] for R-alanine as a function of temperature, where the sum of [HA(], [H2A+], [A-], and [HA°] is 1 mol‚kg-1. - - -, isocoulombic extrapolation of 298.15 K data from ref 1; s, prediction from group additivity model of Yezdimer et al.26

and solution:

∆solvGss° ) RT ln

(

)

RTm°Fw p°

(14)

Here m° ) 1 mol‚kg-1 and p° ) 0.1 MPa. ∆solvG° arises in part as a result of configurational changes in the water caused by the presence of the solute. These are commonly identified with two major effects: the long-range polarization of water caused by the localized charge distribution within the solute ∆solvGpol°, and short-range hydration effects arising from the hydrogen-bonded “structure” of water in the immediate vicinity of the solute ∆solvGhydr°.

∆solvG° ) ∆solvGpol° + ∆solvGhydr°

(15)

The short-range hydration interactions may include hydrogen bonding between the dissolved species and the nearest solvent molecules and a deformation of the bulk solvent structure in the immediate vicinity of the dissolved species. ∆solvGhydr° is difficult to model and is often represented by an empirical function. The Gibbs free energy of polarization ∆solvGpol° may be expressed as

Figure 13. (a) Difference between the experimental values of Cp° and the values of Cp,zwitterionic° calculated for aqueous R-alanine. Symbols represent O, p ) steam saturation pressure; 0, p ) 30.15 MPa. (b) Difference between the experimental values of V° and the values of Vzwitterionic° calculated for aqueous R-alanine. Symbols represent 4, p ) 30.77 MPa; O, p ) 19.96 MPa; 0, p ) 10.05 MPa; 3, p ) 0.1 MPa.

∆solvGpol° ) ∆solvGBorn° + ∆solvGdipole° + ∆solvGquadrupole° + ∆solvGoctopole° + ... (16)

Here Z is the ionic charge, e is the charge on an electron, NA is Avogadro’s number, r is the relative permittivity of the solvent, o is the permittivity of free space, and re is the effectiVe radius of the dissolved species in the bulk solvent. All quantities are in SI units. Although long-range multipole-solvent polarization effects are unimportant for many neutral species, zwitterions present a special case because the charge separation can be quite significant. Amino acids are dipolar zwitterions, and the most significant term in the ∆solvGpol° summation is the second term. Therefore, all other contributions can be neglected. To a first approximation, the Gibbs free energy of polarization for a dissolved neutral dipolar species ∆solvGdipole° in a dielectric continuum can be represented by the equation for a point dipole in a spherical cavity:29

Here ∆solvGBorn° is the ionic contribution to the Gibbs free energy of polarization, and ∆solvGdipole°, ∆solvGquadrupole°, ∆solvGoctopole°, ... are contributions of higher electric moments. When the dissolved species is ionic, often only the first term in eq 16 is significant, so that all other terms can be neglected. This leads to the well-known Born equation for the Gibbs free energy of polarization for a dissolved ionic species ∆solvGBorn°: 28

∆solvGBorn° )

( )

-(Ze)2NA r - 1 8reπo r

(17)


∆solvGdipole° )

(

1 - r 2r + 1

µ2NA 4πore3

Clarke et al.

)

(18)

Here µ is the dipole moment of the charge distribution. All quantities are in SI units. Equation 18 can be used to obtain expressions for ∆solvVdipole°, ∆solvκT,dipole°, and ∆solvCp,dipole°, the standard partial molar volume, compressibility, and heat capacity of polarization for a dissolved neutral dipolar species:

∆solvVdipole° )

∆solvκT,dipole° )

∆solvCp,dipole° ) NA 3

4πore NA

[( [(

4πore3

µ2NA 3

4πore

( )[( -NAµ2

NA 3

4πore

)( )

)( )

∂r 12 3 ∂p (2r + 1)

3

4πore

(

∂r -3 2 ∂p (2r + 1)

( [( ) ( ) (

2

R-alanine

β-alanine

glycine

proline

12.87 2.67

9.50 1.98

12.79 2.65

15.68 3.26

(19)

-

T

)( ) ] )]

∂µ 12Tµ p ∂T p (2 + 1)2 r

(20)

T

+

)( ) ]

)( ) ( )( ) (

amino acid µo, D rcryst, Å

T

∂2r 3 (2r + 1)2 ∂p2

∂r ∂T

TABLE 8: Values of µo and rcryst for r-Alanine, β-Alanine, Glycine and Proline

∂2r ∂r 3Tµ2 12Tµ2 2 2 3 ∂T (2r + 1) ∂T p (2r + 1)

2

-

p

)( ) ]

