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Thermodynamics of solution of L-valine in water
Accepted Manuscript Title: Thermodynamics of solution of L-valine in water Authors: Olga A. Antonova, Valery P. Korolev, Andrey V. Kustov PII: DOI: Reference:
S0040-6031(17)30275-7 https://doi.org/10.1016/j.tca.2017.10.020 TCA 77862
To appear in:
Thermochimica Acta
Received date: Revised date: Accepted date:
5-7-2017 17-10-2017 23-10-2017
Please cite this article as: Olga A.Antonova, Valery P.Korolev, Andrey V.Kustov, Thermodynamics of solution of L-valine in water, Thermochimica Acta https://doi.org/10.1016/j.tca.2017.10.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Thermodynamics of solution of L-valine in water Olga A. Antonova*, Valery P. Korolev and Andrey V. Kustov Krestov Institute of Solution Chemistry, Russian Academy of Sciences, 1, Academicheskaya str., 153045, Ivanovo, Russia, Ivanovo State University of Chemistry and Technology, 7, Sheremetevsky av., 153000, Ivanovo, Russia *Corresponding author: United Physical-Chemical Centre, Institute of Solution Chemistry, Russian Academy of Sciences, 1, Academicheskaya str., 153045, Ivanovo, Russia E-mail address: [email protected] (Olga Antonova) Graphical abstarct 260
280
300
320
340
360 0.016
16
Water - L-Valine 14
0.015
0
solG 12
0.014
-1
0 -TsolS
0.013
6
0.012
0
solY , kJ mol
8
4 0.011 2
0
solH
0.010
0 -2
0.009
Solubility -4
0.008 260
280
300
320
T, K
340
360
X, mol farctions
10
Highlights Enthalpies of L-α-valine solution in water were measured from T=279 to T=323 К Thermodynamic functions and solubility at different temperatures were estimated The prediction agrees well with experimental solubility values
ABSTRACT This paper focuses on the accurate thermodynamic study of solution of L-valine in water in a wide temperature range. Enthalpies of solution of L-valine in water have been calorimetrically determined between T=279 K and T=323 К. Standard enthalpies and heat capacities of solution as well as standard partial molal heat capacities have been calculated and compared with available literature values. The free energy of solution and its enthalpic and entropic terms have been computed using the combination of solubility and calorimetric data via the Gibbs-Helmholtz equation from T=280 K to T=360 K. The temperature dependence of solubility of the amino acid has been also computed and compared with experimental quantities. The satisfactory agreement is found between experimental and predicted solubility values.
Keywords: L-Valine Water Calorimetry Thermodynamics of solution Solubility Prediction 1. Introduction
A major problem of protein chemistry is the determination of the factors which contribute to peculiarities of protein folding and enzyme-substrate interactions in a water-like environment. Proteinwater interactions are important factors that are responsible for stabilizing the native structure of globular proteins. Amino acids and simple peptides are usually used for modeling such interactions in the hope that these investigations should provide a better insight into various aspects of protein stability and biosynthesis. During last several years we have been involved in an intensive and continuing study dealing with the thermodynamic behavior of amino acids in water at different temperatures [1-5]. Enthalpies, free energies, entropies and heat capacities of solution and transfer from water to its mixtures with urea, alcohols or glycols have been obtained and discussed in terms of solute-non-electrolyte pair and triplet interactions occurring in highly diluted solutions [6-9]. Another important point which has been briefly addressed is that for slightly soluble biological species is well
justified to compute temperature changes of thermodynamic functions and solubility values via simple integration of the Gibbs-Helmholtz equation using the temperature dependence of standard enthalpies of solution and the solubility value at the reference temperature [10,11]. Here we extend this approach towards L-valine which is known to be an essential amino acid that cannot be synthesized inside a human body. It is also important that L-valine is more soluble in water than previously studied aromatic amino acids that may require to take into account solute-solute interactions in a saturated solution that can induce the deviation of activity coefficients from unity. Thermodynamic studies of aqueous L-valine solutions are rather scarce. Solution and dilution enthalpies have been obtained at 298 K [12-15] and also at 308 K [16]. Partial molar heat capacities of aqueous L-valine solutions have been obtained from direct heat capacity measurements at 298 K [1719] and also within the narrow temperature range of 288-328 K [20]. The results [20] clearly indicate
that the C p
0 2
values moderately increase with the temperature. We have also found several sources
[21-23] of solubility values of L-valine in water which are in a satisfactory agreement with each other. The present study focuses on the experimental determination of enthalpies of solution of the amino acid both in cold and hot water to compute standard enthalpies, heat capacities of solution and partial molar heat capacities. The combination of calorimetric data with a solubility value at the standard temperature is used to compute free energies and entropies of solution in a wide temperature range via integration of the Gibbs-Helmholtz equation and also to predict the temperature dependence of the amino acid solubility in water.
2. Experimental
2.1. Chemicals L-α-valine (for biochemistry, Merk KGaA, Germany, initial mass fraction >0.990) was dried under reduced pressure for several days at 343 K and then used without further purification. Water was distilled twice.
2.2. Apparatuses and methods
Calorimetric measurements were carried out with a precise isoperibol calorimetric system fitted here with the 60 cm3 titanium vessel. The description of the apparatus and methodology of measurements were presented in detail several times [1,10]. The temperature sensitivity of the calorimeter was of 10-5 K and the temperature stability of the thermostat was better than 10-3 K. The accuracy of the measurements was estimated to be within 1%.
