Activity Coefficient Measurements and Thermodynamic Modeling of

Article pubs.acs.org/jced

Activity Coefficient Measurements and Thermodynamic Modeling of (CaCl2 + L‑Alanine + Water) System Based on Potentiometric Determination at T = (298.2, 303.2, and 308.2) K Bahram Ghalami-Choobar* and Parya Mossayyebzadeh-Shalkoohi Department of Chemistry, Faculty of Science, University of Guilan, P.O. Box: 19141, Rasht 41376, Iran S Supporting Information *

ABSTRACT: In this work, the thermodynamic properties of the ternary (CaCl2 + L-alanine + water) system, using the potentiometric method, were reported. The potentiometric measurements were performed on the galvanic cell of the type: Ag−AgCl|CaCl2·2H2O (m), L-alanine (mA), H2O|Ca−ISE, in various mixed solvent systems containing 0.0 mol·kg−1, 0.1 mol·kg−1, 0.2 mol·kg−1, 0.3 mol·kg−1, and 0.4 mol·kg−1 of L-alanine, over total ionic strengths from 0.0100 mol·kg−1 to 3.0000 mol·kg−1 at T = (298.2, 303.2, and 308.2) K and P = 0.1 MPa. The Ca−ISE was prepared in our laboratory using the ionophore treated by carbon nanotubes. The Debye−Hückel extended equation, Pitzer ion interaction and PSC models were used to correlate the experimental data. The unknown parameters were evaluated and utilized to calculate the thermodynamic properties such as the mean activity coefficients, the osmotic coefficients, the solvent activity, and the excess Gibbs free energy for underinvestigated electrolyte solutions.

1. INTRODUCTION The thermodynamic study of aqueous systems containing amino acids is very important. Particularly, the knowledge of activity coefficients can be very useful as a support for the efficient design and simulation of separation processes such as extraction, precipitation, or drying.1 Amino acids have important functions like being the building blocks of proteins and being the intermediates in metabolism.1,2 In addition, the amino acids can improve growth of plants under salt (such as CaCl2 and NaCl) stress.3 L-Alanine is a nonessential amino acid that can be manufactured by the human body from pyruvate and branched chain amino acids such as valine, leucine, and isoleucine, and does not need to be obtained directly through the diet.4−6 Up till now, some studies have been done about solubility and thermodynamic properties of amino acids in aqueous electrolyte solutions.1,2,7,8 The only available experimental potentiometric data for CaCl2 in L-alanine + water mixed solvent system are those reported by Zhuo group9 and Briggs group10 using an electrochemical cell. They reported the activity coefficients of CaCl2 up to 0.2 mol·kg−1 at 298.2 K. Among the experimental techniques, electrochemical cells with ion-selective electrodes (ISEs) because of rapidity and relative simplicity to generate experimental data are important and efficient tools for the measurements of thermodynamic properties of electrolyte solutions in comparison with the other techniques.11,12 In this work, the results relating to the mean activity coefficient measurements for CaCl2 in the L-alanine + water mixtures using the potentiometric method13 were reported at T = (298.2, 303.2, and 308.2) K and P = 0.1 MPa. This paper is the continuation of the research on ternary and quaternary electrolyte solutions.14−17 The potentiometric measurements were carried out on a galvanic cell containing a solvent polymeric membrane (Ca−ISE) which © XXXX American Chemical Society

treated by carbon nanotubes and Ag−AgCl electrodes over the ionic strength ranging from 0.0100 mol·kg−1 to 3.0000 mol·kg−1 for different series of the molality of L-alanine (mA = 0.0 mol·kg−1, 0.1 mol·kg−1, 0.2 mol·kg−1, 0.3 mol·kg−1, and 0.4 mol·kg−1). The results were interpreted based on Debye−Hückel extended equation, Pitzer ion interaction and PSC models. The unknown parameters have been evaluated for under studied systems. Finally, the values of the mean activity coefficients, the osmotic coefficients, the solvent activity, and the excess Gibbs free energy together with Pitzer and PSC parameters for under investigated systems were obtained.

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 continuously stirred 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 = (298.2, 303.2 and 308.2) K ± 0.1 K. Dibutyl phthalate (DBP), potassium tetrakis(p-chlorophenyl) borate (KTPClPB), high molar mass Received: March 19, 2015 Accepted: September 14, 2015

A

DOI: 10.1021/acs.jced.5b00260 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

very well. The resulting mixture was transferred into a glass dish of 2 cm diameter. The solvent was evaporated. After 2 h, the polymer membrane could be easily removed from the plate. Then the PVC membrane was taken up from the plate and attached to the end of a glass tube with a diameter of 1 cm and height of 5 cm by means of PVC−THF viscose solution. The made electrode was initially conditioned for 48 h in 0.01 mol·dm−3 CaCl2 internal filling solution. The Ag−AgCl electrodes were used as both internal reference electrode and chloride selective electrode. These electrodes were prepared essentially as described elsewhere by electrolysis.18 Both the Ca−ISE and Ag−AgCl electrodes were calibrated against a saturated calomel reference electrode before use in a (10−4 to 1) mol·dm−3 concentration range of pure solution of CaCl2, and showed a good Nernst slope (s) and linear relation (R2). The activity coefficients for CaCl2 in the ternary system (CaCl2 + L-alanine + water) were determined from the emf measurements using the following galvanic cells:

Table 1. Company and Purity Value of Compounds Used chemical used

mass fraction purity

company

CaCl2·2H2O L-alanine tetrahydrofuran (THF) dibutyl phthalate potassium tetrakis(p-chlorophenyl) borate poly(vinyl chloride) polyanetholesulfonic acid sodium salt carbon nanotube

Merck Merck Merck Merck Fluka

> 0.99 0.99−1.01 > 0.99 > 0.99 > 0.98

BDH Laboratory Sigma-Aldrich Neutrino

0.996 0.98 > 0.95

poly(vinyl chloride) (PVC), tetrahydrofuran (THF), L-alanine, calcium chloride (CaCl2·2H2O) and all other reagents used were purchased from chemical companies in Table 1. All of reagents were of analytical reagent grade and were employed without further purification. All primary stock solutions were prepared by using double-distilled water and L-alanine. Density of L-alanine + water mixtures was measured using DMA 4500 density meter from Anton Paar Company. The stock solution of electrolyte were prepared from calcium chloride and L-alanine by adding weighed amounts of solid, using an analytical balance (A&D HR 200) with a resolution of 0.1 mg, and double-distilled water whose specific conductance was less than 2.0 × 10−4 S·m−1. 2.2. Preparation of Electrodes and Data Acquisition. In order to construction of calcium ion selective electrode (Ca−ISE), the polyanetholesulfonic acid sodium salt was used as the ionophore. The procedure used to prepare the Ca−ISE was to mix thoroughly optimized amounts of 28.9 mg of powdered PVC, 58 mg of DBP, and 5.1 mg of KTPClPB in 1.2 cm3 of dry freshly distilled THF. The optimized value (8 mg) of polyanetholesulfonic acid sodium salt that treated by carbon nanotubes in a ratio of 1:5 was added to this solution as an ionophore and mixed

Ag − AgCl|CaCl 2(m), H 2O|Ca−ISE

(A)

Ag − AgCl|CaCl 2(m), L − alanine(mA ), H 2O|Ca−ISE (B)

Here, mA is molality of L-alanine in water and m is the molality of CaCl2 as single salts in mixed solvent. The emf measurements of the galvanic cell were made using standard addition procedure. For this purpose, the concentrated mixed electrolyte solutions were added into the mentioned cell containing a proportion volume of double-distilled water. The standard addition steps were carried out using proper buret and suitable Hamilton syringes (CH-7402 Bonaduz). 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

Table 2. Values of Average Molecular Mass, Dielectric Constant, Density ,Debye−Hückel Constants, Aφ, A, B, and Ax, Parameter Related to Closest Approach Distances, ρ, for Alanine + Water Mixtures mAa mol·kg

−1

εr c

dsb

MS −1

g·mol

kg·dm

−3

Aφ

A −1/2

kg ·mol 1/2

B −1/2

kg ·mol 1/2

−1/2

kg ·mol 1/2

Ax

ρ

−1

·Å

298.2 Kc 0.0 0.1 0.2 0.3 0.4

18.02 18.15 18.28 18.40 18.53

0.9971 0.9999 1.0027 1.0055 1.0082

78.4 80.8 83.1 85.3 87.4

0.3915 0.3746 0.3596 0.3463 0.3343

0.0 0.1 0.2 0.3 0.4

18.02 18.15 18.28 18.40 18.53

0.9957 0.9984 1.0019 1.0041 1.0068

76.6 78.9 81.2 83.3 85.3

0.3949 0.3782 0.3629 0.3497 0.3379

0.0 0.1 0.2 0.3 0.4

18.02 18.15 18.28 18.40 18.53

0.9940 0.9968 1.0001 1.0023 1.0041

74.9 77.1 79.3 81.4 83.4

0.3985 0.3818 0.3666 0.3529 0.3406

0.5097 0.4879 0.4684 0.4510 0.4354

0.3284 0.3240 0.3199 0.3162 0.3128

2.9164 2.7805 2.6597 2.5530 2.4558

14.0402 13.8502 13.6763 13.5176 13.3722

0.5145 0.4928 0.4728 0.4555 0.4402

0.3293 0.3249 0.3208 0.3171 0.3138

2.9418 2.8076 2.6842 2.5777 2.4822

14.0784 13.8899 13.7154 13.5564 13.4143

0.5192 0.4974 0.4776 0.4597 0.4437

0.3301 0.3257 0.3217 0.3179 0.3143

2.9686 2.8337 2.7114 2.6014 2.5019

14.1125 13.9253 13.7533 13.5895 13.4377

303.2 K

308.2 K

a mA indicats the moles number of alanine per kilogram of water. bStandard uncertainties u are as follows: u(dS) = 0.0001 kg·dm−3, u(T) = 0.1 K, and u(p)= 2 kPa with 0.68 level of confidence. cDielectric constant values of pure water at three temperatures were taken from ref 13. Also, these values for alanine + water mixtures at 298.2 K and two other temperatures were obtained from ref 9 and 21, respectively.

