J. CHEM. SOC. FARADAY TRANS., 1994, 90(14), 2027-2035 Some Thermodynamic Properties of Aqueous Amino Acid Systems at 288.15, 298.15, 313.15 and 328.15 K: Group Additivity Analyses of Standard-state Volumes and Heat Capacities Andrew W. Hakin,* Michelle M. Duke, Jocelyn L. Marty and Kathryn E. Preuss Department of Chemistry, University of Lethbridge,4401 University Drive, Lethbridge, Alberta , Canada TIK 3M4 Densities and heat capacities have been measured for aqueous solutions of L-aspartic acid, L-glutamic acid and a-aminobutyric acid at 288.15, 298.15, 313.15 and 328.15 K. These data have been used to calculate apparent molar volumes, V,,,, and apparent molar heat capacities, Cp,,,,2 which in turn have been used to calculate standard-state volumes, Vg, and standard-state heat capacities, Ci, ,.Helgeson, Kirkham and Flowers equa- tions, for neutral organic species in water, have been used to model the calculated standard-state volumes and heat capacities of the amino acids as a function of temperature at constant pressure. These data, and data previously reported for amino acid systems, have been used as input for a group additivity type analysis. The merits of the additivity scheme are discussed, and attempts are made to interpret the predicted trends in the group contributions as a function of temperature. For several years we have been involved with experimental research projects involving the chemistry of Canada's oil sand deposits.'.2 These projects have coincided with our interests in the field of thermodynamics.Indeed, we have often used our knowledge of chemical thermodynamics to elucidate the complicated chemistry of the oil sand deposits and the chemistry of oil extraction processes. The current paper reflects these described interests and, in part, was stimu- lated by a paper from Shock3 in which the stability of aqueous peptide systems was investigated at elevated tem- peratures. Several authors4*' have discussed the role of micro-organisms in the biodegradation of oil deposits. The geology of these deposits dictates that any indigenous life forms must survive a wide range of temperature and pressure conditions. To understand how these organisms are able to exist in such a hostile environment requires the investigation of the ther- modynamic properties of aqueous solutions of organic species which are essential to life, namely aqueous protein systems.Accepting the complexity of such an approach, we have commenced our investigations by focusing our attention on the simple building blocks of protein systems, i.e. aqueous solutions of amino acids and simple peptides. Thermodynamic data reported in the literature usually refer to the standard conditions of 298.15 K and 1 atmo- sphere.6-' * This paper reports densities, p, apparent molar volumes, V2,+, and apparent molar heat capacities, Cp,2, ,, for L-aspartic acid, L-glutamic acid and a-aminobutyric acid in water at 288.15, 298.15, 313.15 and 328.15 K. In addition, we have combined standard-state volume and heat capacity data for L-aspartic acid, L-glutamic acid and a-aminobutyric acid with standard-state thermodynamic data for aqueous amino acid systems reported in our previous to form a thermodynamic data base that covers our experimen- tal temperature range.We have increased the utility of the volume and heat capacity data reported in this paper by using them as input to a semi-empirical modelling procedure proposed by Helge- son, Kirkham and Flowers (HKF).2' The HKF equations allow for the prediction of standard-state thermodynamic properties at elevated temperatures and pressures. However, in the current paper we will restrict our attention to the con- stant pressure variants of these equations. The semi-empirical nature of HKF equations dictates that estimates of standard- state properties at elevated temperatures and pressures are based upon experimental thermodypamic data collected at ambient temperature and pressure.To date, there are only very limited experimental thermodynamic data available for aqueous amino acid solutions with which to compare the estimates produced from these models. However, we are cur- rently working on the construction of a high temperature and pressure densitometer capable of making precise density mea- surements up to 730 K and 40 MPa that should, in part, address this shortfall. The HKF equations reported in this paper provide estimates of standard-state properties which will serve as useful reference points in the future evaluation of this instrument. Thermodynamic data reported in this paper are also used as input to a group additivity scheme that estimates the tem- perature dependences of chemical group contributions to standard-state volumes and heat capacities for aqueous amino acid systems.Although there are several examples in the literature of group additivity schemes being applied to aqueous amino acid systems, these schemes are invariably restricted to 298.15 K, with the notable exception of the work of Privalov and co-worker~.