Thermodynamic Properties Determination and Modeling of the (CaCl2

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Thermodynamic Properties Determination and Modeling of the (CaCl2 + Ca(NO3)2 + L‑Glutamine + H2O) System Using Potentiometric Measurements at T = (293.2, 303.2, and 313.2) K Mojgan Shafaghat-Lonbar and Bahram Ghalami-Choobar* Department of Chemistry, Faculty of Science, University of Guilan, P.O. Box 19141, Rasht, Iran S Supporting Information *

ABSTRACT: The thermodynamic properties of the quaternary (CaCl2 + Ca(NO3)2 + L-glutamine + H2O) system, determined using the potentiometric method, were reported. The potentiometric measurements were performed in aqueous solution containing 2.5% mass fraction of L-glutamine, over total ionic strengths from 0.0100 mol·kg−1 to 4.0000 mol·kg−1 at T = (293.2, 303.2 and 313.2) K and P = 0.1 MPa. Different series of the salt molal ratios r (r = mCaCl2/ mCa(NO3)2= 1, 2.5, 5.0, 7.5, 10.0) and single salt CaCl2 and Ca(NO3)2 solution in aqueous solution containing 2.5% mass fraction of L-glutamine were used for the potentiometric measurements. The Ca-ISE was prepared in our laboratory using the ionophore treated by carbon nanotubes. The Pitzer ion interaction model was used to correlate the experimental data. The mixed ionic interaction parameters (θClNO3 and ψCaClNO3) were evaluated according to Pitzer graphical method. The mixing parameters obtained were used to calculate the values of the mean activity coefficients of Ca(NO3)2, the osmotic coefficients, the solvent activity, the excess Gibbs free energies, the excess enthalpy, excess heat capacity, and the excess entropy for the whole series of the studied mixed electrolyte system. There is a good consistency between the experimental results and Pitzer model.

1. INTRODUCTION In recent years, the experimental and theoretical study on the equilibrium properties of amino acid solutions has experienced a growing interest because of their importance to design efficient separation and purification, drying, desalination, and extraction processes.1−3 Amino acids are the simplest biomolecules and the building blocks of other biomolecules such as peptides and proteins.4 Thus, the investigation of thermodynamic properties such as activity coefficients of amino acids in aqueous electrolyte solutions has been the subject of some studies.5 In addition, such information is useful for the understanding of the molecular interactions in systems, which usually includes proteins and salts in an aqueous medium.6,7 Glutamine is the most abundant free amino acid in the human body, and it has many important metabolic roles that may protect or promote tissue integrity and enhance the immune system.8 Activity coefficients of electrolytes in the presence of some amino acids have been recently studied, but no data on L-glutamine amino acid has been reported up to now. To measure the thermodynamic properties in mixed electrolyte solutions, the most common methods involve the isopiestic vapor pressure,9,10 vapor pressure lowering,11,12 the potentiometric techniques,13,14 and hygrometric method.15,16 Among the various methods, the potentiometric method is proper because of rapidity and relative simplicity to generate experimental data in comparison with the other techniques.17,18 In the last decades, among the main models developed to predict the thermodynamic properties, the Pitzer model with © XXXX American Chemical Society

considerable accuracy has been widely used in the chemical industry. The Pitzer model is based on a modified Debye−Hückel term added to a virial expansion for calculating ion activity coefficients and osmotic coefficients in solutions of high ionic strength.19−21 In continuation to our ongoing research22,23 on the aqueous solutions of electrolyte mixtures (chloride and nitrate) and amino acids (proline and alanine), here we report the results of our study on a quaternary system consisting of calcium chloride, calcium nitrate, and L-glutamine in water. In the present article, the potentiometric measurements were carried out on galvanic cells containing ion selective electrodes (Ca-ISE and NO3-ISE) and Ag−AgCl electrodes over the ionic strength ranging from 0.0100 to 4.0000 mol kg−1 for different series of the salt molal ratios r (r = mCaCl2/mCa(NO3)2= 1, 2.5, 5.0, 7.5, 10.0) and single salt CaCl2 and Ca(NO3)2 solutions in aqueous solution containing 2.5% mass fraction of L-glutamine at T = (293.2, 303.2 and 313.2) K and P = 0.1 MPa. These experimental results were interpreted based on the Pitzer ion interaction model. The unknown parameters have been evaluated for the studied systems. Finally, the values of the mean activity coefficients, the osmotic coefficients, the solvent activity, the excess Gibbs free energy, the excess enthalpy, excess Received: July 1, 2017 Accepted: January 11, 2018

A

DOI: 10.1021/acs.jced.7b00593 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

The resulting mixture was transferred into a glass dish of 2 cm diameter. The solvent was evaporated at room temperature. Then, the PVC membrane was taken up from the plate and attached to the end of a glass tube. The general procedure to prepare a nitrate selective electrode is the same, but there are differences in the amount of substances. It contains 32 mg of PVC, 65 mg of plasticizer DBP, and 3 mg of tridodecyl methylammonium chloride as ionophore. The Ag−AgCl electrodes were used as both internal reference electrodes and chloride selective electrode. These electrodes were prepared essentially as described elsewhere by electrolysis.24 Ca-ISE, NO3-ISE, and Ag−AgCl electrodes were conditioned overnight in the appropriate mixed electrolyte system before each series of measurements. From the preliminary experimental tests performed with different concentrations of internal electrolyte filling solution, the best results were those obtained with 0.1 mol·dm−3 CaCl2 and Ca(NO3)2 electrolyte.

heat capacity, and the excess entropy were obtained with Pitzer parameters for the systems under investigation.

2. EXPERIMENTAL SECTION 2.1. Apparatus and Reagents. All of the potentiometric measurements were made using a digital multimeter (Martini instruments Mi180) whose resolution was 0.1 mV. The output of the multimeter was connected to a personal computer by the RS232 connector for data acquisition. The Mi 5200 software together with Microsoft Excel (Office 2007) software were used for data acquisition and calculations. The solutions were stirred continuously using a magnetic stirrer (Delta model HM-101) at a slow constant rate to avoid concentration gradients in the test solutions. A model GFL circulation water bath was used to control the temperature of the test solution at T = (293.2 ± 0.1, 303.2 ± 0.1 and 313.2 ± 0.1) K. The conductivity measurements were carried out by means of a Metrohm 660 conductometer with a cell type of constant cell 1.17 cm−1 and having an uncertainty of 1%. The power supply current (MP-3003D) was used to prepare the Ag−AgCl wire electrodes. The analytical balance (A&D HR 200) was used to weigh the materials. Dibutyl phthalate (DBP), potassium tetrakis (p-chlorophenyl) borate (KTPClPB), high molecular weight poly(vinyl chloride) (PVC), tetrahydrofuran (THF), calcium chloride (CaCl2.2H2O), calcium nitrate [Ca(NO3)2.4H2O], L-glutamine, and all other reagents used were purchased from the chemical companies listed in Table 1 and all of them were of analytical reagent grade.

3. METHOD 3.1. Potentiometric Measurements and Procedure. At first, the potential of cells (A) and (B) were measured to get the Pitzer parameters and the experimental mean activity coefficients of CaCl2 and Ca(NO3)2 as a single salt aqueous solution containing 2.5% mass fraction of L-glutamine. A. Ca−ISE | CaCl2 (mA), L-glutamine (2.5%) | Ag−AgCl B. Ca−ISE | Ca(NO3)2 (mB), L-glutamine (2.5%) | NO3-ISE mA and mB are the amount of moles of CaCl2 and Ca(NO3)2 as single salts per 1 kilogram of aqueous solution containing 2.5% mass fraction of L-glutamine, respectively. Then, the potentiometric measurements of galvanic cell (C) were performed to obtain the selectivity coefficient of Cl− and NO−3 ions (KClNO3) for different concentrations of Ca(NO3)2 from 1.0 to 1.0 × 10−3 mol kg−1. The value obtained for KClNO3 was very small.

Table 1. Company, Purity, Value, and CAS Registry Number of Compounds Used chemical used CaCl2·2H2O Ca(NO3)2·4H2O L-glutamine

tetrahydrofuran (THF) potassium tetrakis (pchlorophenyl) borate poly(vinyl chloride( dibutyl phthalate polyanetholesulfonic acid sodium salt carbon nanotube tridodecyl methyl ammonium chloride

company Merck Acros Organics Merck Merck Fluka BDH Laboratory Merck SigmaAldrich Neutrino SigmaAldrich

CASRN

mass fraction purity

10035-04-8 13477-34-4

>0.99 >0.99

56-85-9 109-99-9 14680-77-4

>0.99 >0.99 >0.98

9002-86-2

>0.996

84-74-2 55963-78-5

>0.99 0.98

308068-56-6 7173-54-8

>0.95

C. Ca−ISE | Ca(NO3)2 (mB), L-glutamine (2.5%) | Ag−AgCl Finally, the potential of cell (D) was measured for the series of the salt molal ratios r (r = mCaCl2/mCa(NO3)2= 1, 2.5, 5.0, 7.5, 10.0) and different ionic strengths I in the aqueous solution containing 2.5% mass fraction of L-glutamine at T = (293.2, 303.2, and 313.2) K. D. Ca−ISE | CaCl2 (m1), Ca(NO3)2 (m2), L-glutamine (2.5%) | Ag−AgCl The m1 and m2 are the CaCl2 and Ca(NO3)2 mol per 1 kg of aqueous solution containing 2.5% mass fraction of L-glutamine in the quaternary mixture, respectively. The potentiometric

The stock solutions were prepared as follow. At first, the primary stock aqueous solutions containing 2.5% mass fraction of L-glutamine were prepared by using L-glutamine and doubledistilled water whose specific conductance was less than 2.0 × 10−4 S·m−1. Then, the stock electrolyte solutions were prepared by adding the proportion volume of aqueous solutions containing 2.5% mass fraction of L-glutamine into weighted amounts of CaCl2·2H2O and Ca(NO3)2·4H2O. 2.2. Preparation of Electrodes and Potentiometric Measurements. The calcium ion selective electrode was prepared in accordance with the general procedure of PVC membrane construction. For this purpose, an optimized mixture containing of 28.9 mg of powdered PVC, 60 mg of plasticizer DBP, 5.1 mg of additive KTpCIPB, and 6 mg of modified nanotube with sodium polyanetholesulfonic acid sodium salt as ionophore was dissolved in 1.2 mL of dry freshly distilled THF.

