Osmotic Coefficients and Activity Coefficients in Aqueous

Article pubs.acs.org/jced

Osmotic Coefficients and Activity Coefficients in Aqueous Aminoethanoic Acid−NaCl Mixtures at 298.15 K Elena N. Tsurko,*,† Roland Neueder,‡ Rainer Müller,‡ and Werner Kunz‡ †

Research Institute of Chemistry, Karazin National University, Svoboda Sq.4, 61022 Kharkiv, Ukraine Institute of Physical and Theoretical Chemistry, University of Regensburg, Universitaetsstr. 31, 93053 Regensburg, Germany

‡

ABSTRACT: Osmotic coefficients are inferred from vapor pressure osmometry measurements that were performed at T = 298.15 K for ternary amino acid−electrolyte−water systems with variation in the concentrations of amino acid (aminoethanoic acid, glycine) and electrolyte (NaCl) up to high concentrations of aminoethanoic (3 mol·kg−1) and NaCl (3 mol·kg−1). From the consideration of the Gibbs−Duhem equation at mutual data treatment, interparticle interactions in ternary aminoethanoic acid−NaCl−water systems have been deduced in a wide concentration range. A two-parameter fit (third order terms in the power series) according to Bower and Robinson is used for calculation of component activity coefficients.

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INTRODUCTION Ions specifically interact with macromolecules such as proteins and therefore can influence important biological functions like protein solubility and stability, protein−protein interactions, and enzyme activity. The determination of the thermodynamic properties of binary amino acid−water mixtures as well as of ternary amino acid−salt−water mixtures may help to get a deeper insight into the mechanisms underlying these effects which are important for biological function.1 Proteins are macromolecules with highly complex tertiary structures. Steric effects, partial exposition of the amino acid residues to the surrounding solvent, and different dimensional conformations of the amino acid chain stipulate the extraordinary complexity of the resulting structure and biological function of proteins. Amino acid−salt−water systems are the simplest systems for the modeling of interactions between the charged and uncharged parts of these biological macromolecules. One potential starting point for the treatment of phase diagrams are simplified protein models such as coarse-grained peptide models. Molecular modeling and simulation results for protein phase behavior with different types of protein−protein interaction potentials are useful to characterize protein crystallization and to formulate therapeutic proteins.2−4 This theoretical description involves phase equilibria in real protein solutions containing, e.g., albumins, etc. For the elaboration and testing of simple molecular models (models of interparticle interaction potentials, statistical-mechanical models) experimental data on amino acid− salt aqueous solutions are useful. Such models considering van der Waals interactions consisting of Keesom interaction, Debye interaction, London dispersion force, electrostatic interaction, depletion interaction, specific interaction, and hydration force are successfully applied to protein solutions. The effect of © XXXX American Chemical Society

the solvent and salt constituents on the protein phase diagram is especially important.5−7 Data of ternary amino acid−salt−water systems are needed also in this context for the description of membrane protein systems. Membrane proteins possess important functions because their function relies on ionic interactions, especially in the channels.8 To describe phase equilibrium and nonequilibrium processes for complex systems of real proteins, it is necessary to dispose of macroscopic activity coefficients for simple amino acids in salt solutions that may be split into different contributions coming from zwitterions, ions or uncharged species. In recent years many studies of thermodynamic properties of ternary amino acid−salt−water systems have been published. The influence of magnesium acetate and sodium acetate on the transfer properties of L-serine and L-threonine in aqueous solutions at 298.15 K is provided in the work of Banipal et al.9 from speed of sound and flow time measurements. The apparent molar volumes VM, apparent molar adiabatic compressibilities, κS,2, and relative viscosities, ηr, of L-serine and L-threonine were compared with the reported data for DL-α-alanine and DL-αamino-n-butyric acid in aqueous sodium acetate and magnesium acetate solutions. The apparent molar volumes of glycine, DL-αalanine, DL-α-amino-n-butyric acid, DL-valine and DL-leucine in aqueous solutions of 0.5, 1.0, 1.5, and 2.0 mol kg−1 sodium acetate at 310.15 K were studied in the work of Wang et al.10 In the work of Sadowski et al.11 osmotic coefficients and amino acid solubility for electrolyte−amino acid−water systems contained one of the four amino acids: glycine, L-/DL-alanine, Received: March 26, 2014 Accepted: August 5, 2014

A

dx.doi.org/10.1021/je500271z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Article

EXPERIMENTAL SECTION Materials. Chemicals. aminoethanoic acid (glycine, Sigma Bioultra, for molecular biology) CAS 56-40-6; sodium chloride (VWR, Normapur ≥ 99.9 %) CAS 7647-14-5. Aminoethanoic acid and sodium chloride were pulverized and dried at temperatures 353 and 393 K, respectively, under dry nitrogen before use. The solutions were stored under nitrogen. Water from a Millipore purification system with a specific conductivity of 8·10−8 S·cm−1 (298 K) was used for the preparation of solutions. Solutions are prepared by weight with the use of a Mettler AT 201 balance (max 200 g) with an accuracy of 0.001 g, Mettler AE 240 (max 240 g) with an accuracy of 0.0001 g, and Mettler P 1210 (max 1200 g) with an accuracy of 0.010 g dependent on the solution amount. Vapor Pressure Measurements. Osmotic coefficients have been investigated over a wide concentration range ((0.1−3.5) mol·kg−1) with the help of vapor pressure osmometry (Knauer Osmomat, K-7000). The vapor pressure was measured by using two thermistors to obtain voltage changes caused by a change in temperature. A comparison between results obtained with this equipment and those from direct vapor pressure lowering on a classical precise equipment18 has been done elsewhere19 and showed good agreement of both techniques. Special care was taken to keep the drop size and shape equal on both thermistors. For each solution 9 determinations (with zero point adjustment always after three measurements) were performed and the mean measured value was calculated. The measured values MW (the panel reading of the apparatus) are obtained from 3 × 3 measurements. MW values were from 70 to 500 for ternary solutions. Standard deviation σ = 0.5−3 units; relative error δ = (0.2−1) %. The calibration of the apparatus was done with the help of NaCl solutions at 298.15 K in a concentration range of (0.1−3) mol·kg−1.