~~*~~ Experimental L-Aspartic acid (99 +%), L-glutamic acid (99+ Yo),and r-aminobutyric acid (99+ YO),were obtained from Sigma Chemicals Ltd. The acids were purified by repeated rec-rystallization from water and were dried and stored over phosphorus pentoxide in a vacuum oven set at 50°C.The NMR spectra of the amino acids were obtained on a Briiker 250 MHz instrument using D20as an internal standard. The recorded spectra were in excellent agreement with reference spectra.24 All solutions were prepared by weight on the molality con- centration scale using bi-distilled, degassed water. Solutions were stored in sealable 125 ml Nalgene bottles. Densities were measured relative to water with a Sodev 02D vibrating tube, flow den~itometer.~' This instrument routinely measures densities with part-per-million precision. Volumetric heat capacities were measured relative to water using a Picker flow microcalorimeter.26 Small residual heat leaks were corrected for by a calorimetric heat loss correction factor, or f factor.27 This factor was evaluated as J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 f= 0.996 727 2 using standard solutions of sodium chloride in Specific heat capacity data for the aqueous acid systems water. The reported value is assumed to be independent of were calculated from heat capacity ratios, [cpp/(ci,lpy) -13, temperature. at each temperature investigated. Apparent molar heat capac- Details of the densitometer and the flow microcalorimeter, ities, Cp,2, +, were calculated from specific heat data using the and procedures used in their calibration, have been described equation: previously.' 9320,28 Results and Discussion Densities at 288.15, 298.15, 313.15 and 328.15 K for solutions where cpis the specific heat capacity of the solution, and ci, of L-aspartic acid, L-glutamic acid and a-aminobutyric acid in is the specific heat capacity of pure water at the temperature Apparent molar heat capacity data as a function water are reported in Tables 1, 2 and 3, respectively.Appar- of intere~t.~' ent molar volumes, V2,&, were calculated using the equation: of temperature are also contained in Tables 1,2 and 3. Procedures for estimating the uncertainties in apparent molar volumes, 6V2,ql , and apparent molar heat capacities, 6Cp,2, ql have been described previously.' 993' where m is the molality of the solution, M is the molecular The apparent molar volumes and heat capacities of a-weight of the solute, py is the density of pure water at the aminobutyric acid were found to be well modelled by the temperature of interest,29 and p is the density of the solution linear equation : under study.Calculated apparent molar volumes are report- (3)ed for aqueous solutions of L-aspartic acid, L-glutamic acid and a-aminobutyric acid in Tables 1,2 and 3, respectively. where Y represents the extensive thermodynamic property of Table 1 Densities, p, apparent molar volumes, V2,+, heat capacity ratios and apparent molar heat capacities, C,2. + , of aqueous solutions of L-aspartic acid at 288.15, 298.15, 313.15 and 328.15 K" rn/mol kg-Cp,2,+/JK-' mol-' 288.15 K 0.036 27 1.001 287 72.69 (0.14) -1.659 112.6 (1.9) 0.032 63 1.001 075 72.46 (0.15) -1.505 110.2 (2.2) 0.030 42 1 .000 945 72.36 (0.16) -1.403 109.9 (2.3) 0.026 70 1.000714 72.57 (0.19) -1.253 107.3 (2.6) 0.023 97 1.000 553 72.43 (0.21) -1.161 100.4 (2.9) 0.037 47 1.001 357 72.75 (0.13) -1.717 112.5 (1.9) 0.034 55 1.001 187 72.58 (0.15) -1.556 115.1 (2.0) 0.031 21 1.000985 72.62 (0.16) -1.447 109.8 (2.3) 0.027 94 1.000791 72.50 (0.18) -1.309 107.4 (2.5) 0.019 24 1.000 272 72.13 (0.26) -0.9208 101.8 (3.6) 298.15 K 0.036 27 0.999 190 74.00 (0.14) -1.467 139.5 (1.9) 0.032 63 0.998 973 73.98 (0.15) -1.340 136.8 (2.2) 0.030 42 0.998 843 73.99 (0.17) -1.260 135.4 (2.3) 0.026 70 0.998 624 73.94 (0.19) -1.104 132.7 (2.6) 0.023 97 0.998 462 74.02 (0.21) -1.000 134.3 (2.9) 0.037 47 0.999 257 74.01 (0.13) -1.520 139.0 (1.9) 0.034 55 0.999 084 74.03 (0.15) -1.411 137.9 (2.0) 0.031 2 1 0.998 890 73.96 (0.16) -1.280 136.9 (2.3) 0.027 94 0.998 699 73.91 (0.18) -1.161 134.6 (2.5) 0.019 24 0.998 189 73.67 (0.26) -0.8196 129.3 (3.6) 313.15 K 0.036 27 0.994310 75.53 (0.14) -1.298 163.7 (1.9) 0.032 63 0.994 098 75.50 (0.16) -1.214 157.7 (2.2) 0.030 42 0.993 971 75.50 (0.17) -1.063 167.2 (2.3) 0.026 70 0.993 757 75.51 (0.19) -0.942 1 165.8 (2.6) 0.023 97 0.993 607 75.22 (0.21) -0.8735 159.8 (2.9) 0.037 47 0.994 372 75.62 (0.14) -1.372 160.7 (1.9) 0.034 55 0.994 2 13 75.37 (0.15) -1.247 161.7 (2.0) 0.03 1 2 1 0.994 02 1 75.36 (0.16) -1.144 159.4 (2.3) 0.027 94 0.993 831 75.40 (0.18) -1.040 157.3 (2.5) 0.019 24 0.993 336 75.10 (0.26) -0.7273 153.7 (3.6) 328.15 K 0.032 63 0.987 545 76.53 (0.16) -0.9898 188.7 (2.2) 0.030 42 0.987417 76.64 (0.17) -0.9821 181.0 (2.3) 0.026 70 0.987 210 76.51 (0.19) -0.8963 175.2 (2.6) 0.023 97 0.987 058 76.39 (0.21) -0.7990 175.7 (2.9) 0.037 47 0.987 8 13 76.70 (0.14) -1.168 185.9 (1.9) 0.034 55 0.987 655 76.48 (0.15) -1.084 184.1 (2.0) 0.03 1 2 1 0.987 468 76.43 (0.16) -1.022 178.2 (2.3) 0.027 94 0.987 282 76.44 (0.18) -0.8 172 192.9 (2.5) 0.019 24 0.986 792 76.24 (0.27) -0.6637 170.3 (3.6) * Estimated uncertainties for V2,+ and Cp,2, + appear in parentheses.