3. Results
Experimental enthalpies of solution of L-valine were determined in the range of solute molalities from m = 0.003 mol kg-1 to m = 0.03 mol kg-1. Table 1 illustrates enthalpies of solution of L-valine in water at 298 and 308 K. As can be seen the solHm values do not depend on molality for the concentration range studied. Thus, the standard enthalpy of solution or the enthalpy of solution at infinite dilution can be easily computed as the mean value in the range of the experimental enthalpies of solution for each temperature [1,3,10]. We see from Table 1that the agreement between our results and standard enthalpies of solution for L-valine reported elsewhere [12-14,16] is very good.
4. Discussion Tables 1, 2 give the solH0 values for L-valine in water at different temperatures. The temperature dependence of enthalpies of solution is found to fit quite enough to well-known the second-order polynomial [1,4,10]: ΔsolH0 = 2.95(0.06) + 0.151(0.003) (T-298.15) + ½ 0.00128(0.0004) (T-298.15)2,
(1)
R = 0.9994, sf = 0.11 kJ mol-1, where the first term is the enthalpy of solution at the reference temperature of 298 K, the second one is the heat capacity of solution and the third term is its temperature derivative; values in brackets give the standard deviation of the mean. Eq. (1) shows that the heat capacity of solution is positive and slightly increases with the temperature as it is observed for aromatic amino acids such as L-histidine, L-phenylalanine or Ltryptophan [1,2,10]. The heat capacity of solution ΔC0p is known to be the well-established parameter of hydrophobicity [24]. This quantity at the reference temperature (151 J/(mol K))is slightly lower than the ΔC0p value for hydrophobic L-phenylalanine [2,4] or L-tryptophan [10] but three times as larger as the heat capacity of solution for L-histidine [1,4] which contains several hydrophilic centers in its side-chain. It is found that the ΔC0p value increases in the following order: L-glycine, L-alanine [3], L-valine, tryptophan [10], and L-phenylalanine [4], which is in fair agreement with the behaviour of the hydrophobicity parameter of amino acids [25]. Such heat capacity values are usually associated with increasing the number of nearly straight and shorter water-water hydrogen bonds and decreasing the population of more bent H-bonds in the nearest vicinity of non-polar groups. This phenomenon induces increasing energy fluctuations in the hydrophobic hydration shell that results in large and positive heat capacity values [24].
0
To calculate standard partial molar heat capacities C p 2 , we exploit the integral enthalpies of solution method [26] and heat capacity values from Eq. (1):
Cp
0 2
= ΔC0p + Cp cr,
where Cp cr – the heat capacity of crystalline L-valine [27].
(2)
The Cp
cr
- f(T) curve in the range of temperatures of 250-300 K [27] is well described by the
following linear equation: Cp cr = (168.74±0.13) + (0.464±0.005) (T-298.15), R = 0.9996, sf = 0.24 J mol-1 K-1
(3)
The combination of heat capacities of solution obtained with from Eq. (1) and Cp
cr
values
calculated with Eq. (3) results to the following expression for partial molal heat capacities: C p
0 2
=
319.74 + 1.744 (T-298.15). This gives 320 J mol-1 K-1 for the standard partial molar heat capacity of
L-valine in water at 298 K. This quantity is in a good agreement with C p
0 2
values obtained from the
extrapolation of apparent molar heat capacities to an infinite dilution: 307±6 [17], 308±1 [18], 302±1 [19], 306 J mol-1 K-1 [20]. Similarly, we have calculated standard partial molar heat capacities of Lvaline in water at different temperatures. Fig. 1 compares our results with available heat capacity
values. The agreement is found to be rather good in cold water. However, our C p
0 2
values reveal a
stronger temperature dependence that leads to larger heat capacity values at elevated temperatures. Recently, we have shown that for slightly soluble species such as porphyrins [11] or aromatic amino acids [10] it is reasonable to compute thermodynamic functions of solution using the temperature dependence of standard enthalpies and a solubility value at any reference temperature, where activity coefficients are expected to approach to the unity:
ln
T sol H 0 X (T ) 1 dT , X (298.15) R 298.15 Т 2
(4),
where X is the mole fraction of the solute in a saturated solution. However, solubility of L-valine in water is larger than for aromatic amino acids such as Lphenylalanine or L-histidine. Hence, Eq. (1) should be rewritten to take into account the deviation of activity coefficients from the unity:
sol H 0 X (T ) 1 T ln dT ln 2 X (298.15) R 298.15 Т T
,
(5)
298.15
where the last term is the logarithm of the ratio of L-valine activity coefficients at the current and reference temperatures. If this ratio approaches to the unity in the temperature range studied, this term can be omitted and Eq. (1) should predict the temperature dependence of solubility with a good accuracy. We have mentioned above that there are several sources of solubility values of L-valine in water [21-23] which are in a satisfactory agreement with each other. Using the solubility value of X =0.0086 mol fractions at 293 K [21] and Eq. (4), we have predicted the temperature dependence of solubility of L-valine in water and compared these quantities with experimental ones [21]. Fig. 2 illustrates that there is a good agreement between experimental and computed solubility values. The largest deviation does not exceed 0.0007 mol fractions, which leads to the
T
/ 293.15
ratio of 0.93. It indicates that
activity coefficients are only slightly deviate from the unity and free energy of solution and entropic terms can be estimated as in our previous studies [10,11] as follows: solG0 RT ln(1/X)
(6)
-TsolS0 = solG0 - solH0
(7)
Fig. 2 gives experimental and computed thermodynamic functions of L-valine solution in water at different temperatures. The agreement between both sets of quantities is seen to be excellent. The free energy of solution depends slightly on the temperature and the solG0 vs T curve passes through a broad maximum at 350 K. The enthalpic and entropic terms (-TsolS0) change gradually with the temperature. These functions intersect each other at 318 K giving solH0 = (-TsolS0). Both terms are rather small and positive in the middle temperature range. The enthalpy of solution of L-valine becomes negative al low temperatures leading to -TsolS0 = solG0 nearby the temperature of maximal density of water. In contrast, the entropic term changes its sign at elevated temperatures favouring the amino acid transfer from a solid state to a liquid phase.