L-/DL-valine, and L-proline up to the respective amino acid solubility limit and one of 13 salts composed of the ions Li+, Na+, K+, NH4+, Cl−, Br−, I−, NO3−, and SO42− at salt molalities of 0.5, 1.0, and 3.0 mol·kg−1, respectively, were measured at 298.15 K and modeled with the electrolyte perturbed-chain statistical association theory (ePC-SAFT). Different ways are used to evaluate activity coefficient values from properties measured experimentally. In the work of Esteso et al.12 activity coefficients in ternary aminoethanoic acid−NaCl−water systems are obtained from electromotive force measurements of the galvanic cells. Activity coefficients of amino acids are calculated from the NaCl activity coefficient concentration dependence. In several works of Khoshkbarchi et al.13−16 activity coefficients in ternary amino acid−electrolyte− water systems for DL-aminobutyric acid, DL-threonine, DL-alanine and in glycyl glycine−electrolyte−water are received from solubility measurements at 298.15 K. Kumar et al.17 have approximated a large set of activity coefficients, volumes and compressibilities of amino acids in electrolyte solutions using their own experimental data and those of other authors (Esteso et al., Khoshkbarchi et al., etc.) The mentioned properties of both the amino acid/peptide and electrolyte have been approximated for a large series of amino acids (Gly, Ala, Gly-Gly, Pro, β-Ala, Pro, Thr, γ-amino-n-butyric acid, ε-aminocaproic acid, Leu, and Val) and electrolytes (NaCl, NaNO3, NaBr, KCl, NaNO3, KBr, MgCl2, Na2SO4, (CH3)4NBr, (C2H5)4NBr, (C4H9)4NBr, KSCN, and sodium butyrate) with the use of the Pitzer equation. The adjustable parameters for correlating of activity coefficient of amino acid or salt, volume, and compressibility for different amino acids are tabulated in that work. The equations used are based on the second derivative of excess Gibbs free energy of mixing. In our present work osmotic coefficients of aminoethanoic acid−NaCl−water mixtures up to high concentrations of aminoethanoic acid (3 mol·kg−1) and sodium chloride (3 mol·kg−1) were measured. To evaluate activity coefficients from osmotic coefficients in ternary systems it is necessary to develop and to check unified approaches. There are different approaches in the literature but for different kinds of solutes and for data from different methods. The paradigm of calculation of γ1 (activity coefficient of aminoethanoic acid) and γ2 (activity coefficient of NaCl) from osmotic coefficients was proved in this work. Experimental basis of this work are the values of the chemical potential of water in mixtures of aminoethanoic acid with sodium chloride. The aim is to apply the formalism developed as a specimen for activity coefficient evaluation in ternary systems. It is applied first to the properties of the Gly−NaCl−H2O system from own measurements. This system is chosen as a system with well-known reliable properties of the ternary mixture and respective binary solutions. Further, when the procedure is elaborated, ion-specific effects with other salts in amino acids− salt−water systems could be derived. The chemical potentials are inferred from vapor pressure osmometry measurements that were performed at T = 298.15 K for the ternary systems aminoethanoic acid−NaCl−water with variation of concentration of aminoethanoic acid and NaCl (mB = (0.5, 1, 2, and 3) mol·kg−1, mA = 0−3 mol·kg−1) and (mB = (0−3) mol·kg−1, mA = 0.25 mol·kg−1), where mA is the aminoethanoic acid molality in moles per kg of pure water, and mB is the NaCl molality in moles per kg of pure water. Two approaches are used to evaluate the activity coefficients of solution components.

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RESULTS Activity of Water and Osmotic Coefficient. The chemical potential of the solvent in an electrolyte solution is related to the solvent activity via μ1(p , T ) = μ10 (p , T ) + RT ln a1

(1)

where μ1(p,T) is the chemical potential of the solvent in solution, μ10(p,T) is the chemical potential of the pure solvent, R is the gas constant, T is the absolute temperature, and a1 the activity of the solvent in solution. The osmotic coefficient ϕ can be defined in molality concentration scale as ϕ=−

1000 ln a1 vmM1

(2)

where m is the solute molality, ν the stoichiometric coefficient of the solute and M1 the molar mass of the solvent. In a binary solution the osmotic coefficient can be related to the mean activity coefficient γ± of the salt through ϕ(m2) = 1 +

1 m2

∫0

m2

dm ln γ±

(3)

and ln γ± = (ϕ − 1) − B

∫0

m

1−ϕ dm m

(4)



Article

Table 1. Experimental Values of Osmotic Coefficients ϕ at Molalities m for the Systems of Aminoethanoic Acid (1) in Aqueous Solutions of Sodium Chloride (2) + Water (3) at Temperature T = 298.15 Ka

If the solvent is the only volatile component, the liquid−gas equilibrium is given by μ10, g = μ10, L + RT ln a1

(5)

where μ10,g is the chemical potential of the solvent in the gas phase, and μ10,L the chemical potential of the solvent in the liquid phase. The apparatus was calibrated using aqueous sodium chloride solutions, yielding a function which correlates the panel readings with the corresponding concentrations of the sodium chloride solutions. Then the measurements for different amino acid solutions were carried out. From indirect vapor pressure osmometry the values of the osmotic coefficient ϕ of amino acid (AA) and salt (MA) solutions have been obtained with the use of calibration data on NaCl solutions in a given concentration range according to ϕ=

