Effect of temperature on the partial molar volumes and the partial molar compressibilities of α-amino acids in water and in aqueous solutions of strong electrolytes Diana M. Rodrígueza, Carmen M. Romeroa1. a
Departamento de Química, Universidad Nacional de Colombia. Bogotá, Colombia
Abstract Density and sound velocity of glycine, alanine, α-aminobutyric acid, norvaline and norleucine in water and in aqueous solutions of strong electrolytes have been determined in the temperature range from 293.15 to 313.15 K at intervals of 5 K. The electrolytes used are lithium chloride, sodium chloride, potassium chloride, ammonium sulfate and sodium sulfate. The apparent molar volumes and the apparent molar compressibilities were determined as a function of composition at each temperature from the experimental density and sound velocity data. The limiting values of the partial molar volumes and the partial molar adiabatic compressibilities at infinite dilution of the amino acids in water and in aqueous electrolyte solutions were obtained at each temperature. The results confirm that glycine and alanine behave as hydrophilic solutes while aminobutyric acid, norvaline and norleucine exhibit a hydrophobic behavior and this behavior is also observed in the presence of salts. The addition of electrolytes led to an increase of the partial molar volumes and the partial molar compressibilities at infinite dilution suggesting that the cations and anions of the salts interact directly with the zwitterionic group of the α-amino 1
Corresponding autor: Carmen M. Romero. E-mail:
[email protected]. Departamento de Química, Universidad Nacional de Colombia. Calle 44 # 45-67 Bloque B9, Bogotá, Cód. Postal 111311 - Colombia. Phone: 57 1 3165440. Fax (571) 3165220
1
acids, removing water molecules from hydration sphere of the amino acids, therefore reducing their hydration number. The decrease of hydration number reflects a decrease of electrostriction which leads to an increase of the partial molar properties. The results suggest that the dehydrating ability of the salts used show a very good agreement with the increase of the partial molar volume as well as the partial molar compressibility of the αamino acids. Keywords: partial molar volume; partial molar compressibility; α-amino acids; electrolytes; solute-solvent interactions.
1.
Introduction
Amino acids are essential molecules for life: they are the constituent monomers of proteins, and they are part of essential processes in organisms such as cell signaling and regulation of gene expression. -Amino acids in water adopt a zwitterionic form in which is the amine group is protonated
while the carboxyl group is deprotonated, thus the molecule has a zero net charge. Therefore, amino acids can be considered as mixed solutes containing highly hydrophilic groups (amine and carboxyl) and the hydrophobic aliphatic chain. These facts, combined with their biological importance, make the study of the thermodynamic properties of these compounds very interesting and relevant in aqueous solvents, where biological processes occur. The presence of electrolytes has an important effect in the stability and behavior of proteins in aqueous solutions and some authors assume that this is a consequence of their
2
interaction with the peptide groups. However, there is not a general and consistent explanation about the behavior of these molecules in aqueous electrolyte solutions. [1–4]. Amino acids have been considered model compounds that provide useful information to understand the behavior of proteins and the role of solvent structure in the stability of the macromolecules. In fact, apparent molar volumes and the apparent molar compressibilities of these compounds in water are very sensitive to solute-solvent interactions and thus they have been used to provide an insight about hydration properties and solute-solvent interactions[5–10]. Several studies have been reported on the volumes and compressibilities of amino acids in aqueous electrolyte solutions [1,11–16], showing that the addition of salts affects the interaction between the zwitterionic group and the water; in the case of strong electrolytes, this is reflected in positive transfer volumes and compressibilities.
As a continuation of earlier works on the thermodynamic properties of amino acids in aqueous solution [9,17–20], in the actual study we present the partial molar volumes and the partial molar compressibilities of glycine, alanine, α-aminobutyric acid, norvaline and norleucine in water and in aqueous solutions of lithium chloride, sodium chloride, potassium chloride, ammonium sulfate and sodium sulfate at temperatures of (293.15, 298.15, 303.15, 308.15 and 313.15) K, this temperatures were selected since biological systems are of special interest in our group research, therefore a small range of temperatures close to the common body temperature is desired. The α-amino acids were selected because they have a lineal hydrocarbon chain that increases its length by one methylene group, as can be seen in Table 1, allowing the application of additivity approaches to the partial molar volumes and the partial molar compressibilities at infinite
3
dilution. The electrolytes used are commonly found in living organisms, so the mixed solvents used here could simulate the natural environment in which amino acids and other biomolecules are present. Most studies on the thermodynamic properties of amino acids in aqueous solutions have been done on naturally occurring amino acids at 298.15 K, however, very few data are reported in literature for amino acids such as norvaline and norleucine which have a linear hydrocarbon chain, especially at temperatures different from 298.15 K [1,9,21]. In this work, the influence of the temperature on the behavior of the partial molar properties of the five α-amino acids in water and in aqueous solutions of the electrolytes has been used to obtain information about the effect of the salts on solute hydration.
