# Study on Thermodynamic Properties for Binary Systems of Water + L-Cysteine Hydrochloride Monohydrate, Glycerol, and D-Sorbitol at Various Temperatures

Authors: F. Koohyar; A. A. Rostami; M. J. Chaichi; F. Kiani
Journal: Journal of Chemistry
 (2013)

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## Abstract

Viscosities, refractive indices, and densities for aqueous solution of L-cysteine hydrochloride monohydrate ([LCHCMH]) and D-sorbitol, and also densities (ρ), refractive indices (nD), excess molar volumes (VE), and change of refractive indices on mixing (ΔnD) for aqueous solution of glycerol have been measured at several mole fractions and temperatures (between T=303.15 K and T=323.15 K) at atmospheric pressure. The measurements were carried out using a vibrating-tube density meter for density, an Abbe refractometer for refractive index, and an Ubbelohde viscometer for viscosity. From these data for aqueous solution of glycerol, the excess molar volumes and the change of refractive indices on mixing were calculated and fitted to the Redlich-Kister polynomial equation. Also for aqueous solutions of [LCHCMH], glycerol, and D-sorbitol, the density and refractive indices were fitted with the experimental equations to estimate the adjustable parameters and relative deviations. It has been observed for aqueous solution of glycerol that the excess molar volumes and change of refractive indices on mixing increase and decrease with increasing temperature, respectively.


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## Body

## 1. Introduction

Studies on the viscosity and density of binary mixtures along with other thermodynamic properties are being increasingly used as tools for the investigation of the properties of pure components and the nature of intermolecular interactions between liquid mixture components [1]. Also the thermodynamic properties of aqueous solutions play a very important role in variety of fields: chemistry and chemical engineering, separation process (crystallization, evaporation, and desalination), wastewater treatment, pollution control, and oil recovery [2, 3]. Aqueous solutions of alcohols and polyols have attracted a good deal of attention of the scientific community for decades for their unusual nonideal behavior, especially in the low-concentration range. Besides, their study gives important information about the nature of interactions between nonpolar and polar groups with water and how these interactions affect the balance between hydrophobic and hydrophilic effects [4–7].Hydrogen-bonded systems are very interesting because hydrogen bonds play a vital role in chemical, physical, and biological processes. D-sorbitol, water, and glycerol molecules have strong hydrogen bonds [8].The L-cysteine is one of the essential amino acids for body and is found in the blood, hair, and some plants such as, soya (antioxidant). [LCHCMH] is a salt of this amino acid that is very soluble in water and is used in the medical industry [13]. One of the reasons for dissolving of D-sorbitol in water is that it has six OH groups and production of hydrogen bonds between water molecules and these groups. The molecule structure of D-sorbitol is similar to glucose but the solubility of D-sorbitol in water is higher. The measured data for aqueous solution of D-sorbitol play an important role in the fields of food engineering, food and medical industry [14–16], fragile biological material processing, and in the study of inhibitor of the formation of gas hydrate because sugars and polyalcohols exhibit a substantial inhibiting effect on hydrate formation [17, 18]. Glycerol is one type of alcohol that is very soluble in water. It can be due to having three OH groups. Glycerol is using in the pharmaceutical, cosmetic, and food industries because it is nontoxic and possesses good solvent properties for many compounds, both organic and inorganic [19, 20]. It has useful solvent properties, similar to those of water and simple aliphatic alcohols, because it has three alcoholic groups [12]. One of the uses of aqueous solution of [LCHCMH] is in the microbial cultures. Aqueous solution of D-sorbitol is used in the artificial sweeter and some kinds of drugs. Aqueous solution of glycerol is used as a softener in cosmetics and drugs, also antifreeze products. Therefore, the study on thermodynamic properties of aqueous solution of D-sorbitol, [LCHCMH], and glycerol in several temperatures can be used in different industries.


## 2. Experimental

### 2.1. Materials

D-sorbitol, [LCHCMH], and glycerol were purchased from Merck Co. (Darmstadt, Germany). The purity of D-sorbitol and glycerol is 98% and purity of [LCHCMH] is 99%. They are used without further purification. All dilute solutions were prepared from double-distilled water with specific conductivity equal to1.3±0.1μΩ-1·cm-1.