ν(NaCl)m(NaCl)ϕ(NaCl) ν1m(AA) + ν2m(MA)

aminoethanoic acid (1) + NaCl (2), (m2 = 0.50582 mol·kg−1) m1, mol·kg−1

SZ + a

(6)

S = 1.17284 −

4

∑ Djm j (7)

j=1

6202.357τ

(

Ts 2 1 +

τ Ts

)

⎛ τ⎞ + 54.4251 ln⎜1 + ⎟ Ts ⎠ ⎝

− 0.161993τ + 8.59609· 10−5(2Tsτ + τ 2)

NaCl (2) + aminoethanoic acid (1) (m1 = 0.24849 mol·kg−1)

m1, mol·kg−1

m2, mol·kg−1

0 0.9219 0 0.08741 0.7796 0.22284 0.39909 0.7326 0.44648 0.85321 0.7931 0.90609 1.43902 0.7731 1.01168 1.44599 0.8234 1.46210 2.02745 0.8074 2.54545 2.28046 0.8015 2.73572 2.39291 0.7881 2.88719 2.64707 0.8152 3.64729 aminoethanoic acid (1) + NaCl (2), (m2 =1.00000 mol·kg−1)b

m(NaCl) is the molality of a sodium chloride solution showing the same instrument reading (MW) as the amino acid and salt solution, that means the vapor pressure and therefore the solvent activity is equal in both solutions. m(AA) and m(MA) are the molalities of the amino acid and salt and ν1 and ν2 the stoichiometric coefficients. ϕ(NaCl) is the osmotic coefficient calculated with the following equation set developed by Gibbard and Scatchard:20 ϕ=1−

ϕ

aminoethanoic acid (1) + NaCl (2) (m2 = 1.99270 mol·kg−1)

(8)

ϕ

m1, mol·kg−1

ϕ

m2, mol·kg−1

ϕ

0 0.20007 0.39953 0.59989 0.79418 0.98942 1.20356 1.39759 1.58690 1.99320 2.20734 2.60250 2.99114

0.9266 0.9171 0.9086 0.9028 0.9049 0.8905 0.8862 0.8817 0.8889 0.8870 0.8804 0.8840 0.8832

0 0.20001 0.39842 0.60042 0.80410 0.99484 1.19849 1.40141 1.59458 1.79417 1.98993 2.19817 2.38947 2.59746 2.79068 2.99764 3.50741

1.0506 1.0374 1.0254 1.0153 1.0096 1.0044 1.0012 1.0073 0.9903 0.9851 0.9873 0.9831 0.9764 0.9727 0.9709 0.9737 0.9864

where Z = ((1 + X) − (1/(1 + X)) − (2 ln(1 + X)))/X2; τ = T − Ts ; X = a√m; Ts = 298.15 K; a = 1.5. The coefficients Dj of the power series in m of eq 7 are given by 3

Dj = Dj(s) − 0.2516103 ∑ k=0

Dj(k) k!

∫0

τ

tk dt (t + Ts)

a m1 is the molality of aminoethanoic acid in the (water + sodium chloride) system; m2 is the molality of sodium chloride in the (water + aminoethanoic acid) mixed solvent. Standard uncertainties u are u(m) = 0.001 mol·kg−1 and u(ϕ) = 0.01 bData were taken from Sadowski et al.11

(9)

with coefficients Dj(s) and Dj(k) based on precise measurements and given in the paper of Gibbard and Scatchard.20 The activity of water, aw, can be calculated according to ϕ(ν1m(AA) + ν2m(MA))M1 ln a w = − 1000

⎡ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎤ ⎢ν m ⎜ ∂lna1 ⎟ + ν m ⎜ ∂lna 2 ⎟ + 1000 ⎜ ∂lnaw ⎟ ⎥dm 2 2 1 ⎢ 1 1⎝ ∂m1 ⎠ M ⎝ ∂m1 ⎠m2 ⎥⎦ ⎝ ∂m1 ⎠m ⎣ m

(10)

2

2

⎤ ⎡ ⎛ ∂lna1 ⎞ ⎛ ∂lna 2 ⎞ 1000 ⎛ ∂lnaw ⎞ ⎥ + ⎢ν1m1⎜ ⎟ + ν2m2⎜ ⎟ + ⎜ ⎟ dm2 ⎢ M ⎝ ∂m2 ⎠m ⎥⎦ ⎝ ∂m2 ⎠m ⎝ ∂m2 ⎠m ⎣

Osmotic coefficients of aqueous solutions for the ternary systems Gly + NaCl with (m2 = 0.5 mol·kg−1, 1 mol·kg−1, 2 mol·kg−1, 3 mol·kg−1, m1 = 0−3 mol·kg−1 and m2 = 0−3 mol·kg−1, m1 = 0.25 mol·kg−1), where m1 is the amino acid concentration, m2 is the NaCl concentration, at T = 298.15 K are presented in Table 1 and in (Figure 1). Activity Coefficients of Aminoethanoic Acid + NaCl Mixtures. From the consideration of the Gibbs−Duhem equation it follows that 1000 ν1m1d ln a1 + ν2m2d ln a 2 + d ln aw = 0 M

ϕ

0.9761 0 0.9495 0.8804 0.12879 0.8749 0.8884 0.61034 0.8031 0.8754 0.99701 0.8174 0.8944 1.52204 0.8542 0.8804 2.00934 0.8866 0.8654 2.27462 0.9172 0.8937 2.70907 0.9551 0.8961 2.73868 0.9632 0.8544 3.10404 1.0416 aminoethanoic acid (1) + NaCl (2), (m2 = 3.00000 mol·kg−1)b