2. Materials and methods 2.1. Materials The characteristics of the reagents used are presented in Table 1. The mass fraction purity is reported according to the certificates of analysis. Amino acids and salts were used without further purification. They were dried under vacuum at room temperature and kept in a desiccator at least 48 h before use. Water was purified using a Barnstead Easy-Rodi DI 3321 system and degassed before use; the resulting water showed a conductivity less than 1.5 S·m-1 [22,23]. All solutions were prepared by weight using a Mettler balance AT-261 dual range with readability of 1·10-5 g and reproducibility better than 1·10-4 g in the lower range. The concentration of the electrolyte aqueous solutions used as solvents was the same; the selected molality was 0.1500 mol·kg-1. 4
2.2. Methods Densities and sound velocities of the aqueous solutions were measured using a vibrating Utube densimeter, Anton Paar DSA 5000, with a working frequency of 3 MHz and temperature control better than 0.002 K, according to the manufacturer's specifications. The densimeter was calibrated with dry air and purified water at 293.15 K. Density and sound velocity reported data are the average of three independent measurements that were reproducible within 1·10-3 kg·m-3 and 3·10-2 ms-1, respectively, with an uncertainty of 0.150 kg·m-3 for density and 2 ms-1 for sound velocity. The apparent molar volumes V were calculated from the density experimental data using equation (1): (
)
(1)
where M is the molar mass of the α-amino acid, m its molal concentration in the aqueous solution, and
o
is the density of the solvent (either pure water or electrolyte aqueous solution)
is the solution density.
The apparent molar compressibilities, K, of the amino acid in water and in the aqueous solutions of electrolytes were determined, respectively, from the density , and the isentropic compressibility S, of the corresponding solution using the equation
(2)
5
where So is the isentropic compressibility of the solvent. The isentropic compressibilities
S of the aqueous solution at each temperature were calculated from both the sound speed, u, and density measurements by means of the Newton-Laplace equation[24].
S = 1/ ρu2
(3)
The values of density and the isentropic compressibility of water at each temperature, used in calibration were taken from the literature [25,26]. Experimental uncertainties were determined using the method described by Andraos [27]. The uncertainty of the molar properties at infinite dilution was assumed to be equal to those of the most diluted solutions, which presented the biggest error in weighing. 3. Results and discussion Data for density compressibilities
, sound velocity u, apparent molar volumes
and apparent molar
at temperatures of (293.15, 298.15, 303.15, 308.15 and 313.15) K of
the amino acids in water and in the mixed solvents is presented in the supporting material of this paper. The values obtained in this work for the properties of the aqueous solutions of electrolytes used as mixed solvents, are in good agreement with previously published values [14,28–31]. 3.1 Partial Molar Volumes The dependence of the apparent molar volumes of the α-amino acids with the molality at the selected temperatures was fitted by a least squares method to a second order polynomial equation. The value for the apparent molar volume at infinite dilution, which is equal to the partial molar one, ̅ , was obtained by extrapolation. In all cases the apparent molar 6
volume of the α-amino acids in water and in the mixed solvents increases with the concentration. Table 2 shows the partial molar volumes at infinite dilution of the α-amino acids at the selected temperatures; as can be seen, good agreement is found between the results obtained in this work and the values reported in literature. The apparent molar volumes of the α-amino acids in electrolyte aqueous solutions as a function of molality were adjusted using the least squares method to second order polynomial equation; the values of the partial molar volume at infinite dilution obtained by extrapolation are presented in Tables 3 – 7 as well as the partial molar volumes of transfer, defined by Equation 4. ̅
̅
Where, ̅ ̅
̅
(4)
is the partial molar volume of the amino acid in the mixed solvent, and
is the partial molar volume of the amino acid in water ̅
is the partial molar
volume of transfer. Figure 1 shows the partial molar volume of glycine in water and in the salt solutions at the five temperatures of study. It is clear that in all the mixed solvents the value of ̅ is larger than the result in obtained in water and this behavior is the same for all five α-amino acids. According to the co-sphere overlap model [32], the interaction between two ions results in positive values of ̅ negative ̅
, while interactions between a hydrophobic group and an ion give
. Tables 3 – 7 show that in all cases the addition of salts yields positive
values of partial molar volumes of transfer, indicating that the interaction between the zwitterionic group of the amino acids and the hydrated cations and anions of the salts is
7
predominant. Moreover, it is observed that for all five α- amino acids, the effect of the salt over the partial molar volumes follows the order indicated below: ̅
LiCl < ̅
KCl < ̅
NaCl < ̅
(NH4)2SO4 < ̅
Na2SO4