B



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Table 3. Values of Molality of CaCl2, EMF Data, and Mean Activity Coefficient of CaCl2 for (CaCl2 + L-Alanine + Water) System at 298.2 K and P = 0.1 MPa ma mol·kg

was kept constant at T = (298.2, 303.2, and 308.2) K, employing a double-wall container enabling the circulation of thermostated water from a Model GFL circulation.

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

3. THERMODYNAMICS MODELS 3.1. Extended Debye−Hü ckel Equation. The extended Debye−Hückel equation is considered as an ion-interaction19 model that involves electrolyte-specific regression parameters for 2−1 type electrolytes, such as CaCl 2, the extended Debye−Hü c kel equation for the mean activity coefficient, γ ± is given by log γ± = −

2A I + cI + dI 2 − log(1 + 0.001IMS) 1 + Ba I (1)

where I indicates the total ionic strength on a molality scale, a is the ion size parameter, c and d are the ion-interaction parameters, and MS is the average molecular mass of mixed solvent. The A and B are the Debye−Hückel constants given19 by A=

B=

1.8247 × 106ds1/2 (εrT )3/2

50.2901ds1/2 (εrT )1/2

−1

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

Figure 1. Plot of emf versus log(γ±I) for calibration of Ca−ISE and Ag− AgCl electrode pair at T = 298.2 K.

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

(kg1/2·mol−1/2) (2)

(kg1/2·mol−1/2·Å−1) (3)

where d, εr, and T stand for the density, relative permittivity of the solvent, and temperature, respectively. The values of the physical properties (M, ds, and εr) together with the extended Debye−Hückel parameter values (A and B) were shown in Table 2.9,20,21 3.2. Pitzer Model. The Pitzer ion-interaction model was used for the experimental data correlation and calculation of thermodynamic properties for the under investigated system.13 According to the Pitzer model, the mean molal activity coefficient (γ±) for CaCl2 in the mixed solvent is inscribed as

γ±b

Eb mV mA = 0a −54.6 −0.3 24.6 53.0 72.8 85.6 95.2 105.0 113.2 117.4 124.8 135.3 144.6 mA = 0.1 −63.2 −14.4 7.5 35.6 59.4 73.6 83.6 91.3 97.3 102.6 107.2 114.9 121.7 mA = 0.2 −38.9 10.4 32.6 62.3 84.8 97.7 107.5 115.0 121.6 127.2 132.1 140.0 147.0

m mol·kg

γ±

E −1

0.8169 0.6825 0.6179 0.5378 0.4881 0.4660 0.4547 0.4495 0.4482 0.4498 0.4537 0.4669 0.4861

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

0.8242 0.6946 0.6328 0.5580 0.5148 0.4977 0.4903 0.4877 0.4877 0.4893 0.4917 0.4975 0.5026

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

mV mA = 0.3 −23.6 15.3 35.2 63.4 84.1 97.1 106.7 114.3 120.6 126.1 131.1 139.5 146.5 mA = 0.4 −38.3 17.1 34.0 64.9 87.7 100.6 108.8 117.8 123.4 130.4 134.5 143.1 150.1

0.8362 0.7133 0.6535 0.5791 0.5342 0.5160 0.5088 0.5079 0.5115 0.5184 0.5282 0.5555 0.5923 0.8413 0.7215 0.6632 0.5911 0.5485 0.5318 0.5253 0.5245 0.5273 0.5326 0.5399 0.5590 0.5825

0.8306 0.7047 0.6438 0.5687 0.5233 0.5046 0.4966 0.4947 0.4967 0.5018 0.5094 0.5308 0.5593

a

m indicates the moles number of CaCl2 per kilogram of (water + mixture and standard uncertainties u with0.68 level of confidence are follows: u(m) = 0.0001 mol·kg−1, u(T) = 0.1 K, u(p) = 2 kPa. bThe average uncertainties of emf and mean activity coefficient value were calculated in according to data scatter; u(E) = 1.4 mV and u(γ±) = 0.0236. L-alanine)

γ (0) = 2βCaCl BCaCl 2

2

ln γ±CaCl

4 γ 2 2 φ 2 = 2f + BCaCl I+ CCaCl 2I 2 9 9

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

γ

2

(4)

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

(6)

In these equations, α1 and b are assumed to be constant with values of 2.0 and 1.2 kg1/2·mol−1/2, respectively, both in water and

(5) C



Article

Table 4. Values of Molality of CaCl2, EMF data, and mean activity coefficient of CaCl2 for (CaCl2 + L-alanine + water) system at 303.2 K and P = 0.1 MPa ma mol·kg

Eb −1

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000 0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000 0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

γ±b

m −1

mV mA = 0a −26.1 22.2 44.2 73.9 95.7 108.4 117.7 125.2 131.2 136.6 141.4 149.7 159.5 mA = 0.1 −43.9 3.9 24.8 54.8 76.4 89.4 98.7 106.4 113.0 118.9 124.5 134.0 141.0 mA = 0.2 −44.7 6.8 28.5 58.2 80.1 93.7 103.0 110.4 116.9 121.9 127.1 135.8 144.1

E

mol·kg 0.8149 0.6783 0.6123 0.5300 0.4783 0.4549 0.4425 0.4361 0.4336 0.4338 0.4362 0.4458 0.4604

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

0.8221 0.6904 0.6272 0.5503 0.5057 0.4883 0.4811 0.4790 0.4799 0.4827 0.4866 0.4960 0.5056

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

Table 5. Values of Molality of CaCl2, EMF Data, and Mean Activity Coefficient of CaCl2 for (CaCl2 + L-Alanine + Water) System at 308.2 K and P = 0.1 MPa

γ±

ma

mV mA = 0.3 −36.2 13.0 34.9 66.4 88.8 102.2 111.2 118.8 124.6 129.6 134.5 142.8 150.3 mA = 0.4 −39.1 11.7 34.7 66.1 89.2 102.5 112.6 120.2 126.8 132.0 136.6 144.8 154.3

mol·kg

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

0.8391 0.7169 0.6570 0.5826 0.5385 0.5216 0.5159 0.5164 0.5212 0.5291 0.5397 0.5674 0.6027

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

0.8290 0.7017 0.6401 0.5639 0.5178 0.4987 0.4905 0.4884 0.4904 0.4955 0.5031 0.5246 0.5534

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

mV mA = 0a −46.8 1.4 24.6 55.3 77.5 90.5 99.7 107.2 113.1 119.1 124.0 132.4 140.9 mA = 0.1 −64.7 −11.1 11.0 43.3 66.6 80.4 90.6 98.1 103.4 109.0 114.2 122.5 129.6 mA = 0.2 −60.1 −12.9 8.1 32.1 54.7 68.4 79.3 87.2 93.2 98.4 105.8 111.6 119.8

m mol·kg

E −1

0.8124 0.6723 0.6041 0.5180 0.4633 0.4380 0.4244 0.4169 0.4135 0.4127 0.4141 0.4215 0.4335

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

0.8200 0.6858 0.6211 0.5416 0.4945 0.4753 0.4665 0.4630 0.4625 0.4638 0.4662 0.4723 0.4783

0.0033 0.0167 0.0333 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.8333 1.0000

γ±

mV mA = 0.3 −52.0 −1.8 19.8 51.4 73.5 88.2 98.5 106.5 113.1 118.8 124.3 133.0 140.2 mA = 0.4 −49.9 1.4 23.4 53.1 77.1 91.5 101.6 108.7 115.0 120.8 126.0 135.0 143.2

0.8322 0.7047 0.6419 0.5626 0.5133 0.4921 0.4824 0.4791 0.4801 0.4842 0.4909 0.5105 0.5373 0.8374 0.7131 0.6519 0.5755 0.5306 0.5147 0.5110 0.5146 0.5235 0.5368 0.5540 0.5993 0.6595

0.8265 0.6958 0.6320 0.5519 0.5024 0.4813 0.4716 0.4683 0.4692 0.4733 0.4799 0.4992 0.5256

m indicates the moles number of CaCl2 per kilogram of (water + mixture and standard uncertainties u with0.68 level of confidence are follows: u(m) = 0.0001 mol·kg−1, u(T) = 0.1 K, and u(p) = 2 kPa. bThe average uncertainties of emf and mean activity coefficient value were calculated in according to data scatter; u(E) = 1.5 mV and u(γ±) = 0.0238. L-alanine)

in L-alanine + water mixtures. β(0), β(1), and Cφ show solutespecific interaction Pitzer parameters for single salt electrolyte solution so that their values should be determined for CaCl2 in L-alanine + water mixtures. Aφ denotes the Debye−Hückel parameter for the osmotic coefficients defined by eq 719 (εrT )3/2

γ±b

a

m indicates the moles number of CaCl2 per kilogram of (water + L-alanine) mixture and standard uncertainties u with 0.68 level of confidence are follows: u(m) = 0.0001 mol·kg−1, u(T) = 0.1 K, and u(p) = 2 kPa. bThe average uncertainties of emf and mean activity coefficient value were calculated in according to data scatter; u(E) = 1.2 mV and u(γ±) = 0.0189.

