Measurement of thermophysical properties of binary system of (water + ascorbic acid) and ternary systems of (water + ascorbic acid + glycerol) and (water + ascorbic acid + d -sorbitol) at T = 293.15 K to 323.15 K and atmospheric pressure

Journal of Molecular Liquids 281 (2019) 471–479

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Measurement of thermophysical properties of binary system of (water + ascorbic acid) and ternary systems of (water + ascorbic acid + glycerol) and (water + ascorbic acid + D-sorbitol) at T = 293.15 K to 323.15 K and atmospheric pressure Ali Mohammadzadeh Rostami a, Farhoush Kiani b,⁎, Azade Ghorbani-Hasan Saraei a, Fardad Koohyar c,d,⁎⁎, Mina Miranzadeh Omran a a

Department of Agriculture of Food Science Engineering, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran Faculty of Science, Department of Chemistry, Islamic Azad University, Ayatollah Amoli Branch, Amol, Iran Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam d Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam b c

a r t i c l e

i n f o

Article history: Received 29 December 2018 Received in revised form 23 February 2019 Accepted 24 February 2019 Available online 27 February 2019 Keywords: Refractive index Viscosity Ascorbic acid D-Sorbitol Glycerol Temperature Aqueous solutions Binary and ternary systems Change of refractive index on mixing Activation energy for viscous flow

a b s t r a c t Ascorbic acid, D-sorbitol, and glycerol are used as important food additives. In this research work, the thermophysical properties (viscosities and refractive indices) of binary solution of (water + ascorbic acid) and ternary solutions of [(water + ascorbic acid + glycerol)] and [(water + ascorbic acid + D-sorbitol)] were measured in different mass fractions of ascorbic acid (0.03 to 0.21) at temperatures (T = 293.15, 303.15, 313.15, and 323.15) K and atmospheric pressure. For mixtures of this study, the experimental values of viscosity and refractive index increase by increasing solute concentration and decrease by temperature growth. The experimental values of viscosity were correlated with the Jones-Dole and Kampmeyer-Girifalco equations. Also, the experimental values of refractive index were correlated with a semi-empirical equation which its constant, Kr, was suggested and introduced by Koohyar in 2018. Finally, derived thermodynamic properties (change of refractive index on mixing, ΔnD, and activation energy for viscous flow, Ea(vis)) were obtained using refractive index and viscosity data. The obtained data were applied for investigation on interaction between solute and solvent molecules in studied mixtures of this research work. © 2019 Elsevier B.V. All rights reserved.

1. Introduction The study on thermophysical properties of liquids and aqueous solutions has important applications in various fields of food industries such as the design and optimization of processes as well as formulation of various beverages and fruit juices [1–5]. Organic acids and their aqueous solutions have wide usages in food industries [6–9]. There are two main methods for producing organic acid: fermentation and chemical synthesis [10]. Fermentation has advantage over a chemical synthesis because of three reasons. First, the renewable and natural resources (like silage, grains, syrups, molasses, and cheese whey) are used in fermentation

⁎ Corresponding author. ⁎⁎ Correspondence to: F. Koohyar, Division of Computational Physics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam. E-mail addresses: [email protected] (F. Kiani), [email protected] (F. Koohyar).

https://doi.org/10.1016/j.molliq.2019.02.117 0167-7322/© 2019 Elsevier B.V. All rights reserved.

method as a feedstock [11]. Second, the products of fermentation have a higher degree of safety which is so important to human health [12]. Third, the producing of some organic acids by chemical synthesis methods is so difficult [13]. Ascorbic acid (Fig. 1), vitamin C, is one of the most important organic acids which is naturally found in vegetables and fruits such as orange, green pepper, watermelon, grapefruit, kiwi, mango, broccoli, tomato, cabbage, winter squash, and strawberry [14–18]. Ascorbic acid is a good reducing agent. It is readily oxidized at high temperature, in the presence of sunlight and oxygen in air [19]. Ascorbic acid, vitamin C, retains the red color of cured meat and barricades the formation of nitrosamines, which increases cancer risk [20]. It also helps prevent loss of color and flavor in foods when they react with unwanted oxygen [21]. Ascorbic acid is used in food industry as a supplement of beverages and food [22,23], as antioxidants to extend the storage period [24], and change the color of the food in some kind of process or prevent it during storage [25].

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A.M. Rostami et al. / Journal of Molecular Liquids 281 (2019) 471–479

Fig. 1. Structural formulas for ascorbic acid (a) and D-sorbitol (b).