The observed trend is related with the Hofmeister’s series, which is an empiric organization of the ability of the ions to stabilize proteins[33]. It has been found that strongly hydrated anions (such as PO42- and SO42-) and weakly hydrated cations (Ca2+ and Al3+) have a stabilizing effect since they attract water molecules from the hydration sphere of the protein to hydrate themselves, minimizing the hydrophobic interaction. Knowing that amino acids are the constituents units of proteins, it is expected that the same dehydration ability of the ions take place in the systems of this study; thus it could be |proposed that the presence of the salts in solution leads to loose water from the hydration sphere of the amino acids, decreasing the electrostriction and therefore increasing the partial molar volume of the solutes. In order to analyze if the partial molar volume at infinite dilution can be described in terms of group contributions according to a methylene additivity approach based on the dependence of the property on the number of carbon atoms or the number of methylene groups, the partial molar volume at infinite dilution of the amino acids in water and in the mixed solvents was represented by the following equation: V20 V20 ( NH3 , COO ) nV20 (CH 2 )
(5)
Where n represents the number of methylene groups, V20 (CH 2 ) and V20 ( NH3 , COO ) are the volumetric contributions of the methylene, and the amino and carboxylic groups to the partial molar volume of the amino acid; the contribution of the methylene group comprises 8
also the contribution for the hydrogen atom at the end of alkyl. According to Hakin, the number of carbon atoms is approximately equivalent to the number of methylene groups [6,8,34]. The dependence of the partial molar volumes at infinite dilution with the number of methylene groups is well represented by linear equations with the form of equation (5). The group contributions of the methylene and the polar groups are listed in Table 8. As the temperature becomes larger the volumetric contributions ̅
and ̅
increase; the values of the methylene group contribution in water at 298.15 K determined in this work (15.98 cm3 mol-1) agree well with other authors like Millero (15.90 cm3 mol-1)[6] and Mallick (16.11 cm3 mol-1)[35]. It is very interesting that the contribution of the methylene group is smaller in the mixed solvents than in water and it is almost the same no matter the nature of the salt used as cosolute. On the other hand, the polar group contribution is significantly larger in the presence of the electrolytes and the same trend found with the partial molar volumes of transfer is observed with this contribution. This fact enhances the previous observation that the interaction between the zwitterionic group and the ions is dominant over the hydrophobic interaction and that the ion-ion interaction dehydrates the α-amino acid depending on the hydration of the cations and anions of the electrolytes. The partial molar expansibility (Equation 6) of the α-amino acids in water and in the mixed solvents was calculated and the values obtained are shown in Table 9. ̅
̅
(6)
9
The dependence of the partial molar volumes of the amino acids in both water and in the mixed solvents is linear, which is probably a result of the narrow range of temperatures of the study; therefore, the partial molar expansibilities obtained are constant showing that for the systems considered they do not depend on temperature. It can be seen that there are no significant changes in the values of ̅
due to the addition of salts, which led us to
conclude that the concentration of the electrolytes is no enough to shift the relationship between the partial molar volume and the temperature.
3.2 Partial molar compressibility The dependence of the apparent molar compressibilities of the α-amino acids with molality was fitted at all temperatures by a least squares method to second order polynomial equation. The partial molar compressibilities at infinite dilution ̅
obtained by
extrapolation are shown in Table 10. The partial molar compressibilities of the amino acids in water at all temperatures are negative and become larger as the number of methylene groups of the non-polar chain of the amino acid increases. Table 11 shows comparison between our data and the data reported by other authors at 298.15 K. The compressibilities at infinite dilution become less negative as the temperature increases. The dependence of the partial molar compressibilities of the α-amino acids with temperature is well represented by a second order polynomial equation (Equation 7), indicating that ̅
is more sensitive to the changes of temperature than ̅ , since ̅ ⁄
depends on temperature while ̅
is a constant.
10
̅
(7)
In order to study the effect of temperature, we plotted
̅ ⁄
and ̅
as functions of the
number of methylene groups as shown in Figure 2. Until 303.15 K these curves have similar shapes with a minimum in alanine. This results are pretty alike to those found by Chalikian[36] for α,ω-amino acids which show a minimum for γ-amino butyric acid. The data found confirm the previous discussion about the hydrophilic behavior of glycine and alanine, since the change of the partial molar compressibility due to temperature and
̅ ⁄
̅ ⁄
decreases as the carbon chain increases, while for AABA, norvaline and
norleucine as the number of methylene groups become larger, an increase of the values of ̅ ⁄
y ̅ ⁄
, is observed, indicating the importance of hydrophobic interactions. In
the case of (308.15 and 313.15) K, the minimum moves from alanine to AABA, which could mean that the contribution of hydrophilic group becomes larger as the temperature increase, however we don’t have an explanation for this result. Tables 12 – 16 show the partial molar compressibilities at infinite dilution of the α-amino acids in the mixed solvents, as well as the partial molar compressibilities of transfer, defined by Equation 8. ̅ Where ̅
̅
̅
(8)
is the partial molar compressibility of transfer, ̅
is the partial molar
compressibility of the amino acid in the mixed solvent, and ̅
is the partial molar
compressibility of the amino acid in water.