1

1

1

(12)

=0

After transformation and variable separation two equations with split variables are obtained that are used for activity coefficient calculations: ⎛ ∂lna1 ⎞ ⎛ ∂lna1 ⎞ 1000 ⎛ ∂ ln aw ⎞ m1⎜ ⎟ + m2⎜ ⎟ + ⎜ ⎟ =0 ν1M ⎝ ∂m1 ⎠m2 ⎝ ∂m1 ⎠m ⎝ ∂m2 ⎠m

(11)

2

C

1

(13)



Article

Two-Parameter Fit According to Bower and Robinson for Calculation of Component Activity Coefficients. The molal activity coefficient of the amino acid γ1 in the ternary system can be presented as a function of the molality of aminoethanoic acid m1 and molality of NaCl m2 in the form: ∞

ln γ1 =

∞

∑ ∑ Aijm1im2 j(A 00 = 0) (15)

i=0 j=0

According to the classical works of Robinson et al.21−23 for the calculation of component activity coefficients, the quantity Δ is defined by Δ = 2mR ϕR 0 − m1ϕ10 − 2m2ϕ2 0 = −55.51 ln a w − m1ϕ10 − 2m2ϕ2 0 Figure 1. Osmotic coefficients of (aminoethanoic acid + NaCl) mixtures with the background of aminoethanoic acid (m1 = 0.25 mol·kg−1), T = 298.15 K.

where mR is the molality of the standard reference NaCl solution being in equilibrium with the ternary system, ϕR is the molal osmotic coefficient of the standard reference NaCl solution, aw is the activity of the solvent in ternary solution, ϕ10 is the osmotic coefficient of the amino acid in a binary aqueous solution containing amino acid 1 at molality m1 and water, ϕ20 is the osmotic coefficient of sodium chloride in a binary aqueous solution containing sodium chloride 2 at molality m2 and water. ϕ10 value have been interpolated with the use of data from,25 and ϕ20 with the use of data from.20 The values of D = Δ/(m1m2) are given in Table 2.

⎛ ∂ ln a 2 ⎞ ⎛ ∂ ln a 2 ⎞ 1000 ⎛ ∂ ln a w ⎞ m1⎜ ⎟ =0 ⎜ ⎟ + ⎟ + m2⎜ ν1M ⎝ ∂m2 ⎠m1 ⎝ ∂m2 ⎠m ⎝ ∂m1 ⎠m 2

(16)

1

(14)

For the calculation of activity coefficients two methods according to Bower and Robinson21−23 and Mikulin24 are used.

Table 2. Values of D = Δ/(m1m2) at Molalities m for the Systems of Aminoethanoic Acid (1) in Aqueous Solutions of Sodium Chloride (2) + Water (3) at Temperature T = 298.15 K aminoethanoic acid (1) + NaCl (2), (m2 = 0.50582 mol·kg−1) m1, mol·kg−1

Δ/(m1m2)

aminoethanoic acid (1) + NaCl (2), (m2 = 1.99270 mol·kg−1) m1, mol·kg−1

NaCl (2) +aminoethanoic acid (1), m1 = 0.24849 mol·kg−1) m2, mol·kg−1

Δ/(m1m2)

0.08741 −10.99017 0.22284 0.39909 −1.29724 0.44648 0.85321 0.40076 0.90609 1.43902 0.87100 1.01168 1.44599 1.02135 1.46210 2.02745 1.20912 2.54545 2.28046 1.26259 2.73572 2.39291 1.25278 2.88719 2.64706 1.38222 3.64729 aminoethanoic acid (1) + NaCl (2), (m2 = 1.00000 mol·kg−1)

Δ/(m1m2)

−4.38727 0.12879 −0.38931 −1.93375 0.61034 −0.89251 −0.73383 0.99701 −0.83109 −0.56570 1.52204 −0.64786 −0.25620 2.00934 −0.51523 0.05654 2.27462 −0.33588 0.13383 2.70907 −0.15056 0.16090 2.73868 −0.08850 0.19006 3.10404 0.49494 aminoethanoic acid (1) + NaCl (2), (m2 = 3.00000 mol·kg−1)

m1, mol·kg−1

Δ/(m1m2)

m1, mol·kg−1

Δ/(m1m2)

0.20007 0.39953 0.59989 0.79418 0.98942 1.20356 1.39759 1.58690 1.99320 2.20734 2.60250 2.99114

−0.23862 −0.18059 −0.15508 −0.10377 −0.13025 −0.11496 −0.10894 −0.08306 −0.06559 −0.07235 −0.05578 −0.04898

0.20000 0.39842 0.60042 0.80410 0.99483 1.19848 1.40140 1.59458 1.79415 1.98992 2.19817 2.38947 2.59746 2.79068 2.99764 3.50740

−0.05373 −0.07200 −0.07369 −0.06083 −0.05354 −0.04388 −0.02152 −0.04132 −0.03990 −0.02961 −0.02843 −0.03176 −0.03044 −0.02860 −0.02170 −0.00288

D



Article

A two-parameter fitting of the function Δ/(m1m2) has been done with the polynomial:

Table 3. Approximation of D = Δ/(m1m2) with the Equation D = a0 + a1m1 + a2m2 + a3m1m1 + a4m2m2 + a5m1m2, N = 51 Points, for the Systems of Aminoethanoic Acid (1) in Aqueous Solutions of Sodium Chloride (2) + Water (3) at Temperature T = 298.15 Ka