Ascorbic acid dissolves well in water. It has 4 hydroxyl agents (Fig. 1). Hydrogen bonds have a key role for dissolving the organic acids in water. Studying on systems which have hydrogen bond is very important because hydrogen bonds play a vital role in chemical, physical, and biological processes [26]. D-Sorbitol has six OH groups (Fig. 1) and dissolves in water in a high amount (2350 g/L) due to production of hydrogen bonds between water molecules and its hydroxyl groups. D-Sorbitol can be found in apples, pears, peaches, and prunes [27]. It is used in the pharmaceutical, cosmetic, and food industries. For example, D-sorbitol is used to produce low-sugar products such as chocolate, ice cream, and sweets for diabetics. Also, it is used as sustainable and moisturizing in the pharmaceutical industry and cosmetic applications [28]. Glycerol is an alcohol that is extremely soluble in water and is using in the pharmaceutical, food and cosmetic industries [29,30]. Glycerol is relatively a good solvent for oil [31,32] and helps to prevent sugar crystallization [33–35]. In this work, the refractive indices (nD) and viscosities (η) of ternary mixtures of (water + acid ascorbic + D-sorbitol) and (water + ascorbic acid + glycerol) as well as binary mixture of (water + ascorbic acid) were measured in several mole fractions of solutes at temperatures (T = 293.15, 303.15, 313.15 and 323.15) K and atmospheric pressure. The refractive index and viscosity data for pure liquids of this study (glycerol and water) are available in literatures [36], but no experimental data are available for ternary mixtures of this study at comparable conditions. For each chemical of this study, the chemical name, source (origin), CAS No., purity, and purification method are given in Table 1. In addition, the experimental values of refractive index and viscosity for pure liquids of this research work (water and glycerol) with those reported, in the literature, at different temperatures were listed in Table 2. 2. Experimental 2.1. Materials Ascorbic acid, D-sorbitol and glycerol were purchased from Merck Company. The purity of ascorbic acid and glycerol was N99% and purity of D-sorbitol was N98%. They were used without further purification. Mixtures were prepared from known masses of each component in air-tight stoppered glass bottles. All aqueous solutions of this study were prepared using double-distilled water with specific conductivity equal to 1.3 ± 0.1 μΏ −1 cm−1. 2.2. Apparatus and procedure All solutions were prepared by weighing suitable amount of the individual components and mixed in a beaker. The mixtures were

transferred into stopper reagent bottles to prevent water evaporation. All the experiments were repeated five times and average values were reported. A balance (precise 240 A, Switzerland) was used with precision of ±0.0001 g for weighting of solutes. For all studied mixtures, the possible error in the mole fraction was calculated to be lower than ±1 × 10−4. The dynamic viscosity of mixtures was measured using the rotational viscometer (Spindle viscometer, Model V2L, Visco Tech, Spain). This viscometer has the sample chamber fits into a circulating chamber permitting sample to achieve a controlled temperature (between 263.15 K and 373.15 K). The refractive indices (for the sodium D-line, nD) were measured using an Abbe refractometer (CARL ZEISS, Model A, Germany). Both rotational viscometer and Abbe refractometer were connected to a water bath and the temperature was controlled, within ±0.01 K of the desired temperature, using the Schott-Gerate CT 1150 digital thermostat. In this research work, the uncertainties of the refractive index (Abbe refractometer) and viscosity (rotational viscometer) measurements are ±0.0001 and ±0.00001 mPa·s, respectively. The instruments were calibrated at atmospheric pressure with double distilled water before each series of measurements.

3. Results and discussion The thermophysical properties of solutions (viscosity, density, refractive index, and sound velocity) can lead us to better understanding of the interactions between solute and solvent molecules. In this study, the experimental data of refractive indices(nD) (nD) and viscosities (η) have been determined for aqueous solution of acid ascorbic and ternary solutions of (water + acid ascorbic + D-sorbitol) and (water + acid ascorbic + glycerol) at various temperatures and atmospheric pressure. These data are listed in Table 3. Table 3 shows that the values of refractive index and viscosity for solutions of this study can be affected by three factors. The first factor is the concentration of solutions. As it can be seen in Table 3, the values of refractive index and viscosity of solutions increase when the mass fraction (m) and molal concentration of solute (C) increase. As we know, there is interaction between solute and solvent molecules in a solution and the number of these interactions increases when the number of solute molecules (concentration of solute in solution) increases. The second factor is the number of solute species in solution. As it can be seen in Table 3, the values of viscosity and refractive index of ternary solutions of (water + ascorbic acid + D-sorbitol) and (water + ascorbic acid + D-sorbitol) are greater than that of binary solution of (water + ascorbic acid). It is clear that number of solute molecules and consequently, number of solute-solvent interactions increases

Table 1 Sample description table. Chemical name

Source

CAS No.

Purity

Purification method

Method of purity determination

Ascorbic acid D-Sorbitol

Merck Company Merck Company

50-81-7 50-70-4

≥99% ≥98%

None None

FIA HPLC-RI

Glycerol

Merck Company

56-81-5

≥99%

None

GC

A.M. Rostami et al. / Journal of Molecular Liquids 281 (2019) 471–479 Table 2 Comparison of the experimental values of refractive indices, nD, and viscosity, η, for pure liquids of this research work with those reported in the literature at different temperatures. T/ (K)

η/ (mPa·s)

nD Exp.

Lit.

Exp.

Lit.

293.15 303.15 313.15 323.15

Water 1.3336 1.3320 1.3305 1.3294

1.3330 [43] 1.3319 [43] 1.3306 [43] 1.3290 [43]

0.99326 0.79737 0.65355 0.54657

0.9933 [44] 0.7974 [44] 0.6535 [44] 0.5465 [44]

293.15 303.15 313.15 323.15

Glycerol 1.4747 1.4709 1.4671 1.4641

– 1.4710 [36] 1.4670 [36] 1.4640 [36]

1414.85 613.12 283.95 142.04

1410.97 [45] 611.35 [45] 285.47 [45] 140.97 [45]