11
In all cases the partial molar compressibilities of transfer are positive as expected since the electrostriction decreases, leading to a rise of the partial molar volume producing an increase of the partial molar compressibilities of the amino acids. The highest effect on the partial molar compressibilities of transfer is due to Na2SO4 and the effect of the salts can be represented in the following way: ̅
LiCl < ̅
KCl < ̅
NaCl < ̅
(NH4)2SO4 < ̅
Na2SO4
The trend follows the same behavior observed for the partial molar volumes of transfer. The hydration numbers, nH, of the amino acids in water and in the mixed solvents, were determined using the model proposed by Millero [6] and they are presented in Table 16. According to the model, the partial molar volume of an amino acid ̅
can be obtained
using Equation 9. ̅
̅
̅
Where ̅
(9)
is the intrinsic partial molar volume of the amino acid and ̅
is the
electrostriction partial molar volume due to the hydration of the amino acid. The decrease in volume due to electrostriction can be related to the number of water molecules (nH) hydrated to the amino acid: ̅
̅
̅
(10)
̅ is the molar volume of electrostricted water and ̅ is the molar volume of bulk water. The hydration numbers, nH is determined from equation 11: ̅ ̅
(11)
12
Where
is the isentropic compressibility of the solvent (Equation 3) and ̅ is the molar
volume of water, taken from literature[37]. The results presented in Table 17 reflect the dehydration of the α-amino acids due to the addition of salts; these results explain the positive values of ̅
and ̅
. In all cases
and at all temperatures it was found that: nH Water > nH LiCl > nH NaCl > nH KCl > nH (NH4)2SO4 > nH Na2SO4 This is in agreement with the trend found for the effect of salts on partial molar volumes and partial molar compressibilities at infinite dilution. 4. Conclusions Partial molar volumes and partial molar compressibilities at infinite dilutions were determined for glycine, alanine, aminobutyric acid, norvaline and norleucine in water and in aqueous solutions of electrolytes in the temperature range from 293.15 to 313.15 K. From the behavior in water, we conclude that glycine and alanine are hydrophilic solutes, while interactions between AABA, norvaline and norleucine and water are mainly hydrophobic. The addition of salts produces an increase in the partial molar volumes and compressibilities of the α-amino acids, which suggests that the interaction between the zwitterionic group and the anions and cations of the salt is predominant. This interaction between ions leads to removal of water molecules from the hydration sphere of the amino acids to the bulk, reducing the electrostriction which increases the partial molar properties of the solutes.
13
Using the hydration number of the α-amino acids in water and in the mixed solvent, it can be concluded that the dehydrating ability of anions and cations constituting the salts is directly related to the partial molar volumes and compressibilities of transfer, allowing to order the electrolytes according to their effect on the properties of the amino acids and to relate it to the Hofmeister’s series. 5. Acknowledgements This work was supported by the Universidad Nacional de Colombia and the Instituto Colombiano para el Desarrollo de la Ciencia y la Tecnología. Francisco José de Caldas. COLCIENCIAS. through the YOUNG RESEARCHERS NATIONAL PROGRAM and the Universidad Nacional de Colombia grants DIB: 23605 and 046 – 2015 COLCIENCIAS.
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[28] A.J. Ellis, Partial molal volumes of alkali chlorides in aqueous solution to 200ºC, J. Chem. Soc. Inorg. Phys. Theor. (1966) 1579–1584. [29] A.W. Hakin, M.M. Duke, J.L. Marty, K.E. Preuss, 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, J. Chem. Soc. Faraday Trans. 90 (1994) 2027–2035. [30] F. Millero, F. Vinokurova, M. Fernandez, J.P. Hershey, PVT properties of concentrated electrolytes. VI. The speed of sound and apparent molal compressibilities of NaCl, Na2SO4, MgCl2, and MgSO4 solutions from 0 to 100°C, J. Solution. Chem. 16 (1987) 269–284. [31] F.J. Millero, M. Fernandez, F. Vinokurova, Transitions in the speed of sound in concentrated aqueous electrolyte solutions, J. Phys. Chem. 89 (1985) 1062–1064. [32] F. Franks, Water: A Comprehensive Treatise, Plenum Press, New York, 1973. [33] Hofmeister series. http://www1.lsbu.ac.uk/water/hofmeister_series.html (accessed May 2, 2016). [34] D.P. Kharakoz, Volumetric properties of proteins and their analogues in diluted water solutions. 2. Partial adiabatic compressibilities of amino acids at 15-70ºC, J. Phys. Chem. 95 (1991) 5634–5642. [35] B.C. Mallick, N. Kishore, Partial Molar Volumes of Some of α-Amino Acids in Binary Aqueous Solutions of MgSO4·7H2O at 298.15 K, J. Solution. Chem. 35 (2006) 1441–1451. [36] T.V. Chalikian, A.P. Sarvazyan, K.J. Breslauer, Partial molar volumes, expansibilities, and compressibilities of .alpha.,.omega.-aminocarboxylic acids in aqueous solutions between 18 and 55º C, J. Phys. Chem. 97 (1993) 13017–13026. [37] T.J. Bruno, P.D.N. Svoronos, CRC Handbook of Basic Tables for Chemical Analysis, Third Edition, CRC Press, 2010.