D = Δ/(m1m2) = A 01 + A11m1 + 2A 02 m2 + 3A 03m2 2 + A 21m12 + (3/2)A12 m1m2

(17)

neglecting terms higher than third order in the power series in 15. The resulting coefficients of the approximation are the following ones with the use of equation: D = a0 + a1m1 + a 2m2 + a3m1m1 + a4m2m2 + a5m1m2 (18)

where a0 = A01 ; a1 = A11 ; a2 = 2A02 ; a3 = A21 ; a4 = 3A03 ; a5 = (3/2)A12 The coefficients has been found to be equal a0 = 0.03940, a1 = 0.81444, a2 = −1.06995, a3 = 0.02427, a4 = 0.35525, a5 = −0.25150; st. dev. = 0.249. These values are used in further calculations. The statistics of the mutual data treatment is presented in Table 3. Then amino acid activity coefficients in the mixture have been calculated according to ln γ1 = ln γ10 + A 01m2 + A11m1m2 + A 02 m2 2 + A 21m12m2 + A12 m1m2 2 + A 03m2 3

(19)

The corresponding values of activity coefficients in binary systems of aminoethanoic acid in water are calculated as ⎛ ⎛ 2β (1) ⎞ ln γ10 = m⎜⎜2β (0) + ⎜⎜ 2 ⎟⎟ ⎝ α1 m ⎠ ⎝ ⎤⎞ ⎡ ⎛ ⎞ 1 × ⎢1 − ⎜1 + α1m1/2 − α12m⎟ exp( −α1m1/2)⎥⎟⎟ ⎝ ⎠ ⎦⎠ ⎣ 2 (20)

with coefficients β = −0.0099; β = −0.27983; α1 =1.4 from ref 25. The expressions for ln γ2 are obtained by applying the crossdifferentiation relation: (0)

⎛ ∂ ln γ2 ⎞ ⎛ ∂ ln γ1 ⎞ ⎟ ⎟ = 2⎜ ⎜ ⎝ ∂m1 ⎠m ⎝ ∂m2 ⎠m 1

(1)

(21)

2

i.e., assuming 19: 1 1 A 01m1 + A11m12 + A 02 m1m2 2 4 1 1 3 3 + A 21m1 + A12 m12m2 + A 03m1m2 2 6 2 2

ln γ2 = ln γ2 0 +

(22)

The corresponding values of activity coefficients in binary systems of sodium chloride in water are used from ref 20. The results of ln γ1 and ln γ2 calculations are presented in Tables 4 and 5 and in Figure 2 and 3. Calculation of ln γ1 and ln γ2 with Mikulin’s Formulas. In Figure 4 the result of the mutual data set treatment is compared with the ln γ2 of Gly + NaCl + H2O mixtures calculated with simplified Mac Key and Perring formula that is obtained on the basis of Gibbs−Duhem equation: ⎛ ∂ ln γ2 ⎞ ⎛ ∂ ln γ1 ⎞ ν1⎜ ⎟ ⎟ = ν2⎜ ⎝ ∂m1 ⎠m ⎝ ∂m2 ⎠m 1

m1

m2

Dobs

Dcalc

δ2

0.85321 1.43901 1.44599 2.02745 2.28046 2.39291 2.64706 0.90609 1.01168 1.46210 2.54545 2.73572 2.88719 3.64729 0.24849 0.24849 0.24849 0.24849 0.24849 0.24849 0.24849 0.24849 0.24849 0.20007 0.39953 0.59989 0.79418 0.98942 1.20356 1.39759 1.58690 1.99320 2.20734 2.60250 2.99114 0.20000 0.39842 0.60042 0.80410 0.99483 1.19848 1.40140 1.59458 1.79416 1.98992 2.19817 2.38947 2.59746 2.79068 2.99764 3.50740

0.50582 0.50582 0.50582 0.50582 0.50582 0.50582 0.50582 1.99270 1.99270 1.99270 1.99270 1.99270 1.99270 1.99270 3.10404 0.12879 0.61034 0.99701 1.52204 2.00934 2.27462 2.70907 2.73868 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000 3.00000

0.40076 0.87100 1.02135 1.20912 1.26259 1.25278 1.38222 −0.70521 −0.53232 −0.20964 0.12720 0.20792 0.23660 0.27421 0.49494 −0.38931 −0.89251 −0.83109 −0.64786 −0.51523 −0.33588 −0.15056 −0.08850 −0.23352 −0.16167 −0.12077 −0.05445 −0.06683 −0.03837 −0.01946 0.01605 0.05240 0.05363 0.08535 0.10607 −0.05203 −0.06568 −0.06225 −0.04452 −0.03246 −0.01864 0.00828 −0.00797 −0.00381 0.00940 0.01359 0.01275 0.01661 0.02073 0.02998 0.05211

0.15776 0.52775 0.53205 0.88262 1.03004 1.09456 1.23813 −0.41813 −0.38997 −0.27591 −0.04191 −0.00670 0.02008 0.13763 0.14795 0.10032 −0.31856 −0.53565 −0.66038 −0.60090 −0.49759 −0.22041 −0.19664 −0.56365 −0.45427 −0.34634 −0.24354 −0.14208 −0.03294 0.06404 0.15690 0.35031 0.44902 0.62534 0.79135 0.03779 0.04680 0.05401 0.05927 0.06238 0.06374 0.06310 0.06063 0.05617 0.04992 0.04123 0.03140 0.01868 0.00499 −0.01168 −0.06162