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Densities, p, apparent molar volumes, V2,@,heat capacity ratios and apparent molar heat capacities, Cp,2,4, of aqueous solutions of L-glutamic acid at 288.15, 298.15, 313.15 and 328.15 K" m/mol kg -Cp,2,4/J K-' mol-' ~ 288.15 K 0.061 30 1.002 687 88.36 (0.08) -3.012 163.4 (1.2) 0.053 74 1.002251 88.27 (0.09) -2.620 164.8 (1.3) 0.047 82 1.001 906 88.26 (0.10) -2.341 164.0 (1.5) 0.043 02 1.001 628 88.19 (0.12) -2.213 153.4 (1.6) 0.040 49 1.001 478 88.25 (0.12) -2.045 157.6 (1.7) 0.059 55 1.002 582 88.39 (0.08) -2.947 162.1 (1.2) 0.049 83 1.002 02 1 88.29 (0.10) -2.454 162.9 (1.4) 0.044 17 1.001 691 88.28 (0.1 1) -2.227 158.1 (1.6) 0.038 36 1.001355 88.19 (0.13) -1.947 156.4 (1.8) 0.033 3 1 1.001 059 88.21 (0.15) -1.699 155.5 (2.1) 298.15 K 0.061 30 1.O00 545 89.87 (0.08) -2.687 190.8 (1.2) 0.053 74 1.O00 117 89.83 (0.09) -2.373 189.5 (1.3) 0.047 82 0.999 784 89.75 (0.11) -2.210 180.7 (1.5) 0.043 02 0.999 5 11 89.72 (0.12) -1.979 181.5 (1.6) 0.040 49 0.999 366 89.73 (0.12) -1.824 185.6 (1.7) 0.059 55 1.Ooo 447 89.82 (0.08) -2.671 186.4 (1.2) 0.049 83 0.999 897 89.77 (0.10) -2.259 184.4 (1.4) 0.044 17 0.999 576 89.74 (0.1 1) -1.981 186.4 (1.6) 0.038 36 0.999 246 89.70 (0.13) -1.709 187.6 (1.8) 0.033 31 0.998 956 89.75 (0.15) -1.551 179.4 (2.1) 313.15 K 0.061 30 0.995 625 91.55 (0.08) -2.295 222.7 (1.2) 0.053 74 0.995 210 91.47 (0.09) -2.124 213.8 (1.3) 0.047 82 0.994 885 91.41 (0.11) -1.897 213.1 (1.5) 0.043 02 0.994 620 91.37 (0.12) -1.693 214.3 (1.6) 0.040 49 0.994 480 91.35 (0.13) -1.611 212.4 (1.7) 0.059 55 0.995 523 91.61 (0.09) -2.417 209.9 (1.2) 0.049 83 0.994 992 91.50 (0.10) -2.025 209.4 (1.4) 0.044 17 0.994 682 91.42 (0.12) -1.806 199.7 (1.6) 0.038 36 0.994 358 91.43 (0.13) -1.647 208.0 (1.8) 0.033 31 0.994 080 91.36 (0.15) -1.371 206.8 (2.1) 328.15 K 0.061 30 0.989 041 92.79 (0.08) -2.075 240.5 (1.2) 0.053 74 0.988 633 92.71 (0.10) -1.827 239.8 (1.3) 0.047 82 0.988 304 92.86 (0.1 1) -1.672 236.5 (1.5) 0.043 02 0.988 043 92.19 (0.12) -1.512 235.8 (1.6) 0.040 49 0.987 91 1 92.71 (0.13) -1.430 234.5 (1.7) 0.059 55 0.988 945 92.78 (0.09) -1.813 254.9 (1.2) 0.049 83 0.988 422 92.68 (0.10) -1.699 239.3 (1.4) 0.044 17 0.988 110 92.77 (0.12) -1.529 237.6 (1.6) 0.038 36 0.987 799 92.61 (0.13) -1.394 229.7 (1.8) 0.033 3 1 0.987 523 92.62 (0.15) -1.069 247.6 (2.1) 11 Estimated uncertainties for V,, and Cp,,, appear in parentheses.interest, Y&, is the value of Y2,&at infinite dilution, m is the lined by King.'6*34 This method may be summarized using molality of the solution, and S, is the experimental slope.eqn. (4): The appropriate form of eqn. (3) was fitted to our calculated Y2,+-UAY"= y; + Sum (4)V2, and C,2, & data using weighted linear least-squares regression analyses. Weights used in these analyses were cal- where a is the degree of dissociation, AFo is the difference culated as the reciprocals of the square in the uncertainties in between the standard-state thermodynamic properties of the the apparent molar volumes and heat capacities. ionized and the un-ionized species, S, is a constant, and is The acid groups on the side chains of L-glutamic and L-the standard-state thermodynamic property of the non-aspartic acid are known to undergo partial dissociation in dissociated acid.With respect to volume this equation aqueous solution. Over the investigated concentration ranges, requires estimates of the temperature dependence of A-Vo for L-glutamic acid is calculated to show a maximum of ca. 5% each acid. Owing to the unavailability of these data, we have dissociation whilst L-aspartic acid shows a maximum of ca. selected an average value for L-aspartic and L-glutamic acid 8% dissociation. Ignoring the contributions of this ionization of -11.5 cm3 mol-'. This value is based upon the volumes process could lead to the calculation of erroneous standard- of ionization of several other amino acid systems.16 For heat state properties. Correcting calculated standard-state proper- capacities, the temperature dependence of AC; for each acid ties for the ionization contribution requires acid dissociation was estimated from the reported temperature dependence of constants as a function of temperature.These data were the heats of proton i~nization.~~ Our analyses of heat capac- obtained from ref 32 and 33. Standard-state properties for the ity data do not take into account contributions made by the un-ionized (in terms of the side-chain acid group) L-glutamic temperature-dependent state of the involved equilibria or the and L-aspartic acids were calculated using the method out- related thermal effects. In all of our calculations 'relaxation' 2030 J. CHEM. SOC. FARADAY TRANS., 1994, VOL.90 Table 3 Densities, p, apparent molar volumes, V2,+, heat capacity ratios and apparent molar heat capacities, Cp,2, +, of aqueous solutions of a-aminobutyric acid at 288.15, 298.15, 313.15 and 328.15 K" lo(+ cp, 1P; -1)m/mol kg -288.15 K 0.2486 1.005 972 74.99 (0.02) -5.703 216.1 (0.3) 0.1809 1.004 139 74.92 (0.03) -4.181 215.6 (0.4) 0.1614 1.003 598 74.94 (0.03) -3.748 215.4 (0.4) 0.1445 1.003 145 74.86 (0.03) -3.397 214.0 (0.5) 0.1158 1.002 372 74.64 (0.04) -2.743 212.5 (0.6) 0.09325 1.001 718 74.88 (0.05) -2.135 217.0 (0.8) 0.06709 1.OOO 986 74.86 (0.07) -1.535 217.0 (1.1) 0.04556 1.OOO 395 74.65 (0.1 1) -1.086 213.4 (1.5) 298.15 K 0.2486 1.003 771 75.69 (0.02) -5.056 229.1 (0.3) 0.1809 1.001 964 75.70 (0.03) -3.745 228.0 (0.4) 0.1614 1.001 454 75.61 (0.03) -3.345 227.7 (0.4) 0.1445 1.000991 75.65 (0.04) -3.019 227.3 (0.5) 0.1158 1.OOO 220 75.59 (0.04) -2.447 226.2 (0.6) 0.09325 0.999 6 10 75.56 (0.05) -1.948 227.2 (0.8) 0.06709 0.998 894 75.53 (0.08) -1.421 225.9 (1.1) 0.04556 0.998 305 75.54 (0.1 1) -0.9962 223.4 (1.5) 313.15 K 0.2486 0.998 8 15 76.45 (0.02) -4.408 241.7 (0.3) 0.1809 0.997 039 76.47 (0.03) -3.214 242.0 (0.4) 0.1614 0.996 534 76.42 (0.03) -2.889 241.4 (0.4) 0.1445 0.996 092 76.39 (0.04) -2.601 240.9 (0.5) 0.1158 0.995 331 76.36 (0.04) -2.068 242.5 (0.6) 0.09325 0.994 726 76.40 (0.05) -1.678 242.3 (0.8) 0.06709 0.994 028 76.34 (0.08) -1.227 239.9 (1.1) 0.04556 0.993 451 76.35 (0.11) -0.8200 240.3 (1.5) 328.15 K 0.2486 0.1809 0.992 229 0.990 469 77.04 (0.02) 77.06 (0.03) 0.1614 0.1445 0.989 967 0.989 526 77.02 (0.03) 77.02 (0.04) 0.1158 0.09325 0.06709 0.04556 0.988 768 0.988 177 0.987 482 0.986 9 1 1 77.03 (0.04) 77.01 (0.06) 77.01 (0.08) 77.04 (0.1 1) Estimated uncertainties for V2,+ and C,2, + appear in parentheses.contribution^^^ have been assumed to be negligible. The concentration dependence of a was calculated for each acid using eqn. (5) and (6). Initial estimates of a were fed into the Davies equation,32 eqn. (5), to produce estimates of the activity coefficients, y. The computed value of y was in turn entered into eqn. (6) to produce a new estimate of a. This successive approximation procedure was repeated until consistent values of a and y were obtained.The Debye-Huckel constant, A, used in eqn. (5) is the one reported by Robinson and Stokes32 (A = 0.5115 at 298.15 K). Standard-state volumes and heat capacities for the investi- gated aqueous amino acid systems are reported and com- pared with available literature data in Table 4. Table 4 identifies the severe lack of standard-state volume and heat capacity data available in the literature for the amino acid systems investigated in this paper, especially at temperatures removed from 298.15 K. Our reported vg value for a-aminobutyric acid at 298.15 K is in excellent agreement with the data of previous authors,' '-16 with the possible exception of the early work of -3.747 253.5 (0.3) -2.840 251.4 (0.4) -2.455 253.3 (0.4) -2.08 1 256.9 (0.5) -1.845 250.5 (0.6) -1.361 256.2 (0.8) -1.064 250.9 (1.1) -0.7207 251.4 (1.5) Cohn et a1.' Also, our reported v; value at 288.15 K for this system is in good agreement with the result reported by Wadi et d.," but is slightly lower than the value of 75.06 cm3 mol -'reported by Cabani et al.' As one might expect, our reported value for the standard- state volume of L-aspartic acid at 298.15 K is larger than those reported by authors who did not account for the degree of ionization of the acid in their calculations.If the ionization correction is omitted from our calculations, then the V2,& data reported in Table 1 yield vjo2 = 73.63 cm3 mol-'. It therefore appears sensible to conclude that such a correction should not be discounted as being negligible.We also note that the ionization corrected v; value for this system at 298.15 K reported by Mishra and AhluwaliaI6 is in excellent agreement with our value. The value of vg = 71.79 cm3 mol-'reported by Jolicoeur et d6does not appear to agree with other values in the literature. We are unable to account for this discrepancy. Turning to our standard-state volume data for L-glutamic acid at 298.15 K we once again note that our reported value is larger than those reported by authors6*8 who did not account for the ionization of the acid in their calculations. However, our value is in good agreement with the ionization corrected value of Mishra and Ahluwalia.16 If the effects of ionization on the V2,&data reported in Table 2 are dis- counted then we obtain rg = 89.48 cm3 mol- '.This value is in good agreement with the value reported by Jolicoeur et J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 203 1 Table 4 Comparison of calculated P; and Ci, data with literature data T/K V;/crn3 mol-' S,/cm3 mol-2 kg" c,2/J K-' mol-' Scm/JK-' mol-2 kg" L-aspartic acid 288.15 72.84 f0.22 13.63 f6.73 98.8 f4.0 601.2 f125.6 298.15 74.78 f0.1 1 -2.09 f3.51 134.4 & 1.7 358.9 f52.7 C71.79: 74.1,' (D, L) 73.83; 74.8e] (127')313.15 75.98 0.19 7.16 k 6.02 172.3 k7.8 1.0 f242.5 328.15 77.1 1 f0.20 6.05 f6.44 180.4 k12.3 495.7 f392.4 ~-glutamic acid 288.15 88.52 f0.07 3.04 & 1.28 152.3 f5.1 269.0 f100.1 298.15 90.06 f0.10 2.50 f1.90 180.6 f5.8 210.7 f113.0 189.36,' 85.88," 89.85e] (1 77') 313.15 91.62 f0.07 4.90 f1.39 202.3 & 8.9 308.5 f177.1 328.15 92.84 f0.30 4.85 f5.98 227.0 & 12.5 384.8 f244.6 a-aminobutyric acid 288.15 74.67 f0.09 1.33 f0.47 213.4 f1.5 10.5 f7.7 [74.78,/ 75.06g] 298.15 75.51 f0.04 0.76 & 0.19 224.6 f0.5 18.5 f2.6 [76.5,h 75.85,' 75.50,' 75.63' C222.2,' 234.1' 227.2"] 75.54," 75.92,' 75.64"] 313.15 76.34 f0.03 0.50 f0.16 241.3 f0.7 1.8 f3.9 328.15 77.01 f0.02 0.13 f0.09 253.1 f2.6 0.8 f13.8 " For L-aspartic acid and L-glutamic acid S, and Sc refer to S, in eqn.