473

(1) + acid ascorbic (2) + glycerol (3)] (Fig. 2) because this mixture has two solute species and has the maximum molal concentration of solutes (C2 = 13.2477 mol/Kg and C3 = 29.6153 mol kg−1). In this case, the number of solute species and the concentration of solutes are the most effective factors. On the other hand, the minimum values of refractive index have been seen for the binary system of [water (1) + acid ascorbic (2)]. It is clear that this binary solution has only one solute specie (ascorbic acid) and also, has minimum concentration of solutes (please see Table 3). The value of refractive index for [water (1) + acid ascorbic (2) + D-sorbitol (3)], in most molal concentrations and at each given temperature, is greater than refractive index of [water (1) + acid ascorbic (2)] and is lesser than refractive index of [water (1) + acid ascorbic (2) + glycerol (3)]. Of course, in the same concentration of solutes, the maximum value of refractive index must be observed for ternary solution of [water (1) + acid ascorbic (2) + D-sorbitol

when the number of solute species in solution increases. The third factor is structural characters of solute molecules that directly effect on strength of interaction between solute and solvent molecules [29]. 3.1. Refractive indices data Among various thermophysical properties of a solution, refractive index is the most important one that helps us to better understand the strength of interaction between solute and solvent molecules [29]. According to Maxwell's equation, the refractive index of a solution (nD) is related to the permittivity (ε) and the permeability (μ) of this medium as Eq. (1): nD ¼ ðεμ Þ1=2

ð1Þ

For a solution, the permittivity (ε) is the resistance of molecules of this solution against the passing of the light. If the light passes through a solution, interactions occur between the electromagnetic fields of photon (light) and molecules. The strong interaction between solute and solvent molecules causes the light to decrease velocity and consequently, the refractive index of this solution increases. This explanation shows that the refractive index can be a good tool to investigate on power of interaction between solute and solvent molecules in solutions. In 2018, Koohyar introduced a constant, Kr, and showed that for binary aqueous solutions, at constant temperature, we can reach below linear equation by plotting refractive indices versus concentrations of solute [29]: nD ¼ K r c þ nₒ

ð2Þ

In Eq. (2), nD and nₒ are the refractive index of solution and solvent, respectively. C is the molal (or molar) concentration of solute and Kr is a constant that has a direct relationship with power of interaction between solute and solvent molecules. This constant depends on structural properties of solute molecules such as molecular weight, the number of oxygen and nitrogen atoms, and the type and number of agents that are attached to –R [29]. Eq. (2) can be applied for aqueous solution of ascorbic acid in each molal concentration and at each temperature. For ascorbic acid, in aqueous solution and C = 0.5616 mol kg−1, the value of Kr is 0.0258 at 303.15 K. This value is too close to Kr for D-sorbitol in aqueous solution (=0.0259) at the same temperature [36]. The molecular weights of D-sorbitol and ascorbic acid are very close together. Also, both of them have 6 oxygen atoms to generate H-bonding with solvent (water) molecules. On the other hand, the Kr for ascorbic acid is 2.53 times the Kr for glycerol [36]. The molecular weight and number of oxygen atoms for ascorbic acid are 2 times the molecular weight and number of oxygen atoms for glycerol. In this study, at each given temperature, the maximum values of refractive index have been seen for the ternary system of [water

(3)] at each given temperature. As we know, glycerol and Dsorbitol have three and six hydroxyl groups to generate H-bonding, respectively. Therefore, the H-bond between D-sorbitol and water can be stronger than the H-bond between glycerol and water at the same temperatures. In 2013 Koohyar et al., showed that the value of Kr for Dsorbitol (=0.0256) is greater than that of for glycerol (=0.0102) [36]. If the concentrations of solutes are close together, the power of interaction between solute and solvent molecules (Kr) can be the most effective factor [29]. For the ternary solutions of this study, this subject can be seen in m2 = 0.03. In this mass fraction, both two ternary mixtures have the same molal concentrations of ascorbic acid (≈0.2 mol kg−1). Also, the molal concentration of glycerol is 1.8 times the molal concentration of D-sorbitol but it must be noted that Kr for D-sorbitol is 2.5 times the Kr for glycerol. As it can be seen in this case, Kr, compared to concentration of solute, is more effective in value of refractive index of our mixtures. For an aqueous solution, the value of Kr can be obtained by two methods. First method is to plot the refractive index of this solution versus concentration (molal and/or molar) at constant temperature. The result, especially in low concentration of solute, is a linear diagram (Eq. (2)). The slop of this linear diagram is the value of Kr for solute of this aqueous solution. Using this method, only one value is obtained for Kr at constant temperature. For aqueous solution of ascorbic acid, the values of fitting parameters, Kr and nₒ according to Eq. (2), were obtained at various temperatures and listed in Table 4. This table shows that the value of Kr decreases by temperature growth. The molecules move faster at higher temperatures and because of this fact, the power of H-bonding between solute and solvent molecules decreases when temperature increases. In the second method, Eq. (2) can be applied to calculate the value of Kr in each concentration of solute and at given temperature. Using this method, we can calculate one value of Kr for each concentration at each temperature. If we use this method to calculate the value of Kr for ascorbic acid in aqueous solution, it is observed that in the most cases, the value of Kr decreases when molal concentration increases. The solute-solute interaction can increase, and solute-solvent interaction can decrease, when concentration of solute increases in a solution. Moreover, for a solute in solution, the value of activity coefficient decreases as the concentration of solute increases. Koohyar in 2018 introduced a new semi-empirical equation (Eq. (3)) to predict the value of Kr for alkane polyols [R(OH)n, n = 2 to 6 -OH,s) and polyols with one ring (monosaccharide) in aqueous solutions at constant temperature (T = 293.15 K) [29]. These solute molecules (alkane polyols and monosaccharide) have hydroxyl groups and/or oxygen atoms therefore, can generate hydrogen bonds with solvent (water) molecules. i
h K r ¼ MwðsoluteÞ −18:01 5:2  10−6 Nð▬O▬Þ þ 1:28  10−4