2Tµ(1 - r) ∂2µ 2T(1 - r) ∂µ 2 + (21) (2r + 1) ∂T2 p (2r + 1) ∂T p

4.3. Contribution of Amino Acid Dipole Moments to Standard Partial Molar Heat Capacities. The calculations described in section 4.1 suggest that the zwitterion is by far the predominant amino acid species in high-temperature water. Therefore, it is of interest to assess the contribution of the dipole moment ∆solvCp,dipole° to the standard partial molar heat capacities, using an approach similar to the treatment reported for ∆solvVdipole° in our previous work.1 Because the temperature dependence of the mean dipole moment of the amino acids is not well-known,1 we have chosen to use a simpler calculation in which the dipole moment µ was taken to be independent of temperature and equal to the gas-phase value µo, as estimated in ref 1, so that eq 21 becomes

∆solvCp,dipole° )

NA

[(

3Tµo2

)( ) ( )( ) ] ∂2r

4πore3 (2r + 1)2 ∂T2

-

p

12Tµo2

(2r + 1)3

∂r ∂T

2

p

(22)

The effective radius re was taken to be equal to the crystallographic radius.1 Values for µo and rcryst are listed in Table 8. An expression for ∆solvCp,ss° may be obtained from eq 14:1,4

∆solvCp,ss° ) -R + 2RTRw + RT2

( ) ∂Rw ∂T

p

(23)

and, by analogy with eqs 13-15, the standard partial molar heat capacity of the solute may be expressed as

Cp° ) ∆solvCp,nondipole° + ∆solvCp,dipole° + ∆solvCp,ss°

(24)

To illustrate the magnitude of the dipole polarization term, the hydration and intrinsic contributions to solvation have been

Figure 14. (a) Predicted temperature and pressure dependence of Cp° for glycine from the point dipole model, eq 24. Symbols are the values from the experimental isotherms: 0, p ) steam saturation pressure; 4, p ) 30 MPa. Lines are the fitted values from the model. (b) Predicted temperature and pressure dependence of V° for glycine from the point dipole model. Symbols are the values from the experimental isotherms: 4, p ) 30 MPa; O, p ) 20 MPa; 0, p ) 10 MPa. Lines are the fitted values from the model.

represented by an adjustable constant ∆solvCp,nondipole° ) Cp,intr° + ∆solvCp,hydr°, chosen so that the calculated value of Cp° fits the experimental value at 373 K and the highest pressure studied. The standard partial molar heat capacities obtained by fitting eq 24 to the apparent molar heat capacities obtained for glycine at temperatures T g 373 K are shown in Figure 14a. Clearly, the behavior of Cp° at elevated temperatures is consistent with the effects of dipole polarization, as are the results for V° from ref 1. A plot of V° for glycine corresponding to the simpler model used here is shown in Figure 14b. As might be expected,

Amino Acids Under Hydrothermal Conditions the agreement with the experimental results is only qualitative. Glycine is the simplest amino acid, with the most centrosymmetric dipole. Yet, while the temperature and pressure dependencies of ∆solvVdipole° match the data almost exactly, the values for ∆solvCp,dipole° show a much stronger temperature dependence and a slightly stronger pressure dependence than the experimental results. The agreement with V° is probably fortuitous because the temperature dependence of the mean dipole moment, which we ignored, cancels out the increase in the hydrophobic hydration term at elevated temperatures.1 Our neglect of the temperature dependence of µ plays a much larger role in eq 21 than eq 19, and thus has a larger effect on ∆solvCp,dipole°. Similar plots were obtained for R-alanine and proline, using re ) rcryst in eqs 19 and 22, except that both ∆solvCp,dipole° and ∆solvVdipole° show a stronger temperature dependence than the experimental values for Cp° and V°. These additional differences, which are even more pronounced for proline, undoubtedly arise from the presence of hydrophobic organic groups that generate repulsive contributions to ∆solvCp,hydr° and ∆solvVdipole°, and from the off-centered dipole in these more complex amino acids. A more detailed discussion of the contributions to V° is given in ref 1. Briefly, while the dipole contribution is larger than the hydration- and standard-state terms, these terms are not negligible. The hydration term becomes larger for larger molecules, necessitating a more realistic modeling approach in which the presence of hydrophobic groups and the location of the dipole are specifically considered. In their treatments of aqueous ions, Helgeson and co-workers 30 have successfully approximated the primary-sphere hydration effects for MZ+ cations by using an effective radius, re ≈ rcryst + (0.9Z) Å, in the Born equation. Our attempts to develop a similar treatment for Cp° and V° for these dipolar zwitterions, based on eqs 19 and 22 with self-consistent formulas for estimating the effective radius, have not been successful. Clearly a more detailed and rigorous treatment is needed. Acknowledgment. This research was financially supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and by an International Collaborative Research Grant from the International Association for the Properties of Water and Steam (IAPWS). Postgraduate fellowships to R.G.C. from NSERC and Memorial University of Newfoundland are gratefully acknowledged. We are also grateful to the staff of the machine shop and electronic shop at Memorial University for their skillful assistance in modifying and maintaining the high pressure densitometer, to the staff of the amino acid analysis facility at Memorial University for providing the amino acid analyses used in this work, and to the faculty and students at Universite´ Blaise Pascal for their hospitality during R.G.C.’s tenure in Clermont-Ferrand.