(4) whilst for a-aminobutyric acid S, and Sc, refer to S, in eqn. (3). 'Ref. 6. Ref. 7. Ref. 8. Ref. 16. Ref. 17. Ref. 18. Rgf. 9. Ref. 11. j Ref. 10. Ref. 12. Ref. 14. " Ref. 13." Ref. 15. aL6 We are unable to offer an explanation for the very low effective Born coefficient for the neutral organic aqueous value reported by Millero and co-workers.* species of interest, 8 represents a solvent-dependent param- The e;, values at 298.15 K for L-aspartic and L-glutamic eter, and Q and X are defined using the derivatives of the acid, reported by Jolicoeur et uL,~were not corrected for the relative permittivity for water as a function of temperature ionization of the acids. If the Cp,2, data reported in Tables 1 and pressure, eqn. (9) and (10): and 2 for L-aspartic acid and L-glutamic acid are treated in a similar fashion, then we obtain values of ci, = 120.21 J K-' Q=:($) T (9)mol-' and ci, = 172.79 J K-' mol-',respectively. These values are in reasonable agreement with those reported by In E aIn E Jolicoeur et aL6 Literature value^'^^'^^'^ for the standard- state heat capacity of a-aminobutyric acid at 298.15 K are in good agreement with the value that can be calculated from Estimates for Q and X,contained in Table 5, were calculated the Cp,2, data reported in Table 3.at 1 atm and the temperature of interest using a BASIC com-Equations of state for standard-state heat capacities and puter program that followed the procedures described by volumes are reported in the literature in the form of revised Helgeson and Ki~-kharn.~'*~~ Values for 0,c,c1 and c2 were HKF equations for neutral organics in The data obtained by fitting eqn. (7) and (8) to our standard-state data reported in Table 4 have been modelled using constant pres- using multiple regression analysis procedures.To remain sure variants of these equations: consistent with investigations of Shock and Helgeson, we have used the effective Born coefficients reported in ref. 36 V; = 0 + -5: -u),Q (7) and have set 8 = 228 K. The results of our fitting procedures T-8 are reported in Table 5. c;,2 = C' + -c2 + weTX (8) Analysis of and cp,Data for Amino Acids in Water (T-el2 Standard-state volume and heat capacity data reported in where 0,t, c1 and c2 are fitting parameters, o,defines the this paper comprise contributions which shed light on the Table 5 Calculated parameters for eqn. (7) and (8) for aqueous solutions of aspartic acid, glutamic acid and a-aminobutyric acid (4 amino acid 0/cm3 mol-' &m3 K mol-' c,/J K-' mol-' c,/105 J K-' mol-' wJ105 J mol-' " aspartic acid 81.43 f 0.74 -574.91 f53.88 210.41 f8.10 -4.670 f0.4231 -2.049 74 glutamic acid 96.34 f0.15 -571.79 f11.48 230.27 f5.88 -3.8551 f0.3071 -3.044 28 a-aminobutyric acid 79.00 f0.10 -311.10 f7.43 256.57 f4.07 -2.1365 f0.2125 -1.536 36 288.15 6.49 x 10-7 -3.16 x 10-7 298.15 6.69 x 10-~ -3.14 x 10-~ 313.15 7.17 x 10-7 -3.12 x 10-~ 328.15 7.88 x 10-7 -3.17 x 10-7 " Data obtained from ref.36. solvation of the solute species and which give us structural information. The HKF equations utilised in this paper are one type of semi-empirical modelling procedure that has been used to gain access to these contributions.Many other such models have been utilised and dis~ussed.**~~,~~ In the HKF model, the standard-state apparent molar properties defined by eqn. (7) and (8), can be subdivided into two contribution^,^' eqn. (11): Yo,= Y,"+ Y; where subscripts s and e define a non-solvation and a solva-tion contribution, respectively. Further, the non-solvation, or structural, term is taken to represent an intrinsic contribution and a contribution arising from the disruption in the solvent media caused by the presence of the solute species. The solva- tion, or electrostatic, contribution to standard-state proper- ties represents interactions between the solvent and the solute. These contributions are defined using eqn. (12) and (13): vz = -weQ c;, = weTX where we,Q and X have been defined previously.If chemical group additivity schemes are to be applied to our amino acid data then it would appear appropriate to focus our attention on structural contributions to standard- state properties. This may be done by removing the contribu- tions made by solute-solvent interactions to standard-state properties. These contributions are solute specific. Group additivity schemes constructed using this procedure offer the potential of being able to estimate the temperature depen- dence of standard-state volumes and heat capacities of aqueous solutions of peptide and protein systems. To avoid the problems of dealing with the ionic com- ponents of amino acids, previous a~thors~'-~~ have utilised additivity schemes based on neutral N-acetyl amino acid amides, cyclic dipeptides, or small zwitterionic peptides in which the ionic groups are a long way removed from the side chains of interest.The ability to construct an additivity scheme based on the volumetric and thermochemical proper- ties of simple amino acids is therefore very appealing. Group Additivity Analysis We have explored several group additivity schemes for aqueous amino acid systems. In brief, obtaining reliable esti- mates for group contributions