1.4006 × 106ds1/2

−1

0.8341 0.7089 0.6475 0.5706 0.5232 0.5031 0.4941 0.4913 0.4926 0.4970 0.5040 0.5240 0.5511

a

Aφ =

Eb

The Debye−Hückel constant for pure water and the L-alanine + water mixtures were shown in Table 2. 3.3. PSC Model. The PSC model was also used for this ternary system. It introduces composition-dependent terms into the Debye−Hückel expression, and additional short-range parameters for the interaction between the solvent and a single anion and cation in highly concentrated solutions.13−22 Briefly, in the PSC model, the activity coefficients based on mole fractional scale are

kg1/2·mol−1/2 (7) D



Article

ln f±s CaCl = (1 − xI )(x1W1CaCl + x 2W2CaCl) 2

+ 2xI(1 − xI )(x1U1CaCl + x 2U2CaCl) +

8 xI(2 − 3xI )(x12V1CaCl + x 22V2CaCl) 9

+ x1x 2[w12 + 2(x1 − x 2)u12 − (1 − 2xI )Z12CaCl] − x1∞W1CaCl − x 2∞W2CaCl − x1∞x 2∞[w12 + 2(x1∞ − x 2∞)u12 − Z12CaCl]

(9)

where x1∞ =

x1 x1 + x 2

x 2∞ =

x2 x1 + x 2

And w12, u12 are binary interaction parameters related to Margules coefficients for a system containing water (1) and alanine (2). xi is the mole fraction of the species i in the mixture; xI is the mole fraction of the total ions in the solution. In addition, WiCaCl, UiCaCl and ViCaCl are PSC interaction parameters for the binary system, solvent i + CaCl (I = 1 or 2); Z12CaCl is also a model parameter, which accounts for the quaternary short-range PSC interaction.23 The contribution of long-range forces is defined by an extended DH expression including composition-dependent terms

Figure 2. Plot of the values of mean activity coefficient of CaCl2 versus CaCl2 molality at different molality of L-alanine (0.0, 0.1, 0.2, 0.3, and 0.4) at T = 298.2 K and P = 0.1 MPa.

⎡ I1/2(1 − Ix) ⎤ ⎥ = −2A x ⎢(2/ρ)ln(1 + ρIx1/2) − x ln f±DH CaCl2 ⎢⎣ (1 + ρIx1/2) ⎥⎦ +

⎡ g (αI1/2) ⎛ I − 2 4 x +⎜ x xI BCaCl g (αIx1/2) − xI2BCaCl ⎢ ⎢⎣ Ix 9 9 ⎝ Ix

+

1/2 ⎡ ⎤ ⎛ I − 1⎞ 2 4 1 1 ⎢ g (α1Ix ) +⎜ x xI BCaCl g (α1Ix1/2) − xI2BCaCl ⎟exp(−α1Ix1/2)⎥ ⎢⎣ ⎥⎦ 9 9 Ix ⎝ Ix ⎠

(10)

Figure 3. Plot of mean activity coefficient of CaCl2 variation versus CaCl2 molality at different temperature T = (298.2, 303.2, and 308.2) K in the mixed solvent solution with mA = 0.1 mol·kg−1.

where g (αIx1/2) =

expressed by the contribution of short-range (lnfS±) and long-range 22,23 (lnfDH ± ) forces: ln f± = ln f ±s + ln f±DH

⎤ 1⎞ ⎟exp(−αIx1/2)⎥ ⎥⎦ ⎠

Ix =

(8)

2[1 − (1 + αIx1/2)exp(−αIx1/2)] α 2Ix

(11)

1 2 (z MxM + z X2x X) 2

(12)

The BCaCl and B1CaCl are specific parameters for each electrolyte and they indicate the long-range parameters for MX electrolyte in the dilute range; Ix is the ionic strength on the mole fraction basis; α and α1 are given fixed values of 13 and 2,

The lnfS± term is a short-range expression, which can be written as a four-suffix Margules expansion including parameters for the interactions of both the solvent−anion and solvent−cation

Table 6. Adjustable Extended Debye−Hückel Parameters, a, c, and d, for (CaCl2 + L-Alanine + Water) System at 298.2 K, 303.2 K, and 308.2 K and P = 0.1 MPa mA

a

c

0.0 0.1 0.2 0.3 0.4

5.0426 4.9288 5.1641 5.1750 5.1038

0.0456 0.0805 0.0533 0.0505 0.0637

0.0 0.1 0.2 0.3 0.4

4.5972 4.6017 4.8002 4.8001 4.7248

d

σ

a

c

0.0007 0.0010 0.0006 0.0006 0.0005

4.8841 4.7708 5.1019 4.9827 4.9054

0.0455 0.0828 0.0536 0.0507 0.0639

d

σ

0.0022 −0.0065 0.0037 0.0038 0.0031

0.0006 0.0005 0.0006 0.0005 0.0004

mol·kg−1 T = 298.2 K 0.0032 −0.0076 0.0034 0.0057 −0.0002 T = 308.2 K 0.0457 0.0020 0.0816 −0.0070 0.0527 0.0040 0.0509 0.0042 0.0645 0.0088

T = 303.2 K

0.0004 0.0004 0.0004 0.0004 0.0003 E



Article

Table 7. Pitzer Ion-Interaction Parameters, β(0), β(1), and Cφ, of (CaCl2+ L-Alanine + Water) System at 298.2 K, 303.2 K, and 308.2 K and P = 0.1 MPa β(0)

β(1)

0.0 0.1 0.2 0.3 0.4

0.3053 0.3890 0.3084 0.2940 0.3220

1.7085 1.5363 1.5590 1.4780 1.3653

0.0 0.1 0.2 0.3 0.4

0.3103 0.3940 0.3114 0.2990 0.3270

1.4775 1.3823 1.4050 1.3239 1.2112

mA mol·kg

Cφ

σ(γ)

β(0)

β(1)

0.0002 0.0003 0.0020 0.0024 0.0018

0.3081 0.3957 0.3111 0.2968 0.3248

1.6315 1.4592 1.5409 1.4009 1.2882

T = 298.2 K −0.00900 −0.09108 −0.00501 0.01258 −0.03106 T = 308.2 K −0.02313 −0.08818 −0.00506 −0.00247 0.03165

σ(γ)

⎛ 1000 ⎞1/2 Ax = ⎜ ⎟ Aφ ⎝ MS ⎠

0.0002 0.0004 0.0007 0.0007 0.0007

3.000 mol·kg−1 were selected to determine each corresponding potential (EA) using the cell (A). The Nernst equation for cell (A) is

(13)

⎛ ds ⎞1/2 ρ = 2150⎜ ⎟ ⎝ εrT ⎠

(14)

EA = E 0 + s log(γ±0I )

⎡⎛ 2 ⎞ I1/2(1 − Ix) ⎤ ⎥ ln f±CaCl = −2A x ⎢⎜ ⎟ln(1 + ρIx1/2) − x 1/2 2 ⎢⎣⎝ ρ ⎠ (1 + ρIx ) ⎥⎦ +

⎡ g αI1/2 ⎤ 2 4 ( x ) ⎛ Ix − 1 ⎞ +⎜ xI BCaCl g (αIx1/2) − xI2BCaCl ⎢ ⎟exp(−αIx1/2)⎥ ⎢⎣ Ix ⎥⎦ 9 9 ⎝ Ix ⎠

+

1/2 ⎡ ⎛I − 2 4 1 1 ⎢ g (α1Ix ) +⎜ x xI BCaCl g (α1Ix1/2) − xI2BCaCl ⎢ 9 9 Ix ⎝ Ix ⎣

(17)

where the γ± is the mean activity coefficient of CaCl2 in pure water. The E0 is the experimental standard potential of cell (A). Then, measured potentials were plotted against log (γ±I) to check the slope (s) and the linear correlation coefficient (R2) at 298.2 K. It can be noted that the Pitzer parameters of CaCl2 in water system were taken from ref 13 and the activity coefficients (γ± ) were calculated in according to Pitzer model. Amount of R2 in Figure 1 shows the obtained results agree with literature. Figure 1 is also evident that the electrode pair used here has a near Nernst slope (s = 87.3 mV/decade), the experimental standard potential (E0 = 127.8 mV) and linear correlation coefficient (R2 = 0.9992) and it is suitable for our measurements. Furthermore, the comparable calibration were performed the measured potentials against log (γ± I) for CaCl2 in water at T = (303.2 and 308.2) K (see Figures S2 and S3 in Supporting Information). 4.3. Determination of the Mean Activity Coefficients and Pitzer Parameters. After the electrode pair calibration for each series, the emf of the cell (B) was measured at different series of CaCl2 in L-alanine + water mixed solvents through changing of electrolyte concentration by standard addition method. To remove the effect of L-alanine on the measured emf value, both internal filling solution and experiment solution was selected as the same concentration of L-alanine in L-alanine + water mixed solvent. The standard state for the mean activity coefficient was assumed as the real solution in dilute limit, which its value was unit. The mean activity coefficients for CaCl2 in the L-alanine + water mixtures were determined from the emf measurements using the galvanic cell (B) in according to the eq 1818