0.05905 0.11782 0.23941 0.10660 0.05408 0.02503 0.02076 0.08241 0.02026 0.00439 0.02860 0.04606 0.04688 0.01865 0.12040 0.23974 0.32942 0.08728 0.00016 0.00734 0.02615 0.00488 0.01169 0.10899 0.08561 0.05088 0.03576 0.00566 0.00003 0.00697 0.01984 0.08875 0.15633 0.29158 0.46960 0.00807 0.01265 0.01352 0.01077 0.00899 0.00679 0.00301 0.00471 0.00360 0.00164 0.00076 0.00035 0.00000 0.00025 0.00174 0.01293

Σ(x-xi)2 = 3.10686, St.dev. = 0.249; The coefficients: a0 = 0.03940, a1 = 0.81444, a2 = −1.06995, a3 = −0.02427, a4 = 0.35525, a5 = −0.25150.

a

⎛ ∂ ln γ1 ⎞ ⎛ ∂ ln γ1 ⎞ 1 1000 ⎛ ∂ lg a w ⎞ − m1⎜ ⎟ + m2⎜ ⎟ =− ⎜ ⎟ ν1M ⎝ ∂m1 ⎠ ln 10 ⎝ ∂m1 ⎠m ⎝ ∂m2 ⎠m m 2

2

(23)

=0 E

1

2

(24) dx.doi.org/10.1021/je500271z | J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 4. Values of Activity Coefficients γ1 of Aminoethanoic Acid at Molalities m for the Systems of Aminoethanoic Acid (1) in Aqueous Solutions of Sodium Chloride (2) + Water (3) at Temperature T = 298.15 K

Table 5. Values of Activity Coefficients γ2 of Sodium Chloride at Molalities m for the Systems of Aminoethanoic Acid (1) in Aqueous Solutions of Sodium Chloride (2) + Water (3) at Temperature T = 298.15 K

aminoethanoic acid (1) + NaCl (2), (m2 = 0.50582 mol·kg−1)


NaCl (2) + aminoethanoic acid (1), (m1 = 0.24849 mol·kg−1)



NaCl (2) + aminoethanoic acid (1), (m1 = 0.24849 mol·kg−1)

m1, mol·kg−1

m1, mol·kg−1

m2, mol·kg−1

m1, mol·kg−1

m1, mol·kg−1

m2, mol·kg−1

γ1

0.2 0.9068 0.2 0.4 0.9300 0.4 0.6 0.9633 0.6 0.8 1.0037 0.8 1.0 1.0498 1.0 1.2 1.1007 1.2 1.4 1.1562 1.4 1.6 1.2158 1.6 1.8 1.2795 1.8 2.0 1.3470 2.0 2.2 1.4184 2.2 2.4 1.4936 2.4 2.6 1.5725 2.6 2.8 1.6552 2.8 3.0 1.7415 3.0 aminoethanoic acid (1) + NaCl (2), (m2 = 1.00000 mol·kg−1)

γ1

γ1

0.3697 0.2 0.9436 0.4250 0.4 0.9303 0.4920 0.6 0.8857 0.5713 0.8 0.8190 0.6640 1.0 0.7400 0.7715 1.2 0.6567 0.8952 1.4 0.5759 1.0370 1.6 0.5018 1.1987 1.8 0.4369 1.3821 2.0 0.3824 1.5892 2.2 0.3382 1.8220 2.4 0.3041 2.0826 2.6 0.2795 2.3729 2.8 0.2641 2.6948 3.0 0.2581 aminoethanoic acid (1) + NaCl (2), (m2 = 3.00000 mol·kg−1)

m1, mol·kg−1

γ1

m1, mol·kg−1

γ1

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

0.7262 0.7867 0.8600 0.9448 1.0408 1.1484 1.2681 1.4004 1.5463 1.7064 1.8816 2.0728 2.2809 2.5067 2.7512

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

0.2500 0.2852 0.3270 0.3753 0.4304 0.4923 0.5615 0.6379 0.7218 0.8132 0.9118 1.0174 1.1296 1.2478 1.3712

0 0.6844 0 0.2 0.6614 0.2 0.4 0.6473 0.4 0.6 0.6415 0.6 0.8 0.6437 0.8 1.0 0.6538 1.0 1.2 0.6721 1.2 1.4 0.6990 1.4 1.6 0.7355 1.6 1.8 0.7827 1.8 2.0 0.8424 2.0 2.2 0.9166 2.2 2.4 1.0081 2.4 2.6 1.1207 2.6 2.8 1.2589 2.8 3.0 1.4286 3.0 aminoethanoic acid (1) + NaCl (2), (m2 = 1.00000 mol·kg−1)

2

1

1

γ2

m1, mol·kg−1

γ2

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

0.6601 0.6199 0.5877 0.5623 0.5429 0.5287 0.5194 0.5146 0.5140 0.5176 0.5252 0.5371 0.5534 0.5743 0.6002 0.6316

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

0.7166 0.7171 0.7148 0.7094 0.7010 0.6895 0.6750 0.6574 0.6370 0.6139 0.5884 0.5607 0.5311 0.4999 0.4677 0.4346

γ1 =

2

1000 ν2M

∫0

lg aw

[−

ν1m1*γ1* ν1m1 + ν2m2

(27)

where * refers to binary solutions showing the same activity as the ternary solution. Activity coefficient of the salt γ2 in the ternary system could be calculated as

