# Thermophysical Properties of Binary Liquid Systems of Ethanoic Acid, Propanoic Acid, and Butanoic Acid with Benzene or Acetophenone

Authors: R. Ahluwalia; Ritu Gupta; J. L. Vashisht; R. K. Wanchoo
Journal: ISRN Physical Chemistry
 (2013)

---

## Abstract

The density (ρ), viscosity (η), and surface tension (σ) of binary mixtures of carboxylic acids (CAs) (ethanoic acid (EA), propanoic acid (PA), butanoic acid (BA)) + benzene (BEN) or acetophenone (ACT) have been measured at 298.15, 308.15, and 318.15 K. From the experimental results, excess values of molar volume (VE), viscosity (ηE), Gibb's free energy for the activation of low (GE), and surface tension (σE) were evaluated and fitted to a Redlich-Kister type of equation. The parameter “d” of Grunberg and   Nissan expression has also been calculated. From the sign and magnitude of VE, ηE, GE, σE, and “d” values, it is concluded that specific interactions are present in CA+ACT system and these interactions are absent in CA + BEN mixtures. Various viscosity and surface tension models have been used to test the consistency of the data.


---

## Body

## 1. Introduction

Studies on thermophysical properties of binary liquid mixtures containing carboxylic acids are not extensive [1–3]. In view of this, we have undertaken studies on binary mixtures of carboxylic acids (CAs), namely, ethanoic acid (EA), propanoic acid (PA), and butanoic acid (BA) which are self-associated solvents, with a nonpolar solvent benzene (BEN) and polar acetophenone (ACT). These acids exist as cyclic dimers in the pure state. However, trimers also exist which are formed because of strong interactions between ring dimers and monomers [4–6].The excess propertiesVE, ηE, GE, σE, and Grunberg and Nissan parameter “d” computed from the experimental data (density (ρ), viscosity (η), and surface tension) (σ)) of binary mixtures of carboxylic acids (EA, PA, BA) with benzene and acetophenone have been determined. Benzene interacts with acid through Vander Waal's or London dispersion forces and acetophenone forms chemical aggregates with acid through hydrogen bonding. The results are used to theoretically justify the validity of various viscosity and surface tension models. The main thrust of the investigation is to correlate the experimental data in terms of the interacting components of the mixtures and to stress the factors affecting these interactions.


## 2. Experimental Section

Ethanoic acid, propanoic acid, butanoic acid, benzene, and acetophenone were purified by the standard methods described in the literature [7]. Ethanoic acid (BDH, 99% assay) was washed with a calculated amount of acetic anhydride for about 10 h and was subjected to fractional distillation. Propanoic acid and butanoic acid (E. Merck, 99% assay) were dried over anhydrous sodium sulfate for two days and the samples were distilled over potassium permanganate. Benzene (E. Merck, 98.4% assay) was dried by keeping over anhydrous calcium chloride for six to eight hours and then fractionally distilled. Acetophenone (Merck, 99% assay) was also dried by keeping it over anhydrous calcium chloride for two days and distilled at reduced pressure. The purity of all the components was checked by comparing their experimental densities with that of the literature values [7]. For each run, a fresh liquid mixture was prepared on a mass basis (precision of 1 × 10−5 g). The purity of each component with respect to the corresponding literature value is recorded in Table 1.Table 1
Densities (10−3 ρ, kg m−3) of the pure components at 298.15 K.
Component
This work
Lit. values [5]
Ethanoic acid
1.0437
1.04366
Propanoic acid
0.9882
0.9880
Butanoic acid
0.9533
0.9532
Benzene
0.8782
0.8737
Acetophenone
1.0241
1.0238Densities (ρ) of the pure components and their mixtures were measured with a density meter (AP, DMA-48) calibrated at each temperature with ethanol and 1,2-dichloroethane. The densities were measured with an accuracy of 1 × 10−1 kg·m−3.Viscosities (η) were determined using a modified Ubbelohde viscometer [8]. At each temperature, the viscometer was calibrated against the known viscosities of benzene and carbon tetrachloride [9]. The viscometer constants at each temperature were determined from the following
(1)ηρ=at-bt,
where a and b are the temperature-dependent constants. At a particular temperature, an average value of the five consistently measured efflux times t and the densities were used to calculate viscosity. The accuracy of the viscosity measurements is in the order of ±0.0013 mPa·s.Surface tension (σ) of the pure components and their mixtures was determined by the differential capillary rise method [7], using (2). The difference Δh in the liquid levels in two capillaries was measured with a cathetometer reading to 0.05 mm with a vernier constant of 0.01 mm. The surface tension values are accurate to within ±0.02 mN·m−1. Consider
(2)Δh=h1-h2=2σρgA+(B-C),
where A=1/r1-1/r2, B=(1/3)(r2-r1), C=0.129(r22/h2), h1 and h2 are the heights of liquids in capillaries 1 and 2, r1 and r2 are the radii of the capillaries, and g is the acceleration due to gravity (=9.80 m s−2), respectively. The constants A, B, and C of (2) were determined by measuring the Δh for two test liquids (benzene, ethyl ethanoate) of known σ and ρ at 298.15 K. The constant C was separately determined by noting the height of the test liquid in one of the capillaries. The corresponding radius r2 of the capillary was determined from the measured weight of the mercury column of known length. The constants (A, B, and C) were assumed to be temperature independent. For each mixture of the respective systems and pure components, Δh was recorded at three different temperatures over the entire composition range.All the measurements were made at a constant temperature that was maintained with the help of a circulating type ultra cryostat (type MK 70, MLW, Germany) within ±0.02°C.