5. Conclusions
This study focuses on the accurate thermodynamic analysis of L-valine aqueous solutions in a wide temperature range. Enthalpies of solution of L-valine in water have been calorimetrically determined between T = 279 and T = 323 К. Standard enthalpies and heat capacities of solution as well as standard partial molal heat capacities were calculated and compared with available literature values. Our results clearly indicate that both for slightly soluble aromatic amino acids and some aliphatic amino acids it is well justified to compute the temperature dependence of thermodynamic functions of solution via integration of the Gibbs-Helmholtz equation (see Eq. (4)). This approach also provides a simple way to predict quantitatively or at least semi quantitatively solubility values for many biologically active species in a wide temperature range.
References
[1] A.V. Kustov, V.P. Korolev, Thermodynamics of solution of histidine, Thermochim. Acta. 447 (2006) 212-214. [2] A.V. Kustov, V.P. Korolev, The thermodynamic parameters of solution of L-phenylalanine in water, Russ. J. Phys. Chem. A. 81(2) (2007) 193-195. [3] V.P. Korolev, D.V. Batov, N.L. Smirnova, A.V. Kustov, Amino acids in aqueous solution. Effect of molecular structure and temperature on thermodynamics of dissolution, Russ. Chem. Bull., International Edition. 56(4) (2007) 739-742. [4] A.V. Kustov, V.P. Korolev, The thermodynamic characteristics of solution of L-α-histidine and Lα-phenylalanine in water at 273–373 K, Russ. J. Phys. Chem. A. 82 (2008) 1828-1832. [5] V.P. Korolev, O.A. Antonova, N.L. Smirnova, Thermodynamics of aqueous solutions of L-proline at 273-328 K, Russ. J. Phys. Chem. A. 84 (2010) 1827-1831. [6] V.P. Korolev, D.V. Batov, N.L. Smirnova, A.V. Kustov, Thermodynamics of solution of glycine in aqueous urea solution. √ m rule, J. Struct. Chem. 48 (2007) 666-672. [7] A.V. Kustov, N.L. Smirnova, R. Neueder, W. Kunz, Amino acid solvation in aqueous kosmotrope solutions: Temperature dependence of the L-histidine-glycerol interaction, J. Phys. Chem. B. 116(7) (2012) 2325-2329. [8] V.P. Korolev, O.A. Antonova, N.L. Smirnova, Thermodynamic properties and interparticle interactions of L-proline, glycine, and L-alanine in aqueous urea solutions at 288-318 K, J. Therm. Anal. Calorim. 108 (2012) 1-7. [9] V.P. Korolev, O.A. Antonova, N.L. Smirnova, Thermodynamic characteristics, structure, and interactions of L-proline in aqueous solutions of alcohols and urea, J. Struct. Chem. 55(2) (2014) 353-359. [10] A.V. Kustov, O.A. Antonova, N.L. Smirnova, Thermodynamics of solution of L-tryptophan in water, J. Therm. Anal. Calorim. (2017) doi:10.1007/s10973-017-6172-0. [11] A.V. Kustov, N.L. Smirnova, D.B. Berezin, M.B. Berezin, Thermodynamics of solution of protoand mezoporphyrins in N,N-dimethylformamide, J. Chem. Thermodyn. 89 (2015) 123-126. [12] C.H. Spink, M. Auker, Entropies of transfer of amino acids from water to aqueous ethanol solutions, J. Phys. Chem. 74(8) (1970) 1742-1747. [13] B. Palecz, Enthalpies of solution and dilution of some L-α-amino acids in water at 298.15 K, J. Therm. Anal. Calorim. 54 (1998) 257-263. [14] X. Qiu, Q. Lei, . Fang, R. Lin, A calorimetric study on interactions of amino acids with sodium dodecylsulfate and dodecyltrimethylammonium bromide in aqueous solutions at 298.15 K, Thermochim. Acta. 478 (2008) 54-56.