### 2.2. Apparatus and Procedure

All solutions were prepared by weighing suitable amounts of the individual components and mixed in a beaker. The mixtures were transferred into stopper reagent bottles to prevent water evaporation. All of the experiments are repeated three times and average values are reported. For weighting of solutes a balance (Precisa 240 A, Switzerland) was used with a precision of±0.0001 g. Densities (ρ) were measured using a digital vibrating glass tube densimeter (DA-500E, China.). Before each series of measurements, the instrument was calibrated at atmospheric pressure with double-distilled water and dry air. Densities were determined with an uncertainty of ±1×10-4g·cm-3. The dynamic viscosity (η) of the pure components and mixtures was determined from the kinematic viscosities ν measured using an Ubbelhode viscometer with automatic measuring unit (Schott, AVS 400, Germany). Four Ubbelohde tubes with different capillary size (0.36, 0.46, 0.53, and 0.63 mm) were used in the experiments according to the different viscosities of the mixtures. For all measurements, a Schott-Gerate CT 1150 digital thermostat was used to control the temperature within ±0.01 K of the desired temperature. The uncertainty of the time measurement in the viscometer is ±0.01 s. Refractive indices for the sodium D-line nD were measured with an Abbe refractometer (Carl Zeiss, Model A, Germany). A minimum of three independent readings was taken for each composition. The uncertainties of the refractive index and dynamic viscosity are ±1×10-4 and 0.003 (%0.3) mPa·s, respectively. Also the uncertainty of the temperature is ±0.01 K.


## 2.1. Materials

D-sorbitol, [LCHCMH], and glycerol were purchased from Merck Co. (Darmstadt, Germany). The purity of D-sorbitol and glycerol is 98% and purity of [LCHCMH] is 99%. They are used without further purification. All dilute solutions were prepared from double-distilled water with specific conductivity equal to1.3±0.1μΩ-1·cm-1.


## 2.2. Apparatus and Procedure

All solutions were prepared by weighing suitable amounts of the individual components and mixed in a beaker. The mixtures were transferred into stopper reagent bottles to prevent water evaporation. All of the experiments are repeated three times and average values are reported. For weighting of solutes a balance (Precisa 240 A, Switzerland) was used with a precision of±0.0001 g. Densities (ρ) were measured using a digital vibrating glass tube densimeter (DA-500E, China.). Before each series of measurements, the instrument was calibrated at atmospheric pressure with double-distilled water and dry air. Densities were determined with an uncertainty of ±1×10-4g·cm-3. The dynamic viscosity (η) of the pure components and mixtures was determined from the kinematic viscosities ν measured using an Ubbelhode viscometer with automatic measuring unit (Schott, AVS 400, Germany). Four Ubbelohde tubes with different capillary size (0.36, 0.46, 0.53, and 0.63 mm) were used in the experiments according to the different viscosities of the mixtures. For all measurements, a Schott-Gerate CT 1150 digital thermostat was used to control the temperature within ±0.01 K of the desired temperature. The uncertainty of the time measurement in the viscometer is ±0.01 s. Refractive indices for the sodium D-line nD were measured with an Abbe refractometer (Carl Zeiss, Model A, Germany). A minimum of three independent readings was taken for each composition. The uncertainties of the refractive index and dynamic viscosity are ±1×10-4 and 0.003 (%0.3) mPa·s, respectively. Also the uncertainty of the temperature is ±0.01 K.