relies on maximizing the number degrees of freedom in each analysis. In practice, this leads to some restrictions in the number of group contribu- tions and amino acids which can be analysed at one time. Also, the manner in which one separates amino acids into group contributions must be carefully considered.Our analyses are based on a multiple regression procedure that uses matrix mathematics to produce estimates of the required group contributions. In our adopted scheme the structural standard-state volumes and heat capacities are broken down into four group contributions. These contribu- tions are identified in eqn. (14): In addition, two simplifying assumption^^'-^^ are employed to decrease the number of unknowns in our analyses. These assumptions are defined by eqn. (1 5) and (16): (15) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 6 Calculated group contributions of structural components of standard-state volumes and heat capacities at 288.15, 298.15, 313.15 and 328.15 K" ~~ structural group P:/cm3 mol-' C;]J K-' mol-' 288.15 K CH(NH,)CO,H OH C0,H CH2 34.73 (0.34) 15.57 (0.11) 8.74 (0.36) 20.94 (0.36) -22.3 (4.8) 86.2 (1.5) 18.1 (5.0) -4.6 (5.0) 298.15 K CH(NH ,)CO,H OH C0,H CH2 35.54 (0.31) 15.56 (0.10) 8.74 (0.32) 21.83 (0.32) -0.4 (2.8) 83.1 (0.9) 19.3 (2.9) 9.5 (2.9) 313.15 K CH(NH,)CO,H OH C0,H CH, 36.03 (0.29) 15.69 (0.09) 8.96 (0.30) 22.40 (0.30) 20.5 (1.7) 80.1 (0.5) 26.7 (1.8) 21.8 (1.8) 328.15 K CH(NH ,)CO,H CH, OH- 36.28 (0.21') 15.85 (0.07) 8.95 (0.23) 37.5 (1.2) 77.5 (0.4) 27.2 (1.2) C0,H 22.91 (0.23) 23.4 (1.2) Calculated standard errors are contained in parentheses.For example, the non-solvation contributions to thermody- namic standard-state properties of L-threonine can be rep- resented by eqn.(17): P:(L-threonine) = P'(L-threonine) -Y~(L-threonine) Standard-state volume and heat capacity data for glycine, L-alanine, L-serine, L-threonine, L-valine, L-leucine, L-isoleucine, L-glutamic acid, L-aspartic acid and a-aminobutyric acid at 288.15, 298.15, 313.15 and 328.15 K were used as the input data set for this scheme.19920 The resultant estimates of group contributions to volumes and heat capacities at each tem- perature are reported in Table 6 together with their calcu- lated standard errors. Tables 7 and 8 compare experimental standard-state volumes and heat capacities with those which can be calcu- lated for our data set of ten amino acids. The differences between the experimental and the calculated values are similar in magnitude to the estimated uncertainties in our standard-state properties, and therefore afford us a high degree of confidence in our analysis procedures.In comparing our group contributions to those obtained in other studies, we caution the reader that the present paper looks at structural group contributions to standard-state heat capacities. In other words, the y: contribution to of eqn. (11). In previous investigations, Yg itself was used for group contributions and so any comparisons that we make inher- ently assume that contributions made by Yz to for each group are small. We have been unable to calculate the elec- trostatic contributions of each group that we investigated.However, based on the magnitude of calculated 7: values for the amino acids our assumption appears valid, at least to a first approximation. Group contributions to standard-state heat capacities of aqueous organic species have been calculated by several However, with the exception of the temperature-dependent study of Makhatadze and Priva10v~~ these studies are restricted to the standard temperature of 298.15 K. Hedwig et report group contributions to standard-state heat capacities at 298.15 K. These values were J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 7 Comparison of experimental and calculated standard-state volumes (cm3 mol-') at 288.15, 298.15, 313.15 and 328.15 K T = 288.15 K T = 298.15 K T = 313.15 K T = 328.15 K amino acid expt.calc. expt. calc. expt. calc. expt. calc. L-alanine" 59.67 58.80 60.47 59.62 61.14 60.37 61.53 60.92 L-serine" 59.70 60.02 60.66 60.86 61.63 61.78 62.22 62.28 L-threonine" 76.18 75.86 76.90 76.70 77.93 77.78 78.52 78.46 L-valineb 90.08 90.04 90.80 90.85 91.67 91.88 92.57 92.75 L-leucineb 106.81 105.97 107.73 106.78 109.00 107.97 110.18 109.03 L-glutamic acid 88.52 88.78 90.06 90.5 3 9 1.62 92.00 92.84 93.29 L-aspartic acid 72.84 72.57 74.78 74.30 75.98 75.60 77.11 76.66 L-isoleucineb 104.9 106.02 105.76 106.84 107.04 108.03 108.09 109.10 glycine" 42.48 43.14 43.26 43.97 44.01 44.58 44.5 1 44.96 a-aminobutyric acid 74.67 74.64 75.51 75.46 76.34 76.37 77.01 77.1 1 " Experimental data from ref. 19. Experimental data from ref.20. Table 8 Comparison of experimental and calculated standard-state heat capacities (J K-' mol-') at 288.15, 298.15, 313.15 and 328.15 K T = 288.15 K T = 298.15 K T = 313.15 K T = 328.15 K amino acid expt. calc. expt. calc. expt. calc. expt. calc. ~ L-alanine" 126.3 117.1 141.2 134.6 153.7 151.4 166.5 165.4 L-serine" 89.0 95.9 114.1 116.2 140.0 142.1 157.9 158.1 L-threonine" 192.8 185.9 205.3 203.2 228.5 226.4 240.2 240.0 L-valineb 294.4 29 1 .O 305.8 302.2 3 16.3 3 13.2 325.2 322.1 L-leucineb 