ð3Þ

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Table 3 The refractive indices (nD) and viscosities (η) for aqueous solutions of ascorbic acid, [water (1) + acid ascorbic (2) + D-sorbitol (3)] and [water (1) + ascorbic acid (2) + glycerol (3)] as a function of mass fractions (m2, m3) and molalities (C2, C3) at different temperatures and atmospheric pressure. m3

m2

– – – – – – –

0.03 0.06 0.09 0.12 0.15 0.18 0.21

– – – – – – –

0.03 0.06 0.09 0.12 0.15 0.18 0.21

– – – – – – –

0.03 0.06 0.09 0.12 0.15 0.18 0.21

– – – – – – –

0.03 0.06 0.09 0.12 0.15 0.18 0.21

C3

C2

(mol/kg)

(mol/kg)

Water (1) + ascorbic acid (2) T = 293.15 K – – – – – – – T = 303.15 K – – – – – – – T = 313.15 K – – – – – – – T = 323.15 K – – – – – – –

η/ (mPa·s)

0.1756 0.3624 0.5616 0.7743 1.0020 1.2464 1.5093

1.3376 1.3433 1.3482 1.3525 1.3573 1.3631 1.3682

1.02161 1.32120 1.56650 1.93790 2.25542 2.40241 2.68254

0.1756 0.3624 0.5616 0.7743 1.0020 1.2464 1.5093

1.3365 1.3420 1.3464 1.3507 1.3556 1.3612 1.3662

0.98200 1.21900 1.43890 1.78220 2.00360 2.25760 2.42510

0.1756 0.3624 0.5616 0.7743 1.0020 1.2464 1.5093

1.3352 1.3405 1.3448 1.3492 1.3538 1.3593 1.3641

0.91400 1.13150 1.32600 1.53970 1.77170 1.92140 2.10110

0.1756 0.3624 0.5616 0.7743 1.0020 1.2464 1.5093

1.3340 1.3387 1.3432 1.3474 1.3521 1.3578 1.3623

0.86300 1.05560 1.22220 1.40620 1.60500 1.71113 1.88031

1.3502 1.3676 1.3865 1.4070 1.4291 1.4531 1.4799

15.70980 20.47040 23.55642 27.29402 33.928952 40.75942 49.68210

1.3487 1.3656 1.3841 1.4041 1.4262 1.4499 1.4758

15.01817 19.03523 23.01805 26.07886 31.01280 36.91284 45.39156

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.03 0.06 0.09 0.12 0.15 0.18 0.21

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.03 0.06 0.09 0.12 0.15 0.18 0.21

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.03 0.06 0.09 0.12 0.15 0.18 0.21

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.03 0.06 0.09 0.12 0.15 0.18 0.21

Water (1) + ascorbic acid (2) + glycerol (3) T = 293.15 K 1.2482 0.1958 2.9348 0.4604 5.3405 0.8377 9.0491 1.4195 15.5128 2.4334 29.6153 4.6456 – 13.2485 T = 303.15 K 1.2482 0.1958 2.9348 0.4604 5.3405 0.8377 9.0491 1.4195 15.5128 2.4334 29.6153 4.6456 – 13.2485 T = 313.15 K 1.2482 0.1958 2.9348 0.4604 5.3405 0.8377 9.0491 1.4195 15.5128 2.4334 29.6153 4.6456 – 13.2485 T = 323.15 K 1.2482 0.1958 2.9348 0.4604 5.3405 0.8377 9.0491 1.4195 15.5128 2.4334 29.6153 4.6456 – 13.2485

0.03 0.06 0.09

water (1) + ascorbic acid (2) + D-sorbitol (3) T = 293.15 K 0.7021 0.1980 0.8033 0.4154 0.9149 0.6551

0.11 0.12 0.13

nD

1.3472 1.3637 1.3817 1.4012 1.4233 1.4468 1.4718

14.01273 18.02481 21.05276 24.07366 29.10777 35.10821 41.14670

1.3458 1.3619 1.3794 1.3986 1.4207 1.4439 1.4681

13.12341 16.82481 19.34775 22.06867 26.80285 31.90285 39.14185

1.3543 1.3612 1.3673

9.77750 11.93820 13.81460

A.M. Rostami et al. / Journal of Molecular Liquids 281 (2019) 471–479

475

Table 3 (continued) m3

m2

0.14 0.15 0.16 0.17

0.12 0.15 0.18 0.21

0.11 0.12 0.13 0.14 0.15 0.16 0.17

0.03 0.06 0.09 0.12 0.15 0.18 0.21

0.11 0.12 0.13 0.14 0.15 0.16 0.17

0.03 0.06 0.09 0.12 0.15 0.18 0.21

0.11 0.12 0.13 0.14 0.15 0.16 0.17

0.03 0.06 0.09 0.12 0.15 0.18 0.21

C3

C2

(mol/kg)

(mol/kg)

1.0385 1.1763 1.3308 1.5052 T = 303.15 K 0.7021 0.8033 0.9149 1.0385 1.1763 1.3308 1.5052 T = 313.15 K 0.7021 0.8033 0.9149 1.0385 1.1763 1.3308 1.5052 T = 323.15 K 0.7021 0.8033 0.9149 1.0385 1.1763 1.3308 1.5052