Figure 1. Plot the cell potential against log(γ±I) for calibration of Ca-ISE and Ag−AgCl electrode pair at T = 303.2 K. B



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double-wall container enabling the circulation of thermostated water from a model GFL circulation. It can be noted, the standard state for the mean activity coefficients was assumed to be the real solution in the dilution limit. 3.2. Pitzer Model. The Pitzer ion interaction model was used for the experimental data correlation and calculation of thermodynamic properties for ternary (CaCl2 + L-glutamine + H2O) and (Ca(NO3)2 + L-glutamine + H2O) and quaternary

measurements of the galvanic cell were made using standard addition procedure. In each series and for each standard addition step, data collection was performed for every 10 s interval and for 10 min (for concentrated solutions) to 20 min (for dilute solutions) using a multimeter (Martini instruments Mi 180) connected to a personal computer. As usual, all measurements were performed under stirring conditions and the temperature was kept constant at T = (293.2, 303.2, and 313.2) K, employing a

Table 2. Total Ionic Strengths (I), Molality of CaCl2 (mA), Molality of L-Glutamine (m2), the Cell Potential Data (E) and Experimental Mean Activity Coefficients of CaCl2 (γ±CaCl2) for (CaCl2 + L-Glutamine + H2O) System at T = (293.2, 303.2, and 313.2) K and P = 0.1 MPa I

mAa

m2a

Eb

mol· kg−1

mol· kg−1

mol· kg−1

mV

0.0116 0.0518 0.0989 0.2483 0.4962 0.7426 0.9875 1.2309 1.4729 1.7135 1.9526 2.4268 2.8954 3.3586 3.8165

0.0039 0.0173 0.0330 0.0828 0.1654 0.2475 0.3292 0.4103 0.4910 0.5712 0.6509 0.8089 0.9651 1.1195 1.2722

T = 293.2 K 0.1755 0.1754 0.1753 0.1750 0.1744 0.1739 0.1734 0.1728 0.1723 0.1718 0.1713 0.1703 0.1692 0.1682 0.1673

−86.6 −46.5 −28.4 −2.0 17.0 29.2 37.8 44.9 50.9 56.0 60.5 68.8 76.0 82.0 88.5

I

mAa

m2a

Eb

γ±CaCl2b

mol· kg−1

mol· kg−1

mol· kg−1

mV

1.0587 0.8246 0.7576 0.6858 0.6196 0.6051 0.5945 0.5947 0.5989 0.6033 0.6089 0.6342 0.6649 0.6908 0.7441

0.0116 0.0497 0.0996 0.2493 0.4977 0.7440 0.9889 1.2328 1.4748 1.7153 1.9547 2.4290 2.8982 3.3617 3.8200

0.0039 0.0166 0.0332 0.0831 0.1659 0.2480 0.3296 0.4109 0.4916 0.5718 0.6516 0.8097 0.9661 1.1206 1.2733

T = 303.2 K 0.1755 0.1754 0.1753 0.1750 0.1744 0.1739 0.1734 0.1728 0.1723 0.1718 0.1713 0.1703 0.1692 0.1682 0.1673

−86.5 −42.0 −18.6 8.8 32.6 44.1 51.5 59.1 65.4 71.1 75.9 84.3 92.1 99.1 106.7

I

mAa

m2a

Eb

γ±CaCl2b

mol· kg−1

mol· kg−1

mol· kg−1

mV

γ±CaCl2b

1.0376 0.8256 0.7834 0.6644 0.6403 0.5875 0.5418 0.5355 0.5323 0.5353 0.5360 0.5433 0.5643 0.5897 0.6395

0.0117 0.0612 0.0998 0.2488 0.4975 0.7682 0.9885 1.2318 1.4736 1.7141 1.9529 2.4272 2.8955 3.3588 3.8165

0.0039 0.0204 0.0333 0.0829 0.1658 0.2561 0.3295 0.4106 0.4912 0.5714 0.6510 0.8091 0.9652 1.1196 1.2722

T = 313.2 K 0.1755 0.1754 0.1753 0.1750 0.1744 0.1738 0.1734 0.1728 0.1723 0.1718 0.1713 0.1703 0.1692 0.1682 0.1673

−103.5 −48.1 −27.3 0.6 23.2 38.5 46.4 53.6 58.6 63.2 67.4 74.1 80.3 88.3 95.9

0.9144 0.7568 0.8062 0.6779 0.6175 0.6000 0.5750 0.5585 0.5331 0.5178 0.5080 0.4882 0.4824 0.5142 0.5536

aa

mA is expressed per kilogram of aqueous L-glutamine solution, m2 is the molality of L-glutamine in the solvent. Standard uncertainties u are u(m) = 0.0001 mol·kg−1, u(T) = 0.1 K, u(p) = 2 kPa. bThe average standard uncertainties of cell potential and mean activity coefficient value were calculated in according to the law of uncertainty propagation: u(E) = 0.1 mV and u(γ±) = 0.0060 at 293.2, u(E) = 0.2 mV and u(γ±) = 0.0065 at 303.2, and u(E) = 0.2 mV and u(γ±) = 0.0050 at 313.2 K.

Table 3. Total Ionic Strengths (I), Molality of Ca(NO3)2 (mB), Molality of L-Glutamine (m2), the Cell Potential Data (E) and Experimental Mean Activity Coefficients of Ca(NO3)2 (γ±Ca(NO3)2) for (Ca(NO3)2 + L-Glutamine + H2O) System at T = (293.2, 303.2, and 313.2) K and P = 0.1 MPa I

mBa

m2a

mol·kg−1 mol·kg−1 mol·kg−1 T = 293.2 K 0.0068 0.0023 0.0501 0.0167 0.0995 0.0332 0.2485 0.0828 0.4940 0.1647 0.7368 0.2456 0.9764 0.3255 1.2137 0.4046 1.4480 0.4827 1.6795 0.5598 1.9392 0.6464 2.3583 0.7861 2.7982 0.9327 3.2286 1.0762

0.1755 0.1753 0.1751 0.1744 0.1734 0.1723 0.1713 0.1703 0.1692 0.1682 0.1671 0.1653 0.1634 0.1616

Eb mV −41.4 14.8 34.5 58.1 78.0 89.1 97.2 103.0 108.3 112.6 116.1 122.0 126.5 131.9

I γ±Ca(NO3)2b

mBa

m2a

mol·kg−1 mol·kg−1 mol·kg−1

T = 303.2 K 0.9522 0.0099 0.8047 0.0503 0.7684 0.0997 0.6628 0.2489 0.6367 0.4942 0.6124 0.7366 0.6014 0.9764 0.5843 1.2133 0.5818 1.4477 0.5769 1.6792 0.5599 1.9084 0.5578 2.3583 0.5442 2.7984 0.5622 3.2286 3.6494

0.0033 0.0168 0.0332 0.0830 0.1647 0.2455 0.3255 0.4044 0.4826 0.5597 0.6361 0.7861 0.9328 1.0762 1.2165

0.1755 0.1753 0.1751 0.1744 0.1734 0.1723 0.1713 0.1703 0.1692 0.1682 0.1673 0.1653 0.1634 0.1616 0.1598

Eb mV −104.1 −52.0 −31.4 −4.2 16.0 28.0 36.3 43.0 47.4 52.0 56.1 60.3 66.6 71.0 74.0

I γ±Ca(NO3)2b

mBa

m2a

mol·kg−1 mol·kg−1 mol·kg−1

T = 313.2 K 0.9185 0.0099 0.8318 0.0501 0.7664 0.1002 0.6797 0.2486 0.6179 0.4943 0.5887 0.7368 0.5660 0.9766 0.5540 1.2133 0.5280 1.4479 0.5207 1.6793 0.5165 1.9082 0.4725 2.3585 0.4787 2.7984 0.4719 3.2286 0.4557 3.6494

0.0033 0.0167 0.0334 0.0829 0.1648 0.2456 0.3255 0.4044 0.4826 0.5598 0.6361 0.7862 0.9328 1.0762 1.2165

0.1755 0.1753 0.1751 0.1744 0.1734 0.1723 0.1713 0.1703 0.1692 0.1682 0.1673 0.1653 0.1634 0.1616 0.1598

Eb mV

γ±Ca(NO3)2b

−130.0 −77.8 −58.0 −30.7 −11.0 1.0 9.0 14.5 19.2 23.4 26.6 31.0 36.0 41.1 45.0

0.9073 0.8372 0.7509 0.6775 0.6097 0.5829 0.5570 0.5274 0.5077 0.4955 0.4793 0.4416 0.4314 0.4347 0.4315

a

mB is expressed per kilogram of aqueous L-glutamine solution, m2 is the molality of L-glutamine in the solvent. Standard uncertainties u are u(m) = 0.0001 mol·kg−1, u(T) = 0.1 K, u(p) = 2 kPa. bThe average standard uncertainties of cell potential and mean activity coefficient value were calculated in according to the law of uncertainty propagation: u(E) = 0.6 mV and u(γ±) = 0.0155 at 293.2, u(E) = 0.5 mV and u(γ±) = 0.0100 at 303.2, and u(E) = 0.2 mV and u(γ±) = 0.0055 at 313.2 K. C



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Table 4. Pitzer Ion-Interaction Parameter Values (β(0), β(1), and Cφ) for Single Electrolyte of CaCl2 and Ca(NO3)2 in Aqueous Solution Containing 2.5% Mass Fraction of LGlutamine β / kg mol−1 (0)

T/K

β / kg mol−1 (1)

ln γ±CaCl = 2f γ + 2

ln γ±Ca(NO ) = 2f γ + 3

(φ)

C / kg2 mol−2

σ(γ)a

ref

a

0.0508 −0.1670 −0.2598

293.2 303.2 313.2

−0.0233 −0.1108 −0.2272

3.1360 0.1183 3.7794 0.2238 4.3836 0.2332 Ca(NO3)2 3.4391 0.1038 3.7203 0.1128 4.1479 0.1723

0.0175 0.0174 0.0098

this work this work this work

0.0094 0.0104 0.0095

this work this work this work

2

(1)

4 γ 2 2 ϕ BCa(NO3) I + C I2 2 9 9 Ca(NO3)2 (2)

CaCl2 293.2 303.2 313.2

4 γ 2 2 ϕ 2 BCaCl 2 I + CCaCl 2I 9 9

where ⎤ ⎡ I 2 f γ = −Aϕ⎢ + ln(1 + b I )⎥ ⎦ ⎣1 + b I b γ (0) BMX = 2βMX +

σ is standard deviation of the fitting.

(3)

(0) 2βMX

α12I

⎤ ⎡ ⎛ α2 ⎞ × ⎢1 − ⎜1 + α1 I − 1 I ⎟ exp( −α1 I )⎥ ⎢⎣ 2 ⎠ ⎝ ⎦⎥

20

(CaCl2 + Ca(NO3)2 + L-glutamine + H2O) systems. According to the Pitzer model, the mean molal activity coefficients (γ±) for CaCl2 and Ca(NO3)2 as single salts in the aqueous solution containing 2.5% mass fraction of L-glutamine are written as

(4)

In these equations, α1 and b are assumed constant with an amount of 2.0 and 1.2 kg1/2·mol−1/2, respectively, and I is the

Table 5. Total Ionic Strengths (I), Molality of CaCl2 (m1), Molality of L-Glutamine (m2), the Cell Potential Data (E) and Experimental Mean Activity Coefficients of CaCl2 (γ±CaCl2) for (CaCl2 + Ca(NO3)2 + L-Glutamine + H2O) System at T = 293.2 K and P = 0.1 MPa I

m1a

m2a

Eb

mol·kg−1

mol·kg−1

mol·kg−1

mV

0.0019 0.0082 0.0167 0.0414 0.0826 0.1234 0.1637 0.2037 0.2434 0.2828 0.3217 0.3987 0.4744 0.5487 0.6218

0.1755 0.1753 0.1752 0.1747 0.1739 0.1731 0.1723 0.1715 0.1708 0.1700 0.1692 0.1678 0.1663 0.1648 0.1634

−50.3 −13.6 4.5 40.5 66.0 78.5 87.2 93.9 99.5 104.4 108.4 115.4 121.6 127.2 132.4

0.0034 0.0146 0.0293 0.0733 0.1461 0.2184 0.2904 0.3617 0.4329 0.5035 0.5735 0.7124 0.8496 0.9850 1.1143

0.1755 0.1754 0.1753 0.1749 0.1743 0.1737 0.1731 0.1725 0.1719 0.1714 0.1708 0.1697 0.1685 0.1674 0.1664