(ν1m1 + ν2m2)γ2 ν2m2*γ * =

γ2

0.6713 0 0.6281 0.2 0.7306 0.5892 0.4 0.6746 0.5542 0.6 0.6432 0.5224 0.8 0.6234 0.4934 1.0 0.6112 0.4670 1.2 0.6043 0.4427 1.4 0.6020 0.4203 1.6 0.6037 0.3996 1.8 0.6090 0.3804 2.0 0.6180 0.3624 2.2 0.6301 0.3455 2.4 0.6459 0.3296 2.6 0.6658 0.3145 2.8 0.6892 0.3001 3.0 0.7168 aminoethanoic acid (1) + NaCl (2), (m2 = 3.00000 mol·kg−1)

where * refers to binary solution isopiestic with mixed (ternary) solution. So, activity coefficients of the amino acid γ1 in the ternary system could be calculated with approximate formula as

(25)

as simplified calculation formula for activity coefficients of mixed solutions of two electrolytes without common ion (also nonelectrolyte-electrolyte) that obey Zdanovskii rule (the assumption used: solution properties are additive and water activity and volume are constant in isopiestic solutions). The expression of Mc Key and Perring26 for solutions of two electrolytes of different kind was obtained in different way and corrected by Mikulin.24 The corrected formula is lg

γ2

m1, mol·kg−1

⎛ ∂ ln γ2 ⎞ ⎛ ∂ ln γ2 ⎞ 1 1000 ⎛ ∂ lg a w ⎞ − m1⎜ ⎟ + m2⎜ ⎟ =− ⎜ ⎟ ν1M ⎝ ∂m2 ⎠ ln 10 ⎝ ∂m1 ⎠m ⎝ ∂m2 ⎠m m =0

γ2

γ2 =

0.4343 ⎛ ∂m ⎞ 1 1 + ]d(lg a w ) ⎟ − 2 ⎜ m m2* m ⎝ ∂ lg x ⎠a

ν2m2*γ2* ν1m1 + ν2m2

(28)

So the activity coefficients of sodium salt with the background of aminoethanoic acid have been evaluated with the help of

w

(26) F



Article

Figure 2. Activity coefficients of aminoethanoic acid (ln γ1) in mixtures with the background of NaCl (a) and with the background of aminoethanoic acid, m1 = 0.25 mol·kg−1 (b), T = 298.15 K.

Figure 3. Activity coefficients of sodium chloride (ln γ2) in mixtures with the background of NaCl (a) and with the background of aminoethanoic acid, m1 = 0.25 mol·kg−1 (b), T = 298.15 K.

activity coefficient values in the corresponding isopiestic binary solutions.26,20 Data from two different calculation procedures (formulas 22 and 28 respectively) are shown in Figure 4.

■

DISCUSSION Osmotic coefficients decrease with increasing aminoethanoic acid concentration and increase with increasing NaCl background concentration. For mixtures with the background of aminoethanoic acid (m1 = 0.25 mol·kg−1) osmotic coefficients as a function of NaCl concentration pass through a minimum. Osmotic coefficients are in good agreement with published data also obtained by vapor pressure osmometry but measured with a different apparatus (Gonotec Osmomat 070).11 At m2 = 1.0 mol·kg−1 values for the osmotic coefficient were lower but with higher error at m2 = 0.5 mol·kg−1 because of low signal at small concentrations. Absolute values of osmotic coefficients are lower than 1 (negative deviations from ideal state) at low ionic strengths and higher than 1 (positive deviations from ideal state) at high ionic strengths. This is typical of a simple salt solution and a hint for only minor interactions between amino acid and salt. Dependence of γ1 from the molality of aminoethanoic acid at a constant NaCl molality increases with increasing amino acid concentration m1 and that from the molality of NaCl at a constant aminoethanoic acid molality decreases with NaCl

Figure 4. Activity coefficients of NaCl (lnγ2) in a mixture on the background of aminoethanoic acid (m1 = 0.25 mol·kg−1) and in binary NaCl−water solutions, T = 298.15 K.

concentration m2. Also in the work of Kumar et al. the ln γAJW activity coefficients of aminoethanoic acid in Gly-NaCl-H2O mixtures decrease with NaCl background concentration.17 The solubility of aminoethanoic acid has been determined in aqueous G