[15] X. Wang, Y. Guo, Q. Zheng, R. Lin, Transfer enthalpies of amino acids and glycine peptides from water to aqueous solutions of trimethylamine N-oxide at 298.15 K, Thermochim. Acta. 587 (2014) 48-51. [16] A.K. Mishra, J.C. Ahluwalia, Enthalpies, heat capacities and apparent molal volumes of transfer of some amino acids from water to aqueous t-butanol, J. Chem. Soc. Faraday Trans. I. 77 (1981) 1469-1483. [17] C.H. Spink, I. Wadsö, Thermochemistry of solutions of biochemical model compounds. 4. The partial molar heat capacities of some amino acids in aqueous solution, J. Chem. Thermodyn. 7 (1975) 561-572. [18] G. DiPaola, B. Belleau, Apparent molal heat capacities and volumes of amino acids in aqueous polyol solutions, Can. J. Chem. 56 (1978) 1827-1831. [19] C. Jolicoeur, B. Riedl, D. Desrochers, L.L. Lemelin, R. Zamojska, O. Enea, Solvation of amino acid residues in water and urea-water mixtures:volumes and heat capacities of 20 amino acids in water and in 8 Molar urea at 250 C, J. Solut. Chem. 15 (1986) 109-128. [20] M.M. Duke, A.W. Hakin, R.M. McKay, K.E. Preuss, The volumetric and thermochemical properties of aqueous solutions of L-valine, L-leucine, and L-isoleucine at 288.15, 298.15, 313.15, and 328.15 K, Can. J. Chem. 72 (1994) 1489-1494. [21] Chuntao Zhang, Bangyu Liu, Xin Wang, Hairong Wang, Haitao Zhang, Measurement and correlation of solubility of L-valine in water + (ethanol, N,N-dimethylformamide, acetone, isopropyl alcohol) from 293.15 K to 343.15 K, J. Chem. Eng. Data. 59(9) (2014) 2732–2740. [22] G.D. Fasman, Handbook of biochemistry and molecular biology, 3rd ed. Physical and chemical data, CRC Press: Cleveland, v1, 1976. [23] I. Kurosawa, A.S. Teja, R.W. Rousseau, Solid-liquid equilibria in L-leucine + L-valine + water. Fluid Phase Equilibria. 228-229 (2005) 83-87. [24] B. Madan, K. Sharp, Heat Capacity Changes Accompanying Hydrophobic and Ionic Solvation: A Monte Carlo and Random Network Model Study, J. Phys. Chem. 100 (1996) 7713-7721. [25] B. Palecz, Enthalpic homogeneous pair interaction coefficients of L-α-amino acids as a hydrophobicity parameter of amino acid side chain, J. Amer. Chem. Soc. 124 (2002) 6003-6008. [26] C.M. Criss, J.W. Cobble, The thermodynamic properties of high temperature aqueous solutions. I. standard partial molal heat capacities of sodium chloride and barium chloride from 0 to 100 0, J. Amer. Chem. Soc. 83(15) (1961) 3223-3228. [27] J.O. Hutchens, A.G. Cole, J.W. Stout, Heat capacities from 11 to 3050 K, entropies, and free energies of formation of L-valine, L- isoleucine, and L-leucine, J. Phys. Chem. 67 (1963) 11281130.
360
350
_ -1 -1 Cp 2, J mol K
340
330
320
310
300
290
280
290
300
310
320
330
T, K
Fig. 1. The comparison of standard partial molal heat capacities C p
0 2
of L-valine in water computed
from Eqs. (1-3) () with those determined via the extrapolation of apparent molar heat capacities to an infinite dilution (empty symbols): – the data of [17], - [18], - [19], - [20]; ▲ – this value was obtained from the temperature dependence of the enthalpy of solution of [16].
260
280
300
320
340
360 0,016
16 0,015
14 12
0,014
6
0,012
0
solY , kJ mol
0,013 8
4 0,011
X, mol farctions
-1
10
2 0,010
0 -2
0,009
-4 0,008 260
280
300
320
340
360
T, K Fig. 2. Thermodynamic functions of solution of L-valine in water: points are experimental values; lines are a calculation according to Eqs. (4-7). Left-hand scale: experimental free energies () [21] and enthalpies () of solution; dotted line gives the entropic term (-T∆solS0). Right-hand scale: calculated (solid line) and experimental () solubility values of L-valine in water [21].
Table 1 Experimental (solHm/kJ mol-1) and standard (solH0/kJ mol-1) enthalpies of solution of L-valine in water 298.15 K
298.15 K
308.15 K
mVala
∆solHm
∆solH0
∆solH0
0.00401
3.00
3.09±0.04b (this work)
4.590.06 (this work)
0.00593
3.00
0.01025
3.01
3.10±0.17 [12]
4.43±0.15 [16]
0.00652
3.04
3.12±0.07 [13]
0.00467
3.05
3.15±0.01 [14]
0.00694
3.06
3.15±0.01 [15]
0.00743
3.07
3.00±0.14 [16]
0.00399
3.09
0.00539
3.11
0.00456
3.12
0.00101
3.14
0.00360
3.15
0.00409
3.17
0.00533
3.22
a
From here on mVal denotes valine molality, mol kg-1.
b
Uncertainties represent the twice standard deviation of the mean ± 2
(x
m
xi ) 2 / n(n 1) .
The experimental pressure is 101.33 kPa. Standard uncertainties for temperature, pressure and molality are u(T)=±0.01 K, u(p)=±0.5 kPa and u(mVal)=±1.10-5mol kg-1, respectively.