−56.4 7.4 30.0 57.0 78.1 90.5 99.6 106.9 113.1 118.4 122.9 130.7 137.7 142.9 148.6

r=1 0.0116 0.0495 0.1004 0.2486 0.4956 0.7401 0.9823 1.2222 1.4603 1.6966 1.9302 2.3921 2.8462 3.2924 3.7310 r = 7.5 0.0117 0.0498 0.0997 0.2494 0.4966 0.7426 0.9872 1.2299 1.4719 1.7117 1.9498 2.4220 2.8885 3.3491 3.7885

γ±CaCl2b

I

m1a

m2a

Eb

mol·kg−1

mol·kg−1

mol·kg−1

mV

γ±CaCl2b

0.0028 0.0118 0.0239 0.0592 0.1182 0.1766 0.2345 0.2920 0.3491 0.4056 0.4619 0.5731 0.6827 0.7906 0.8970

0.1755 0.1754 0.1752 0.1748 0.1741 0.1734 0.1728 0.1721 0.1714 0.1708 0.1701 0.1688 0.1675 0.1663 0.1650

23.0 56.0 73.9 95.9 113.9 124.5 132.4 138.7 143.7 148.6 152.6 159.7 166.4 172.6 176.7

0.9452 0.7557 0.7255 0.6642 0.6499 0.6454 0.6520 0.6620 0.6670 0.6863 0.6994 0.7369 0.7938 0.8633 0.8864

0.0046 0.0151 0.0305 0.0761 0.1505 0.2252 0.2990 0.3728 0.4458 0.5184 0.5906 0.7337 0.8747 1.0141 1.1517

0.1755 0.1754 0.1753 0.1749 0.1743 0.1738 0.1732 0.1726 0.1720 0.1715 0.1709 0.1698 0.1687 0.1676 0.1665

−20.5 11.8 31.7 57.8 78.0 89.0 100.2 107.8 113.2 118.3 123.0 131.1 137.0 144.3 151.5

0.8395 0.7435 0.7127 0.6752 0.6653 0.6393 0.6970 0.7185 0.7180 0.7307 0.7491 0.7878 0.8029 0.8813 0.9843

r = 2.5 0.0116 0.0495 0.1004 0.2486 0.4964 0.7416 0.9849 1.2264 1.4662 1.7037 1.9399 2.4072 2.8671 3.3206 3.7673 r = 10 0.4432 0.0152 0.7390 0.0500 0.7391 0.1005 0.6783 0.2512 0.6518 0.4967 0.6384 0.7432 0.6354 0.9866 0.6385 1.2302 0.6456 1.4713 0.6534 1.7107 0.6588 1.9488 0.6742 2.4213 0.7012 2.8866 0.7097 3.3466 0.7476 3.8006 1.1471 0.7427 0.6048 0.6622 0.6736 0.6377 0.6115 0.5918 0.5785 0.5703 0.5600 0.5487 0.5476 0.5528 0.5635

I

m1a

m2a

Eb

mol·kg−1

mol·kg−1

mol·kg−1

mV

γ±CaCl2b

0.0036 0.0140 0.0278 0.0691 0.1381 0.2063 0.2744 0.3419 0.4089 0.4757 0.5419 0.6733 0.8209 0.9313 1.0580

0.1755 0.1754 0.1753 0.1749 0.1742 0.1736 0.1730 0.1724 0.1718 0.1712 0.1706 0.1694 0.1681 0.1671 0.1659

−15.1 18.4 34.4 58.4 77.0 90.1 96.2 102.6 107.3 112.2 116.6 124.7 131.8 137.0 142.7

0.9276 0.7844 0.6978 0.6558 0.6339 0.6746 0.6295 0.6337 0.6258 0.6398 0.6563 0.7036 0.7420 0.7863 0.8469

r=5 0.0130 0.0505 0.0999 0.2487 0.4971 0.7427 0.9879 1.2309 1.4720 1.7124 1.9509 2.4239 2.9554 3.3527 3.8087

a m1 is expressed per kilogram of aqueous L-glutamine solution, m2 is the molality of L-glutamine in the solvent, and r is the salts molal ratio (r = mCaCl2/mCa(NO3)2). Standard uncertainties u are u(m) = 0.0001 mol·kg−1, u(T) = 0.1 K, u(p) = 2 kPa. bThe average standard uncertainties of cell potential and mean activity coefficient value were calculated in according to the law of uncertainty propagation; u(E) = 0.1 mV and u(γ±) = 0.0067 for r = 1, u(E) = 0.1 mV and u(γ±) = 0.0069 for r = 2.5, u(E) = 0.2 mV and u(γ±) = 0.0081 for r = 5, u(E) = 0.2 mV and u(γ±) = 0.0060 for r = 7.5 and u(E) = 0.2 mV and u(γ±) = 0.0081 for r = 10.

D



Article

total ionic strength on a molality scale. β(0), β(1), and Cφ symbolize the parameters of Pitzer equation for single salt electrolyte solutions in aqueous solution containing 2.5% mass fraction of L-glutamine and indicate the virial coefficients in relating to the binary (β(0), β(1)) and ternary (Cφ) interactions. Aφ denotes the Debye−Hückel parameter for the osmotic function defined by eq 5: Aϕ =

1.4006 ×

According to the Pitzer model, the mean activity coefficient values for CaCl2 in the quaternary system consisting of calcium chloride and calcium nitrate into the L-glutamine + water aqueous solution containing 2.5% mass fraction of L-glutamine were calculated using eq 6: ϕ γ ln γ±CaCl = 2f γ + 2mCa mCl (2BCaCl − BCaCl )/I 2 2 2

106ds1/2 1/2 −1/2 kg mol 3/2

(εrT )

ϕ γ + 2mCa mNO3(2BCa(NO − BCa(NO )/I 3)2 3)2

(5)

γ ϕ ) + [(mCl + 2mCa )/3][2(BCaCl − BCaCl 2 2

−3

where ds is the solvent density (kg m ), εr is the solvent relative permittivity; and T is the kelvin temperature. The values of this parameter for L-glutamine + water aqueous solution containing 2.5% mass fraction of L-glutamine are 0.3324, 0.3399, and 0.3475 kg1/2 mol−1/2 at 293.2, 303.2, and 313.2 K, respectively. In this work εr values for aqueous solution containing 2.5% mass fraction of L-glutamine were determined by using the mixing rule and reported data in the literature.25−27

ϕ ϕ + (2ICCaCl /3 2 )] + (2/3 2 )mCa (mCl CCaCl 2 2 ϕ γ ϕ + mNO3CCa(NO ) + (mNO3 /3)[2(BCa(NO − BCa(NO ) 3)2 3)2 3)2 ϕ + (2ICCa(NO /3 2 ) + 4θC lNO3 + (mCl + 2mCa ) 3)2

× ψCaClNO ]

(6)

3


m1a

m2a

Eb

mol·kg−1

mol·kg−1

mol·kg−1

mV

γ±CaCl2b

0.0019 0.0083 0.0168 0.0416 0.0829 0.1238 0.1644 0.2046 0.2446 0.2842 0.3235 0.4012 0.4777 0.5529 0.6270

0.1755 0.1753 0.1752 0.1747 0.1739 0.1731 0.1723 0.1715 0.1707 0.1700 0.1692 0.1677 0.1662 0.1648 0.1633

−106.0 −61.0 −39.3 −12.3 7.3 19.9 29.2 36.5 42.3 48.5 53.7 60.7 66.6 72.2 79.9

0.8348 0.7547 0.7140 0.6482 0.5856 0.5722 0.5698 0.5699 0.5676 0.5865 0.6042 0.6012 0.6028 0.6161 0.6846

0.0037 0.0149 0.0294 0.0732 0.1460 0.2183 0.2902 0.3615 0.4324 0.5030 0.5729 0.7114 0.8482 0.9825 1.1165

0.1755 0.1754 0.1753 0.1749 0.1743 0.1737 0.1731 0.1725 0.1720 0.1714 0.1708 0.1697 0.1685 0.1674 0.1663

−93.5 −49.1 −25.9 0.5 22.1 34.7 42.6 50.6 57.1 62.1 66.2 73.6 80.5 87.4 94.5

0.8348 0.7402 0.7308 0.6304 0.5900 0.5679 0.5368 0.5431 0.5479 0.5442 0.5395 0.5396 0.5493 0.5722 0.6111

r=1 0.0116 0.0496 0.1007 0.2494 0.4973 0.7429 0.9863 1.2277 1.4674 1.7055 1.9410 2.4071 2.8659 3.3174 3.7619 r = 7.5 0.0124 0.0505 0.1001 0.2488 0.4964 0.7423 0.9868 1.2291 1.4702 1.7101 1.9479 2.4188 2.8839 3.3406 3.7961

I

m1a

m2a

Eb

mol·kg−1

mol·kg−1

mol·kg−1

mV

0.0028 0.0118 0.0237 0.0593 0.1184 0.1768 0.2348 0.2922 0.3492 0.4057 0.4617 0.5725 0.6814 0.7886 0.8941

0.1755 0.1754 0.1752 0.1748 0.1741 0.1734 0.1728 0.1721 0.1714 0.1708 0.1701 0.1688 0.1676 0.1663 0.1651

0.0036 0.0150 0.0302 0.0756 0.1508 0.2254 0.2996 0.3738 0.4473 0.5204 0.5932 0.7377 0.8807 1.0221 1.1621

0.1755 0.1754 0.1753 0.1749 0.1743 0.1738 0.1732 0.1726 0.1720 0.1715 0.1709 0.1698 0.1687 0.1677 0.1666

r = 2.5 0.0116 0.0496 0.0995 0.2492 0.4974 0.7427 0.9861 1.2274 1.4668 1.7037 1.9392 2.4045 2.8619 3.3122 3.7552 r = 10 0.0119 0.0496 0.0995 0.2496 0.4977 0.7438 0.9888 1.2335 1.4760 1.7174 1.9577 2.4345 2.9061 3.3729 3.8348

I

m1a

m2a

Eb

γ±CaCl2b

mol·kg−1

mol·kg−1

mol·kg−1

mV

γ±CaCl2b

−88.0 −46.6 −27.3 −1.6 17.0 30.1 37.2 43.7 47.6 53.2 59.0 66.5 72.5 77.2 81.7

0.8414 0.7537 0.7026 0.6453 0.5907 0.6048 0.5734 0.5687 0.5400 0.5574 0.5910 0.5980 0.6202 0.6241 0.6515

r=5 0.0130 0.0505 0.0999 0.2487 0.4971 0.7427 0.9879 1.2309 1.4720 1.7124 1.9509 2.4239 2.9554 3.3527 3.8087

0.0036 0.0140 0.0278 0.0691 0.1381 0.2063 0.2744 0.3419 0.4089 0.4757 0.5419 0.6733 0.8209 0.9313 1.0580

0.1755 0.1754 0.1753 0.1749 0.1743 0.1736 0.1730 0.1724 0.1718 0.1712 0.1706 0.1694 0.1682 0.1671 0.1660

−15.1 18.4 34.4 58.4 77.0 90.1 96.2 102.6 107.3 112.2 116.6 124.7 131.8 137.0 142.7

0.8548 0.7397 0.6912 0.6491 0.5960 0.5712 0.5557 0.5362 0.5213 0.5029 0.5176 0.5065 0.5050 0.5278 0.5188