## 3. Results and Discussion

The experimental data of densities (‎ρ), refractive indices (nD), and dynamic viscosities (η) for aqueous solution of [LCHCMH] and D-sorbitol at (303.15, 308.15, 313.15, 318.15 and 323.15) K, also densities (‎ρ), refractive indices (nD), excess molar volumes (VE), and change of refractive indices on mixing (ΔnD) for aqueous solution of glycerol at (303.15, 313.15, and 323.15) K are listed in Tables 2 and 3. The densities and refractive indices of pure water and glycerol at different temperatures are listed in Table 1.Table 1
Experimental value of density (ρ) and refractive index (nD) of pure liquids along with the corresponding values available in the literature at various temperatures (K).
Liquid
T (K)
ρ (g/cm3)
n
D
Experimental
Literature
Experimental
Literature
water
303.15
0.9957
0.99565a
1.3320
1.3319b
313.15
0.9922
0.99221a
1.3305
1.3306b
323.15
0.9880
0.98804b
1.3290
1.3290b
glycerol
303.15
1.2557
1.25560c
1.4710
not available
313.15
1.2493
1.24950c
1.4670
not available
323.15
1.2428
1.24290c
1.4640
not available
aRef. [9].
bRef. [10].
cRef. [11, 12].Table 2
Experimental densities (ρ), viscosities (η) and refractive indices (nD) as functions of mole fraction of [LCHCMH] and D-sorbitol (x1) for binary systems of [LCHCMH] (2) + water (1) and D-sorbitol (2) + water (1) at the various temperatures (K) and atmospheric pressure.
x
1
ρ (g/cm3)
η (mPa·s)
n
D
x
1
ρ (g/cm3)
η (mPa·s)
n
D
[LCHCMH] (2) + water (1)
D-sorbitol (2) + water (1)
T = 303.15 K
0.010
1.0252
0.8529
1.3480
0.002
0.9982
0.8134
1.3340
0.020
1.0534
1.1265
1.3605
0.004
1.0063
0.8647
1.3370
0.040
1.0988
1.5062
1.3830
0.006
1.0138
0.9160
1.3400
0.080
1.1637
2.4858
1.4175
0.008
1.0210
0.9675
1.3425
0.100
1.1903
3.3911
1.4310
0.010
1.0278
1.0191
1.3455
0.110
1.2029
3.9700
1.4370
0.012
1.0342
1.0708
1.3480
0.120
1.2151
4.6266
1.4425
0.014
1.0401
1.1226
1.3505
0.130
1.2268
5.3488
1.4475
0.016
1.0457
1.1745
1.3530
0.140
1.2378
6.1192
1.4525
0.018
1.0508
1.2266
1.3550
0.150
1.2478
6.9147
1.4570
0.020
1.0554
1.2787
1.3570
0.160
1.2562
7.7061
1.4615
0.022
1.0598
1.3310
1.3590
0.170
1.2643
8.4592
1.4660
0.024
1.0636
1.3834
1.3605
0.180
1.2715
9.1336
1.4700
0.026
1.0671
1.4359
1.3625
0.190
1.2765
9.9717
1.4740
0.028
1.0702
1.4885
1.3640
T = 308.15 K
0.010
1.0234
0.7892
1.3472
0.002
0.9962
0.7471
1.3335
0.020
1.0509
1.0228
1.3597
0.004
1.0048
0.7869
1.3365
0.040
1.0962
1.3563
1.3819
0.006
1.0122
0.8221
1.3394
0.080
1.1613
2.2369
1.4164
0.008
1.0195
0.8763
1.3420
0.100
1.1866
2.9551
1.4300
0.010
1.0253
0.9231
1.3447
0.110
1.1983
3.3869
1.4360
0.012
1.0312
0.9658
1.3471
0.120
1.2093
3.8827
1.4415
0.014
1.0376
1.0081
1.3497
0.130
1.2198
4.4510
1.4464
0.016
1.0428
1.0535
1.3520
0.140
1.2298
5.1008
1.4514
0.018
1.0482
1.1053
1.3543
0.150
1.2391
5.8416
1.4560
0.020
1.0526
1.1472
1.3562
0.160
1.2467
6.5236
1.4606
0.022
1.0570
1.2027
1.3580
0.170
1.2543
7.2175
1.4647
0.024
1.0615
1.2453
1.3600
0.180
1.2611
8.0144
1.4690
0.026
1.0648
1.2914
1.3615
0.190
1.2658
8.8263
1.4730
0.028
1.0676
1.3555
1.3632
T = 313.15 K
0.010
1.0217
0.7275
1.3465
0.002
0.9948
0.6825
1.3330
0.020
1.0491
0.9082
1.3590
0.004
1.0030
0.7202
1.3360
0.040
1.0944
1.2733
1.3810
0.006
1.0102
0.7581
1.3385
0.080
1.1588
1.9680
1.4155
0.008
1.0173
0.7961
1.3415
0.100
1.1833
2.5717
1.4290
0.010
1.0236
0.8344
1.3440
0.110
1.1944
2.9513
1.4350
0.012
1.0296
0.8728
1.3465
0.120
1.2048
3.3866
1.4405
0.014
1.0354
0.9114
1.3490
0.130
1.2146
3.8784
1.4455
0.016