Ax and ρ were calculated for whole series and were shown in Table 2. Therefore, the mean activity coefficients on the mole fraction scale are determined in according to eq 1522

⎤ 1⎞ ⎟exp(−α1Ix1/2)⎥ ⎥⎦ ⎠

+ (1 − xI )(x1W1CaCl + x 2W2CaCl) + 2xI (1 − xI )(x1U1CaCl + x 2U2CaCl) 8 xI (2 − 3xI )(x12V1CaCl + x 22V2CaCl) 9

+ x1x 2[w12 + 2(x1 − x 2)u12 − (1 − 2xI )Z12CaCl] − x1∞W1CaCl − x 2∞W2CaCl − x1∞x 2∞[w12 + 2(x1∞ − x 2∞)u12 − Z12CaCl]

(15)

The molal-based activity coefficient (γ) can be related to the mole-fraction-based activity coefficient (f) by fi = γi[1 + (3mMS/1000)]

T = 302.2 K −0.01863 −0.08274 −0.00410 −0.00328 −0.00909

0.0005 0.0014 0.0008 0.0006 0.0011

respectively. The Debye−Hückel parameter on the mole-fraction basis (Ax) and the parameter related to closest approach distances ρ were calculated using the eqs 13 and 14

+

Cφ

−1

(16)

where m is the molal concentration of the solute species i.

4. RESULTS AND DISCUSSION 4.1. Evaluation of densitometry data. Densities of L-alanine + water mixtures were measured with the accuracy about ± 0.0001 kg·dm−3 at T = (298.2, 303.2, and 308.2) K (Table 1). Comparison between experimental density values and literature data24 indicated a good agreement (see figure S1 in Supporting Information). 4.2. Calibration of Ca−ISE and Ag/AgCl Electrode Pairs. The amount of CaCl2 ionic strength (I) from 0.0100 to

E B = E 0 + s log(γ±m)

(18)

In Tables 3 to 5 were illustrated the values of measured emf and the obtained mean activity coefficients of the CaCl2 electrolyte in several different mixtures of L-alanine + water as a function of CaCl2 molality at T = (298.2, 303.2, and 308.2) K. Also, Figure 2 presents the variation of the CaCl2 mean activity coefficients versus the CaCl2 molality in water, and different molality of L-alanine in mixed solvents at T = 298.2 K. It can be F



Article

Table 8. Values of Ionic Strength I, Osmotic Coefficient φ, Excess Free Gibbs Energy GE/RT, and Solvent Activity as of (CaCl2 + LAlanine + Water) System for Different Series of Alanine Molality Based on Pitzer Model at 298.2 K and P = 0.1 MPa φb

Ia mol·kg

GE/RTb

asb

φ

I

−1

mol·kg mA = 0

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9377 0.8930 0.8744 0.8590 0.8602 0.8689 0.8807 0.8943 0.9093 0.9256 0.9430 0.9805 1.0209

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9404 0.8983 0.8816 0.8707 0.8781 0.8914 0.9057 0.9198 0.9333 0.9459 0.9573 0.9764 0.9895

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9428 0.9022 0.8856 0.8732 0.8774 0.8887 0.9029 0.9189 0.9363 0.9550 0.9747 1.0169 1.0622

GE/RT

as

−0.0012 −0.0122 −0.0315 −0.1058 −0.2539 −0.4156 −0.5831 −0.7524 −0.9211 −1.0871 −1.2491 −1.5563 −1.8347

0.9998 0.9992 0.9984 0.9960 0.9919 0.9878 0.9834 0.9790 0.9743 0.9694 0.9644 0.9535 0.9417

−0.0012 −0.0118 −0.0304 −0.1020 −0.2443 −0.3988 −0.5585 −0.7198 −0.8806 −1.0395 −1.1953 −1.4951 −1.7758

0.9998 0.9992 0.9983 0.9959 0.9918 0.9876 0.9832 0.9787 0.9740 0.9692 0.9643 0.9540 0.9432

−1

mA = 0.3 −0.0014 −0.0138 −0.0356 −0.1198 −0.2887 −0.4744 −0.6687 −0.8673 −1.0678 −1.2681 −1.4668 −1.8554 −2.2266

0.9998 0.9992 0.9984 0.9961 0.9923 0.9883 0.9843 0.9801 0.9757 0.9712 0.9666 0.9568 0.9463

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9448 0.9054 0.8892 0.8768 0.8809 0.8925 0.9074 0.9245 0.9435 0.9642 0.9864 1.0347 1.0877

−0.0013 −0.0131 −0.0339 −0.1135 −0.2710 −0.4418 −0.6184 −0.7974 −0.9770 −1.1561 −1.3342 −1.6862 −2.0326

0.9998 0.9992 0.9984 0.9961 0.9921 0.9879 0.9837 0.9793 0.9749 0.9704 0.9658 0.9567 0.9475

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9467 0.9087 0.8932 0.8822 0.8879 0.9002 0.9148 0.9306 0.9470 0.9640 0.9813 1.0165 1.0516

−0.0013 −0.0126 −0.0326 −0.1094 −0.2625 −0.4295 −0.6028 −0.7784 −0.9540 −1.1278 −1.2984 −1.6259 −1.9300

0.9998 0.9992 0.9984 0.9960 0.9920 0.9879 0.9836 0.9792 0.9747 0.9699 0.9650 0.9546 0.9434

mA = 0.1

mA = 0.4

mA = 0.2

a

I indicates the ionic strength of CaCl2 per kilogram of (water + L-alanine) mixture and standard uncertainties u with 0.68 level of confidence are follows: u(I) = 0.0001 mol·kg−1, u(T) = 0.1 K, and u(p) = 2 kPa. bThe average standard uncertainties of osmotic coefficient, excess Gibbs energy, and solvent (water + L-alanine) activity were calculated with 0.68 level of confidence; u(φ) = 0.0064, u(GE/RT) = 0.0055 and u(as) = 0.0001.

the temperature. Also, the comparable trends were observed with 0.2 molal, 0.3 molal, and 0.4 molal of L-alanine in L-alanine + water mixtures (see Figures S6 to S8 in Supporting Information). At the same time, when the molality of electrolyte is fixed, the values of the mean activity coefficient increase with increasing the mlality of L-alanine in L-alanine + water mixtures. This can be interpreted in terms of the electrostatic interaction and structural interaction models. The electrostatic effect can be represented as the interaction of ions with L-alanine which the amino acid and the ions of the salt are considered to be hard and inflexible and the solvent is treated as a dielectric continuum. The structural interaction can be described in terms of the molecular parameters

observed that at low molality of electrolyte, the values of the mean activity coefficients decrease with increasing the molality of electrolyte, and then increase with increasing the molality of electrolyte at high molality at the same values of L-alanine molality in L-alanine + water mixtures and temperature. As well, the similar trends were observed to change the activity coefficients at T = (303.2 and 308.2) K (see Figures S4 and S5 in Supporting Information). Figure 3 indicates the values of the activity coefficients of CaCl2 in solution with 0.1 molal of L-alanine mixed solvent. A comparison of data in Tables 3 to 5 and Figure 3 show the activity coefficients of CaCl2 in mixture decrease with rising G



Article

Table 9. Values of Ionic Strength I, Osmotic Coefficient φ, Excess Free Gibbs Energy GE/RT, and Solvent Activity as of (CaCl2 + LAlanine + Water) System for Different Series of Alanine Molality Based on Pitzer Model at 303.2 K and P = 0.1 MPa φb

Ia mol·kg

GE/RTb

asb

φ

I

−1

mol·kg mA = 0

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9368 0.8908 0.8711 0.8539 0.8535 0.8613 0.8722 0.8848 0.8989 0.9139 0.9298 0.9637 0.9994

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9395 0.8961 0.8785 0.8662 0.8731 0.8870 0.9025 0.9182 0.9337 0.9485 0.9624 0.9872 1.0069

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9422 0.9008 0.8838 0.8707 0.8745 0.8859 0.9002 0.9164 0.9342 0.9533 0.9735 1.0167 1.0630

GE/RT

as

−0.0013 −0.0124 −0.0320 −0.1082 −0.2609 −0.4283 −0.6026 −0.7798 −0.9573 −1.1333 −1.3064 −1.6399 −1.9508

0.9998 0.9992 0.9984 0.9960 0.9920 0.9879 0.9836 0.9792 0.9747 0.9699 0.9650 0.9546 0.9435

−0.0012 −0.0120 −0.0310 −0.1044 −0.2509 −0.4102 −0.5746 −0.7402 −0.9044 −1.0655 −1.2222 −1.5186 −1.7872

0.9998 0.9992 0.9984 0.9959 0.9919 0.9876 0.9832 0.9787 0.9739 0.9690 0.9638 0.9529 0.9412