−91.0 −51.4 −28.0 −0.2 19.8 31.5 41.0 49.5 54.7 59.6 63.5 70.4 76.3 81.2 87.0

0.9795 0.7384 0.7245 0.6456 0.5776 0.5423 0.5371 0.5506 0.5349 0.5297 0.5172 0.5108 0.5076 0.5040 0.5243

a

m1 is expressed per kilogram of aqueous L-glutamine solution, m2 is the molality of L-glutamine in the solvent, and r is the salts molal ratio (r = mCaCl2/mCa(NO3)2). Standard uncertainties u are u(m) = 0.0001 mol·kg−1, u(T) = 0.1 K, u(p) = 2 kPa. bThe average standard uncertainties of cell potential and mean activity coefficient value were calculated in according to the law of uncertainty propagation; u(E) = 0.3 mV and u(γ±) = 0.0094 for r = 1, u(E) = 0.3 mV and u(γ±) = 0.0085 for r = 2.5, u(E) = 0.3 mV and u(γ±) = 0.0075 for r = 5, u(E) = 0.2 mV and u(γ±) = 0.0060 for r = 7.5 and u(E) = 0.3 mV and u(γ±) = 0.0079 for r = 10. E



Article

The quantities of BϕMX and BγMX have been calculated from the eqs 7 and 8:19,21 ϕ 1 ° + βMX BMX = βMX exp( −α1 I )

303.2, and 313.2 K), as a preliminary step. The measured potentials were plotted against log (γ±I) to check the slope (s) and the linear correlation coefficient (R2). It can be noted that the activity coefficients (γ±) were calculated according to eq 1. The degree of the linear correlation coefficient (R2 = 0.9993) and a near Nernst slope (s = 81.1 mV) in Figure 1 indicates that the electrode pair used here are well suited for our measurements. 4.2. Determination of Activity Coefficients and Pitzer Parameters for Ternary Systems. After the calibration of Ca-ISE and Ag-AgCl electrodes, the mean activity coefficients CaCl2 in aqueous solution containing 2.5% mass fraction of L-glutamine were determined based on cell potential measurements using the galvanic cell (A) considering the Nernst equation. Similarly, the mean activity coefficients Ca(NO3)2 in ternary (Ca(NO3)2 + L-glutamine + H2O) system were determined based on potentiometric measurements using the galvanic cell (B). The values of measured cell potential and the obtained mean activity coefficients of the single salt CaCl2 and Ca(NO3)2 in

(7)

γ 1 ° + (2βMX BMX = 2βMX /α12I )

× [1 − (1 + α1 I − α12I /2)exp(−α1 I )]

(8)

The θClNO3 and ψCaClNO3 indicate the unknown mixing ion interaction parameters which were determined according to the Pitzer graphical method.28

4. RESULTS AND DISCUSSION 4.1. Calibration of Electrode Pair of Ca-ISE and Ag− AgCl. To check the response of the electrodes, the potential of the cell (A) was first measured in single salt CaCl2 in aqueous solution containing 2.5% mass fraction of L-glutamine with ionic strength ranging from 0.0100 to 4.0000 mol kg−1, at T = (293.2,


m1a

m2a

Eb

mol·kg−1

mol·kg−1

mol·kg−1

mV

γ±CaCl2b

0.0019 0.0083 0.0166 0.0417 0.0826 0.1240 0.1646 0.2047 0.2446 0.2841 0.3232 0.4003 0.4761 0.5487 0.6218

0.1755 0.1753 0.1752 0.1747 0.1739 0.1731 0.1723 0.1715 0.1707 0.1700 0.1692 0.1677 0.1663 0.1648 0.1634

−148.3 −106.0 −93.1 −50.0 −32.0 −7.6 5.2 13.5 20.1 26.2 30.4 37.2 44.2 49.6 55.7

0.9312 0.7309 0.5272 0.7219 0.6097 0.8157 0.8865 0.9035 0.9135 0.9362 0.9281 0.9075 0.9348 0.9465 1.0058

0.0037 0.0146 0.0296 0.0732 0.1460 0.2184 0.2902 0.3616 0.4325 0.5030 0.5728 0.7115 0.8482 0.9832 1.1165

0.1755 0.1754 0.1753 0.1749 0.1743 0.1737 0.1731 0.1725 0.1720 0.1714 0.1708 0.1697 0.1685 0.1674 0.1663

−95.5 −53.1 −33.1 −6.6 11.8 23.6 31.7 38.8 43.1 47.8 52.6 59.6 65.7 71.7 78.0

0.8192 0.7637 0.6975 0.6383 0.5649 0.5437 0.5254 0.5250 0.5012 0.4983 0.5075 0.5119 0.5136 0.5332 0.5704

r=1 0.0117 0.0498 0.0999 0.2501 0.4955 0.7442 0.9875 1.2284 1.4674 1.7046 1.9389 2.4019 2.8567 3.2924 3.7311 r = 7.5 0.0125 0.0495 0.1005 0.2489 0.4964 0.7425 0.9866 1.2294 1.4705 1.7101 1.9475 2.4189 2.8839 3.3429 3.7961

I

m1a

m2a

Eb

mol·kg−1

mol·kg−1

mol·kg−1

mV

0.0028 0.0119 0.0238 0.0593 0.1181 0.1766 0.2344 0.2919 0.3491 0.4058 0.4620 0.5731 0.6827 0.7906 0.8970

0.1755 0.1754 0.1752 0.1748 0.1741 0.1734 0.1728 0.1721 0.1714 0.1708 0.1701 0.1688 0.1675 0.1663 0.1650

0.0037 0.0152 0.0301 0.0757 0.1507 0.2250 0.2990 0.3727 0.4457 0.5184 0.5900 0.7335 0.8746 1.0140 1.1516

0.1755 0.1754 0.1753 0.1749 0.1743 0.1738 0.1732 0.1726 0.1720 0.1715 0.1709 0.1698 0.1687 0.1676 0.1665

r = 2.5 0.0117 0.0498 0.0999 0.2492 0.4959 0.7417 0.9845 1.2262 1.4662 1.7042 1.9402 2.4070 2.8673 3.3205 3.7672 r = 10 0.0123 0.0502 0.0995 0.2498 0.4972 0.7425 0.9867 1.2299 1.4708 1.7108 1.9471 2.4208 2.8865 3.3464 3.8007

I

m1a

m2a

Eb

γ±CaCl2b

mol·kg−1

mol·kg−1

mol·kg−1

mV

γ±CaCl2b

−102.0 −55.6 −34.6 −8.1 12.9 25.7 34.4 41.7 47.5 52.1 55.5 63.3 69.1 74.2 80.5

0.8265 0.7609 0.7052 0.6178 0.5768 0.5627 0.5480 0.5458 0.5416 0.5337 0.5183 0.5259 0.5239 0.5258 0.5582

r=5 0.0117 0.0501 0.1003 0.2488 0.4969 0.7420 0.9864 1.2286 1.4690 1.7081 1.9453 2.4153 2.8790 3.3364 3.7876

0.0033 0.0139 0.0279 0.0691 0.1380 0.2061 0.2740 0.3413 0.4081 0.4745 0.5404 0.6709 0.7997 0.9268 1.0521

0.1755 0.1754 0.1753 0.1749 0.1743 0.1736 0.1730 0.1724 0.1718 0.1712 0.1706 0.1694 0.1682 0.1671 0.1660

−53.6 −16.2 3.3 27.5 43.9 55.8 64.6 71.3 76.9 81.1 86.3 92.8 98.5 104.4 110.0

0.8499 0.7186 0.7002 0.6479 0.5696 0.5738 0.5838 0.5899 0.5980 0.5940 0.6171 0.6255 0.6492 0.6789 0.7449

−88.5 −45.8 −25.3 0.7 22.1 34.6 41.8 48.5 56.6 61.4 65.1 72.0 78.3 84.5 87.7

0.8788 0.7589 0.7005 0.6000 0.5659 0.5476 0.5094 0.4977 0.5283 0.5232 0.5125 0.5022 0.5040 0.5172 0.5245

a

m1 is expressed per kilogram of aqueous L-glutamine solution, m2 is the molality of L-glutamine in the solvent, and r is the salts molal ratio (r = mCaCl2/mCa(NO3)2). Standard uncertainties u are u(m) = 0.0001 mol·kg−1, u(T) = 0.1 K, u(p) = 2 kPa. bThe average standard uncertainties of cell potential and mean activity coefficient value were calculated in according to the law of uncertainty propagation; u(E) = 0.3 mV and u(γ±) = 0.0097 for r = 1, u(E) = 0.2 mV and u(γ±) = 0.0071 for r = 2.5, u(E) = 0.2 mV and u(γ±) = 0.0066 for r = 5, u(E) = 0.2 mV and u(γ±) = 0.0063 for r = 7.5 and u(E) = 0.2 mV and u(γ±) = 0.0062 for r = 10. F



Article

mixture of L-glutamine and water at T = (293.2, 303.2 and 313.2) K were listed in Tables 2 and 3, respectively. The Pitzer ion-interaction parameters for CaCl2 (β0CaCl2, β1CaCl2 ϕ and CCaCl ) were obtained by an iteration minimization 2 procedure on the results of eq 3 employing the Microsoft Excel (solver) program. As the same way, these parameters for Ca(NO3)2 (β0Ca(NO3)2, β1Ca(NO3)2, and CϕCa(NO3)2) were determined by using eq 4. The obtained results were illustrated in Table 4 for the investigated ternary systems at T = (293.2, 303.2, and 313.2) K. As can be seen, increasing the temperature reduces β0CaCl2 at the same concentration of L-glutamine. Also, the amounts β1CaCl2 and CϕCaCl2 are increased with increasing temperature. 4.3. Evaluation of the Mean Activity Coefficients for Quaternary System. The experimental mean activity coefficients of CaCl2 were evaluated for various series of salt molal ratio by using the galvanic cell (D) from the Nernst equation:

Figure 3. Values of mean activity coefficients CaCl2 against total ionic strength at different temperature T = (293.2, 303.2 and 313.2) K for molal ratio r = mCaCl2/mCa(NO3)2 = 10 in the aqueous solution containing 2.5% mass fraction of L-glutamine.

temperature. Also, a similar tendency was seen with r = 1, 2.5, 5, and 7.5 (see Figures S3 to S6 in Supporting Information). 4.4. Determination of Mixed Ionic Interaction Parameters (θClNO3, ψCaClNO3). The mixed ionic interaction parameters (θClNO3,ψCaClNO3) were determined for the quaternary system studied based on the Pitzer graphical method, in according to the following relation:

E D = E′ + k log[(m1 + m2)(2m1)2 γ±3CaCl + K ClNO3 2

× (m1 + m2)(2m2)2 γ±3Ca(NO ) ]

(9)

3 2

Because KClNO3 is so small, the second term within brackets on the right of eq 9 can be neglected, therefore we get the simplified form of eq 10:

⎞ 3 1⎛ 1 Δln γ±CaCl = θClNO3 + ⎜mCa + mCl ⎟ 2 ⎝ ⎠ 4mNO3 2 2

E D = E′ + k log[(m1 + m2)(2m1)2 γ±3CaCl ] 2

= E° + s log(γ±I )

(10)

(11)

Table 8. Pitzer Mixing Interaction Parameters Obtained (θClNO3 and ψCaClNO3) for the (CaCl2 + Ca(NO3)2 + L-Glutamine + H2O) Quaternary System at T = (293.2, 303.2, and 313.2) K and P = 0.1 MPa

The values for the mean ionic activity coefficient of CaCl2 in the mixture over total ionic strengths from 0.0100 to 4.0000 mol· kg−1 for different series of salt molal ratio r = mCaCl2/mCa(NO3)2= 1.0, 2.5, 5.0, 7.5, and 10.0 were illustrated in Tables 5 to 7 at 293.2, 303.2, and 313.2 K, respectively. As well, Figure 2 presents

r T = 293.2 K 1 2.5 5 7.5 meana ud 10 T = 303.2 K 1 2.5 7.5 meanb ud 5 10 T = 313.2 K 2.5 7.5 10 meanc ud 1 5