1.0407
0.9502
1.3510
0.140
1.2239
4.4260
1.4505
0.018
1.0459
0.9891
1.3535
0.150
1.2326
5.0270
1.4550
0.020
1.0506
1.0282
1.3555
0.160
1.2411
5.6776
1.4595
0.022
1.0549
1.0676
1.3575
0.170
1.2478
6.3723
1.4635
0.024
1.0591
1.1071
1.3590
0.180
1.2539
7.1039
1.4680
0.026
1.0628
1.1467
1.3610
0.190
1.2591
7.8638
1.4720
0.028
1.0651
1.1866
1.3625
T = 318.15 K
0.010
1.0203
0.6712
1.3457
0.002
0.9925
0.6283
1.3325
0.020
1.0474
0.8248
1.3582
0.004
1.0012
0.6625
1.3353
0.040
1.0924
1.1123
1.3802
0.006
1.0082
0.6978
1.3380
0.080
1.1565
1.7845
1.4147
0.008
1.0152
0.7286
1.3408
0.100
1.1803
2.2926
1.4282
0.010
1.0211
0.7647
1.3432
0.110
1.1910
2.5753
1.4342
0.012
1.0270
0.7960
1.3458
0.120
1.2015
2.9296
1.4397
0.014
1.0332
0.8293
1.3480
0.130
1.2115
3.3496
1.4447
0.016
1.0382
0.8716
1.3502
0.140
1.2205
3.8327
1.4497
0.018
1.0434
0.9013
1.3525
0.150
1.2292
4.4079
1.4540
0.020
1.0477
0.9433
1.3545
0.160
1.2375
5.0173
1.4584
0.022
1.0526
0.9822
1.3565
0.170
1.2445
5.7185
1.4624
0.024
1.0564
1.0148
1.3581
0.180
1.2491
6.3015
1.4668
0.026
1.0592
1.0604
1.3601
0.190
1.2545
7.0022
1.4708
0.028
1.0628
1.0893
1.3615
T = 323.15 K
0.010
1.0182
0.6181
1.3450
0.002
0.9908
0.5854
1.3320
0.020
1.0459
0.7690
1.3575
0.004
0.9986
0.6131
1.3345
0.040
1.0908
1.0179
1.3795
0.006
1.0059
0.6414
1.3375
0.080
1.1538
1.5936
1.4140
0.008
1.0129
0.6702
1.3400
0.100
1.1776
2.0479
1.4275
0.010
1.0194
0.6996
1.3425
0.110
1.1885
2.3364
1.4335
0.012
1.0256
0.7295
1.3450
0.120
1.1987
2.6703
1.4390
0.014
1.0313
0.7600
1.3470
0.130
1.2084
3.0522
1.4440
0.016
1.0366
0.7910
1.3495
0.140
1.2176
3.4831
1.4490
0.018
1.0415
0.8226
1.3515
0.150
1.2261
3.9632
1.4530
0.020
1.0461
0.8547
1.3535
0.160
1.2339
4.4916
1.4575
0.022
1.0502
0.8874
1.3555
0.170
1.2408
5.0663
1.4615
0.024
1.0538
0.9206
1.3570
0.180
1.2465
5.6846
1.4655
0.026
1.0571
0.9544
1.3590
0.190
1.2506
6.3421
1.4695
0.028
1.0599
0.9887
1.3605Table 3
Experimental densities (ρ), refractive indices (nD), excess molar volumes (VE)and change of refractive indices on mixing (ΔnD) as functions of mole fraction of glycerol (x1) for binary system of glycerol (2) + water (1) at the various temperatures (K) and atmospheric pressure.
x
1
ρ (g/cm3)
n
D
V
E (cm3/mol)
ΔnD
T = 303.15 K
0.000
0.9956
1.3320
0.0000
0.0000
0.010
1.0070
1.3380
−0.0170
0.0046
0.021
1.0187
1.3440
−0.0372
0.0090
0.036
1.0330
1.3510
−0.0629
0.0140
0.047
1.0428
1.3560
−0.0819
0.0175
0.071
1.0631
1.3665
−0.1266
0.0247
0.099
1.0842
1.3770
−0.1812
0.0312
0.133
1.1053
1.3880
−0.2261
0.0375
0.175
1.1269
1.3995
−0.2731
0.0432
0.227
1.1489
1.4110
−0.3192
0.0475
0.294
1.1710
1.4230
−0.3559
0.0502
0.382
1.1928
1.4345
−0.3675
0.0493
0.439
1.2036
1.4405
−0.3601
0.0475
0.589
1.2250
1.4525
−0.3082
0.0392
0.692
1.2356
1.4585
−0.2553
0.0303
0.824
1.2460
1.4655
−0.1673
0.0189
1.000
1.2557
1.4710
0.0000
0.0000
T = 313.15 K
0.000
0.9922
1.3305
0.0000
0.0000
0.010
1.0034
1.3360
−0.0162
0.0041
0.021
1.0150
1.3420
−0.0366
0.0086
0.036
1.0290
1.3490
−0.0592
0.0136
0.047
1.0388
1.3540
−0.0801
0.0171
0.071
1.0588
1.3645
−0.1228
0.0243
0.099
1.0795
1.3745
−0.1733
0.0305
0.133
1.1003
1.3855
−0.2161
0.0368
0.175
1.1218
1.3970
−0.2658
0.0426
0.227
1.1435
1.4085
−0.3100
0.0470
0.294
1.1652
1.4200
−0.3416
0.0494
0.382
1.1868
1.4310
−0.3535
0.0483
0.439
1.1975
1.4370
−0.3464
0.0466
0.589
1.2187
1.4490
−0.2952
0.0380
0.692
1.2291
1.4540
−0.2382
0.0290
0.824
1.2393
1.4605
−0.1450
0.0175
1.000
1.2493
1.4670
0.0000
0.0000
T = 323.15 K
0.000
0.9880
1.3290
0.0000