Article

(4) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria ; 3rd ed.; Prentice Hall: NJ, 1999. (5) King, R. S.; Blanch, H. W.; Prausnitz, J. M. Molecular thermodynamics of aqueous two-phase systems for bioseparations. AIChE J. 1988, 34, 1585−1594. (6) Tavares, F. W.; Prausnitz, J. M. Analytic calculation of phase diagrams for solutions containing colloids or globular proteins. Colloid Polym. Sci. 2004, 282, 620−632. (7) Wu, J.-Z.; Prausnitz, J. M. Phase equilibria in a system of “breathing” molecules. Fluid Phase Equilib. 2002, 194−197, 689−700. (8) Eisenberg, B. Ionic channels in biological membranes − electrostatic analysis of a natural nanotube. Contemp. Phys. 1998, 39, 447−466. (9) Banipal, T. S.; Kaur, D.; Banipal, P. K.; Singh, G. Thermodynamic and transport properties of l-serine and l-threonine in aqueous sodium acetate and magnesium acetate solutions at T = 298.15 K. J. Chem. Thermodyn. 2007, 39, 371−384. (10) Wang, J.; Yan, Z.; Zhuo, K.; Lu, J. Partial molar volumes of some α-amino acids in aqueous sodium acetate solutions at 308.15 K. Biophys. Chem. 1999, 89, 179−188. (11) Held, C.; Reschke, T.; Müller, R.; Kunz, W.; Sadowski, G. Measuring and modeling aqueous electrolyte/amino-acid solutions with ePC-SAFT. J. Chem. Thermodyn. 2014, 68, 1−12. (12) Rodriguez-Raposo, R.; Fernandez-Merida, L.; Esteso, M. A. Activity coefficients in (electrolyte+amino acid)(aq). The dependence of the ion-zwitterion interactions on the strength and on the molality of the amino acid analyzed in terms of Pitzer’s equations. J. Chem. Thermodyn. 1994, 26, 1121−1128. (13) Soto, A.; Arce, A.; Khoshkbarchi, M. K.; Vera, J. H. Effect of the anion and the cation of an electrolyte on the solubility of DLaminobutyric acid in aqueous solutions: measurements and modeling. J. Biophys. Chem. 1998, 73, 77−83. (14) Vera, J. H.; Chung, Y. M. Activity coefficients of the peptide and the electrolyte in ternary systems water + glycyl-glycine + NaCl, +NaBr, + KCl and +KBr at 298.2 K. Biophys. Chem. 2001, 92, 77−88. (15) Soto-Campos, A. M.; Khoshbarchi, M. K.; Vera, J. H. Interaction of DL-threonine with NaCl and NaNO3 in aqueous solutions. EMF measurements with ion-selective electrodes. J. Chem. Thermodyn. 1997, 29, 609−622. (16) Soto-Campos, A. M.; Khoshbarchi, M. K.; Vera, J. H. Effect of the anion and the cation of an electrolyte on the activity coefficient of DLalanine in aqueous solutions. Fluid Phase Equilib. 1998, 142, 193−204. (17) Saritha, C.; Satpute, D. B.; Badarayani, R.; Kumar, A. Correlations of thermodynamic properties of aqueous amino acid − electrolyte mixtures. J. Solution Chem. 2009, 38, 95−114. (18) Barthel, J.; Neueder, R. Precision Apparatus for the static determination of the vapor pressure of solutions. GIT Fachz. Lab. 1984, 28, 1002−1012. (19) Widera, B.; Neueder, R.; Kunz, W. Vapor pressures and osmotic coefficients of aqueous solutions of SDS, C6TAB, and C8TAB at 25°C. Langmuir 2003, 19, 8226−8229. (20) Gibbard, H. F.; Scatchard, G.; Rousseau, R. A.; Creek, J. L. Liquidvapor equilibrium of aqueous sodium chloride, from 298 to 373 K and from 1 to 6 mol kg−1, and related properties. J. Chem. Eng. Data 1973, 19, 281−288. (21) Bower, V. E.; Robinson, R. A. The thermodynamics of the ternary system: urea-sodium chloride-water at 25°. J. Phys. Chem. 1963, 67, 1524−1527. (22) Robinson, R. A.; Stokes, R. H.; Marsch, K. N. Coefficients in the ternary systems water + sucrose + sodium chloride. J. Chem. Thermodyn. 1970, 2, 745−750. (23) Wen, W.-Y.; Chen, C.-m. L. Activity coefficients for two ternary systems: water-urea-tetramethylammonium bromide and water-ureatetrabutylammonium bromide at 25°. J. Phys. Chem. 1969, 73, 2895− 2901. (24) Mikulin, G. I., Ed.; Questions of Physical Chemistry of Electrolyte Solutions; Khimija: Leningrad, 1968 (in Russian).

NaCl solution showing an increase with rising NaCl background concentration from 1 to 3 mol·kg−1.11 This observation is in agreement with the decrease of the activity coefficient of aminoethanoic acid lnγ1 with rising NaCl background concentration in the present work. The prediction of aminoethanoic acid solubility in the presence of salts with the e-PC-SAFT model also yields in an increase of aminoethanoic acid solubility with rising NaCl concentration.11 This fact is in accordance with the Debye−MacAuley equation:27 ln γ1 =

2 2 D0 − D nj ∑ νjzj e 2D0 2ε0 ni akT

(29)

where nj is the electrolyte (j) concentration; ni is the nonelectrolyte (i) concentration; D0 and D are dielectric constants of the solvent (water) and its mixture with nonelectrolyte; k represents the Boltzmann constant; zi and νi represent charge and valence number, respectively; e is the electron charge; ε0 the absolute dielectric permeability; T the absolute temperature and a represents the radius of ions of the type j. (D0 − D) is negative in the case of aminoethanoic acid, because the dielectric constant increases with rising amino acid concentration in the case of aminoethanoic acid.28 Activity coefficients of the amino acid at a constant aminoethanoic acid molality decrease with ionic strength increase (NaCl background concentration). The dependence of γ1 = f(m1) is practically linear which is in accordance with the Long−MacDevit equation for activity coefficients of nonelectrolytes:29 ln γi = kimi + kjmj

(30)

The dependence of γ1 = f(m2) is also linear, which could be concluded from eq 30 at constant kimi and from Sechenov’s law. The negative value of kj reflects the salting-in effect in the aminoethanoic acid−NaCl−water system. The dependence of γ1 from NaCl concentration at a constant aminoethanoic acid background is expressed stronger in comparison with the dependence of γ2 = f(m2). Activity coefficients of NaCl γ2 decrease with increasing aminoethanoic acid concentration and the γ2 values become lower with higher NaCl background concentration. γ2 values pass through a minimum at constant aminoethanoic acid concentration.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +38-057707-5660. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS E.T. is very grateful to the German Academic Exchange Service (DAAD) for sponsoring these measurements. REFERENCES

(1) Kunz, W., Ed.; Specific Ion Effects; World Scientific: London, 2009. (2) Jiang, J. W.; Prausnitz, J. M. Molecular thermodynamics for protein precipitation with a polyelectrolyte. J. Phys. Chem. B 1999, 103, 5560− 5569. (3) Li, J. G.; Rajagopalan, R.; Jiang, J. W. Role of solvent in protein phase behaviour: influence of temperature dependent potential. J. Chem. Phys. 2008, 128, 235104. H



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Osmotic Coefficients and Activity Coefficients in Aqueous

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