Table 2 Experimental (solHm/kJ mol-1) and standard (solH0/kJmol-1) enthalpies of solution of L-valine in water at different temperatures mVal
solHm
T = 279.15 K
mVal
solHm
T = 283.15 K
mVal
solHm
T = 288.15 K
0.00476
0.28
0.00318
0.91
0.00343
1.39
0.00302
0.28
0.00360
0.92
0.00508
1.45
0.00430
0.30
0.00366
0.94
0.00452
1.45
0.00461
0.31
0.00219
0.96
0.00298
1.46
solH0 = 0.290.02
solH0 = 0.930.02
solH0 = 1.440.03
7.24 T = 293.15 K
6.31 T = 303.15 K
T = 308.15 K
0.00381
2.10
0.00128
3.51
0.00734
4.52
0.00317
2.12
0.00812
3.55
0.00811
4.57
0.00482
2.18
0.00473
3.62
0.00124
4.59
0.00362
2.18
0.00574
3.67
0.00922
4.67
solH0 = 2.150.04
solH0 = 3.590.07
solH0 = 4.590.06
T = 313.15 K
T = 318.15 K
T = 323.15 K
0.00923
5.29
0.00151
6.01
0.00121
7.11
0.02111
5.40
0.00541
6.07
0.00416
7.16
0.01700
5.52
0.00497
6.08
0.00422
7.19
0.00217
5.53
0.00413
6.12
0.00340
7.21
solH0 = 5.440.11
solH0 = 6.070.05
solH0 = 7.170.04
Uncertainties for the experimental quantities represent the twice standard deviation of the mean. The experimental pressure is 101.33 kPa. Standard uncertainties for temperature, pressure and molality are u(T)=±0.01 K, u(p)=±0.5 kPa and u(mVal)=±1.10-5mol kg-1, respectively.
S0040-6031(17)30275-7 https://doi.org/10.1016/j.tca.2017.10.020 TCA 77862
To appear in:
Thermochimica Acta
Received date: Revised date: Accepted date:
5-7-2017 17-10-2017 23-10-2017
Please cite this article as: Olga A.Antonova, Valery P.Korolev, Andrey V.Kustov, Thermodynamics of solution of L-valine in water, Thermochimica Acta https://doi.org/10.1016/j.tca.2017.10.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Thermodynamics of solution of L-valine in water Olga A. Antonova*, Valery P. Korolev and Andrey V. Kustov Krestov Institute of Solution Chemistry, Russian Academy of Sciences, 1, Academicheskaya str., 153045, Ivanovo, Russia, Ivanovo State University of Chemistry and Technology, 7, Sheremetevsky av., 153000, Ivanovo, Russia *Corresponding author: United Physical-Chemical Centre, Institute of Solution Chemistry, Russian Academy of Sciences, 1, Academicheskaya str., 153045, Ivanovo, Russia E-mail address: [email protected] (Olga Antonova) Graphical abstarct 260
280
300
320
340
360 0.016
16
Water - L-Valine 14
0.015
0
solG 12
0.014
-1
0 -TsolS
0.013
6
0.012
0
solY , kJ mol
8
4 0.011 2
0
solH
0.010
0 -2
0.009
Solubility -4
0.008 260
280
300
320
T, K
340
360
X, mol farctions
10
Highlights Enthalpies of L-α-valine solution in water were measured from T=279 to T=323 К Thermodynamic functions and solubility at different temperatures were estimated The prediction agrees well with experimental solubility values
ABSTRACT This paper focuses on the accurate thermodynamic study of solution of L-valine in water in a wide temperature range. Enthalpies of solution of L-valine in water have been calorimetrically determined between T=279 K and T=323 К. Standard enthalpies and heat capacities of solution as well as standard partial molal heat capacities have been calculated and compared with available literature values. The free energy of solution and its enthalpic and entropic terms have been computed using the combination of solubility and calorimetric data via the Gibbs-Helmholtz equation from T=280 K to T=360 K. The temperature dependence of solubility of the amino acid has been also computed and compared with experimental quantities. The satisfactory agreement is found between experimental and predicted solubility values.
Keywords: L-Valine Water Calorimetry Thermodynamics of solution Solubility Prediction 1. Introduction
A major problem of protein chemistry is the determination of the factors which contribute to peculiarities of protein folding and enzyme-substrate interactions in a water-like environment. Proteinwater interactions are important factors that are responsible for stabilizing the native structure of globular proteins. Amino acids and simple peptides are usually used for modeling such interactions in the hope that these investigations should provide a better insight into various aspects of protein stability and biosynthesis. During last several years we have been involved in an intensive and continuing study dealing with the thermodynamic behavior of amino acids in water at different temperatures [1-5]. Enthalpies, free energies, entropies and heat capacities of solution and transfer from water to its mixtures with urea, alcohols or glycols have been obtained and discussed in terms of solute-non-electrolyte pair and triplet interactions occurring in highly diluted solutions [6-9]. Another important point which has been briefly addressed is that for slightly soluble biological species is well
justified to compute temperature changes of thermodynamic functions and solubility values via simple integration of the Gibbs-Helmholtz equation using the temperature dependence of standard enthalpies of solution and the solubility value at the reference temperature [10,11]. Here we extend this approach towards L-valine which is known to be an essential amino acid that cannot be synthesized inside a human body. It is also important that L-valine is more soluble in water than previously studied aromatic amino acids that may require to take into account solute-solute interactions in a saturated solution that can induce the deviation of activity coefficients from unity. Thermodynamic studies of aqueous L-valine solutions are rather scarce. Solution and dilution enthalpies have been obtained at 298 K [12-15] and also at 308 K [16]. Partial molar heat capacities of aqueous L-valine solutions have been obtained from direct heat capacity measurements at 298 K [1719] and also within the narrow temperature range of 288-328 K [20]. The results [20] clearly indicate
that the C p
0 2
values moderately increase with the temperature. We have also found several sources
[21-23] of solubility values of L-valine in water which are in a satisfactory agreement with each other. The present study focuses on the experimental determination of enthalpies of solution of the amino acid both in cold and hot water to compute standard enthalpies, heat capacities of solution and partial molar heat capacities. The combination of calorimetric data with a solubility value at the standard temperature is used to compute free energies and entropies of solution in a wide temperature range via integration of the Gibbs-Helmholtz equation and also to predict the temperature dependence of the amino acid solubility in water.