Figure 2. Plot of the mean activity coefficients for CaCl2 versus total ionic strength at different molal ratio (r = mCaCl2/mCa(NO3)2) at T = 293.2 K and P = 0.1 MPa.

the mean activity coefficients of CaCl2 against total ionic strength for various series of salt molal ratios at T = 293.2 K. It can be observed that with rising the ratio of CaCl2 to Ca(NO3)2, activity coefficient of CaCl2 will decrease. As well, the same trends were observed to change the activity coefficients at T = (303.2 and 313.2) K (see Figures S1 and S2 in Supporting Information). In addition, the temperature comparison of activity coefficient data for r = 10 is shown in Figure 3, and it is clear that the activity coefficient of CaCl2 in a mixture decreases by increasing the

θClNO3 (kg·mol−1)

ψCaClNO3 (kg2·mol−2)

0.023 0.374 0.659 0.815 0.468 ±0.174 1.911

−0.155 −0.066 −0.355 −0.567 −0.286 ±0.111 −0.817

0.327 0.497 0.546 0.457 ±0.066 0.180 0.432

−0.279 −0.374 −0.537 −0.397 ±0.075 −0.340 −0.752

0.324 0.399 0.348 0.357 ±0.022 0.971 1.071

−0.253 −0.232 −0.236 −0.240 ±0.006 −0.608 −0.467

a

The value of molal ratio r = 10 was excluded to calculate the mean values. bThe values of molal ratio r = 5 and 10 were excluded to calculate the mean values. cThe values of molal ratio r = 1 and 5 were excluded to calculate the mean values. du is standard uncertainty value for θClNO3 and ψCaClNO3. G


Journal of Chemical & Engineering Data Δln γ±CaCl = (ln γ±CaCl )exp − (ln γ±CaCl )cal 2

2

2

Article

high ionic strengths. The results obtained were illustrated for different series of salt molal ratio in Table 8. 4.5. Calculation of Thermodynamic Properties. The parameters obtained were used for predicting the thermodynamic properties of the system under investigation by the Pitzer model. The osmotic coefficients (φ), the mean activity coefficients of Ca(NO3)2, solvent activity (as), and the excess Gibbs free energy (GE) were calculated for all of the series under

(12)

where (ln γ±CaCl2)cal is related to the values calculated in eq 6 with ψCaClNO3 = 0 and θClNO3 = 0. The Pitzer mixing parameters were determined from the intercept and slope of the linear regression plot of the left side of eq 11 versus 1/2(mCa + 1/2mCl). These parameters account for the short-range interactions between two anion and two anions plus cation which are important only at

Table 9. Calculated Values of Mean Activity Coefficients for Ca(NO3)2 (γ±Ca(NO3)2), Osmotic Coefficients (φ), Excess Gibbs Free Energy (GE/RT) and Solvent Activity (as) as a Function of Ionic Strength, for the (CaCl2 + L-Glutamine + H2O) and (CaCl2 + Ca(NO3)2 + L-Glutamine + H2O) Systems at 293.2 K and P = 0.1 MPa I/(mol·kg−1) r = pure CaCl2 0.0116 0.0518 0.0989 0.2483 0.4962 0.7426 0.9875 1.2309 1.4729 1.7135 1.9526 2.4268 2.8954 3.3586 3.8165 r = 7.5 0.0117 0.0498 0.0997 0.2494 0.4966 0.7426 0.9872 1.2299 1.4719 1.7117 1.9498 2.4220 2.8885 3.3491 3.7885 r = 2.5 0.0116 0.0495 0.1004 0.2486 0.4964 0.7416 0.9849 1.2264 1.4662 1.7037 1.9399 2.4072 2.8671 3.3206 3.7673

γ±Ca(NO3)2

φ

GE/RT

I/(mol·kg−1)

as

0.9499 0.9282 0.9242 0.9276 0.9326 0.9335 0.9338 0.9355 0.9398 0.9472 0.9579 0.9899 1.0356 1.0944 1.1658

−0.0014 −0.0110 −0.0258 −0.0819 −0.1875 −0.3007 −0.4185 −0.5395 −0.6621 −0.7850 −0.9068 −1.1417 −1.3566 −1.5421 −1.6898

0.9998 0.9991 0.9983 0.9958 0.9915 0.9873 0.9832 0.9790 0.9748 0.9705 0.9661 0.9567 0.9463 0.9345 0.9213

0.8475 0.7715 0.7446 0.7382 0.7690 0.8077 0.8481 0.8897 0.9330 0.9781 1.0252 1.1268 1.2395 1.3642 1.4970

0.9504 0.9310 0.9288 0.9383 0.9518 0.9597 0.9658 0.9721 0.9799 0.9896 1.0015 1.0327 1.0735 1.1235 1.1798

−0.0014 −0.0103 −0.0256 −0.0794 −0.1770 −0.2779 −0.3799 −0.4817 −0.5829 −0.6819 −0.7780 −0.9582 −1.1164 −1.2464 −1.3397

0.9998 0.9991 0.9983 0.9957 0.9913 0.9870 0.9826 0.9782 0.9738 0.9693 0.9647 0.9550 0.9445 0.9330 0.9210

0.8472 0.7694 0.7397 0.7260 0.7432 0.7669 0.7912 0.8159 0.8411 0.8671 0.8942 0.9522 1.0158 1.0856 1.1619

0.9511 0.9336 0.9336 0.9488 0.9702 0.9846 0.9957 1.0059 1.0163 1.0275 1.0400 1.0689 1.1033 1.1429 1.1872

−0.0014 −0.0101 −0.0253 −0.0762 −0.1662 −0.2551 −0.3416 −0.4252 −0.5054 −0.5818 −0.6540 −0.7838 −0.8909 −0.9722 −1.0249

0.9998 0.9991 0.9983 0.9957 0.9912 0.9866 0.9821 0.9775 0.9729 0.9683 0.9635 0.9537 0.9434 0.9325 0.9209

r = 10 0.0152 0.0500 0.1005 0.2512 0.4967 0.7432 0.9866 1.2302 1.4713 1.7107 1.9488 2.4213 2.8866 3.3466 3.8006 r=5 0.0130 0.0505 0.0999 0.2487 0.4971 0.7427 0.9879 1.2309 1.4720 1.7124 1.9509 2.4239 2.9554 3.3527 3.8087 r=1 0.0116 0.0495 0.1004 0.2486 0.4956 0.7401 0.9823 1.2222 1.4603 1.6966 1.9302 2.3921 2.8462 3.2924 3.7310 H

γ±Ca(NO3)2

φ

GE/RT

as

0.8335 0.7717 0.7451 0.7403 0.7733 0.8145 0.8576 0.9024 0.9488 0.9972 1.0482 1.1584 1.2806 1.4165 1.5669

0.9461 0.9305 0.9279 0.9362 0.9479 0.9544 0.9593 0.9647 0.9718 0.9810 0.9927 1.0241 1.0657 1.1173 1.1782

−0.0020 −0.0104 −0.0259 −0.0807 −0.1792 −0.2828 −0.3875 −0.4935 −0.5987 −0.7023 −0.8034 −0.9946 −1.1637 −1.3046 −1.4109

0.9997 0.9991 0.9983 0.9957 0.9914 0.9870 0.9827 0.9784 0.9740 0.9696 0.9650 0.9554 0.9449 0.9334 0.9208

0.8415 0.7702 0.7431 0.7346 0.7614 0.7955 0.8311 0.8675 0.9050 0.9440 0.9847 1.0723 1.1829 1.2752 1.3922

0.9489 0.9318 0.9305 0.9419 0.9583 0.9685 0.9765 0.9843 0.9931 1.0035 1.0158 1.0467 1.0919 1.1329 1.1873

−0.0016 −0.0105 −0.0255 −0.0782 −0.1735 −0.2701 −0.3671 −0.4627 −0.5564 −0.6478 −0.7357 −0.8983 −1.0556 −1.1504 −1.2297

0.9998 0.9991 0.9983 0.9957 0.9913 0.9868 0.9824 0.9779 0.9734 0.9688 0.9642 0.9543 0.9423 0.9324 0.9201

0.8465 0.7665 0.7337 0.7110 0.7122 0.7193 0.7270 0.7349 0.7433 0.7525 0.7625 0.7859 0.8140 0.8471 0.8852

0.9515 0.9351 0.9363 0.9541 0.9785 0.9947 1.0069 1.0175 1.0277 1.0382 1.0492 1.0738 1.1019 1.1333 1.1674

−0.0014 −0.0100 −0.0250 −0.0746 −0.1603 −0.2434 −0.3228 −0.3985 −0.4702 −0.5380 −0.6013 −0.7140 −0.8064 −0.8767 −0.9237

0.9998 0.9991 0.9983 0.9956 0.9911 0.9865 0.9819 0.9774 0.9727 0.9681 0.9634 0.9538 0.9439 0.9336 0.9229



Article

investigation with common cation [m1 CaCl2 + m2 Ca(NO3)2] according to eq5: ϕ−1=

ϕ γ ln γ±Ca(NO ) = 2f γ + 2mCa mCl (2BCaCl − BCaCl )/I 2 2 3 2

ϕ γ + 2mCa mNO3(2BCa(NO − BCa(NO )/I + [(mNO3 + 2mCa )/3] 3)2 3)2

2 {−AϕI[ I /(1 + b I )] mCl + mNO3 + mCa

γ ϕ ϕ × [2(BCa(NO − BCa(NO ) + (2ICCa(NO /3 2 )] 3)2 3)2 3)2

ϕ ϕ + mCl mCa BCaCl + mNO3mCaBCa(NO + mCl mNO3θClNO3 2 3)2

+

zCa zCl

1/2 ϕ + mCl (mCa )2 CCaCl 2

zCa zCl

ϕ ϕ + (2/3 2 )mCa (mCl CCaCl + mNO3CCa(NO ) 2 3)2

1/2

γ ϕ ϕ + (mCl /3)[2(BCaCl − BCaCl ) + (2ICCaCl /3 2 ) + 4θClNO3 2 2 2

mNO3

ϕ ×(mCa )2 CCa(NO + mCl mNO3mCa ψCaClNO } 3)2 3

+ (mNO3 + 2mCa )ψCaClNO ]

(14)

3

(13)


γ±Ca(NO3)2

φ

GE/RT

I/(mol·kg−1)

as

0.9500 0.9849 0.9625 0.9831 0.9663 0.9337 0.9117 0.8963 0.8873 0.8846 0.8883 0.9222 0.9713 1.0444 1.1400

−0.0014 −0.0104 −0.0259 −0.0817 −0.1891 −0.3089 −0.4390 −0.5783 −0.7241 −0.8748 −1.0285 −1.3355 −1.6286 −1.8917 −2.1101

0.9998 0.9991 0.9982 0.9955 0.9912 0.9873 0.9835 0.9799 0.9762 0.9724 0.9685 0.9596 0.9495 0.9374 0.9229

0.8423 0.7690 0.7424 0.7312 0.7461 0.7634 0.7790 0.7935 0.8074 0.8215 0.8359 0.8671 0.9020 0.9411 0.9850

0.9495 0.9323 0.9307 0.9364 0.9373 0.9302 0.9212 0.9135 0.9086 0.9073 0.9101 0.9284 0.9637 1.0150 1.0824

−0.0015 −0.0106 −0.0256 −0.0789 −0.1787 −0.2868 −0.4021 −0.5232 −0.6492 −0.7790 −0.9106 −1.1740 −1.4281 −1.6604 −1.8643