0.0000
0.010
0.9991
1.3340
−0.0160
0.0036
0.021
1.0105
1.3400
−0.0261
0.0081
0.036
1.0244
1.3470
−0.0572
0.0131
0.047
1.0340
1.3520
−0.0758
0.0167
0.071
1.0538
1.3625
−0.1175
0.0239
0.099
1.0743
1.3720
−0.1673
0.0296
0.133
1.0950
1.3830
−0.2116
0.0360
0.175
1.1160
1.3945
−0.2535
0.0419
0.227
1.1375
1.4060
−0.2965
0.0464
0.294
1.1590
1.4170
−0.3268
0.0484
0.382
1.1804
1.4275
−0.3369
0.0469
0.439
1.1911
1.4335
−0.3322
0.0452
0.589
1.2120
1.4455
−0.2744
0.0370
0.692
1.2222
1.4495
−0.2106
0.0270
0.824
1.2323
1.4560
−0.1139
0.0157
1.000
1.2428
1.4640
0.0000
0.0000The value ofVE for aqueous solution of glycerol was calculated from the density data using:
(1)VE=(x1M1+x2M2)ρ-(x1M1ρ1+x2M2ρ2).
In this equation x1, x2 are mole fractions, M1, M2 are the molar masses, and ρ1, ρ2are the densities of pure components 1, 2, respectively.The change of refractive index on mixing (ΔnD) for aqueous solution of glycerol was calculated from:
(2)ΔnD=nD-(x1nD1+x2nD2).
In this equation x1, x2 are mole fractions, nD,nD1,nD2 are the refractive indices of the mixture and the pure components 1, 2, respectively.The values ofΔnD and VE for aqueous solution of [LCHCMH] and D-sorbitol cannot be calculated directly because for the calculation of ΔnD and VE for mixture we need the refractive indices and densities of the pure components of this mixture. For the solid components such as D-sorbitol and [LCHCMH] the density, refractive index, and viscosity are not available in literature at different temperatures.The value ofΔnD or VE for each mixture was fitted to the Redlich-Kister polynomial equation according to [21]:
(3)Y=x1(1-x1)∑i=0nAi(2x1-1)i.
Here Y=VE or ΔnD and Ai are adjustable parameters and x1 is the mole fraction.In each case, the optimum number of coefficientsAi was determined from an examination of the variation of the standard deviation:
(4)σ(Y)=[∑(Ycal-Yexp)2n-m]1/2,
where n is the total number of experimental values and m is the number of parameters.For aqueous solution of glycerol the values of these parameters,Ai, along with the standard errors (σ) are listed in Table 4.Table 4
Redlich-Kister fitting coefficientsAi and the standard deviation σ of VE and ΔnD for aqueous solution of glycerol at various temperatures (K).
T (K)
Property
A
0
A
1
A
2
A
3
σ
303.15
V
E (cm3/mol)
−1.3792
−0.9382
−0.3966
0.9522
0.049
ΔnD
0.4746
−0.2054
0.0826
0.0989
0.001
313.15
V
E (cm3/mol)
−1.3288
−0.9510
−0.2533
0.8318
0.016
ΔnD
0.1731
0.1120
0.0826
0.0558
0.001
323.15
V
E (cm3/mol)
−1.2586
−0.9996
−0.0742
0.6850
0.007
ΔnD
0.1680
0.1197
0.0731
0.0488
0.001The experimental data that are listed in Tables2 and 3 and Figure 1 show that the density, viscosity, and refractive index at each experimental temperature increase as the mole fraction of solutions increases. In the case of each mole fractions of solute, the density, viscosity, and refractive index of solutions decrease with increasing temperature.Figure 1
Variation of viscosities,η, against mole fraction of [LCHCMH], x2, for binary system of water (1) + [LCHCMH] (2) at T (K) = ◆, 303.15; ▪, 313.15; ▲, 323.15.The thermodynamic property values for solutions of this study can be dependent on two factors. The first factor is the concentration of solutions. The second factor is the power of bonds between solvent and solute molecules (in solution) due to the values of polarity (dipole-dipole interaction and the hydrogen bonds) and electrical charge of solute molecules. The second factor