−1

mA = 0.3 −0.0014 −0.0139 −0.0362 −0.1222 −0.2955 −0.4868 −0.6875 −0.8934 −1.1018 −1.3107 −1.5189 −1.9288 −2.3250

0.9998 0.9992 0.9984 0.9962 0.9923 0.9884 0.9844 0.9803 0.9760 0.9716 0.9670 0.9575 0.9474

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9440 0.9032 0.8859 0.8716 0.8739 0.8841 0.8976 0.9131 0.9301 0.9485 0.9679 1.0097 1.0545

−0.0014 −0.0133 −0.0345 −0.1159 −0.2774 −0.4528 −0.6342 −0.8178 −1.0016 −1.1845 −1.3656 −1.7212 −2.0669

0.9998 0.9992 0.9984 0.9961 0.9921 0.9880 0.9838 0.9794 0.9749 0.9703 0.9657 0.9562 0.9466

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

0.9458 0.9064 0.8899 0.8774 0.8828 0.8962 0.9128 0.9313 0.9513 0.9724 0.9944 1.0408 1.0895

−0.0013 −0.0128 −0.0330 −0.1109 −0.2664 −0.4362 −0.6125 −0.7914 −0.9702 −1.1471 −1.3209 −1.6544 −1.9640

0.9998 0.9992 0.9984 0.9960 0.9920 0.9879 0.9837 0.9793 0.9747 0.9700 0.9650 0.9546 0.9434

mA = 0.1

mA = 0.4

mA = 0.2

a I indicates the ionic strength of CaCl2 per kilogram of (water + L-alanine) mixture and standard uncertainties u with 0.68 level of confidence are follows: u(I) = 0.0001 mol·kg−1, u(T) = 0.1 K, and u(p) = 2 kPa. bThe average standard uncertainties of osmotic coefficient, excess Gibbs energy, and solvent (water + L-alanine) activity were calculated with 0.68 level of confidence; u(φ) = 0.0081, u(GE/RT) = 0.0075 and u(as) = 0.0001.

(c and d) and physical properties. However, the obtained adjustable parameters do not show any regular trend with increasing molality of alanine. 4.5. Determination of Pitzer Parameters. Pitzer ioninteraction parameters (β(0), β(1), and Cφ) were obtained by an iteration minimization procedure employing the Microsoft Excel (solver) program. The obtained results were listed for the investigated systems at T = (298.2, 303.2, and 308.2) K in Table 7. The parameters (β(0), β(1), andCφ) are solute-specific parameters and indicate the virial coefficients in relating to the binary(β(0), and β(1)) and ternary(Cφ) interactions.13 It was observed, β(0)

which arises the contribution to the specific interaction from each of the groups in the L-alanine.10 4.4. Estimation of Debye−Hückel Parameters. The extended Debye−Hückel was used to correlate the experimental activity coefficient data for under investigated electrolyte system at T = (298.2, 303.2, and 308.2) K. The adjustable parameters (a, c, and d) were obtained by an iteration minimization procedure employing the Microsoft Excel (solver) program. The adjustable parameters were found for CaCl2 in various L-alanine + water system were illustrated in Table 6. It can be noted that the explicit relation is not observed between adjustable parameters H



Article

Table 10. Values of Ionic Strength I, Osmotic Coefficient φ, Excess Free Gibbs Energy GE/RT, and Solvent Activity as of (CaCl2 + L-Alanine + Water) System for Different Series of Alanine Molality Based on Pitzer Model at 308.2 K and P = 0.1 MPa φb

Ia mol·kg

GE/RTb

asb

φ

I

−1

mol·kg

GE/RT

as

0.9431 0.9010 0.8827 0.8667 0.8679 0.8777 0.8912 0.9069 0.9244 0.9432 0.9632 1.0061 1.0522

−0.0013 −0.0126 −0.0326 −0.1105 −0.2674 −0.4400 −0.6201 −0.8034 −0.9873 −1.1698 −1.3495 −1.6960 −2.0198

0.9998 0.9992 0.9984 0.9960 0.9920 0.9880 0.9837 0.9794 0.9748 0.9701 0.9652 0.9548 0.9436

0.9450 0.9044 0.8870 0.8734 0.8792 0.8949 0.9152 0.9387 0.9648 0.9932 1.0236 1.0900 1.1630

−0.0012 −0.0121 −0.0315 −0.1065 −0.2564 −0.4193 −0.5866 −0.7539 −0.9180 −1.0768 −1.2285 −1.5049 −1.7376

0.9998 0.9992 0.9984 0.9960 0.9919 0.9876 0.9832 0.9785 0.9735 0.9683 0.9628 0.9508 0.9374

−1

mA = 0 0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000 mA = 0.1 0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000 mA = 0.2 0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

mA = 0.3

0.9356 0.8874 0.8659 0.8455 0.8427 0.8494 0.8597 0.8720 0.8858 0.9006 0.9162 0.9490 0.9834

−0.0014 −0.0142 −0.0370 −0.1258 −0.3061 −0.5061 −0.7168 −0.9335 −1.1535 −1.3746 −1.5955 −2.0324 −2.4577

0.9998 0.9992 0.9984 0.9962 0.9924 0.9886 0.9846 0.9805 0.9763 0.9720 0.9675 0.9581 0.9482

0.9386 0.8937 0.8749 0.8605 0.8655 0.8782 0.8927 0.9075 0.9220 0.9357 0.9485 0.9706 0.9871

−0.0014 −0.0135 −0.0351 −0.1184 −0.2849 −0.4665 −0.6551 −0.8468 −1.0396 −1.2320 −1.4235 −1.8019 −2.1737

0.9998 0.9992 0.9984 0.9961 0.9922 0.9881 0.9839 0.9796 0.9752 0.9707 0.9662 0.9569 0.9477

0.9410 0.8976 0.8789 0.8628 0.8644 0.8747 0.8886 0.9047 0.9225 0.9416 0.9619 1.0053 1.0518

−0.0013 −0.0130 −0.0338 −0.1143 −0.2764 −0.4545 −0.6402 −0.8292 −1.0187 −1.2070 −1.3924 −1.7502 −2.0851

0.9998 0.9992 0.9984 0.9961 0.9921 0.9881 0.9839 0.9795 0.9750 0.9703 0.9654 0.9551 0.9440

0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000 mA = 0.4 0.0100 0.0500 0.1000 0.2500 0.5000 0.7500 1.0000 1.2500 1.5000 1.7500 2.0000 2.5000 3.0000

a

I indicates the ionic strength of CaCl 2 per kilogram of (water + L-alanine) mixture and standard uncertainties u with 0.68 level of confidence are follows: u(I) = 0.0001 mol·kg−1, u(T) = 0.1 K, and u(p) = 2 kPa. bThe average standard uncertainties of osmotic coefficient, excess Gibbs energy, and solvent (water + L-alanine) activity were calculated with 0.68 level of confidence; u(φ) = 0.0084, u(GE/RT) = 0.0079 and u(as) = 0.0001.

which can be identified with the total binary ionic interactions increase with increasing of temperature at the same molality of alanine. As well, β(1) which can be identified with the interactions between unlike-charged ions decrease with increasing molality of alanine at the same temperature. 4.6. Calculation of Thermodynamic Properties by Pitzer Model. The obtained parameters were used to calculate the thermodynamic properties of under investigation system by the Pitzer model. The osmotic coefficients (φ) and the excess Gibbs free energy for all of series under investigation can be calculated using the following equations:

φCaCl = 1 − 2

2Aφ I 1+b I

+

4 φ 4 2 φ 2 BCaCl 2 I + CCaCl 2I 9 27 (19)

φ BCaCl = β (0) + β (1)exp( −α1 I ) 2

(20)

G E = RTI(1 − φ + ln γ±)

(21)

The values of these thermodynamic properties were illustrated in Tables 8 to 10 for different series of alanine molality at T = (298.2, 303.2, and 308.2) K, respectively. Figure 4 shows the I



J

0.0017 0.0018 0.0021 439.3088 440.1872 441.3123

σ

85.47914 85.4819 85.48555

Z12CaCl

−778.039 −777.919 −777.863

V2CaCl

−392.371 −391.305 −390.019

U2CaCl

114.47 112.6591 107.7389

W2 CaCl

55.396 49.67525 32.53357

B1CaCl

0.072 −0.329 −1.00694

BCaCl

−0.058 0.334 1.054302 19.148 17.98369 17.86924

−38.2729 −36.8977 −35.7825

u12 w12 V1CaCl

0 0.003192 0.006171 K

298.2 303.2 308.2

variation of the excess Gibbs free energy against the ionic strength variation at 298.2 K. It can be seen that the excess Gibbs free energy enlarges by increasing the molality of alanine in the mixtures. As it was mentioned before, this can be interpreted in terms of the interaction model. For the studied system here, there are the polar groups in L-alanine that can interact with Ca2+ and Cl−. Additionally, the corresponding variations were observed to change excess Gibbs free energy at T = (303.2 and 308.2) K (see Figures S9 and S10 in Supporting Information). Moreover, Figure 5 indicates the values of excess Gibbs free energy in mixture with 0.1 molal of L-alanine in L-alanine + water mixtures. It can be seen the values of excess Gibbs free energy decrease with rising temperature. In addition, the similar tendency was seen with 0.2 molal, 0.3 molal, and 0.4 molal of L-alanine mixed solvent (see Figures S11 to S13 in Supporting Information). 4.7. Determination of PSC Parameters and Calculation of Thermodynamic Properties. For our work, the PSC model was also applied to correlate the experimental data. In this approach, the L-alanine + water mixture was considered as a mixed solvent containing water (1) and L-alanine (2). The corresponding parameters were then determined, as described below, for this approach. First, the long-range (BCaCl and B1CaCl) and short-range (W1CaCl, U1CaCl, V1CaCl) binary interaction parameters were determined based on eq 15 for binary system containing water and CaCl2 by using the mean activity coefficient data. The obtained parameters were illustrated in Table 11 at T = (298.2, 303.2, and 308.2) K. It can be observed that there

U1CaCl

Figure 5. Plot of excess Gibbs free energy variation versus CaCl2 molality at different temperature T = (298.2, 303.2, and 308.2) K in the mixed solvent solution with mA = 0.1 mol·kg−1.