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18
Table 1: Sample description
Source
CAS Number
Purity (mass fraction)
Glycine
Aldrich
56-40-6
>0.98
Alanine
Sigma
56-41-7
>0.99
AABA
Aldrich
2835-81-6
>0.99
Norvaline
Sigma
760-78-1
>0.99
Norleucine
Sigma
327-57-1
>0.99
LiCl
Sigma
7447-41-1
>0.99
NaCl
Merck
7647-14-5
>0.995
KCl
Merck
7447-40-7
>0.995
(NH4)2SO4
Carlo Erba
7783-20-2
0.99
Na2SO4
Merck
7757-82-6
0.99
Name
Lithium chloride Sodium chloride Potassium chloride Ammonium sulfate Sodium sulfate
Chemical Structure
19
Table 2: Partial molar volumes of α-amino acids in water from T = 293.15 to 313.15 K at 75 kPa. ̅
T/K 293.15 298.15 303.15 308.15 313.15 T/K 293.15 298.15 303.15 308.15 313.15
/ Glycine Literature Alanine Literature 42.8[38] 60.01[39] 42.90 60.03 43.3[5] 43.33[40] 60.38 60.41[41] 60.43[6] 43.33 43.89[39] 60.63[39] 43.86 60.72 44.2[10] 60.96[43] 44.31 61.00 44.52[39] 61.20[5] 44.63 61.35 ̅ / Norvaline Literature Norleucine Literature 91.03[9] 106.88[9] 91.06 106.89 91.77 [9] 91.70[7] 107.56 107.58[9] 107.60[5] 91.74 92.21[9] 108.22[9] 92.26 108.25 92.68[21] 108.16[21] 92.76 108.84 -109.20[5] 93.51 109.58
AABA 74.98 75.56 75.92 76.40 77.00
Literature 74.98[9] 75.64[9]75.62[42] 75.89[9] 76.20[10] 77.40[7]
a. (̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality b. u(P) = 1 kPa c. u(T) = 0.01 K
20
Table 3: Partial molar volumes at infinite dilution of α-amino acids in aqueous lithium chloride 0.1500 m and partial molar volumes of transfer from water to the aqueous electrolyte solution from T = 293.15 to 313.15 K at 75 kPa.
T/K
Glycine ̅ /
̅
293.15 298.15 303.15 308.15 313.15
43.19 43.64 44.17 44.57 44.95
0.29 0.31 0.30 0.31 0.31
a. b. c. d.
Alanine / ̅ / 60.25 60.63 60.98 61.25 61.58
T/K
Norvaline ̅ /
̅
293.15 298.15 303.15 308.15 313.15
91.21 91.90 92.42 92.92 93.71
0.16 0.16 0.17 0.16 0.19
̅ 0.23 0.26 0.27 0.26 0.25 Norleucine / ̅ 107.00 107.67 108.39 108.96 109.62
AABA / ̅ /
̅
75.15 75.74 76.11 76.58 77.20
0.17 0.20 0.19 0.19 0.20
/ ̅
/
/
0.12 0.10 0.13 0.12 0.03
(̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
21
Table 4: Partial molar volumes at infinite dilution of α-amino acids in aqueous sodium chloride 0.1500 m and partial molar volumes of transfer from water to the aqueous electrolyte solution from T = 293.15 to 313.15 K at 75 kPa.
T/K
Glycine ̅ /
̅
293.15 298.15 303.15 308.15 313.15
43.36 43.78 44.31 44.71 45.08
0.46 0.45 0.44 0.45 0.44
a. b. c. d.
Alanine / ̅ / 60.40 60.75 61.08 61.35 61.70
T/K
Norvaline ̅ /
̅
293.15 298.15 303.15 308.15 313.15
91.35 92.05 92.56 93.06 93.82
0.30 0.31 0.31 0.30 0.30
̅ 0.38 0.38 0.37 0.36 0.37 Norleucine / ̅ 107.16 107.83 108.56 109.13 109.86
AABA / ̅ /
̅
75.31 75.88 76.25 76.72 77.32
0.33 0.34 0.33 0.33 0.32
/ ̅
/
/
0.28 0.26 0.30 0.29 0.27
(̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
22
Table 5: Partial molar volumes at infinite dilution of α-amino acids in aqueous potassium chloride 0.1500 m and partial molar volumes of transfer from water to the aqueous electrolyte solution from T = 293.15 to 313.15 K at 75 kPa.
T/K
Glycine ̅ /
̅
293.15 298.15 303.15 308.15 313.15
43.27 43.68 44.25 44.61 45.01
0.37 0.35 0.38 0.35 0.37
Alanine / ̅ / 60.33 60.67 61.00 61.29 61.63
T/K
Norvaline ̅ /
̅
293.15 298.15 303.15 308.15 313.15
91.29 91.97 92.48 92.98 93.78
0.24 0.23 0.23 0.22 0.26
̅ 0.31 0.30 0.29 0.30 0.30 Norleucine / ̅ 107.10 107.76 108.47 109.05 109.80
AABA / ̅ /
̅
75.24 75.80 76.17 76.64 77.26
0.26 0.26 0.25 0.25 0.26
/ ̅
/
/
0.22 0.19 0.21 0.21 0.21
a. (̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality b. u(P) = 1 kPa c. u(T) = 0.01 K d. u(m salt) = 1·10-4 mol·kg-1
23
Table 6: Partial molar volumes at infinite dilution of α-amino acids in aqueous ammonium sulfate 0.1500 m and partial molar volumes of transfer from water to the aqueous electrolyte solution from T = 293.15 to 313.15 K at 75 kPa.