In Eq. (3), Mw is the molar mass of solute and N(\\O\\) is the number of hydroxyl groups and/or oxygen atoms that are existed in solute molecule (atoms that can generate hydrogen bond with solvent molecules). Ascorbic acid (similar to alcohols) has hydroxyl groups and oxygen atoms. According to Eq. (3), the calculated (theoretical) value of Kr for ascorbic acid, in aqueous solution, is 0.0252 L mol−1 at 293.15 K. This value is the same that is calculated as the experimental value of Kr for ascorbic acid, in aqueous solution and C = 0.7743 mol kg−1. ascorbic acid has a negative and also, a positive deviation from Eq. (3) [29]. The values of these negative and positive deviations can be equal together. The negative deviation can be due to existing carbonyl group in molecule of ascorbic acid. Carbonyl is an electron acceptor. Thus, this group can has electron withdrawing effect on ring, and consequently on hydroxyl group, in ascorbic acid. In this condition, weaker hydrogen bonds are formed between solute and solvent molecules. The positive deviation can be due to generate ions when ascorbic acid solve in water (aqueous solution). It is well known that the interaction between ion and water molecule is stronger than interaction between neutral molecule and water molecule.

η/ (mPa·s)

nD

0.9207 1.2166 1.5484 1.9230

1.3742 1.3818 1.3899 1.3985

15.94080 18.28770 19.99420 22.25540

0.1980 0.4154 0.6551 0.9207 1.2166 1.5484 1.9230

1.3528 1.3594 1.3651 1.3717 1.3792 1.3871 1.3954

9.22510 11.34210 13.10240 15.11620 17.13970 18.88180 20.84200

0.1980 0.4154 0.6551 0.9207 1.2166 1.5484 1.9230

1.3514 1.3577 1.3632 1.3696 1.3766 1.3843 1.3925

8.63210 10.82420 12.40880 14.29260 16.10240 17.70390 19.53020

0.1980 0.4154 0.6551 0.9207 1.2166 1.5484 1.9230

1.3502 1.3561 1.3615 1.3678 1.3743 1.3817 1.3895

7.99420 10.25620 11.81640 13.47180 15.10240 16.50940 18.22240

The refractive index data can be fitted by an equation according to temperature as the below: nD ¼ a þ bT

ð4Þ

In Eq. (4), nD is the refractive index of the solution, T is the temperature and (a) and (b) are constants. For all solutions of this study, in various mass fractions, parameters (a) and (b) are listed in Table 5. As it can be seen in this table, for all solutions of this study the value of constant (a) increases when mass fraction increases. In Eq. (4), the constant (a) is the value of refractive index of a solution when the temperature tends to zero (in T → 0). As we mentioned, the value of refractive index of a mixture increases by increasing of concentration or mass fraction. Table 5 shows that the constants (a) and (b) have positive and negative values, respectively. According to Eq. (4), the negative value of the constant (b) shows decrease the refractive index of a solution when temperature increases. This effect can be seen in Table 3. As it can be seen in this table, for all solutions of this study, the value of refractive index decreases with temperature growth (Fig. 3). Table 4 Fitting parameters (Kr and nₒ from Eq. (2)) for binary mixture of (water + ascorbic acid) at various temperatures.

Fig. 2. The refractive index (nD) versus mass fraction (m2) for ( ): ternary mixture of [water (1) + ascorbic acid (2) + glycerol (3)], ( ): [water (1) + ascorbic acid (2) + Dsorbitol (3)], and ( ): [water (1) + ascorbic acid (2)] at T = 293.15 K.

Kr/ (L mol−1)

nₒ

nₒ(exp)

T = 293.15 K 0.0226

1.3347

1.3330a

0.001275

T = 303.15 K 0.0220

1.3336

1.3319a

0.001276

T = 313.15 K 0.0214

1.3323

1.3306a

0.001278

T = 323.15 K 0.0212

1.3309

1.3290a

0.001430

RDðfor nₒÞ ¼ a

  nₒ−nₒð expÞ 

Ref. [42].

nₒð expÞ:

RD (for nₒ)

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Table 5 Fitting parameters (a and b from Eq. (4)) for refractive indices of mixtures of this study in various mass fractions, m2. m2

a

b

m2

Water (1) + ascorbic acid (2) 0.3 1.373111 −0.000121 0.6 1.388272 −0.000153 0.9 1.396803 −0.000166 1.2 1.401719 −0.000168 1.5 1.408318 −0.000174 1.8 1.415201 −0.000178 2.1 1.426214 −0.000198 Water (1) + ascorbic acid (2) +

a

m2

b

Water (1) + ascorbic acid (2) + glycerol (3) 0.3 1.393273 −0.000147 0.6 1.423248 −0.000190 0.9 1.455957 −0.000237 1.2 1.489315 −0.000281 1.5 1.511415 −0.000281 1.8 1.543027 −0.000307 2.1 1.595311 −0.000394

1.394392 1.410986 1.423748 1.436461 1.455321 1.470183 1.486112

−0.000137 −0.000170 −0.000193 −0.000213 −0.000251 −0.000274 −0.000299

γ × 105

m2

α

β × 104

γ × 105

1.5 1.8 2.1

0.9052 −7.5061 −2.5152

−0.0885 0.4304 0.1240

2.1253 −5.8337 −1.1002

1.2352 0.8366 5.1156

−0.0186 0.0102 −0.2496

0.8004 0.3678 4.3828

0.8327 4.5182 2.2452

2.6289 −52.5185 −14.9821

Water (1) + ascorbic acid (2) + D-sorbitol (3) 0.3 −47.9112 2.9351 −36.4683 1.5 −13.1804 0.6 −15.9217 1.1357 −9.3549 1.8 −73.0169 0.9 −0.4066 0.1780 7.0060 2.1 −36.9033 1.2 −35.0803 2.2851 −23.1419