## 3. Results

Experimental densities of pure components and their literature values at 298.15 K are given in Table1. Experimental values of ρ, η, and σ were fitted to (3) using nonlinear regression technique [10]. The computed coefficients of (3) and standard errors are listed in Table 3.Equation (3) fits the experimental data within the average uncertainty in the temperature range of 298.15 K–318.15 K and 0<x1<1(3)Y(T,x1)=[a0exp(a1T)(bo+b1x1+b2x12+b3x13)]1/2.Based on the regular solution theory [11], Grunberg and Nissan proposed an empirical expression for viscosities of real mixtures:
(4)d=1(x1x2)[lnηmix-x1lnη1-x2lnη2],
where η1 and η2 refer to the dynamic viscosities of the pure liquid components 1 and 2, respectively, x1 and x2 are the mole fractions of components 1 and 2, respectively, in the mixture, and “d” is a parameter which denotes the measure of strength of interaction between the two components. The values of “d” are reported in Table 2.Table 2
Mole fraction of first componentx1, density, viscosity, and surface tension for various systems.
(a)
System: ethanoic acid (1) + benzene (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
x
1
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
0.0000
0.8782
0.6035
28.21
—
0.8669
0.5294
26.75
—
0.8560
0.4588
25.24
—
0.1465
0.8899
0.6157
28.02
−0.5760
0.8792
0.5599
26.63
−0.2350
0.8685
0.4941
25.20
−0.0080
0.2786
0.9035
0.6165
27.89
−0.7652
0.8926
0.5451
26.54
−0.6631
0.8822
0.4746
25.18
−0.5441
0.3984
0.9181
0.6258
27.73
−0.8931
0.9073
0.5380
26.46
−0.9022
0.8967
0.4682
25.16
−0.7692
0.5074
0.9335
0.6517
27.61
−0.9683
0.9226
0.5528
26.39
−1.0121
0.9119
0.4941
25.15
−0.7465
0.6071
0.9496
0.6964
27.51
−0.9991
0.9387
0.5906
26.33
−1.0263
0.9279
0.5477
25.14
−0.5641
0.6986
0.9666
0.7587
27.41
−0.9972
0.9556
0.6470
26.28
−0.9831
0.9449
0.6167
25.13
−0.2991
0.7829
0.9845
0.8364
27.33
−0.9733
0.9737
0.7158
26.23
−0.9122
0.9629
0.6859
25.13
0.0009
0.8607
1.0032
0.9265
27.25
−0.9330
0.9924
0.7904
26.18
−0.8450
0.9817
0.7418
25.12
0.3209
0.9329
1.0229
1.0263
27.17
−0.8784
1.0120
0.8647
26.14
−0.8561
1.0012
0.7728
25.12
0.6777
1.0000
1.0437
1.1310
27.10
—
1.0325
0.9487
26.10
—
1.0213
0.7667
25.11
—
(b)
System: propanoic acid (1) + benzene (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
x
1