W1CaCl

Figure 4. Plot of excess Gibbs free energy of (CaCl2 + L-alanine + water) system against total ionic strength at T = 298.2 K.

T

Table 11. Long-range, BCaCl and B1CaCl, and short-range, W1CaCl, U1CaCl, V1CaCl, Binary Interaction Parameters, Margules Parameters, w12 and u12, and Ternary Short-Range PSC Interaction Parameters, W2CaCl, V2CaCl, U2CaCl, and Z12CaCl, of (CaCl2 + L-Alanine + Water) System at 298.2 K, 303.2 K, and 308.2 K and P = 0.1 MPa

Article



Article

Table 12. Values of Mole Fraction of the Total Ions in the Solutions xI, Activity Coefficient of CaCl2 Based on Mole Fractional Scale f±, Activity Coefficient of L-Alanine Based on Mole Fractional Scale fA, Excess Free Gibbs Energy Per Mole gE/RT for (CaCl2 + L-Alanine + Water) System at Different Series of Molality of Alanine Based on PSC Model at 298.2 K and P = 0.1 MPa xIa

f±CaCl2b

0.0002 0.0009 0.0018 0.0045 0.0089 0.0133 0.0177 0.0220 0.0263 0.0306 0.0348 0.0431 0.0513

0.8172 0.6824 0.6172 0.5363 0.4868 0.4652 0.4545 0.4497 0.4486 0.4504 0.4545 0.4683 0.4889

0.0002 0.0009 0.0018 0.0045 0.0090 0.0134 0.0178 0.0222 0.0265 0.0308 0.0350 0.0434 0.0516

0.8248 0.6956 0.6335 0.5580 0.5146 0.4984 0.4928 0.4931 0.4973 0.5045 0.5142 0.5404 0.5750

0.0002 0.0009 0.0018 0.0045 0.0091 0.0135 0.0179 0.0223 0.0267 0.0310 0.0353 0.0437 0.0520

0.8316 0.7077 0.6487 0.5787 0.5419 0.5317 0.5320 0.5382 0.5486 0.5622 0.5789 0.6203 0.6726

fAb

gE/RT

xI

f±CaCl2

0.0000 −0.0002 −0.0006 −0.0022 −0.0052 −0.0085 −0.0119 −0.0153 −0.0188 −0.0222 −0.0255 −0.0320 −0.0380

0.0002 0.0009 0.0018 0.0046 0.0091 0.0136 0.0181 0.0225 0.0269 0.0312 0.0355 0.0440 0.0523

0.8377 0.7187 0.6627 0.5983 0.5686 0.5649 0.5717 0.5847 0.6022 0.6235 0.6484 0.7083 0.7826

1.0218 1.0550 1.0961 1.2152 1.3891 1.5155 1.5799 1.5755 1.5044 1.3770 1.2096 0.8279 0.4863

0.0000 −0.0001 −0.0004 −0.0017 −0.0044 −0.0073 −0.0105 −0.0138 −0.0171 −0.0205 −0.0239 −0.0305 −0.0370

0.0002 0.0009 0.0018 0.0046 0.0092 0.0137 0.0182 0.0226 0.0270 0.0314 0.0357 0.0443 0.0527

0.8434 0.7291 0.6760 0.6174 0.5952 0.5986 0.6127 0.6334 0.6591 0.6894 0.7239 0.8062 0.9075

1.0210 1.0531 1.0928 1.2069 1.3704 1.4847 1.5365 1.5204 1.4403 1.3076 1.1388 0.7657 0.4414

0.0001 0.0000 −0.0003 −0.0013 −0.0036 −0.0063 −0.0092 −0.0124 −0.0156 −0.0190 −0.0224 −0.0294 −0.0365

fA

gE/RT

1.0202 1.0512 1.0895 1.1985 1.3519 1.4543 1.4939 1.4670 1.3787 1.2413 1.0719 0.7080 0.4005

0.0001 0.0001 −0.0001 −0.0009 −0.0029 −0.0053 −0.0081 −0.0111 −0.0143 −0.0177 −0.0213 −0.0287 −0.0363

1.0194 1.0494 1.0861 1.1902 1.3335 1.4244 1.4523 1.4152 1.3194 1.1781 1.0086 0.6544 0.3633

0.0001 0.0002 0.0001 −0.0005 −0.0022 −0.0044 −0.0070 −0.0100 −0.0132 −0.0166 −0.0203 −0.0282 −0.0365

mA = 0.3

mA = 0

mA = 0.1

mA = 0.4

mA = 0.2

a

Mean uncertainty value for the mole fraction of the total ions in the solution is u(xI) = 0.0001, and uncertainty of temperature and pressure are u(T) = 0.1 K and u(p) = 2 kPa, respectively. bThe average standard uncertainty for activity coefficients of CaCl2 and activity coefficients of alanine based on mole fractional scale with 0.68 level of confidence are u( f±CaCl2) = 0.0040 and u( fA) = 0.0282, respectively.

energy per mole22 and activity coefficient of alanine in mole fraction (fA) based26,27 can be written

is the very agreement between the obtained results with literature22 at T = 298.2 K. Then, the Margules parameters (w12 and u12) for binary water + L-alanine mixture were calculated using the isopiestic data from literature25 in according to Margules equation13,26 at T = (298.2, 303.2, and 308.2) K. Finally, the ternary short-range PSC interaction parameters (W2CaCl, V2CaCl, U2CaCl, and Z12CaCl) were obtained by fitting over the whole set of experimental data (with L-alanine molality from 0.1 to 0.4). All obtained parameters were listed in Table 11. Consequently, the PSC parameters obtained were used to calculate the thermodynamic properties of under investigation system. According to the PSC model, the excess Gibbs free

⎛ 4A I ⎞ ⎡ (1 + ρIx1/2) ⎤ 2 gE ⎥ + xIBCaCl g (αIx1/2) = − ⎜ x x ⎟ln⎢ 9 RT ⎝ ρ ⎠ ⎢⎣ 1 + ρ(Ix°)1/2 ⎥⎦ +

2 1 xIBCaCl g (α1Ix1/2) + xI(x1W1CaCl + x 2W2CaCl) 9

+ xI2(x1U1CaCl + x 2U2CaCl) 8 + xI2(x12V1CaCl + x 22V2CaCl) + x1x 2[w12 + u12(x1 − x 2) 9 + xIZ12CaCl] K

(22) DOI: 10.1021/acs.jced.5b00260 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 13. Values of Mole Fraction of the Total Ions in the Solutions xI, Activity Coefficient of CaCl2 Based on Mole Fractional Scale f±, Activity Coefficient of L-Alanine Based on Mole Fractional Scale fA, Excess Free Gibbs Energy Per Mole (gE/RT) for (CaCl2 + L-Alanine + Water) System at Different Series of Molality of Alanine Based on PSC Model at 303.2 K and P = 0.1 MPa xIa

f±CaCl2b

0.0002 0.0009 0.0018 0.0045 0.0089 0.0133 0.0177 0.0220 0.0263 0.0306 0.0348 0.0431 0.0513

0.8153 0.6786 0.6121 0.5287 0.4766 0.4531 0.4408 0.4343 0.4318 0.4320 0.4344 0.4449 0.4617

0.0002 0.0009 0.0018 0.0045 0.0090 0.0134 0.0178 0.0222 0.0265 0.0308 0.0350 0.0434 0.0516

0.8228 0.6915 0.6280 0.5498 0.5035 0.4851 0.4775 0.4759 0.4782 0.4834 0.4911 0.5128 0.5424

0.0002 0.0009 0.0018 0.0045 0.0091 0.0135 0.0179 0.0223 0.0267 0.0310 0.0353 0.0437 0.0520

0.8298 0.7037 0.6433 0.5705 0.5306 0.5179 0.5158 0.5198 0.5279 0.5392 0.5533 0.5892 0.6350

fAb

gE/RT

xI

f±CaCl2

0.0000 −0.0002 −0.0006 −0.0022 −0.0053 −0.0086 −0.0122 −0.0157 −0.0193 −0.0229 −0.0264 −0.0333 −0.0397

0.0002 0.0009 0.0018 0.0046 0.0091 0.0136 0.0181 0.0225 0.0269 0.0312 0.0355 0.0440 0.0523

0.8358 0.7147 0.6571 0.5897 0.5566 0.5500 0.5542 0.5645 0.5793 0.5978 0.6195 0.6725 0.7385