388.1 382.4 397.5 390.6 406.8 398.8 411.9 405.5 L-glutamic acid 152.3 173.2 180.6 203.7 202.3 232.2 227.0 247.6 L-aspartic acid 98.8 77.9 134.4 11 1.3 172.3 142.4 180.4 159.8 L-isoleucineb 372.9 383.1 383.8 391.3 392.8 399.6 399.5 406.3 glycine" 15.2 29.6 37.6 50.2 57.8 70.0 76.8 86.4 a-aminobutyric acid 213.4 207.2 224.6 221.6 241.3 235.7 253.1 247.3 " Experimental data from ref.19. Experimental data from ref. 20. obtained from an analysis of several amino acids, peptides The methylene group contribution to standard-state heat and N-acetylamides. In addition, Nichols et a1." have report- capacities decreases with increasing temperature. As dis-ed group contributions to standard-state heat capacities cussed previously, with side-chain contributions,20 this trend based on an analysis of amides and other relatively simple reflects the apolar nature of the methylene group and its compounds. Group contributions reported by Makhatadze hydrophobic character. With increasing temperature the and Priva10v~~ are calculated from the partial molar heat structure-promoting ability of this group is decreased.Use of capacities of various peptides and organic compounds that the assumptions defined by eqn. (15) and (16) dictates that the model amino acid side chains. All of these authors agree that trends in the contributions of H atoms and CH, groups to a methylene group should contribute ca. 90 J K-' mol-' to standard-state heat capacities mirror that displayed by the observed standard-state heat capacities. This value is in very methylene group. Hydrophobic solvation is most dominant good agreement with our calculated value of 83.1 J K-' with the methyl group. mol-'. Also, our estimates for the contributions of a hydro- Group contributions to standard-state heat capacities for gen atom and a methyl group to observed standard-state the CH(NH2)C02H, OH and C02H groups are seen to heat capacities, 41.55 J K-' mol-' and 124.7 J K-' mol-', respectively, are in good agreement with the values reported 1oo.oo(tin ref.42, but are noticeably less than the values reported in ref. 50. It has been suggested4' that these differences can be attributed to the chemical homogeneity of the compounds 80.00 i tt rstudied in ref. 50 which leads to a non-unique set of coeffi- 60.00-Icients. Estimates of the H atom and methyl group contribu- -tions calculated in ref. 23 are also larger than those we have ,-40.00-calculated in our analysis. At present this apparent discrep- L 20.00-ancy cannot be resolved because our group-analysis scheme 7 is restricted by the number of unknowns that can be solved 2 0.00-for at one time, i.e. insufficient degrees of freedom.With an 'c, increased data base of thermodynamic data for aqueous -20.00-amino acids we should, in time, be able to modify our group I 1 I 1 Ianalysis to solve directly for the H atom and the CH, group -40.00 contributions. This would remove the requirement of the assumptions defined by eqn. (1 5) and (16). The temperature dependences of group contributions to the structural components of standard-state heat capacities are shown in Fig. 1. 2034 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 I I t40.00 I I I1 our current data set is too limited and does not permit the estimation of structural contributions of the peptide group 35.004 (CONH) to standard-state volumes and heat capacities.Hence, we are currently working on extending the data sets I 30.001 t used in our analyses by measuring the volumetric and ther- mochemical properties of several other amino acid and dipeptide systems. The results of these studies will be report- ed in future publications. 15.00 A.W.H. is grateful to the Natural Sciences and Engineering 10.0 ] 0 -I-Research Council of Canada (NSERC) for operating support and to the University of Lethbridge for equipment funding. r7 u K.E.P. is grateful to NSERC for the award of an Under- 5.00.) 280.00 290.00 300.00 graduate Student Research Award. 310.00 320.00 330.00 TI References Fig.2 Temperature dependence of the group contributions to struc- 1 L. Barta, A. W. Hakin and L. G. Hepler, in Oil Field Chemistry, tural components of standard-state volumes. (0)CH(NH,)CO,H, OH,(.)(0)(*I Enhanced Recovery and Production Stimulation, ACS Symp. Ser. CH, 7 COP. 396, ed. J. K. Borchardt and T. F. Yen, American Chemical Society, Washington DC, 1989, ch. 23. A. W. Hakin and M. M. Duke, in Proceedings Fine Tails Sympo- increase with increasing temperature. These trends are indica- 2 tive of the polar nature of these groups and reflect the role of hydrophilic hydration. Although there are some variations in specific values, we note that our group contributions to standard-state heat capacities follow the same general tem- sium, ed.J. K. Liu, Fine Tails Fundamentals Consortium, Edmonton, 1993. 3 E. L. Shock, Geochim. Cosmochim. Acta, 1992,56,3481. 4 L. R. Brown, Chem. Eng. Prog., 1987,83,35. 5 I. Rubinstein, C. Spykerelle and D. W. S. Westlake, Geochim. Cosmochim. Acta, 1977,41, 1341. perature dependences as those reported by Makhatadze and ~rivalov.