The viscosity of a solution is a measure of its resistance to gradual deformation by shear stress or tensile stress. Viscosity data are mostly used as a key physicochemical property in understanding the flow of raw materials, processing intermediates and final products [37]. Viscosity of solutions can be affected by temperature, concentration, and pressure [38]. For a solution, the relationship between viscosity and temperature can be defined by Kampmeyer-Girifalco equation as the bellow [39]: ð5Þ

In Eq. (5), η is the viscosity of the solution, T is temperature and α, β, γ are constants. The values of these constants were calculated for all solutions of this study and these data are listed in Table 6. According to Eq. (5), in given concentration, the value of viscosity decreases with temperature growth (Fig. 4). As it can be in Table 3, for all solutions of this study in each mass fraction, the value of viscosity decreases when temperature increases. The interaction between solute and solvent molecules can be weaker when temperature increases. In addition, the viscosity data of a solution, including ions, can be fitted by Jones-Dole equation [40]: η=η0 ¼ 1 þ AC1=2 þ BC

β × 104

Water (1) + ascorbic acid (2) + glycerol (3) 0.3 −2.0535 0.1714 −2.2306 1.5 0.6 0.7952 1.1469 0.4119 1.8 0.9 −6.6491 0.4624 −6.6595 2.1 1.2 −4.3624 0.3235 −4.4968

3.2. Viscosity data

logη ¼ α þ β=T þ γ=T2

α

Water (1) + ascorbic acid (2) 0.3 −5.3099 0.3336 −4.3365 0.6 1.9793 −0.1330 3.3326 0.9 −0.0047 −0.0229 2.0210 1.2 −5.2940 0.2543 −1.2329

D-sorbitol(3)

0.3 0.6 0.9 1.2 1.5 1.8 2.1

Table 6 Fitting parameters (α, β, and γ from Eq. (5)) for viscosities of mixtures of this study in various mass fractions, m2.

ð6Þ

Fig. 3. The refractive indices (nD) versus molal concentration (C) for binary mixture of (water + ascorbic acid) at T = ( ): 293.15 K, ( ): 303.15 K, ( ): 313.15 K, and ( ): 323.15 K.

In Eq. (6), C is the concentration of solute in solution. A and B are constants. η and η0 are the viscosities of solution and solvent, respectively. Constants of Jones-Dole equation (A and B) were calculated for all solutions of this study at T = 293.15, 303.15, 313.15, and 323.15 K and were listed in Table 7. Table 3 and Fig. 5 show that at given temperature, the values of viscosity for mixtures of this study fall in the below order: ηðwaterþascorbic acidþglycerolÞ Nηðwaterþascorbic acidþd‐sorbitolÞ Nηðwaterþascorbic acidÞ ð7Þ

Also, as it can be seen in Table 7, at a given temperature, the values of constants B (from Jones-Dole equation) fall in the below orders:

jBjðwaterþascorbic acidþglycerolÞ N jBjðwaterþascorbic acidþd‐sorbitolÞ N jBjðwaterþascorbic acidÞ

ð8Þ

The above order (Eq. (8)) can be seen about values of the constant A (from Jones-Dole equation) for all solutions of this study. The comparison of orders 7 and 8 shows that the values of constants of Jones-Dole equation can show the power of interaction between solvent and solute molecules [41]. In a solution, the value of viscosity can have a direct relationship with the power of interaction between solvent and solute molecules. In this research work (in refractive index data section), the same result was obtained for mixtures of this study about the order of the power of interactions between solute and solvent molecules.

Fig. 4. The viscosities (ƞ) versus molal concentration (C2) for ternary mixture of [water (1) + ascorbic acid (2) + D-sorbitol (3)] at T = ( ): 293.15 K, ( ): 303.15 K, ( ): 313.15 K, and ( ): 323.15 K.

A.M. Rostami et al. / Journal of Molecular Liquids 281 (2019) 471–479 Table 7 Jones-Dole equation parameters (A and B from Eq. (6)) for mixtures of this study at various temperatures. T/ (K)

A

B

(dm3/2 mol-1/2)

(dm3 mol−1)

A

B

(dm3/2 mol-1/2)

(dm3 mol−1)

313.15 323.15

0.5595 1.0846

1.0738 0.7680

Water (1) + ascorbic acid (2) + glycerol (3) 293.15 31.3576 −5.4985 313.15 303.15 37.9423 −6.9744 323.15

43.5951 48.4029

−8.1199 −9.0192

Water (1) + ascorbic acid (2) + D-sorbitol (3) 293.15 20.1047 −4.0293 313.15 303.15 24.5289 −5.2610 323.15

28.7784 32.6151

−6.4396 −7.4388

Water (1) + ascorbic acid (2) 293.15 −0.4939 1.6209 303.15 0.0101 1.4434

T/ (K)

3.3.1. The change of refractive index on mixing For solutions, the value of change of refractive index on mixing (ΔnD) is calculated using the below equation: ΔnD ¼ nD −