J. Phys. Chem. B, Vol. 104, No. 49, 2000 11793 Supporting Information Available: Tables S1, S2, S3, and S4 list the densities relative to water (F - Fw) and the apparent molar volumes V0 for aqueous solutions of R-alanine, β-alanine, glycine, and proline as a function of molality at 298 K. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Clarke, R. G.; Tremaine, P. R. J. Phys. Chem. B 1999, 103, 5131. (2) Hakin, A. W.; Daisley, D. C.; Delgado, L.; Liu, J. L.; Marriott, R. A.; Marty, J. L.; Tompkins, G. J. Chem. Thermodyn. 1998, 30, 583. (3) Amend, J. P.; Helgeson, H. C. J. Chem. Soc., Faraday Trans. 1997, 93, 1927. (4) Hneˇdkovsky´, L.; Hynek, V.; Majer, V.; Wood, R. In Steam, Water and Hydrothermal Systems: Physics and Chemistry Meeting the Needs of Industry; Tremaine, P., Hill, P., Irish, D. E., Balakrishnan, P. V., Eds.; NRC Research Press: Ottawa, 2000. Proceedings of the 13th International Conference on Properties of Water and Steam, Toronto, Canada, Sept 1216, 1999; Paper TTP3.4. (5) Xiao, C.; Bianchi, H.; Tremaine, P. R. J. Chem. Thermodyn. 1997, 29, 261. (6) Archer, D. G. J. Phys. Chem. Ref. Data. 1992, 21, 793. (7) Hill, P. G. J. Phys. Chem. Ref. Data. 1990, 19, 1233. (8) Harvey, A. H.; Peskin, A. P.; Klein, S. A. NIST/ASME Steam Properties. NIST Standard Reference Database 10, Version 2.11, 1997. (9) Carter, R. W.; Wood, R. H. J. Chem. Thermodyn. 1991, 23, 1037. (10) Picker, P.; Ludec, P. A.; Desnoyers, J. E. J. Chem. Thermodyn. 1971, 3, 631. (11) Desnoyers, J. E.; deVisser, C.; Perron, G.; Picker, P. J. Solution Chem. 1976, 5, 605. (12) Xie, W.; Tremaine, P. R. J. Solution Chem. 1999, 28, 291. (13) Perrin, D. D.; Armarego, W. L. F. Purification of Laboratory Chemicals, 3rd ed.; Pergamon Press: New York, 1988. (14) Xiao, C.; Tremaine, P. R. J. Chem. Eng. Data 1996, 41, 1075. (15) Hakin, A. W.; Duke, M. M.; Klassen, S. A.; McKay, R. M.; Preuss, K. E. Can. J. Chem. 1994, 72, 362. (16) Gucker, F. T.; Allen, T. W. J. Am. Chem. Soc. 1942, 64, 191. (17) Hakin, A. W.; Copeland, A. K.; Liu, J. L.; Marriott, R. A.; Preuss, K. E. J. Chem. Eng. Data 1997, 42, 84. (18) Spink, C. H.; Wadso¨, I. J. Chem. Thermodyn. 1975, 7, 561. (19) Mesmer, R. E.; Marshall, W. L.; Palmer, D. A.; Simonson, J. M.; Holmes, H. F. J. Solution Chem. 1988, 17, 699. (20) Atkins, P. W. Physical Chemistry, 4th ed.; W. H. Freeman and Company: New York, 1990. (21) Kikuchi, M.; Sakurai, M.; Katsutoshi, N. J. Chem. Eng. Data 1995, 40, 935. (22) Kharakoz, D. P. J. Phys. Chem. 1991, 95, 5634. (23) Chalikian, T. V.; Sarvazyan, A. P.; Breslauer, K. J. J. Phys. Chem. 1993, 97, 13017. (24) Criss, C. M.; Wood, R. H. J. Chem. Thermodyn. 1996, 28, 723. (25) Shvedov, D.; Tremaine, P. R. J. Solution Chem. 1997, 26, 1113. (26) Yezdimer, E. M.; Sedlbauer, J.; Wood, R. H. Chem. Geol. 2000, 164, 259. Note that values of V° from ref 2 are incorrectly tabulated by Yezdimer et al. in their Table 2. (27) Sedlbauer, J.; O’Connell, J. P.; Wood, R. H. Chem. Geol. 2000, 163, 43. (28) Born, M. Z. Phys. 1920, 1, 45. (29) Beveridge, D. L.; Schnuelle, D. W. J. Phys. Chem. 1975, 79, 2562. (30) Shock, E. L.; Oelkers, E. H.; Johnson, J. W.; Sverjensky, D. A.; Helgeson, H. C. J. Chem. Soc., Faraday Trans. 1992, 88, 803 and references cited therein.

Apparent Molar Heat Capacities of Aqueous -Alanine, -Alanine

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