T/K
Glycine ̅ /
̅
293.15 298.15 303.15 308.15 313.15
43.71 44.13 44.71 45.09 45.50
0.81 0.80 0.84 0.83 0.86
a. b. c. d.
Alanine / ̅ / 60.74 61.10 61.43 61.70 62.07
T/K
Norvaline ̅ /
̅
293.15 298.15 303.15 308.15 313.15
91.69 92.38 92.89 93.38 94.14
0.64 0.64 0.64 0.62 0.62
̅ 0.72 0.73 0.72 0.71 0.74 Norleucine / ̅ 107.50 108.18 108.89 109.43 110.19
AABA / ̅ /
̅
75.65 76.23 76.58 77.06 77.68
0.67 0.69 0.66 0.67 0.68
/ ̅
/
/
0.62 0.61 0.63 0.59 0.60
(̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
24
Table 7: Partial molar volumes at infinite dilution of α-amino acids in aqueous sodium sulfate 0.1500 m and partial molar volumes of transfer from water to the aqueous electrolyte solution from T = 293.15 to 313.15 K at 75 kPa.
T/K
Glycine ̅ /
̅
293.15 298.15 303.15 308.15 313.15
44.01 44.43 45.01 45.39 45.80
1.11 1.10 1.14 1.13 1.16
a. b. c. d.
Alanine / ̅ / 61.04 61.40 61.72 62.00 62.36
T/K
Norvaline ̅ /
̅
293.15 298.15 303.15 308.15 313.15
91.99 92.68 93.19 93.68 94.43
0.94 0.94 0.94 0.92 0.91
̅ 1.02 1.03 1.01 1.01 1.03 Norleucine / ̅ 107.78 108.46 109.17 109.72 110.47
AABA / ̅ /
̅
75.94 76.53 76.88 77.36 77.97
0.96 0.99 0.96 0.97 0.97
/ ̅
/
/
0.90 0.89 0.91 0.88 0.88
(̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
25
Table 8: Group contributions to the partial molar volume of the α-amino acids in water and in the aqueous electrolyte solution from T = 293.15 to 313.15 K at 75 kPa.
T/K 293.15 298.15 303.15 308.15 313.15 T/K 293.15 298.15 303.15 308.15 313.15
a. b. a. c. d.
Water ̅ /
LiCl 0.1500 m ̅
/ 15.90 27.47 15.98 27.77 16.03 28.11 16.08 28.41 16.21 28.59 KCl 0.1500 m ̅ / ̅ 15.86 15.95 15.99 16.06 16.17
/ 27.86 28.14 28.50 28.74 28.98
̅
/ ̅
15.86 27.79 15.93 28.12 15.99 28.45 16.05 28.72 16.15 28.97 (NH4)2SO4 0.1500 m ̅ / ̅ 15.85 15.94 15.98 16.04 16.15
/ 28.30 28.59 28.95 29.22 29.48
/
NaCl 0.1500 m ̅ ̅ / / 15.86 27.95 15.94 28.24 16.00 28.56 16.06 28.83 16.17 29.05 Na2SO4 0.1500 m ̅ / ̅ 15.85 15.93 15.98 16.03 16.14
/ 28.61 28.90 29.26 29.53 29.78
u(̅ ) = 0.17 cm3 mol-1 (max) u(̅ ) = 0.56 cm3 mol-1 (max) u(m salt) = 1·10-4 mol·kg-1 u(P) = 1 kPa u(T) = 0.01 K
26
Table 9: Partial molar expansibility of α-amino acids in water and in the aqueous electrolyte solution from T = 293.15 to 313.15 K at 75 kPa. ̅ Amino acid Glycine Alanine AABA Norvaline Norleucine a. b. c. d.