N X

xi nDi

Table 8 The values of changes of refractive index on mixing, ΔnD, for mixtures of this study in wide range of mole fractions of ascorbic acid, x2, at different temperatures and at atmospheric pressure. ΔnD

x2

T = 293.15 K

3.3. Derived thermodynamic properties

ð9Þ

i¼0

In Eq. (9), nD is the refractive index of the mixture, nDi is the refractive index of the pure component i, and xi is the mole fraction of component i in the mixture. N is the number of components. The values of ΔnD for binary and ternary solutions of this study were calculated at different temperatures and listed in Table 8. This table shows that in all studied mole fractions and at all studied temperatures, the sign of ΔnD is positive for all solutions of this study. It can show that in these solutions, the interaction between solute and solvent molecules is stronger than interaction between solute-solute and solvent-solvent molecules. Also, as it can be seen in Table 8 and Fig. 6, for all solutions of this study, in most mole fractions, the value of ΔnD decreases by temperature growth. It is well known that the molecules move faster, and strength of interaction between these molecules become weaker, when temperature increases. On the other hand, Table 8 and Fig. 7 show the below order regarding the values of ΔnD for solutions of this study at given temperature: ΔnDðwaterþascorbic acidþglycerolÞ N ΔnDðwaterþascorbic acidþd‐sorbitolÞ N ΔnDðwaterþascorbic acidÞ

ð10Þ

477

T = 303.15 K

T = 313.15 K

T = 323.15 K

0.0032 0.0065 0.0100 0.0138 0.0177 0.0220 0.0265

Water (1) + ascorbic acid (2) 0.00341 0.00341 0.00786 0.00765 0.01142 0.01071 0.01431 0.01359 0.01759 0.01697 0.02181 0.02098 0.02520 0.02427

0.00341 0.00744 0.01040 0.01337 0.01645 0.02036 0.02344

0.00380 0.00723 0.01038 0.01315 0.01632 0.02042 0.02320

0.0034 0.0078 0.0136 0.0215 0.0331 0.0517 0.0865

Water (1) + ascorbic acid (2) + glycerol (3) 0.01279 0.01244 0.01230 0.02459 0.02382 0.02334 0.03610 0.03501 0.03412 0.04644 0.04497 0.04371 0.05366 0.05238 0.05130 0.05380 0.05251 0.05153 0.03612 0.03445 0.03313

0.01252 0.02320 0.03352 0.04287 0.05054 0.05061 0.03166

0.0035 0.0073 0.0115 0.0160 0.0210 0.0265 0.0326

Water (1) + ascorbic acid (2) + D-sorbitol (3) 0.01839 0.01798 0.01785 0.02364 0.02291 0.02249 0.02794 0.02681 0.02617 0.03285 0.03141 0.03056 0.03828 0.03673 0.03538 0.04399 0.04224 0.04067 0.04993 0.04787 0.04619

0.01823 0.02245 0.02603 0.03031 0.03461 0.03959 0.04470

interactions are effective in sign and value of ΔnD. Order of Eq. (10) has a good agreement with Eq. (7) as well as explanations about values of refractive index of our studied solutions in this research work. The Redlich-Kister polynomial equation is applied to fit ΔnD data as the below [42]:

Y ¼ x2 ð1−x2 Þ

n X

Ai ð2x2 −1Þi

ð11Þ

i¼0

In the above equation, x2 is the mole fraction of solute, Y is thermodynamic properties and Ai is adjustable parameter. The optimum number of coefficients Ai was calculated using an examination of the variation of the standard deviation:

In aqueous solutions, the value of ΔnD can show the power of interactions between solute and solvent molecules. Of course, it must be noted that both concentration of solutes and power of solute-solvent

"

 2 #1=2 ∑ Y ðcalÞ −Y ð expÞ δY ¼ n−m

Fig. 5. The viscosity (ƞ) versus mass fraction (m2) for ( ): ternary mixture of [water (1) + ascorbic acid (2) + glycerol (3)], ( ): [water (1) + ascorbic acid (2) + D-sorbitol (3)], and ( ): [water (1) + ascorbic acid (2)] at T = 293.15 K.

Fig. 6. The value of change of refractive index on mixing (ΔnD) for ternary mixture of [water (1) + ascorbic acid (2) + glycerol (3)] at T = ( ): 293.15 K, ( ): 303.15 K, ( ): 313.15 K, and ( ): 323.15 K.

ð12Þ

478

A.M. Rostami et al. / Journal of Molecular Liquids 281 (2019) 471–479

0.06

Table 10 The values of parameter A and the activation energy for viscous flow, Ea(vis), (according to Eq. (13)) for aqueous solutions of this study in various mass fractions, m2.

0.05

nD

0.04

m2

A

0.03

Water (1) + ascorbic acid (2) 0.03 0.1442 4.8048 0.06 0.1037 6.2170 0.09 0.0943 6.8697 0.12 0.0451 9.2153

0.02 0.01 0 0

0.02

0.04

0.06

0.08

0.1

x2 Fig. 7. The value of change of refractive index on mixing (Δn D ) for ( ): ternary mixture of [water (1) + ascorbic acid (2) + glycerol (3)], ( ): [water (1) + ascorbic acid (2) + D -sorbitol (3)], and ( ): [water (1) + ascorbic acid (2)] at T = 293.15 K.

where, n is the total number of experimental values and m is the number of parameters. The value of Redlich-Kister parameters (Ai) along with the standard deviation (δ) for ΔnD of solutions of this study were calculated and listed in Table 9. 3.3.2. Activation energy for viscous flow For solutions, activation energy for viscous flow, Ea(vis), is the needed energy for moving one layer of solution (including solute and solvent molecules) upon adjacent layer. The value of Ea(vis) for a solution can be obtained using its viscosity at different temperatures according to the below equation [38]: EaðvisÞ RT