0.9998 0.9991 0.9983 0.9957 0.9915 0.9874 0.9834 0.9795 0.9757 0.9718 0.9679 0.9595 0.9501 0.9395 0.9271

0.9510 0.9345 0.9347 0.9463 0.9552 0.9543 0.9496 0.9444 0.9401 0.9377 0.9375 0.9443 0.9611 0.9875 1.0226

0.8450 0.7673 0.7377 0.7194 0.7224 0.7276 0.7309 0.7330 0.7345 0.7360 0.7376 0.7424 0.7497 0.7595 0.7718

−0.0014 −0.0102 −0.0250 −0.0765 −0.1694 −0.2663 −0.3669 −0.4709 −0.5778 −0.6868 −0.7974 −1.0199 −1.2379 −1.4457 −1.6372

0.9998 0.9991 0.9983 0.9957 0.9913 0.9870 0.9829 0.9789 0.9749 0.9710 0.9671 0.9590 0.9506 0.9415 0.9317

r = 10 0.0119 0.0496 0.0995 0.2496 0.4977 0.7438 0.9888 1.2335 1.4760 1.7174 1.9577 2.4345 2.9061 3.3729 3.8348 r=5 0.0117 0.0499 0.1000 0.2489 0.4966 0.7419 0.9865 1.2283 1.4689 1.7083 1.9457 2.4154 2.8789 3.3364 3.7877 r=1 0.0116 0.0496 0.1007 0.2494 0.4973 0.7429 0.9863 1.2277 1.4674 1.7055 1.9410 2.4071 2.8659 3.3174 3.7619 I

γ±Ca(NO3)2

φ

GE/RT

as

0.8446 0.7703 0.7434 0.7332 0.7501 0.7695 0.7873 0.8042 0.8206 0.8372 0.8544 0.8916 0.9333 0.9803 1.0329

0.9500 0.9320 0.9298 0.9344 0.9335 0.9251 0.9151 0.9068 0.9017 0.9007 0.9042 0.9253 0.9652 1.0234 1.0991

−0.0015 −0.0103 −0.0255 −0.0797 −0.1813 −0.2918 −0.4104 −0.5363 −0.6671 −0.8020 −0.9394 −1.2144 −1.4790 −1.7206 −1.9272

0.9998 0.9991 0.9983 0.9957 0.9915 0.9874 0.9835 0.9796 0.9758 0.9719 0.9679 0.9594 0.9496 0.9384 0.9253

0.8452 0.7689 0.7410 0.7277 0.7391 0.7526 0.7644 0.7749 0.7848 0.7947 0.8048 0.8269 0.8520 0.8806 0.9126

0.9506 0.9331 0.9321 0.9399 0.9435 0.9386 0.9312 0.9244 0.9198 0.9182 0.9201 0.9347 0.9640 1.0073 1.0639

−0.0014 −0.0103 −0.0254 −0.0780 −0.1754 −0.2794 −0.3898 −0.5048 −0.6241 −0.7468 −0.8712 −1.1202 −1.3616 −1.5859 −1.7841

0.9998 0.9991 0.9983 0.9957 0.9914 0.9873 0.9832 0.9793 0.9754 0.9715 0.9676 0.9593 0.9502 0.9400 0.9285

0.8442 0.7641 0.7311 0.7047 0.6941 0.6861 0.6771 0.6676 0.6581 0.6491 0.6409 0.6272 0.6174 0.6113 0.6085

0.9512 0.9355 0.9368 0.9511 0.9638 0.9656 0.9624 0.9574 0.9523 0.9477 0.9443 0.9414 0.9443 0.9527 0.9661

−0.0014 −0.0102 −0.0252 −0.0753 −0.1646 −0.2563 −0.3503 −0.4467 −0.5457 −0.6471 −0.7501 −0.9600 −1.1718 −1.3817 −1.5863

0.9998 0.9991 0.9983 0.9956 0.9912 0.9869 0.9827 0.9786 0.9746 0.9707 0.9668 0.9591 0.9514 0.9434 0.9352


Journal of Chemical & Engineering Data ⎛ 18.42ϕI ⎞ ⎟ as = exp⎜ − ⎝ ⎠ I

Article

(293.2, 303.2, and 313.2) K, respectively. Figure 4 shows that the mean activity coefficient of Ca(NO3)2 (γ±Ca(NO3)2) increases by increasing the total ionic strength for various series of salt molal ratios in the mixture at T = 293.2 K. Additionally, the corresponding variations were observed to change the mean activity coefficient of Ca(NO3)2 at T = (303.2 and 313.2) K (see Figures S7 and S8 in Supporting Information). As well, Figure 5 indicates the plot of the excess Gibbs free energy against total ionic strength at T = 293.2 K. It can be seen

(15)

GE /RT = 3[m1(1 − ϕ + ln γCaCl ) + m2 2

× (1 − ϕ + ln γCa(NO ) )]

(16)

3 2

The values of these thermodynamic properties were illustrated for different series of salt molal ratio in Tables 9−11 at T =


γ±Ca(NO3)2

φ

GE/RT

I/(mol·kg−1)

as

0.9505 0.9332 0.9331 0.9362 0.9256 0.9026 0.8822 0.8618 0.8458 0.8352 0.8306 0.8399 0.8742 0.9328 1.0145

−0.0014 −0.0136 −0.0254 −0.0781 −0.1794 −0.3052 −0.4195 −0.5574 −0.7055 −0.8620 −1.0248 −1.3618 −1.6989 −2.0202 −2.3097

0.9998 0.9989 0.9983 0.9957 0.9916 0.9873 0.9841 0.9806 0.9773 0.9740 0.9706 0.9631 0.9544 0.9439 0.9312

0.9499 0.9355 0.9359 0.9431 0.9392 0.9241 0.9062 0.8895 0.8761 0.8671 0.8629 0.8700 0.8978 0.9457 1.0128

0.8402 0.7686 0.7407 0.7249 0.7252 0.7251 0.7233 0.7213 0.7204 0.7215 0.7251 0.7407 0.7693 0.8121 0.8710

−0.0016 −0.0102 −0.0254 −0.0765 −0.1722 −0.2776 −0.3926 −0.5168 −0.6490 −0.7880 −0.9317 −1.2282 −1.5242 −1.8066 −2.0626

0.9998 0.9991 0.9983 0.9957 0.9914 0.9874 0.9837 0.9801 0.9765 0.9731 0.9695 0.9620 0.9534 0.9434 0.9316

0.8430 0.7659 0.7364 0.7146 0.7057 0.6967 0.6865 0.6764 0.6675 0.6606 0.6560 0.6546 0.6641 0.6847 0.7173

0.9510 0.9366 0.9382 0.9495 0.9518 0.9421 0.9287 0.9154 0.9043 0.8964 0.8924 0.8963 0.9167 0.9528 1.0038

−0.0014 −0.0102 −0.0249 −0.0751 −0.1659 −0.2637 −0.3679 −0.4791 −0.5966 −0.7190 −0.8452 −1.1041 −1.3630 −1.6112 −1.8391

0.9998 0.9991 0.9983 0.9957 0.9913 0.9872 0.9833 0.9795 0.9759 0.9723 0.9686 0.9610 0.9527 0.9434 0.9327

r = 10 0.0123 0.0502 0.0995 0.2498 0.4972 0.7425 0.9867 1.2299 1.4708 1.7108 1.9471 2.4208 2.8865 3.3464 3.8007 r=5 0.0117 0.0501 0.1003 0.2488 0.4969 0.7420 0.9864 1.2286 1.4690 1.7081 1.9453 2.4153 2.8790 3.3364 3.7876 r=1 0.0117 0.0498 0.0999 0.2501 0.4955 0.7442 0.9875 1.2284 1.4674 1.7046 1.9389 2.4019 2.8567 3.2924 3.7311 J

γ±Ca(NO3)2

φ

GE/RT

as

0.8408 0.7683 0.7417 0.7265 0.7284 0.7298 0.7294 0.7289 0.7295 0.7321 0.7372 0.7563 0.7888 0.8363 0.9009

0.9500 0.9351 0.9353 0.9417 0.9365 0.9203 0.9014 0.8839 0.8700 0.8607 0.8564 0.8640 0.8932 0.9434 1.0135

−0.0015 −0.0104 −0.0251 −0.0771 −0.1738 −0.2806 −0.3978 −0.5249 −0.6602 −0.8028 −0.9494 −1.2551 −1.5593 −1.8493 −2.1120

0.9998 0.9991 0.9983 0.9957 0.9915 0.9875 0.9838 0.9802 0.9767 0.9732 0.9698 0.9622 0.9536 0.9435 0.9315

0.8432 0.7673 0.7394 0.7219 0.7194 0.7166 0.7122 0.7076 0.7042 0.7027 0.7036 0.7136 0.7356 0.7707 0.8203

0.9508 0.9358 0.9368 0.9454 0.9437 0.9305 0.9142 0.8987 0.8862 0.8776 0.8735 0.8797 0.9051 0.9492 1.0110

−0.0014 −0.0104 −0.0252 −0.0759 −0.1701 −0.2725 −0.3840 −0.5034 −0.6302 −0.7632 −0.9008 −1.1839 −1.4666 −1.7364 −1.9818

0.9998 0.9991 0.9983 0.9957 0.9914 0.9874 0.9835 0.9799 0.9763 0.9728 0.9692 0.9616 0.9531 0.9433 0.9319

0.8422 0.7629 0.7308 0.7017 0.6821 0.6630 0.6438 0.6256 0.6093 0.5954 0.5840 0.5694 0.5650 0.5704 0.5856

0.9510 0.9367 0.9388 0.9515 0.9564 0.9489 0.9371 0.9249 0.9143 0.9063 0.9014 0.9016 0.9153 0.9412 0.9798

−0.0014 −0.0102 −0.0249 −0.0751 −0.1640 −0.2605 −0.3614 −0.4680 −0.5801 −0.6968 −0.8166 −1.0628 −1.3101 −1.5441 −1.7689

0.9998 0.9991 0.9983 0.9956 0.9913 0.9871 0.9831 0.9793 0.9756 0.9719 0.9683 0.9609 0.9530 0.9445 0.9349



Article

T = (303.2 and 313.2) K. Also, Figure 6 shows variation of the excess Gibbs free energy against the ionic strength variation for r = 10. It can be seen the values of excess Gibbs free energy decrease with rising temperature. In addition, a similar tendency was seen for other salt molal ratios (r = 1, 2.5, 5, and 7.5) in aqueous solution containing 2.5% mass fraction of L-glutamine (presented in Figures S11 to S14). 4.6. Temperature Dependence of Thermodynamic Properties. The excess enthalpy (HE) and excess heat capacity (CPE) were calculated by using temperature dependence parameters for quaternary system. According to the Pitzer model, excess Gibbs free energy for a system under investigation is calculated by eq 17:29 0 GE /nRT = − Aϕ(4I /b)ln(1 + b I ) + 2mCa mCl {βCaCl

Figure 4. Values of mean activity coefficient of Ca(NO3)2 versus ionic strength for different series of molal ratio at T = 293.2 K and P = 0.1 MPa

+

1 (2βCaCl /α 2I )[1 2

2

− (1 + α I )exp( − α I )]

0 ϕ + mCa CCaCl / 2 } + 2mCa mNO3{βCa(NO ) 2

3 2

+

1 (2βCa(NO /α 2I )[1 3)2

− (1 + α I )

ϕ × exp(− α I )] + mCa CCa(NO / 2 } + 2mCl 3)2

× mNO3[θClNO3 + (1/2)mCa ψCaClNO ]

(17)

3

All of the parameters in Pitzer model (Aφ, β(0), β(1), Cφ, θ, and ψ) depend on the temperature and suitable analytical form should be used to describe the temperature-dependence of these parameters. The following general equation was found to reproduce the parameters in pitzer model:30 Figure 5. Excess Gibbs free energy changes against total ionic strength at different molal ratios (r = mCaCl2/mCa(NO3)2) at T = 293.2 K in the aqueous solution containing 2.5% mass fraction of L-glutamine.