2. Experimental
2.1. Chemicals L-α-valine (for biochemistry, Merk KGaA, Germany, initial mass fraction >0.990) was dried under reduced pressure for several days at 343 K and then used without further purification. Water was distilled twice.
2.2. Apparatuses and methods
Calorimetric measurements were carried out with a precise isoperibol calorimetric system fitted here with the 60 cm3 titanium vessel. The description of the apparatus and methodology of measurements were presented in detail several times [1,10]. The temperature sensitivity of the calorimeter was of 10-5 K and the temperature stability of the thermostat was better than 10-3 K. The accuracy of the measurements was estimated to be within 1%.
3. Results
Experimental enthalpies of solution of L-valine were determined in the range of solute molalities from m = 0.003 mol kg-1 to m = 0.03 mol kg-1. Table 1 illustrates enthalpies of solution of L-valine in water at 298 and 308 K. As can be seen the solHm values do not depend on molality for the concentration range studied. Thus, the standard enthalpy of solution or the enthalpy of solution at infinite dilution can be easily computed as the mean value in the range of the experimental enthalpies of solution for each temperature [1,3,10]. We see from Table 1that the agreement between our results and standard enthalpies of solution for L-valine reported elsewhere [12-14,16] is very good.
4. Discussion Tables 1, 2 give the solH0 values for L-valine in water at different temperatures. The temperature dependence of enthalpies of solution is found to fit quite enough to well-known the second-order polynomial [1,4,10]: ΔsolH0 = 2.95(0.06) + 0.151(0.003) (T-298.15) + ½ 0.00128(0.0004) (T-298.15)2,
(1)
R = 0.9994, sf = 0.11 kJ mol-1, where the first term is the enthalpy of solution at the reference temperature of 298 K, the second one is the heat capacity of solution and the third term is its temperature derivative; values in brackets give the standard deviation of the mean. Eq. (1) shows that the heat capacity of solution is positive and slightly increases with the temperature as it is observed for aromatic amino acids such as L-histidine, L-phenylalanine or Ltryptophan [1,2,10]. The heat capacity of solution ΔC0p is known to be the well-established parameter of hydrophobicity [24]. This quantity at the reference temperature (151 J/(mol K))is slightly lower than the ΔC0p value for hydrophobic L-phenylalanine [2,4] or L-tryptophan [10] but three times as larger as the heat capacity of solution for L-histidine [1,4] which contains several hydrophilic centers in its side-chain. It is found that the ΔC0p value increases in the following order: L-glycine, L-alanine [3], L-valine, tryptophan [10], and L-phenylalanine [4], which is in fair agreement with the behaviour of the hydrophobicity parameter of amino acids [25]. Such heat capacity values are usually associated with increasing the number of nearly straight and shorter water-water hydrogen bonds and decreasing the population of more bent H-bonds in the nearest vicinity of non-polar groups. This phenomenon induces increasing energy fluctuations in the hydrophobic hydration shell that results in large and positive heat capacity values [24].
0
To calculate standard partial molar heat capacities C p 2 , we exploit the integral enthalpies of solution method [26] and heat capacity values from Eq. (1):
Cp
0 2
= ΔC0p + Cp cr,
where Cp cr – the heat capacity of crystalline L-valine [27].