is effective in excess thermodynamic properties [22].For mixtures of this study the maximum values of density and refractive index are perceived for aqueous solution of [LCHCMH]. In this solution the second factor is very effective due to the electrical charge of ions of solute molecules (Cl− and R-NH3+).Also the minimum values of density and refractive index are perceived for aqueous solution of D-sorbitol. In this solution the first factor is very effective due to a low concentration of solute in the solution.Among the several thermodynamic properties, the excess molar volumes have been of much consideration for the practical target of determining composition from the density measurement. Excess molar volumes could also supply information on the possible interactions between components of a binary system, such as molecular associations and dipole-dipole and dipole-induced-dipole interactions [23].Three factors can be effective in the value of excess molar volumes [24, 25]. The first factor is the specific forces between molecules, such as H-bond and charge-transfer complexes. The positive excess molar volumes for the solution can be a result of the breaking of the H-bonds (weaker hydrogen bonds) and complexes between solvent and solute. Forming hydrogen bonds (stronger H-bonds) and complexes bring negative values of excess molar volumes. The second factor is the physical forces between molecules including electrostatic forces between charged particles, permanent dipoles, induction forces between a permanent dipole and an induced dipole, forces of attraction (dispersion forces), and repulsion between nonpolar molecules. Physical forces between molecules are usually weak. The sign of excess molar volume values can be positive or negative but these absolute values are small. The third factor is the structural characteristics of the component, arising from geometrical fitting of one component into the other's structure, due to the differences in form and size of component and free volume.As seen in Figure2, the values of VE for aqueous solution of glycerol over the entire range of mole fractions at all experimental temperatures are negative. In this solution the third factor (the structural characteristics of the component, arising from geometrical fitting of one component into the other's structure) is very effective due to the small size of water molecules and better hydrogen bonding formation with three OH of glycerol and water [26].Figure 2
Variation of excess molar volumes,VE, against mole fraction of glycerol, x2, for binary system of water (1) + glycerol (2) at T (K) = ◆, 303.15; ▪, 313.15; ▲, 323.15.The value ofVE increases as the temperature increases. The distance between molecules in this solution increases with increasing of the temperature and the interaction between molecules in this solution decreases.Also as seen in Figure3, the values of ΔnD for aqueous solution of glycerol over the entire range of mole fractions at all temperatures (in this study) are positive. The value of ΔnD decreases as the temperature increases.Figure 3
Variation of change of refractive indices on mixing, ΔnD, against mole fraction of glycerol, x2, for binary system of water (1) + glycerol (2) at T (K) = x, 303.15; ▪, 313.15; ◆, 323.15.It is clear that the minimum and maximum values ofVE and ΔnD for aqueous solution of glycerol appear at xglycerol≈0.4 and xglycerol≈0.35, respectively.The refractive index (nD) for aqueous solutions obeys from the following equation [27]:
(5)nD=Anc+nD*,
where nD is the refractive index of aqueous solutions, An is the constant that depends on physical and chemical properties of solute molecules, c is the molar concentration of aqueous solutions, and nD*  is the refractive index of water at determinate temperature.As seen in Figure4, the correlation between refractive index and molar concentration for mixtures of this study is linear with high association coefficient (R2=0.9998) and we can obtain the value of constant An for [LCHCMH] and glycerol solution at 313.15 K from this diagram according to (5), [An[LCHCMH]=0.0280L·mol-1 and An[glycerol]=0.0102L·mol-1].Figure 4
The linearity between refractive indices,nD, and molar concentration of [LCHCMH] and glycerol, c, at T (K) = 313.15 for binary systems of: □, (glycerol + water); Δ, ([LCHCMH] + water).For mixtures of this study, the values ofAn, nD* and relative deviations between the experimental values of nD* in literature (refractive index of water) [10], and calculated values of nD* from (5) at different temperatures are listed in Table 5.Table 5
Value of constantsAn, nD* (from (5) and relative deviation of nD* for aqueous solution of [LCHCMH], D-sorbitol, and glycerol at various temperatures (K).
T (K)
System
A
n (L/mol)
n
D
*
n
D
*
RD (fornD*)
Literature
303.15
[LCHCMH] + water
0.0282
1.3324
1.3319b
0.00038
313.15
0.0280
1.3309
1.3306b
0.00023
323.15
0.0278
1.3299
1.3290b
0.00068
303.15
D-sorbitol + water
0.0259
1.3318
1.3319b
0.00008
313.15
0.0256
1.3306
1.3306b
0.00000
323.15
0.0246
1.3296
1.3290b
0.00045
303.15
glycerol + water
0.0104
1.3327
1.3319b
0.00060
313.15
0.0102
1.3310
1.3306b
0.00030
323.15
0.0100
1.3293
1.3290b
0.00023
bRef. [28].For aqueous solutions of glycerol (5) at 313.15 K has the general form:
(6)nD=0.0102c+1.3310.
According to (6), having the refractive index of aqueous solution of glycerol at 313.15 K, we can obtain the molar concentration of the solution in the same temperature, and vice versa.For aqueous solution of glycerol the calculated refractive indices according to (6) and the experimental ones at 313.15 K in different molar concentrations of glycerol are listed in Table 6. The low relative deviations for experimental and calculated values of nD for aqueous solution of glycerol indicate that the experimental values are well fitted in (5) and (6) at 313.15 K.Table 6
Experimental and calculated refractive indices (nD) from (6) and relative deviation of nD as function of molar concentrations of glycerol (c) for aqueous solution of glycerol at T = 313.15 K.
c
n
D
RD (fornD)
c
n
D
RD (fornD)
(mol/L)
exp
cal
(mol/L)
exp
cal
1.00
1.3410
1.3408
0.00015
6.50
1.3975
1.3969
0.00043
2.00
1.3515
1.3510
0.00037
7.00
1.4025
1.4020
0.00036
3.00
1.3615
1.3612
0.00022
7.50
1.4075
1.4071
0.00028
4.00
1.3720
1.3714
0.00044
8.00
1.4125
1.4122
0.00021
5.00
1.3820
1.3816
0.00029
8.50
1.4175
1.4173
0.00014
6.00
1.3920
1.3918
0.00014
9.00
1.4230
1.4224
0.00042Also as seen in Figure5, for solution of this study the relation between density and refractive index is linear. These lines (ρ versus nD) are close together. The relation between density and refractive index can be due to the interaction between the solute and solvent molecules. In these solutions the solvent is water and the kind of interaction between solute and solvent is the H-bond. Therefore, we expect the same results for variation of density versus refractive index. In Figure 5 we see the same slope of the lines (ρ versus nD). Therefore, the quantities of slopes can be depend on the kinds of solvent-solute interaction.Figure 5