1.0161 1.0508 1.0941 1.2206 1.4098 1.5538 1.6361 1.6475 1.5884 1.4678 1.3014 0.9071 0.5422

0.0000 −0.0002 −0.0005 −0.0017 −0.0044 −0.0075 −0.0107 −0.0141 −0.0176 −0.0211 −0.0247 −0.0317 −0.0386

0.0002 0.0009 0.0018 0.0046 0.0092 0.0137 0.0182 0.0226 0.0270 0.0314 0.0357 0.0443 0.0527

0.8414 0.7248 0.6701 0.6083 0.5823 0.5825 0.5935 0.6111 0.6336 0.6604 0.6911 0.7648 0.8556

1.0182 1.0520 1.0939 1.2157 1.3948 1.5266 1.5957 1.5946 1.5252 1.3978 1.2288 0.8414 0.4936

0.0000 −0.0001 −0.0003 −0.0013 −0.0036 −0.0064 −0.0094 −0.0126 −0.0160 −0.0195 −0.0231 −0.0304 −0.0378

fA

gE/RT

1.0203 1.0531 1.0937 1.2108 1.3799 1.4996 1.5560 1.5430 1.4641 1.3308 1.1599 0.7802 0.4492

0.0001 0.0000 −0.0001 −0.0009 −0.0029 −0.0054 −0.0082 −0.0113 −0.0146 −0.0181 −0.0218 −0.0295 −0.0375

1.0223 1.0542 1.0934 1.2058 1.3650 1.4729 1.5169 1.4927 1.4051 1.2666 1.0946 0.7232 0.4086

0.0001 0.0002 0.0001 −0.0005 −0.0021 −0.0044 −0.0071 −0.0101 −0.0134 −0.0170 −0.0207 −0.0289 −0.0376

mA = 0.3

mA = 0

mA = 0.1

mA = 0.4

mA = 0.2

a

Mean uncertainty value for the mole fraction of the total ions in the solution is u(xI) = 0.0001, and uncertainty of temperature and pressure are u(T) = 0.1 K and u(p) = 2 kPa, respectively. bThe average standard uncertainty for activity coefficients of CaCl2 and activity coefficients of alanine based on mole fractional scale with 0.68 level of confidence are u( f±CaCl2) = 0.0029 and u( fA) = 0.0349, respectively ln fA =

2Ax Ix3/2 (1 + ρx1/2 )

−

Figure 6 shows that at low molality of electrolyte, the activity coefficient values of alanine increase with increasing the molality of CaCl2 and then decrease with increasing the molality of electrolyte at high molality at the same values of L-alanine molality in L-alanine + water mixtures at T = 298.2 K. Also, Figure 6 indicates that there is the linear relationship between logarithm of alanine activity coefficient and concentration added salt (CaCl2) at below 0.1667 molal and over 0.5 molal of electrolyte. The other hand, the variation of activity coefficient generally obeys the Setschenow rule28

2 2 2 1 Ix BCaCl exp(− αIx1/2) − Ix2BCaCl exp(− α1Ix1/2) 9 9

+ x I[(1 − x 2)W2CaCl − x1W1CaCl] + x I2[(1 − 2x 2)U2CaCl 8 − 2x1U1CaCl] + x I2[x 2(2 − 3x 2)V2CaCl − 3x12V1CaCl] 9 + x1IX(1 − 2x 2)Z12CaCl + x1{(1 − x 2)w12 + [2(x1 − x 2)(1 − x 2) − x1]u12}

(23)

The values of the excess Gibbs free energy per mole and activity coefficients of alanine and CaCl2 on mole fraction based were illustrated for different series of L-alanine molality in Tables 12 to 14.

log γA = ksm L

(24) DOI: 10.1021/acs.jced.5b00260 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 14. Values of Mole Fraction of the Total Ions in the Solutions xI, Activity Coefficient of CaCl2 Based on Mole Fractional Scale f±, Activity Coefficient of L-Alanine Based on Mole Fractional Scale fA, Excess Free Gibbs Energy Per Mole gE/RT for (CaCl2 + L-Alanine + Water) System at Different Series of Molality of Alanine Based on PSC Model at 308.2 K and P = 0.1 MPa xIa

f±CaCl2b

0.0002 0.0009 0.0018 0.0045 0.0089 0.0133 0.0177 0.0220 0.0263 0.0306 0.0348 0.0431 0.0513

0.8128 0.6726 0.6036 0.5161 0.4603 0.4347 0.4209 0.4134 0.4099 0.4093 0.4111 0.4200 0.4352

0.0002 0.0009 0.0018 0.0045 0.0090 0.0134 0.0178 0.0222 0.0265 0.0308 0.0350 0.0434 0.0516

0.8203 0.6854 0.6193 0.5367 0.4864 0.4654 0.4561 0.4530 0.4541 0.4582 0.4648 0.4843 0.5114

0.0002 0.0009 0.0018 0.0045 0.0091 0.0135 0.0179 0.0223 0.0267 0.0310 0.0353 0.0437 0.0520

0.8271 0.6974 0.6343 0.5567 0.5123 0.4966 0.4924 0.4946 0.5010 0.5108 0.5234 0.5561 0.5984

fAb

gE/RT

xI

f±CaCl2

0.0000 −0.0002 −0.0007 −0.0022 −0.0054 −0.0090 −0.0127 −0.0164 −0.0202 −0.0240 −0.0278 −0.0351 −0.0420

0.0002 0.0009 0.0018 0.0046 0.0091 0.0136 0.0181 0.0225 0.0269 0.0312 0.0355 0.0440 0.0523

0.8334 0.7085 0.6482 0.5758 0.5379 0.5280 0.5296 0.5377 0.5505 0.5670 0.5868 0.6356 0.6969

1.0656 1.1045 1.1531 1.2969 1.5180 1.6951 1.8078 1.8433 1.7990 1.6824 1.5092 1.0762 0.6574

0.0001 −0.0001 −0.0004 −0.0017 −0.0045 −0.0077 −0.0111 −0.0147 −0.0183 −0.0220 −0.0258 −0.0332 −0.0405

0.0002 0.0009 0.0018 0.0046 0.0092 0.0137 0.0182 0.0226 0.0270 0.0314 0.0357 0.0443 0.0527

0.8391 0.7189 0.6614 0.5944 0.5632 0.5597 0.5678 0.5828 0.6028 0.6272 0.6555 0.7239 0.8087

1.0728 1.1109 1.1583 1.2978 1.5090 1.6732 1.7713 1.7924 1.7354 1.6096 1.4316 1.0028 0.6012

0.0002 0.0001 −0.0001 −0.0011 −0.0035 −0.0064 −0.0096 −0.0130 −0.0165 −0.0202 −0.0240 −0.0317 −0.0395

fA

gE/RT

1.0800 1.1172 1.1634 1.2985 1.4997 1.6512 1.7352 1.7423 1.6736 1.5394 1.3575 0.9340 0.5495

0.0003 0.0003 0.0002 −0.0006 −0.0026 −0.0052 −0.0082 −0.0114 −0.0149 −0.0185 −0.0224 −0.0304 −0.0388

1.0871 1.1234 1.1684 1.2990 1.4902 1.6291 1.6993 1.6932 1.6134 1.4718 1.2868 0.8696 0.5021

0.0005 0.0005 0.0005 −0.0001 −0.0018 −0.0041 −0.0068 −0.0099 −0.0134 −0.0171 −0.0210 −0.0294 −0.0385

mA = 0.3

mA = 0

mA = 0.1

mA = 0.4

mA = 0.2

a

Mean uncertainty value for the mole fraction of the total ions in the solution is u(xI) = 0.0001, and uncertainty of temperature and pressure are u(T) = 0.1 K and u(p) = 2 kPa, respectively. bThe average standard uncertainty for activity coefficients of CaCl2 and activity coefficients of alanine based on mole fractional scale with 0.68 level of confidence are u( f±CaCl2) = 0.0036 and u( fA) = 0.0525, respectively.

The ks is the Setschenow coefficient which indicates the salting effect of CaCl2 on alanine. Adding salt to an aqueous solution of a compound can result in either an increase (salting out) or a decrease (salting in) in activity coefficient of a compound.29 The value of ks indicates on enlargement the activity coefficient of alanine at low concentration of CaCl2. It can be noted, the region of dilute salt solutions (below 0.5 molal) cannot interpreted by the Setschenow rule because of the increasing errors,30 whereas the activity coefficient values of alanine reduce with increasing the molality of electrolyte at upper 0.5 molal of electrolyte of CaCl2. Figure 7 shows the ks values and the plot of log(γA) variation for high molality of CaCl2 at different L-alanine + water

mixtures at 298.2 K. It is known that each of the organic compounds (nonelectrolyte) brings about an increase in the dielectric constant when added to water, its activity coefficients decrease with increasing the molality of electrolyte. These results are in agreement with literature.31 In addition, the similar trends were observed for log(γA) variations at T = (303.2 and 308.2) K (see Figures S14 and S15 in Supporting Information). Figure 8 shows the activity coefficient of alanine in mixture decreases with rising the molality of alanine in the fixed ionic strength at T = 298.2 K. Moreover, Figure 9 shows the logarithm of alanine activity coefficient versus its molailty at T = (298.2, 303.2, and 308.2) K. It can be seen that logarithm of alanine M



Article

activity coefficient decrease with its molailty and increase with temperature.