F(T ) = a T + bT /T + c T ln T

(18)

The values of aT, bT, and cT were obtained by an iteration minimization procedure on results of eq 18 employing the Microsoft Excel (solver) program for values of Aφ, β(0), β(1), Cφ, θ, and ψ. The results were listed in Table 12. The temperaturedependence parameters were used to calculate of excess enthalpy and heat capacity values. Temperature differentiation of the excess Gibbs free energy expression (eq 17) gives the excess enthalpy according to eq 19: 0 H E /nRT 2 = Aϕ′(4I /b) ln(1 + b I ) − 2mCa mCl {βCaCl ′ 2

+

1 (2βCaCl ′/α 2I )[1 2

− (1 + α I ) exp(−α I )]

0 ϕ ′ + mCa CCaCl ′/ 2 } − 2mCa mNO3{βCa(NO ) 2 3 2

+ Figure 6. Excess Gibbs free energy changes against total ionic strength at different temperatures for molal ratio r = mCaCl2/mCa(NO3)2 = 10.

1 (2βCa(NO ′/α 2I )[1 3)2

− (1 + α I ) exp(−α I )]

ϕ + mCa CCa(NO ′/ 2 } − 2mCl mNO3[θClNO3′ 3)2

+ (1/2)mCa ψCaClNO ′]

that the excess Gibbs free energy is reduce by increasing the salt molal ratio in the aqueous solution containing 2.5% mass fraction of L-glutamine. Furthermore, Figures S9 and S10 show the excess Gibbs free energy changes versus total ionic strength at

(19)

3

The equation for excess heat capacity (CEP) follows directly from temperature differentiation of the excess enthalpy

Table 12. Values of Parameters aT, bT, and cT in eq 18 for Pitzer Model Interaction Parameters (β0MX, β1MX, CϕMX, θClNO3 and ψCaClNO3), and Debye−Hückel Parameter (Aφ) βCaCl20 aT bT cT

26.825 0.612 −4.717

βCaCl21 −104.131 −2.274 18.884

CCaCl2ϕ −9.791 −0.126 1.747

βCa(NO3)20

βCa(NO3)21 −57.413 −1.210 10.708

17.523 0.496 −3.088 K

CCa(NO3)2ϕ −5.765 −0.033 1.032

θClNO3 9.974 0.324 −1.671

ψCaClNO3 −4.137 1.150 0.669

Aϕ −0.986 0.958 0.231



Article

Table 13. Values of Ionic Strength (I), Excess Enthalpy (HE/nsRT), Excess Heat Capacity (cEP/nsRT) and Excess Entropy (SE/nsR) of the (CaCl2 + L-Glutamine + H2O) and (CaCl2 + Ca(NO3)2 + L-Glutamine + H2O) Systems at T = 293.2 K and P = 0.1 MPa I

HE

cEP

SE

I

HE

cEP

SE

I

HE

cEP

SE

mol·kg−1

nsRT

nsRT

nsR

mol·kg−1

nsRT

nsRT

nsR

mol·kg−1

nsRT

nsRT

nsR

0.0005 −0.0003 −0.0068 −0.0427 −0.0802 −0.0242 0.1566 0.4710 0.9203 1.4948 2.1851 3.8706 5.8743 8.0887 10.3292

0.0000 0.0000 0.0000 −0.0003 −0.0004 0.0001 0.0015 0.0038 0.0072 0.0114 0.0164 0.0286 0.0431 0.0591 0.0752

0.0019 0.0100 0.0187 0.0367 0.0968 0.2537 0.5365 0.9528 1.5032 2.1767 2.9631 4.8288 6.9908 9.3352 11.6690

0.0006 0.0023 0.0024 0.0036 0.0643 0.2465 0.5700 1.0380 1.6466 2.3880 3.2473 5.2802 7.6447 10.2381 12.9648

0.0000 0.0000 0.0000 0.0000 0.0004 0.0017 0.0039 0.0071 0.0112 0.0163 0.0221 0.0360 0.0521 0.0697 0.0883

0.0020 0.0123 0.0274 0.0782 0.2247 0.4899 0.8928 1.4365 2.1169 2.9261 3.8487 5.9943 8.4512 11.1150 13.8887

r = pure CaCl2 0.0116 0.0004 0.0518 −0.0013 0.0989 −0.0095 0.2483 −0.0566 0.4962 −0.1247 0.7426 −0.1083 0.9875 0.0272 1.2309 0.2927 1.4729 0.6884 1.7135 1.2083 1.9526 1.8429 2.4268 3.4097 2.8954 5.2866 3.3586 7.3657 3.8165 9.5400 r=5 0.0130 0.0005 0.0505 0.0000 0.0999 −0.0057 0.2487 −0.0366 0.4971 −0.0615 0.7427 0.0109 0.9879 0.2114 1.2309 0.5477 1.4720 1.0179 1.7124 1.6177 1.9509 2.3348 2.4239 4.0779 2.9554 6.4496 3.3527 8.4268 3.8087 10.8219

0.0000 0.0000 −0.0001 −0.0004 −0.0008 −0.0007 0.0002 0.0020 0.0047 0.0082 0.0126 0.0232 0.0360 0.0502 0.0650

0.0018 0.0097 0.0163 0.0253 0.0628 0.1924 0.4457 0.8322 1.3505 1.9933 2.7497 4.5514 6.6432 8.9078 11.2298

0.0000 0.0000 0.0000 −0.0002 −0.0003 0.0004 0.0020 0.0045 0.0080 0.0125 0.0178 0.0305 0.0479 0.0623 0.0798

0.0022 0.0104 0.0198 0.0415 0.1120 0.2811 0.5785 1.0104 1.5744 2.2656 3.0705 4.9763 7.5053 9.5773 12.0517

r = 10 0.0152 0.0500 0.1005 0.2512 0.4967 0.7432 0.9866 1.2302 1.4713 1.7107 1.9488 2.4213 2.8866 3.3466 3.8006 r = 2.5 0.0116 0.0495 0.1004 0.2486 0.4964 0.7416 0.9849 1.2264 1.4662 1.7037 1.9399 2.4072 2.8671 3.3206 3.7673

0.0005 −0.0005 −0.0076 −0.0464 −0.0903 −0.0430 0.1266 0.4307 0.8659 1.4260 2.1026 3.7591 5.7256 7.9021 10.1810

0.0000 0.0000 0.0000 −0.0003 −0.0005 −0.0001 0.0012 0.0035 0.0066 0.0107 0.0156 0.0275 0.0415 0.0571 0.0734

0.0026 0.0099 0.0183 0.0343 0.0889 0.2398 0.5141 0.9243 1.4645 2.1282 2.9061 4.7538 6.8894 9.2068 11.5919

0.0005 0.0008 −0.0028 −0.0222 −0.0165 0.0952 0.3390 0.7215 1.2402 1.8861 2.6515 4.4895 6.6488 9.0289 11.5275

0.0000 0.0000 0.0000 −0.0001 0.0000 0.0010 0.0029 0.0058 0.0096 0.0144 0.0201 0.0336 0.0494 0.0668 0.0851

0.0019 0.0109 0.0224 0.0540 0.1498 0.3503 0.6806 1.1467 1.7457 2.4680 3.3055 5.2733 7.5398 10.0012 12.5526

r = 7.5 0.0117 0.0498 0.0997 0.2494 0.4966 0.7426 0.9872 1.2299 1.4719 1.7117 1.9498 2.4220 2.8885 3.3491 3.7885 r=1 0.0116 0.0495 0.1004 0.2486 0.4956 0.7401 0.9823 1.2222 1.4603 1.6966 1.9302 2.3921 2.8462 3.2924 3.7310

Table 14. Values of Ionic Strength (I), Excess Enthalpy (HE/nsRT), Excess Heat Capacity (cEP/nsRT) and Excess Entropy (SE/nsR) of the (CaCl2 + L-Glutamine + H2O) and (CaCl2 + Ca(NO3)2 + L-Glutamine + H2O) Systems at T = 303.2 K and P = 0.1 MPa HE

I mol·kg

−1

nsRT

r = pure CaCl2 0.0116 0.0004 0.0497 −0.0014 0.0996 −0.0103 0.2493 −0.0594 0.4977 −0.1315 0.7440 −0.1192 0.9889 0.0116 1.2328 0.2727 1.4748 0.6632 1.7153 1.1774 1.9547 1.8069 2.4290 3.3618 2.8982 5.2272 3.3617 7.2930 3.8200 9.4530 r=5 0.0117 0.0004 0.0499 −0.0003 0.1000 −0.0064

cEP nsRT

SE nsR

0.0000 0.0000 −0.0001 −0.0004 −0.0009 −0.0008 0.0001 0.0019 0.0045 0.0080 0.0123 0.0229 0.0356 0.0497 0.0644

0.0018 0.0091 0.0155 0.0222 0.0577 0.1897 0.4507 0.8510 1.3874 2.0522 2.8354 4.6973 6.8558 9.1847 11.5631

0.0000 0.0000 0.0000

0.0019 0.0101 0.0191

HE

I mol·kg

−1

r = 10 0.0119 0.0496 0.0995 0.2496 0.4977 0.7438 0.9888 1.2335 1.4760 1.7174 1.9577 2.4345 2.9061 3.3729 3.8348 r = 2.5 0.0116 0.0496 0.0995

cEP

nsRT

nsRT

0.0004 −0.0007 −0.0081 −0.0485 −0.0969 −0.0541 0.1120 0.4133 0.8471 1.4084 2.0883 3.7548 5.7432 7.9449 10.2521

0.0000 0.0000 −0.0001 −0.0003 −0.0007 −0.0004 0.0008 0.0028 0.0058 0.0096 0.0142 0.0256 0.0391 0.0541 0.0698

0.0005 0.0006 −0.0034

0.0000 0.0000 0.0000 L

SE nsR

I mol·kg

−1

r = 7.5 0.0019 0.0124 0.0096 0.0505 0.0174 0.1001 0.0312 0.2488 0.0844 0.4964 0.2378 0.7423 0.5224 0.9868 0.9496 1.2291 1.5142 1.4702 2.2105 1.7101 3.0276 1.9479 4.9692 2.4188 7.2222 2.8839 9.6655 3.3406 12.1793 3.7961 r=1 0.0019 0.0116 0.0108 0.0496 0.0216 0.1007

HE

cEP

SE

nsRT

nsRT

nsR

0.0004 −0.0006 −0.0076 −0.0451 −0.0867 −0.0356 0.1396 0.4476 0.8882 1.4557 2.1379 3.8029 5.7835 7.9612 10.2676

0.0000 0.0000 −0.0001 −0.0003 −0.0006 −0.0002 0.0010 0.0030 0.0060 0.0099 0.0146 0.0259 0.0394 0.0542 0.0699

0.0020 0.0099 0.0180 0.0338 0.0920 0.2512 0.5417 0.9707 1.5374 2.2347 3.0485 4.9769 7.2116 9.6216 12.1319