(2)
The Cp
cr
- f(T) curve in the range of temperatures of 250-300 K [27] is well described by the
following linear equation: Cp cr = (168.74±0.13) + (0.464±0.005) (T-298.15), R = 0.9996, sf = 0.24 J mol-1 K-1
(3)
The combination of heat capacities of solution obtained with from Eq. (1) and Cp
cr
values
calculated with Eq. (3) results to the following expression for partial molal heat capacities: C p
0 2
=
319.74 + 1.744 (T-298.15). This gives 320 J mol-1 K-1 for the standard partial molar heat capacity of
L-valine in water at 298 K. This quantity is in a good agreement with C p
0 2
values obtained from the
extrapolation of apparent molar heat capacities to an infinite dilution: 307±6 [17], 308±1 [18], 302±1 [19], 306 J mol-1 K-1 [20]. Similarly, we have calculated standard partial molar heat capacities of Lvaline in water at different temperatures. Fig. 1 compares our results with available heat capacity
values. The agreement is found to be rather good in cold water. However, our C p
0 2
values reveal a
stronger temperature dependence that leads to larger heat capacity values at elevated temperatures. Recently, we have shown that for slightly soluble species such as porphyrins [11] or aromatic amino acids [10] it is reasonable to compute thermodynamic functions of solution using the temperature dependence of standard enthalpies and a solubility value at any reference temperature, where activity coefficients are expected to approach to the unity:
ln
T sol H 0 X (T ) 1 dT , X (298.15) R 298.15 Т 2
(4),
where X is the mole fraction of the solute in a saturated solution. However, solubility of L-valine in water is larger than for aromatic amino acids such as Lphenylalanine or L-histidine. Hence, Eq. (1) should be rewritten to take into account the deviation of activity coefficients from the unity:
sol H 0 X (T ) 1 T ln dT ln 2 X (298.15) R 298.15 Т T
,
(5)
298.15
where the last term is the logarithm of the ratio of L-valine activity coefficients at the current and reference temperatures. If this ratio approaches to the unity in the temperature range studied, this term can be omitted and Eq. (1) should predict the temperature dependence of solubility with a good accuracy. We have mentioned above that there are several sources of solubility values of L-valine in water [21-23] which are in a satisfactory agreement with each other. Using the solubility value of X =0.0086 mol fractions at 293 K [21] and Eq. (4), we have predicted the temperature dependence of solubility of L-valine in water and compared these quantities with experimental ones [21]. Fig. 2 illustrates that there is a good agreement between experimental and computed solubility values. The largest deviation does not exceed 0.0007 mol fractions, which leads to the
T
/ 293.15
ratio of 0.93. It indicates that
activity coefficients are only slightly deviate from the unity and free energy of solution and entropic terms can be estimated as in our previous studies [10,11] as follows: solG0 RT ln(1/X)
(6)
-TsolS0 = solG0 - solH0
(7)
Fig. 2 gives experimental and computed thermodynamic functions of L-valine solution in water at different temperatures. The agreement between both sets of quantities is seen to be excellent. The free energy of solution depends slightly on the temperature and the solG0 vs T curve passes through a broad maximum at 350 K. The enthalpic and entropic terms (-TsolS0) change gradually with the temperature. These functions intersect each other at 318 K giving solH0 = (-TsolS0). Both terms are rather small and positive in the middle temperature range. The enthalpy of solution of L-valine becomes negative al low temperatures leading to -TsolS0 = solG0 nearby the temperature of maximal density of water. In contrast, the entropic term changes its sign at elevated temperatures favouring the amino acid transfer from a solid state to a liquid phase.
5. Conclusions
This study focuses on the accurate thermodynamic analysis of L-valine aqueous solutions in a wide temperature range. Enthalpies of solution of L-valine in water have been calorimetrically determined between T = 279 and T = 323 К. Standard enthalpies and heat capacities of solution as well as standard partial molal heat capacities were calculated and compared with available literature values. Our results clearly indicate that both for slightly soluble aromatic amino acids and some aliphatic amino acids it is well justified to compute the temperature dependence of thermodynamic functions of solution via integration of the Gibbs-Helmholtz equation (see Eq. (4)). This approach also provides a simple way to predict quantitatively or at least semi quantitatively solubility values for many biologically active species in a wide temperature range.
References
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[15] X. Wang, Y. Guo, Q. Zheng, R. Lin, Transfer enthalpies of amino acids and glycine peptides from water to aqueous solutions of trimethylamine N-oxide at 298.15 K, Thermochim. Acta. 587 (2014) 48-51. [16] A.K. Mishra, J.C. Ahluwalia, Enthalpies, heat capacities and apparent molal volumes of transfer of some amino acids from water to aqueous t-butanol, J. Chem. Soc. Faraday Trans. I. 77 (1981) 1469-1483. [17] C.H. Spink, I. Wadsö, Thermochemistry of solutions of biochemical model compounds. 4. The partial molar heat capacities of some amino acids in aqueous solution, J. Chem. Thermodyn. 7 (1975) 561-572. [18] G. DiPaola, B. Belleau, Apparent molal heat capacities and volumes of amino acids in aqueous polyol solutions, Can. J. Chem. 56 (1978) 1827-1831. [19] C. Jolicoeur, B. Riedl, D. Desrochers, L.L. Lemelin, R. Zamojska, O. Enea, Solvation of amino acid residues in water and urea-water mixtures:volumes and heat capacities of 20 amino acids in water and in 8 Molar urea at 250 C, J. Solut. Chem. 15 (1986) 109-128. [20] M.M. Duke, A.W. Hakin, R.M. McKay, K.E. Preuss, The volumetric and thermochemical properties of aqueous solutions of L-valine, L-leucine, and L-isoleucine at 288.15, 298.15, 313.15, and 328.15 K, Can. J. Chem. 72 (1994) 1489-1494. [21] Chuntao Zhang, Bangyu Liu, Xin Wang, Hairong Wang, Haitao Zhang, Measurement and correlation of solubility of L-valine in water + (ethanol, N,N-dimethylformamide, acetone, isopropyl alcohol) from 293.15 K to 343.15 K, J. Chem. Eng. Data. 59(9) (2014) 2732–2740. [22] G.D. Fasman, Handbook of biochemistry and molecular biology, 3rd ed. Physical and chemical data, CRC Press: Cleveland, v1, 1976. [23] I. Kurosawa, A.S. Teja, R.W. Rousseau, Solid-liquid equilibria in L-leucine + L-valine + water. Fluid Phase Equilibria. 228-229 (2005) 83-87. [24] B. Madan, K. Sharp, Heat Capacity Changes Accompanying Hydrophobic and Ionic Solvation: A Monte Carlo and Random Network Model Study, J. Phys. Chem. 100 (1996) 7713-7721. [25] B. Palecz, Enthalpic homogeneous pair interaction coefficients of L-α-amino acids as a hydrophobicity parameter of amino acid side chain, J. Amer. Chem. Soc. 124 (2002) 6003-6008. [26] C.M. Criss, J.W. Cobble, The thermodynamic properties of high temperature aqueous solutions. I. standard partial molal heat capacities of sodium chloride and barium chloride from 0 to 100 0, J. Amer. Chem. Soc. 83(15) (1961) 3223-3228. [27] J.O. Hutchens, A.G. Cole, J.W. Stout, Heat capacities from 11 to 3050 K, entropies, and free energies of formation of L-valine, L- isoleucine, and L-leucine, J. Phys. Chem. 67 (1963) 11281130.