5. CONCLUSIONS The galvanic cell consisting of a Ca−ISE and Ag−AgCl electrodes were used to study the thermodynamic properties of CaCl2 + alanine + H2O system at T = (298.2, 303.2, and 308.2) K. The emf measurements were made for CaCl2 in various alanine + water mixtures containing 0.0 molal, 0.1 molal, 0.2 molal, 0.3 molal, and 0.4 molal of alanine over the entire range of total ionic strengths. The parameters of both Pitzer and PSC models were determined for the whole data set of ternary system. Meanwhile, the parameters a, c, and d were obtained for the extended Debye−Hückel equation. Results show that the adjustable parameters of Pitzer’s model have the explicit relation. But, the Debye−Hückel adjustable parameters do not show any regular trend. The obtained parameters were used to calculate the thermodynamic properties such as of osmotic coefficients (ϕ), excess Gibbs free energy and activity coefficient of alanine. It can be concluded, the variation of L-alanine activity coefficient with increasing the molality of CaCl2 obeys the Setschenow rule.

Figure 6. Plot of log(γA) variation against molality of CaCl2 for different L-alanine + water mixtures at 298.2 K.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00260. Plot of measured densities and literature data, plots of emf versus log(γ±I), plots of the values of mean activity coefficient of CaCl2 versus CaCl2 molality, plots of excess Gibbs free energy of (CaCl2 + L-alanine + water) system against total ionic strength, plots of mean activity coefficient of CaCl2 variation versus CaCl2 molality at different temperature, plots of excess Gibbs free energy variation versus CaCl2 molality at different temperature, plots of lg(γA) variation against molality of CaCl2. (PDF)

Figure 7. Plot of log(γA) variation against molality of CaCl2 for high concentrations at different L-alanine + water mixtures at 298.2 K.

■

AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS We gratefully acknowledge the graduate office of University of Guilan for supporting this work.

Figure 8. Plot of log(γA) variation against molality of L-alanine for various total ionic strength at 298.2 K.

ABBREVIATIONS m molal concentration of CaCl2 mA molal concentration of L-alanine I total ionic strength on the molal concentration scale x1 mole fraction of water x2 mole fraction of L-alanine xI mole fraction of the total ions in the solution Ix ionic strength on the mole fraction basis the ionic strength for reference state Ix0 MS average molecular mass ds density of alanine + water mixtures E electromotive force data E0 the experimental standard potential S the slope of Nernst equation

Figure 9. Plot of log(γA) variation against molality of L-alanineon in the fixed total ionic strength (I = 2) at T = (298.2, 303.2, and 308.2)K. N


Journal of Chemical & Engineering Data A B a c d b as GE Ax f± fA gE w12 u12 BCaCl B1CaCl WiCaCl UiCaCl ViCaCl Z12CaCl

Article

(8) Tomé, L. I. N.; Pinho, S. P.; Jorge, M.; Gomes, J. R. B.; Coutinho, J. AP. Salting-in with a salting-out agent: explaining the cation specific effects on the aqueous solubility of amino acids. J. Phys. Chem. B 2013, 117, 6116−6128. (9) Zhang, X. K.; Zhuo, K. L.; Ma, J. J.; Liu, H. X.; Wang, J. J. Activity coefficients of CaCl2 in Glycine+water and Alanine+water mixtures at 298.15 K. Chem. J. Chinese. U. 2009, 30, 1844−1850. (10) Briggs, C. C.; Lilley, T. H.; Rutherford, J.; Woodhead, S. The activity of Calcium chloride in aqueous solutions of some amino acids at 25°C. J. Solution Chem. 1974, 3, 649−658. (11) Ghalami-Choobar, B.; Mahdavi, V.; Pourpanah, S. Activity coefficient determinations of KCl in the KCl + formamide + water mixed solvent system based on potentiometric measurements at 298.2 K. J. Solution Chem. 2012, 41, 89−99. (12) Lu, J.; Li, S. N.; Zhai, Q.; Jiang, Y. C.; Hu, M. C. Activity coefficient determination for the ternary systems CsCl in N-Methylformamide or Urea + Water mixtures at T = 298.15 K. J. Solution Chem. 2013, 42, 1782−1793. (13) Pitzer, K. S. Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, FL, 1991. (14) Ghalami-Choobar, B.; Mahmoodi, N.; MossayyebzadehShalkoohi, P. Thermodynamic properties determination of ternary mixture (NaCl + Na2HPO4+ water) using potentiometric measurements. J. Chem. Thermodyn. 2013, 57, 108−113. (15) Ghalami-Choobar, B.; Shekofteh-Gohari, M.; Sayyadi-Nodehi, F. Thermodynamic study of ternary electrolyte KCl + 1-PrOH + water system based on Pitzer and Pitzer − Simonson − Clegg models using potentiometric measurements. J. Mol. Liq. 2013, 188, 49−54. (16) Ghalami-Choobar, B.; Sayyadi-Nodehi, F. Thermodynamic study of the quaternary electrolyte (NaCl + NaNO3 + HCONH2 + H2O) system using potentiometric measurements at T = (298.2 and 303.2) K. J. Chem. Thermodyn. 2012, 49, 104−113. (17) Ghalami-Choobar, B.; Shafaghat-Lonbar, M. Thermodynamic investigation of the ternary mixed electrolyte (NaCl + Na2HCit + H2O) system using potentiometric measurements at T = (298.2 and 308.2) K. J. Chem. Thermodyn. 2014, 78, 69−78. (18) Bates, R. G. Determination of pH, Theory and Practice, 2nd ed.; Wiley: New York, 1964. (19) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions; Reinhold: New York, 1958. (20) Ma, L.; Li, S. N.; Zhai, Q.; Jiang, Y. C.; Hu, M. C. Thermodynamic study of RbF/CsF in amino acid aqueous solution based on Pitzer, modified Pitzer and extended Debye−Hückel models at 298.15K by a Potentiometric Method. Ind. Eng. Chem. Res. 2013, 52, 11767−11772. (21) Zhuo, K. L.; Chen, Y.; Kang, L.; Xu, S.; Wang, J. Dielectric constants for binary amino acid-water solutions from (278.15 to 313.15) K. J. Chem. Eng. Data 2009, 54, 137−141. (22) Clegg, S. L.; Pitzer, K. S.; Brimblecombe, P. Thermodynamics of multicomponent, miscible, ionic solutions. 2. Mixtures including unsymmetrical electrolytes. J. Phys. Chem. 1992, 96, 9470−9479. (23) Farelo, F.; Lopes, A.; Ferra, M. I. A. Activity coefficients of potassium chloride and sodium chloride in the quaternary system KClNaCl-Water-Ethanol. J. Solution Chem. 2002, 31, 845−860. (24) Hakin, A. W.; Duke, M. M.; Klassen, S. A.; MC Kay, R. M.; Preuss, K. E. Apparent molar heat capacities and volumes of some aqueous solutions of aliphatic amino acids at 288.15, 298.15, 313.15, and 328.15 K. Can. J. Chem. 1994, 72, 362−368. (25) Romero, C. M.; Gonźalez, M. E. Osmotic and activity coefficients of glycine, dl-α-alanine and dl-α-aminobutyric acid in aqueous solutions at temperatures between 288.15 and 303.15K. Fluid Phase Equilib. 2006, 250, 99−104. (26) Cui, R. F.; Hu, M. C.; Jin, L. H.; Li, S. N.; Jiang, Y. C.; Xia, S. P. Activity coefficients of rubidium chloride and cesium chloride in methanol−water mixtures and a comparative study of Pitzer and Pitzer− Simonson−Clegg models (298.15 K). Fluid Phase Equilib. 2007, 251, 137−144. (27) Hu, Y. F.; Guo, T. M. Thermodynamics of electrolytes in aqueous systems containing both ionic and nonionic solutes. Application of the Pitzer−Simonson−Clegg equations to activity coefficients and

extended Debye−Hückel parameter extended Debye−Hückel parameter the ion size parameter the extended Debye−Hückel ion-interaction parameter the extended Debye−Hückel ion-interaction parameter constant with value of 1.2 kg1/2·mol−1/2 solvent activity excess free Gibbs energy Debye−Hückel parameter on a mole fraction basis activity coefficients of CaCl2 based on mole fractional scale activity coefficients of L-alanine based on mole fractional scale excess free Gibbs energy per mole binary interaction parameters binary interaction parameters long-range parameter for CaCl2 in the dilute range long-range parameter for CaCl2 in the dilute range PSC interaction parameter for the binary system PSC interaction parameter for the binary system PSC interaction parameter for the binary system quaternary short-range PSC interaction parameter

Greek Letters

εr Aφ ρ β(0) β(1) Cφ φ γ± γA α α1 ν

■

dielectric constant of alanine + water mixtures Debye−Hückel parameter for the osmotic coefficients parameter related to closest approach distances interaction Pitzer parameters for single salt electrolyte solution interaction Pitzer parameters for single salt electrolyte solution interaction Pitzer parameters for single salt electrolyte solution osmotic coefficient activity coefficient of CaCl2 based on molality scale activity coefficient of alanine based on molality scale fixed value of 13 constant with value of 2 numbers of ions in CaCl2

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Activity Coefficient Measurements and Thermodynamic Modeling of

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