ð13Þ

η ¼ Ae

In Eq. (13), η is viscosity of solution, A is called the pre-exponential factor and Ea(vis) is the activation energy for viscous flow (kJ mol−1). Table 9 The Redlich-Kister polynomial equation constants (Ai) along with the standard deviation (δ) for ΔnD of solutions made by water, ascorbic acid, D-sorbitol, and glycerol at different temperatures. A0 × 108

A1 × 108

A2 × 108

A3 × 108

A4 × 108

δ

−0.1875

0.1567

0.1250

0.2703

1.2500

0.4693

0.0063

0.2732

0.0013

1.4413

−0.0019

1.4927

−0.0025

2.1514

−0.0013

0.7900

Water (1) + ascorbic acid (2) −2.9471

Ea (vis)

m2

A

(kJ mol−1)

−4.3449

2.0509

2.9756

20.5862

29.7996

0.2800

0.2992

T = 293.15 K −2.7550 −1.0750 T = 303.15 K 1.8752 0.7250 T = 313.15 K 18.7625 7.2500 T = 323.15 K 0.1623 0.0500

Water (1) + ascorbic acid (2) + glycerol (3) T = 293.15 K 0.0237 0.0323 0.0198 0.0074 T = 303.15 K −0.0353 −0.0483 −0.0298 −0.0112 T = 313.15 K −0.0470 −0.0644 −0.0396 −0.0149 T = 323.15 K −0.0233 −0.0321 −0.0198 −0.0075 Water (1) + ascorbic acid (2) + D-sorbitol (3) T = 293.15 K 2.9469 4.3448 2.7550 1.0750 T = 303.15 K 1.9044 2.8473 1.8150 0.7125 T = 313.15 K 5.0142 7.3297 4.6325 1.8000 T = 323.15 K 8.2514 11.9296 7.5075 2.9000

0.1875

0.1345

0.1250

0.4757

0.3125

0.3377

0.0500

0.2959

Ea (vis) (kJ mol−1)

0.15 0.18 0.21

0.0460 0.0445 0.0442

9.5083 9.8039 10.0549

Water (1) + ascorbic acid (2) + glycerol (3) 0.03 1.9945 5.0629 0.15 0.06 2.2944 5.3452 0.18 0.09 2.3804 5.6511 0.21 0.12 2.4080 5.9656

2.4592 2.8088 3.1029

6.4074 6.5273 6.7638

Water (1) + ascorbic acid (2) + D-sorbitol (3) 0.03 1.004 5.5745 0.15 0.06 2.1640 4.1763 0.18 0.09 2.3315 4.3491 0.21 0.12 2.3712 4.6631

2.0992 2.2847 2.3231

5.2923 5.3122 5.5272

For aqueous solutions of this study, the values of Ea(vis) (as well as constants A) were obtained in each mass fraction of ascorbic acid. Obtained data were listed in Table 10. This table shows that for all solutions of this study, the value of Ea(vis) increases as the mass fraction of ascorbic acid (or number of solute molecules) increases. It is clear that when the number of solute molecules increases, the number of interaction between species (in two adjacent layers of solution) increases and therefore in this situation, there is need more energy (Ea(vis)) to move one layer of solution upon another layer. 4. Conclusions In the present work, the experimental values of viscosity and refractive index were measured for the binary system of (water + acid ascorbic) as well as ternary systems of (water + acid ascorbic + glycerol) and (water + acid ascorbic + D-sorbitol) at T = (293.15, 303.15, 313.15 and 323.15) K and atmospheric pressure over the wide range of mass fractions. The change of refractive index on mixing, ΔnD, and activation energy for viscous flow, Ea(vis) were obtained using refractive index and viscosity data, respectively. Results show that for all solutions of this study, the experimental values of viscosity and refractive index increase by increasing concentration of solutes and decrease by temperature growth. Among three mixtures that we studied in this research work, aqueous solution of (ascorbic acid + glycerol) has the highest value of viscosity and refractive index at each studied temperature. Viscosity data were correlated by Jones-Dole and Kampmeyer-Girifalco equations. The constants of Jones-Dole equation (A and/or B) can lead us to better understanding of interactions between solute and solvent molecules. In addition, refractive index data were correlated by a linear equation. For a series of homologous solute molecules, the constant of this linear equation, Kr, can be applied to investigate on interactions between solute and solvent molecules. In this study, the values of ΔnD, Kr and B show the same result about power of interactions between solute and solvent molecules in our studied solutions. References [1] A.L. Santana, I.C.N. Debien, M.A.A. Meireles, High-pressure phase equilibrium methodologies applied to food systems, Food Public Health 5 (2015) 184–202. [2] L. Oteroa, A. Ouseguib, B. Guignona, A. Le Bailb, P.D. Sanz, Evaluation of the thermophysical properties of tylose gel under pressure in the phase change domain, Food Hydrocoll. 20 (2006) 449–460. [3] M.A. Masuelli, Study of bovine serum albumin solubility in aqueous solutions by intrinsic viscosity measurements, Adv. Phys. Chem. 2013 (2013), 360239. (8 pages). [4] P.K. Banipal, V. Singh, T.S. Banipal, H. Singh, Ultrasonic studies of some mono-, di-, and tri-saccharides in aqueous sodium acetate solutions at different temperatures, Z. Phys. Chem. 227 (2013) 1707–1722.

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