~~ 6 C. Jolicoeur, B. Riedl, D. Desrochers, L. L. Lemelin, R. The temperature dependences of group contributions to the structural components of standard-state volumes are shown in Fig. 2. The methylene group contribution to standard-state volumes at 298.15 K is in good agreement 7 8 Zamojska and 0.Enea, J. Solution Chem., 1986, 15, 109. L. G. Longsworth, in Electrochemistry in Biology and Medicine, ed. T.S. Hedlovsky, Wiley-Interscience, New York, 1955, ch. 12. F. J. Millero, A. LoSurdo and C. Shin, J. Phys. Chem., 1978, 82, 784. with the value of 15.9 cm3 mol-' reported in ref. 11 and is in 9 E. J. Cohn, T. L. McMeekin, J. T. Edsall and M. H. Blanchard, fair agreement with the value of 16.9 cm3 mol-' reported by Millero et a1.* The value of 16.9 cm3 mol-' may also be cal- culated from the standard-state volume data reported by Makhatadze et al.22We also note that our calculated contri- butions for the OH and C02H groups at 298.15 K are in good agreement with the values of 8.1 and 21.6 cm3 mol-' that were calculated in ref. 11 using a molecular modelling 10 11 12 13 J. Am. Chem. Soc., 1934,56,784. C. H. Spink and I. Wadso, J. Chem. Thermodynam., 1975,7,561. S.Cabani, G. Conti, E. Matteoli and M. R. Tine, J. Chem. Soc., Faraday Trans. I, 1981,77, 2377. H. D. Ellerton, G. Reinfields, D. E. Mulcahy and P. J. Dunlop, J. Phys. Chem., 1964,68, 398. J. C. Ahluwalia, C. Ostiguy, G. Perron and J. E. Desnoyers, Can. J. Chem., 1977,55,3364. procedure. Agreement is less satisfactory with the same group contributions that can be calculated from the data contained in ref. 22. The trends in these data as a function of temperature are more difficult to interpret. However, for the CH(NH2)C02H 14 15 16 17 18 G. DiPaola and B. Belleau, Can. J. Chem., 1978,56, 1827. M. R. Tine, Ph.D. Thesis, Universita di Pisa, 1977. A. K. Mishra and J. C. Ahluwalia, J. Phys. Chem., 1984,88,86. R. K. Wadi, M. N. Islam and R.K. Goyal, Indian J. Chem. A., 1990,29,1055. S. Cabani, G. Conti, E. Matteoli and M. R. Tine, J. Chem. Soc., and C02H groups the data appear to follow previously docu- mented behaviour, i.e. the volume contributions of these groups increase with increasing temperature, a feature indica- tive of hydrophilic hydration. However, the volume contribu- tion of the hydrophobic methylene group and the hydrophilic OH group are almost independent of temperature. These 19 20 21 Faraday Trans. I, 1981,77,2385. A. W. Hakin, M. M. Duke, S. A. Klassen, R. M. McKay and K. E. Preuss, Can. J. Chem., in the press. M. M. Duke, A. W. Hakin, R. McKay and K. E. Preuss, Can. J. Chem., in the press. H. C. Helgeson, D. H. Kirkham and G. C. Flowers, Am. J. Sci., 1981,281,1249. trends are not so readily explained. Once again we arrive at 22 G.I. Makhatadze, V. N. Medvedkin and P. L. Privalov, Bio- the conclusion that obtaining reliable structural information from volume data is a more difficult proposition than obtain- ing structural information from heat capacity data. This con- clusion is re-emphasised by closer inspection of the temperature dependences of group contributions to standard- state volumes which can be calculated from the data con- 23 24 25 polymers, 1990,30, 1001. G. I. Makhatadze and P. L. Privalov, J. Mol. Biol., 1990, 213, 375. C. J. Pouchert and J. R. Campbell, The AIdrzch Library ofNMR Spectra, The Aldrich Chemical Co., Gillingham, 1974, vol. 111. P. Picker, E. Tremblay and C. Jolicoeur, J. Solution Chem., 1974, 3, 377.tained in ref. 22. In the 288.15-328.15 K temperature range, data amassed by the latter authors predict volume decreases for the C02H and OH groups with increasing temperature whilst the reverse trend is shown for the methylene group with increasing temperature. Such patterns appear to contra- dict those that one would predict based on the hydrophilic 26 27 28 29 P. Picker, P.-A. Leduc, P. R. Philip and J. E. Desnoyers, J. Chem. Thermodynam., 1971,3,631. J. E. Desnoyers, C. DeVisser, G. Perron and P. Picker, J. Solu-tion Chem., 1976,5,605. A. W. Hakin, S. A. M. Mudrack and C. L. Beswick, Can. J. Chem., 1993,71,925. G.S. Kell, J. Chem. Eng. Data, 1967, 12, 66. and hydrophobic characters of these groups. One goal of our investigations into the thermodynamic properties of aqueous amino acid systems is to develop an analysis procedure that will allow us to estimate standard- state volumes and heat capacities for peptide and perhaps protein systems, as a function of temperature.Unfortunately, 30 31 32 33 G. S. Kell, in Water-A Comprehensive Treatise, ed. F. Franks, Plenum Press, New York, 1972, vol. I, pp. 363-412. G. R. Hedwig, J. Solution Chem., 1988, 17, 383. R. A. Robinson and R. H. Stokes, Electrolyte Solutions, Butter-worths, London, 2nd edn. (revised), 1965. Handbook of Biochemistry Selected Data for Molecular Biology, ed. H. A. Sober CRC Press, Boca Raton, 2nd. edn., 1970. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 2035 34 E. J. King, J. Phys. Chem., 1969,73, 1220. 43 T. E. Leslie and T. H. Lilley, Biopolymers, 1985,24, 695. 35 J. W. Larson, K. G. Zeeb and L. G. Hepler, Can. J. Chem., 1982, 44 S. Cabani, G. Conti and E. Matteoli, Biopolymers, 1977, 16, 465. 60,2141. 45 K. P. 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Paper 4/00629A; Received 1st February, 1994