Variation of densities,ρ, against refractive indices, nD, at T (K) = 303.15 for binary systems of: ◆, (water + [LCHCMH]); ▪, (water + D-sorbitol); ▲, (water + glycerol).A third-order polynomial was found to satisfactorily correlate the change of density with various compositions [28]:
(7)ρ=b∘+b1x1+b2x12+b3x13.
In this equation, x1 is the mole fractions of [LCHCMH], D-sorbitol, and glycerol, and b∘, b1, b2, and b3 refer to the fit coefficients. Fit parameters are listed in Table 7 for the mixtures.Table 7
Coefficientsbi of the polynomial (7), and relative deviation (RD) between b∘ (density of pure water in literature) and experimental b∘ (that obtain from (7) at various temperatures for different binary mixtures.
T (K)
b
∘ (g/cm3)
b
1 (g/cm3)
b
2(g/cm3)
b
3(g/cm3)
b
∘ (g/cm3)
RD (forb∘)
Literature
[LCHCMH] (2) + water (1)
303.15
1.0046
2.4795
−6.3416
3.5316
0.99565a
0.0090
313.15
0.9965
2.8025
-
11.2350
20.0310
0.99221a
0.0043
323.15
0.9937
2.7695
−11.1250
19.6010
0.98804b
0.0057
D-sorbitol (2) + water (1)
303.15
0.9898
4.3269
−52.3920
14.9970
0.99565a
0.0059
313.15
0.9870
4.1404
-
48.5530
30.4230
0.99221a
0.0053
323.15
0.9827
4.1708
−49.1770
−44.9920
0.98804b
0.0054
glycerol (2) + water (1)
303.15
1.0023
0.8796
−1.1677
0.5452
0.99565a
0.0067
313.15
0.9988
0.8683
−1.1532
0.5390
0.99221a
0.0066
323.15
0.9944
0.8591
−1.1427
0.5353
0.98804b
0.0064
aRef. [9].
bRef. [28].For different aqueous solutions in each temperature,b∘ in (7) is the density of pure water (solvent).
(8)x1=0⇒ρ=b∘.
We calculate the relative deviation (RD) between b∘ in literature (density of pure water [28]) and experimental b∘ (that obtained from (7)) and list those in Table 7. The low values of relative error in this case indicate that the experimental b∘ is very close to density of pure water. Thus, for these study mixtures (7) can be used in correlation of density with mole fraction of solute. The relative deviation (RD) for b∘ was calculated according to following equation:
(9)RD=|b∘(lit)-b∘(exp)b∘(lit)|,
where b∘(lit) is the value of b∘ found in literature (density of pure water) and b∘(exp) is the value of b∘ from (7).The RD fornD* was calculated according to the following equation:
(10)RD=|nD*-nD(c)*nD*|,
where nD(c)* is the calculated value of refractive index of water from (5) and nD* is the experimental value of refractive index of water (in literature) at the same temperature.


## 4. Conclusions

The experimental viscosities, densities, and refractive indices for the binary system of ([LCHCMH] + water) and (D-sorbitol + water) at (303.15, 308.15, 313.15, 318.15, and 323.15) and also densities, refractive indices data for (glycerol + water) at (303.15, 313.15, and 323.15) K were obtained over a wide range of composition. For aqueous solution of glycerol, from the experimental density and refractive index, values of excess molar volume and change of refractive index on mixing were calculated.It was found that for aqueous solution of glycerol, all these calculated quantities for excess molar volume and change of refractive index on mixing are negative and positive, respectively. The Redlich-Kister polynomial equation was applied successfully for the correlation ofΔnD and VE.



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