360
350
_ -1 -1 Cp 2, J mol K
340
330
320
310
300
290
280
290
300
310
320
330
T, K
Fig. 1. The comparison of standard partial molal heat capacities C p
0 2
of L-valine in water computed
from Eqs. (1-3) () with those determined via the extrapolation of apparent molar heat capacities to an infinite dilution (empty symbols): – the data of [17], - [18], - [19], - [20]; ▲ – this value was obtained from the temperature dependence of the enthalpy of solution of [16].
260
280
300
320
340
360 0,016
16 0,015
14 12
0,014
6
0,012
0
solY , kJ mol
0,013 8
4 0,011
X, mol farctions
-1
10
2 0,010
0 -2
0,009
-4 0,008 260
280
300
320
340
360
T, K Fig. 2. Thermodynamic functions of solution of L-valine in water: points are experimental values; lines are a calculation according to Eqs. (4-7). Left-hand scale: experimental free energies () [21] and enthalpies () of solution; dotted line gives the entropic term (-T∆solS0). Right-hand scale: calculated (solid line) and experimental () solubility values of L-valine in water [21].
Table 1 Experimental (solHm/kJ mol-1) and standard (solH0/kJ mol-1) enthalpies of solution of L-valine in water 298.15 K
298.15 K
308.15 K
mVala
∆solHm
∆solH0
∆solH0
0.00401
3.00
3.09±0.04b (this work)
4.590.06 (this work)
0.00593
3.00
0.01025
3.01
3.10±0.17 [12]
4.43±0.15 [16]
0.00652
3.04
3.12±0.07 [13]
0.00467
3.05
3.15±0.01 [14]
0.00694
3.06
3.15±0.01 [15]
0.00743
3.07
3.00±0.14 [16]
0.00399
3.09
0.00539
3.11
0.00456
3.12
0.00101
3.14
0.00360
3.15
0.00409
3.17
0.00533
3.22
a
From here on mVal denotes valine molality, mol kg-1.
b
Uncertainties represent the twice standard deviation of the mean ± 2
(x
m
xi ) 2 / n(n 1) .
The experimental pressure is 101.33 kPa. Standard uncertainties for temperature, pressure and molality are u(T)=±0.01 K, u(p)=±0.5 kPa and u(mVal)=±1.10-5mol kg-1, respectively.
Table 2 Experimental (solHm/kJ mol-1) and standard (solH0/kJmol-1) enthalpies of solution of L-valine in water at different temperatures mVal
solHm
T = 279.15 K
mVal
solHm
T = 283.15 K
mVal
solHm
T = 288.15 K
0.00476
0.28
0.00318
0.91
0.00343
1.39
0.00302
0.28
0.00360
0.92
0.00508
1.45
0.00430
0.30
0.00366
0.94
0.00452
1.45
0.00461
0.31
0.00219
0.96
0.00298
1.46
solH0 = 0.290.02
solH0 = 0.930.02
solH0 = 1.440.03
7.24 T = 293.15 K
6.31 T = 303.15 K
T = 308.15 K
0.00381
2.10
0.00128
3.51
0.00734
4.52
0.00317
2.12
0.00812
3.55
0.00811
4.57
0.00482
2.18
0.00473
3.62
0.00124
4.59
0.00362
2.18
0.00574
3.67
0.00922
4.67
solH0 = 2.150.04
solH0 = 3.590.07
solH0 = 4.590.06
T = 313.15 K
T = 318.15 K
T = 323.15 K
0.00923
5.29
0.00151
6.01
0.00121
7.11
0.02111
5.40
0.00541
6.07
0.00416
7.16
0.01700
5.52
0.00497
6.08
0.00422
7.19
0.00217
5.53
0.00413
6.12
0.00340
7.21
solH0 = 5.440.11
solH0 = 6.070.05
solH0 = 7.170.04
Uncertainties for the experimental quantities represent the twice standard deviation of the mean. The experimental pressure is 101.33 kPa. Standard uncertainties for temperature, pressure and molality are u(T)=±0.01 K, u(p)=±0.5 kPa and u(mVal)=±1.10-5mol kg-1, respectively.