Water 8.8 6.5 9.8 12.0 13.0
/ LiCl 0.1500 m 8.9 6.5 9.8 12.0 13.0
NaCl 0.1500 m 8.7 6.4 9.7 11.9 13.4
KCl 0.1500 m 8.8 6.4 9.8 12.0 13.4
(NH4)2SO4 0.1500 m 9.0 6.5 9.7 11.8 13.2
Na2SO4 0.1500 m 9.1 6.5 9.8 11.8 13.3
u( ̅ ) = 0.6 cm3 mol-1 K-1 (max) u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
27
Table 10: Partial molar compressibilities at infinite dilution of the α-amino acids in water from T = 293.15 to 313.15 K at 75 kPa. T/K 293.15 298.15 303.15 308.15 313.15
̅ / Glycine 28.49 25.10 22.80 19.20 16.78
Alanine 29.53 25.93 23.85 20.26 17.97
AABA 31.67 26.56 24.44 21.74 18.82
Norvaline 34.75 30.03 25.72 22.97 19.63
Norleucine 38.34 34.52 28.31 24.62 22.46
a. ( ̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality b. u(P) = 1 kPa c. u(T) = 0.01 K
28
Table 11: Literature comparison of the partial molar compressibilities at infinite dilution of the α-amino acids in water at 298.15 K. ̅
Glycine
/ This work 25.10
Literature 25.97[6] 26.6[34] 24.09[44] 27.16[44] 26.40[43]
Alanine
25.93
25.56[6] 25.1[34] 26.28[45] 24.74[44] 25.16[43]
AABA
26.56
27.1[34] 29.95[46]
Norvaline
30.03
29.0[34]29.70[46]
Norleucine
34.52
30.3[34]
α-amino acid
a. ( ̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality b. u(T) = 0.01 K
29
Table 12: Partial molar compressibilities at infinite dilution and partial molar compressibilities of transfer of the α-amino acids in aqueous lithium chloride 0.1500 m from T = 293.15 to 313.15 K at 75 kPa. Glycine T/K 293.15 298.15 303.15 308.15 313.15
̅
/
27.32 23.32 21.22 17.12 15.61
Alanine ̅
̅
/
1.17 1.78 1.58 2.08 1.17
27.34 24.47 21.83 18.43 16.32
Norvaline T/K 293.15 298.15 303.15 308.15 313.15 a. b. c. d.
̅
32.61 28.14 23.46 20.34 17.66
/
AABA / ̅
/
2.19 1.46 2.02 1.83 1.65
̅
29.76 24.77 22.53 20.12 17.40
/ ̅
/
1.91 1.79 1.91 1.62 1.42
Norleucine ̅
2.14 1.89 2.26 2.63 1.97
/ - ̅
36.68 32.59 26.63 22.09 20.02
/
̅
/
1.66 1.93 1.68 2.53 2.44
( ̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
30
Table 13: Partial molar compressibilities at infinite dilution and partial molar compressibilities of transfer of the α-amino acids in aqueous sodium chloride 0.1500 m from T = 293.15 to 313.15 K at 75 kPa. Glycine ̅
T/K 293.15 298.15 303.15 308.15 313.15
Alanine ̅
/
25.02 21.70 19.71 15.67 14.07
̅
/
3.47 3.40 3.09 3.53 2.71
25.62 22.76 19.29 17.05 14.25
AABA / ̅
3.91 3.17 4.56 3.21 3.72
Norvaline T/K 293.15 298.15 303.15 308.15 313.15 a. b. c. d.
̅
30.72 26.24 21.66 18.49 15.88
/
/
̅
/ ̅
28.08 22.13 20.69 18.21 15.05
/
3.59 4.43 3.75 3.53 3.77
Norleucine ̅
4.03 3.79 4.06 4.48 3.75
/
̅
34.28 30.22 24.21 20.95 18.73
/
̅
/
4.06 4.30 4.10 3.67 3.73
( ̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
31
Table 14: Partial molar compressibilities at infinite dilution and partial molar compressibilities of transfer of the α-amino acids in aqueous potassium chloride 0.1500 m from T = 293.15 to 313.15 K at 75 kPa. Glycine ̅
T/K 293.15 298.15 303.15 308.15 313.15
Alanine ̅
/
25.71 22.39 20.26 16.42 14.64
̅
/
2.78 2.71 2.54 2.78 2.14
26.33 22.99 20.46 17.62 14.88
AABA / ̅
3.20 2.94 3.39 2.64 3.09
Norvaline T/K 293.15 298.15 303.15 308.15 313.15 a. b. c. d.
̅
31.34 27.02 22.36 19.24 16.58
/
/
̅
/ ̅
28.62 23.26 21.27 18.75 15.77
/
3.05 3.30 3.17 2.99 3.05
Norleucine ̅
3.41 3.01 3.36 3.73 3.05
/
̅
35.47 31.39 25.43 21.24 19.14
/
̅
/
2.87 3.13 2.88 3.38 3.32
( ̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
32
Table 15: Partial molar compressibilities at infinite dilution and partial molar compressibilities of transfer of the α-amino acids in aqueous ammonium sulfate 0.1500 m from T = 293.15 to 313.15 K at 75 kPa. Glycine ̅
T/K 293.15 298.15 303.15 308.15 313.15
Alanine ̅
/
23.75 20.56 18.56 14.71 13.16
̅
/
4.74 4.54 4.24 4.49 3.62
24.41 21.52 18.56 16.39 13.74
AABA / ̅
5.12 4.41 5.29 3.87 4.23
Norvaline T/K 293.15 298.15 303.15 308.15 313.15
a. b. c. d.