0.0006 0.0020 0.0017

0.0000 0.0000 0.0000

0.0020 0.0122 0.0269



Article

Table 14. continued I

HE

cEP

SE

I

HE

cEP

SE

I

HE

cEP

SE

mol·kg−1

nsRT

nsRT

nsR

mol·kg−1

nsRT

nsRT

nsR

mol·kg−1

nsRT

nsRT

nsR

r=5 0.2489 0.4966 0.7419 0.9865 1.2283 1.4689 1.7083 1.9457 2.4154 2.8789 3.3364 3.7877

−0.0391 −0.0681 −0.0008 0.1934 0.5212 0.9826 1.5719 2.2770 3.9882 6.0170 8.2590 10.6098

−0.0003 −0.0005 0.0000 0.0013 0.0035 0.0067 0.0107 0.0155 0.0272 0.0410 0.0562 0.0722

r = 2.5 0.2492 0.4974 0.7427 0.9861 1.2274 1.4668 1.7037 1.9392 2.4045 2.8619 3.3122 3.7552

0.0389 0.1073 0.2786 0.5832 1.0260 1.6068 2.3188 3.1482 5.1084 7.3785 9.8449 12.3939

−0.0248 −0.0228 0.0848 0.3239 0.7011 1.2135 1.8520 2.6085 4.4243 6.5552 8.9014 11.3619

−0.0002 −0.0002 0.0006 0.0022 0.0048 0.0083 0.0126 0.0178 0.0301 0.0446 0.0606 0.0774

according to eq 20:

0.0517 0.1466 0.3510 0.6908 1.1719 1.7914 2.5388 3.4059 5.4441 7.7932 10.3471 12.9991

r=1 0.2494 0.4973 0.7429 0.9863 1.2277 1.4674 1.7055 1.9410 2.4071 2.8659 3.3174 3.7619

0.0011 0.0586 0.2382 0.5603 1.0285 1.6392 2.3846 3.2498 5.3002 7.6886 10.3106 13.0680

0.0000 0.0004 0.0016 0.0038 0.0070 0.0112 0.0162 0.0221 0.0361 0.0524 0.0702 0.0890

0.0765 0.2232 0.4945 0.9105 1.4752 2.1849 3.0317 3.9999 6.2602 8.8605 11.6923 14.6543

Ultimately, values of excess entropy were determined by eq 21. GE HE SE = − nRT nRT nR

CPE/nRT 2 = 2HE/nRT 3 + Aϕ″(4I /b)ln(1 + b I ) 0 1 − 2mCa mCl {βCaCl ″ + (2βCaCl ″ /α 2I ) 2

2

Tables 13−15 include calculated excess enthalpy, excess heat capacity, and entropy values. Figure 7 represents excess enthalpy changes versus increasing ionic strength for different molal ratio at T = 293.2 K. In addition, Figures S15 and S16 indicate the corresponding variations to change excess enthalpy at T = (303.2 and 313.2) K. 4.7. Evaluation of CaCl2 and Ca(NO3)2 Molality Dependence. The molalities of CaCl2 and Ca(NO3)2 were obtained in

ϕ × [1 − (1 + α I ) exp( −α I )] + mCa CCaCl ″/ 2 } 2 0 ″ + (2β1 − 2mCa mNO3{βCa(NO ″ /α 2I )[1 ) Ca(NO ) 3 2

3 2

ϕ − (1 + α I ) exp(−α I )] + mCa CCa(NO ″/ 2 } 3)2

− 2mCl mNO3[θClNO3″ + (1/2)mCa ψCaClNO ″]

(20)

3

(21)

Table 15. Values of Ionic Strength (I), Excess Enthalpy (HE/nsRT), Excess Heat Capacity (cEP/nsRT) and Excess Entropy (SE/nsR) of the (CaCl2 + L-Glutamine + H2O) and (CaCl2 + Ca(NO3)2 + L-Glutamine + H2O) Systems at T = 313.2 K and P = 0.1 MPa HE

I mol·kg

−1

nsRT

r = pure CaCl2 0.0117 0.0004 0.0612 −0.0028 0.0998 −0.0101 0.2488 −0.0573 0.4975 −0.1271 0.7682 −0.1081 0.9885 0.0112 1.2318 0.2631 1.4736 0.6404 1.7141 1.1376 1.9529 1.7450 2.4272 3.2489 2.8955 5.0504 3.3588 7.0483 3.8165 9.1365 r=5 0.0117 0.0004 0.0501 −0.0003 0.1003 −0.0062 0.2488 −0.0378 0.4969 −0.0658 0.7420 −0.0005 0.9864 0.1873 1.2286 0.5053 1.4690 0.9519 1.7081 1.5217

cEP nsRT

SE nsR

0.0000 0.0000 −0.0001 −0.0004 −0.0009 −0.0007 0.0001 0.0018 0.0044 0.0077 0.0119 0.0221 0.0344 0.0480 0.0622

0.0018 0.0108 0.0154 0.0208 0.0522 0.1971 0.4306 0.8205 1.3459 1.9996 2.7698 4.6107 6.7492 9.0685 11.4462

0.0000 0.0000 0.0000 −0.0003 −0.0004 0.0000 0.0013 0.0034 0.0065 0.0104

0.0019 0.0101 0.0190 0.0381 0.1043 0.2720 0.5713 1.0088 1.5821 2.2849

HE

I mol·kg

−1

r = 10 0.0123 0.0502 0.0995 0.2498 0.4972 0.7425 0.9867 1.2299 1.4708 1.7108 1.9471 2.4208 2.8865 3.3464 3.8007 r = 2.5 0.0117 0.0498 0.0999 0.2492 0.4959 0.7417 0.9845 1.2262 1.4662 1.7042

cEP

nsRT

nsRT

SE nsR

0.0004 −0.0008 −0.0079 −0.0470 −0.0936 −0.0527 0.1068 0.3953 0.8103 1.3477 1.9911 3.5847 5.4759 7.5677 9.7598

0.0000 0.0000 −0.0001 −0.0003 −0.0006 −0.0004 0.0007 0.0027 0.0055 0.0092 0.0136 0.0244 0.0373 0.0515 0.0665

0.0020 0.0097 0.0172 0.0302 0.0802 0.2280 0.5047 0.9203 1.4705 2.1504 2.9405 4.8397 7.0352 9.4171 11.8719

0.0005 0.0005 −0.0033 −0.0240 −0.0222 0.0815 0.3119 0.6769 1.1739 1.7947

0.0000 0.0000 0.0000 −0.0002 −0.0002 0.0006 0.0021 0.0046 0.0080 0.0122

0.0019 0.0108 0.0216 0.0511 0.1437 0.3452 0.6797 1.1560 1.7705 2.5137

M

I mol·kg

−1

r = 7.5 0.0125 0.0495 0.1005 0.2489 0.4964 0.7425 0.9866 1.2294 1.4705 1.7101 1.9475 2.4189 2.8839 3.3429 3.7961 r=1 0.0117 0.0498 0.0999 0.2501 0.4955 0.7442 0.9875 1.2284 1.4674 1.7046

HE

cEP

SE

nsRT

nsRT

nsR

0.0004 −0.0005 −0.0074 −0.0436 −0.0838 −0.0342 0.1352 0.4340 0.8608 1.4098 2.0691 3.6824 5.5997 7.7191 9.9409

0.0000 0.0000 −0.0001 −0.0003 −0.0006 −0.0002 0.0009 0.0030 0.0059 0.0096 0.0141 0.0251 0.0381 0.0526 0.0677

0.0020 0.0097 0.0180 0.0329 0.0883 0.2434 0.5278 0.9508 1.5099 2.1978 3.0008 4.9106 7.1240 9.5256 12.0036

0.0006 0.0020 0.0017 0.0012 0.0561 0.2320 0.5444 0.9976 1.5874 2.3060

0.0000 0.0000 0.0000 0.0000 0.0004 0.0016 0.0037 0.0068 0.0108 0.0157

0.0020 0.0122 0.0266 0.0763 0.2201 0.4925 0.9058 1.4657 2.1675 3.0027



Article

Table 15. continued HE

I mol·kg

−1

r=5 1.9453 2.4153 2.8790 3.3364 3.7876

nsRT 2.2036 3.8614 5.8265 7.9964 10.2721

cEP nsRT 0.0150 0.0263 0.0397 0.0545 0.0700

SE

HE

I −1

nsR

mol·kg

3.1044 5.0453 7.2931 9.7327 12.2539

r = 2.5 1.9402 2.4070 2.8673 3.3205 3.7672

SE

cEP

nsRT

nsRT

2.5291 4.2938 6.3725 8.6620 11.0664

0.0172 0.0292 0.0434 0.0590 0.0754

I

nsR 3.3743 5.3979 7.7355 10.2732 12.9054

mol·kg

−1

r=1 1.9389 2.4019 2.8567 3.2924 3.7311

HE

cEP

SE

nsRT

nsRT

nsR

3.1387 5.1074 7.3944 9.8364 12.4632

0.0214 0.0348 0.0504 0.0670 0.0849

3.9553 6.1702 8.7045 11.3805 14.2321

electrodes for different series of salt molal ratio r = 1.0, 2.5, 5.0, 7.5, and 10.0. The thermodynamic investigation of the system studied shows that potentiometric measurements can be used as an alternative method for the determination of the thermodynamic properties of mixed electrolytes in mixed solvent systems. The ion-interaction parameters of Pitzer were determined for the whole data set of ternary (CaCl2 + L-glutamine + H2O) and (Ca(NO3)2 + L-glutamine + H2O) systems. Also, the Pitzer mixing parameters were obtained for the quaternary (CaCl2 + Ca(NO3)2 + L-glutamine + H2O) system using the Pitzer graphical method. The thermodynamic properties such as osmotic coefficients, mean activity coefficient of Ca(NO3)2, excess Gibbs free energy, activity of solvent, excess enthalpy, excess heat capacity, and excess entropy were calculated by using the obtained Pitzer parameters. Results show that the Pitzer model describes experimental data satisfactorily.

Figure 7. Plot of excess enthalpy variation against total ionic strength at different molal ratio (r = mCaCl2/mCa(NO3)2) at T = 293.2 K in the aqueous solution containing 2.5% mass fraction of L-glutamine.

■

isoactivity positions calculated by using the Pitzer model for different series of the salt molal ratios r (r = mCaCl2/mCa(NO3)2= 1, 2.5, 5.0, 7.5, 10.0) and single salt CaCl2 and Ca(NO3)2 solution in aqueous solution containing 2.5% mass fraction of L-glutamine at T = (293.2, 303.2 and 313.2). Figure 8 represents the

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00593. Plots of mean activity coefficients, excess Gibbs free energy, and excess enthalpy variations versus total ionic strength; plots of molality of Ca(NO3)2 versus molality of CaCl2 at different temperatures (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +981333367262. Fax: +981333367262. E-mail: [email protected]. ORCID

Bahram Ghalami-Choobar: 0000-0002-3599-1153 Funding

We gratefully acknowledge the graduate Office University of Guilan for supporting of this work. Notes

Figure 8. Dependence of molality of Ca(NO3)2 versus molality CaCl2 for different constant activities of mixed solvent at T = 293.2 K.

The authors declare no competing financial interest.

■

isoactivity plots of the molality of Ca(NO3)2 versus molality CaCl2 for different activities of mixed solvent at T = 293.2 K. The linear relation between the molality of Ca(NO3)2 and molality CaCl2 shows that electrolytes have similar hydrophilic behavior. In additional, Figures S17 and S18 indicate the corresponding plots (303.2 and 313.2) K.

REFERENCES

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Article

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O


Thermodynamic Properties Determination and Modeling of the (CaCl2

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