̅
29.73 25.37 20.87 17.85 15.41
/
/
̅
/ ̅
27.25 21.84 19.89 17.50 14.60
/
4.42 4.72 4.55 4.24 4.22
Norleucine ̅
5.02 4.66 4.85 5.12 4.22
/
̅
33.42 29.51 23.78 20.58 18.46
/
̅
/
4.92 5.01 4.53 4.04 4.00
( ̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
33
Table 16: Partial molar compressibilities at infinite dilution and partial molar compressibilities of transfer of the α-amino acids in aqueous sodium sulfate 0.1500 m from T = 293.15 to 313.15 K at 75 kPa. Glycine ̅
T/K 293.15 298.15 303.15 308.15 313.15
Alanine ̅
/
21.50 18.41 13.79 12.28 10.33
̅
/
6.99 6.69 9.01 6.92 6.45
AABA / ̅
22.37 19.77 14.74 13.75 11.72
7.16 6.16 9.11 6.51 6.25
Norvaline T/K 293.15 298.15 303.15 308.15 313.15 a. b. c. d.
̅
27.37 23.23 17.25 16.01 14.08
/
/
̅
/ ̅
24.63 21.15 16.00 15.98 13.04
/
7.04 5.41 8.44 5.76 5.78
Norleucine ̅
7.38 6.80 8.47 6.96 5.55
/
̅
30.41 24.61 18.94 17.00 15.12
/
̅
/
7.93 9.91 9.37 7.62 7.34
( ̅ ) obtained by extrapolation from the apparent molar volumes as a function of molality u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1
34
Table 17: Hydration numbers of the α-amino acids in water and in the aqueous electrolyte solution from T = 293.15 to 313.15 K at 75 kPa. nH (Water) Glycine Alanine AABA 293.15 3.46 3.59 3.85 298.15 3.10 3.20 3.28 303.15 2.86 2.99 3.06 308.15 2.43 2.57 2.75 313.15 2.14 2.30 2.40 nH (LiCl 0.1500 m) T/K Glycine Alanine AABA 293.15 3.37 3.38 3.68 298.15 2.93 3.07 3.11 303.15 2.70 2.78 2.87 308.15 2.20 2.37 2.59 313.15 2.02 2.11 2.25 nH (NaCl 0.1500 m) T/K Glycine Alanine AABA 293.15 3.10 3.18 3.48 298.15 2.73 2.87 2.79 303.15 2.52 2.46 2.64 308.15 2.02 2.20 2.35 313.15 1.83 1.85 1.96 nH (KCl 0.1500 m) T/K Glycine Alanine AABA 293.15 3.18 3.26 3.55 298.15 2.82 2.89 2.93 303.15 2.58 2.61 2.71 308.15 2.12 2.27 2.42 313.15 1.90 1.93 2.05 nH ((NH4)2SO4 0.1500 m) T/K Glycine Alanine AABA 293.15 3.00 3.08 3.44 298.15 2.64 2.76 2.80 303.15 2.41 2.41 2.58 308.15 1.93 2.15 2.30 313.15 1.74 1.82 1.93 nH (Na2SO4 0.1500 m) T/K Glycine Alanine AABA 293.15 2.75 2.87 3.15 298.15 2.39 2.57 2.75 303.15 1.82 1.94 2.11 308.15 1.63 1.83 2.12 313.15 1.38 1.57 1.75 u(nH) = 0.64 (max) u(P) = 1 kPa u(T) = 0.01 K u(m salt) = 1·10-4 mol·kg-1 T/K
a. b. c. d.
Norvaline 4.22 3.71 3.22 2.91 2.51
Norleucine 4.66 4.27 3.55 3.12 2.87
Norvaline 4.03 3.53 2.98 2.61 2.29
Norleucine 4.53 4.09 3.39 2.84 2.59
Norvaline 3.81 3.31 2.76 2.38 2.06
Norleucine 4.25 3.81 3.09 2.70 2.43
Norvaline 3.88 3.40 2.85 2.48 2.15
Norleucine 4.39 3.95 3.24 2.74 2.49
Norvaline 3.75 3.25 2.71 2.34 2.04
Norleucine 4.22 3.78 3.09 2.70 2.44
Norvaline 3.51 3.02 2.27 2.13 1.89
Norleucine 3.90 3.20 2.49 2.26 2.02
35
46.00 45.50 45.00 44.50 44.00 43.50 43.00 42.50 290.00
295.00
300.00
305.00
310.00
315.00
T/K
Figure 1: Partial molar volumes at infinite dilution of glycine in water and in the aqueous electrolyte solution at different temperatures.
36
14.00
A
13.00 12.00 11.00 10.00 9.00 8.00 7.00 6.00
𝟏
1.150E-04
̅ 𝟐 ⁄𝝏𝑻 /𝒄𝒎𝟑 𝒎𝒐𝒍 𝝏𝑲
𝟏
𝑮𝑷𝒂
𝟏
1.250E-04
𝑲
0
1
2
3 -CH₂
4
5
6
B
1.050E-04 9.500E-05 8.500E-05 7.500E-05 6.500E-05 5.500E-05 4.500E-05 3.500E-05 0
1
2
3
4
5
6
-CH₂
Figure 2: (A) Partial molar expansibilities of the α-amino acids as a function of the ̅ ⁄ methylene groups. (B) of the α-amino acids as a function of the methylene groups.
37