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
0.0000
0.8782
0.6035
28.21
—
0.8669
0.5294
26.75
—
0.8560
0.4588
25.24
—
0.1164
0.8877
0.6299
27.79
−0.1880
0.8766
0.5533
26.38
−0.1531
0.8658
0.4809
24.95
−0.0851
0.2287
0.8974
0.6452
27.42
−0.3151
0.8863
0.5619
26.06
−0.3290
0.8756
0.4889
24.69
−0.2620
0.3254
0.9063
0.6617
27.12
−0.3742
0.8954
0.5722
25.80
−0.4092
0.8847
0.5081
24.47
−0.2471
0.4415
0.9178
0.6954
26.76
−0.3831
0.9071
0.5995
25.49
−0.4180
0.8965
0.5483
24.22
−0.1361
0.5425
0.9288
0.7408
26.46
−0.3430
0.9181
0.6404
25.23
−0.3583
0.9075
0.5992
24.01
0.0273
0.6401
0.9403
0.7985
26.17
−0.2711
0.9295
0.6944
24.97
−0.2530
0.9189
0.6572
23.81
0.2271
0.7345
0.9520
0.8638
25.89
−0.1764
0.9413
0.7553
24.73
−0.1171
0.9307
0.7128
23.62
0.4525
0.8181
0.9629
0.9242
25.65
−0.0772
0.9522
0.8095
24.52
0.0241
0.9416
0.7516
23.45
0.6797
0.9143
0.9761
0.9886
25.37
0.0556
0.9654
0.8616
24.27
0.2091
0.9547
0.7697
23.27
1.0053
1.0000
0.9882
1.0305
25.13
—
0.9774
0.8858
24.07
—
0.9666
0.7412
23.10
—
(c)
System:  butanoic acid (1) + benzene (2)
Temp.
T = 298.15, K
T = 308.15, K
T= 318.15, K
x
1
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
0.0000
0.8782
0.6035
28.21
—
0.8669
0.5294
26.75
—
0.8560
0.4588
25.24
—
0.0965
0.8844
0.6554
27.84
−0.0821
0.8737
0.5723
26.43
−0.0502
0.8629
0.4944
24.99
0.0442
0.1938
0.8909
0.7002
27.52
−0.2023
0.8806
0.6046
26.16
−0.2071
0.8699
0.5501
24.77
0.2503
0.2918
0.8978
0.7427
27.20
−0.3081
0.8877
0.6437
25.89
−0.2583
0.8772
0.6162
24.56
0.3907
0.3906
0.9049
0.7987
26.91
−0.3482
0.8949
0.6954
25.65
−0.2540
0.8846
0.6849
24.37
0.4783
0.4902
0.9124
0.8763
26.63
−0.3304
0.9026
0.7645
25.42
−0.2031
0.8923
0.7501
24.19
0.5266
0.5906
0.9202
0.9788
26.35
−0.2691
0.9105
0.8516
25.20
−0.1171
0.9003
0.8078
24.01
0.460
0.6917
0.9279
1.1049
26.08
−0.1782
0.9186
0.9534
24.97
−0.0074
0.9085
0.8558
23.84
0.5413
0.7937
0.9360
1.2480
25.81
−0.0671
0.9268
1.0620
24.75
0.1182
0.9169
0.8944
23.67
0.5170
0.8964
0.9444
1.3954
25.55
0.0573
0.9351
1.1645
24.53
0.2564
0.9253
0.9262
23.51
0.4754
1.0000
0.9533
1.5283
25.31
—
0.9434
1.2421
24.33
—
0.9335
0.9562
23.35
—
(d)
System: ethanoic acid (1) + acetophenone (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
x
1
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
0.0000
1.0241
1.6589
38.74
—
1.0156
1.3469
37.67
—
1.0069
1.0082
36.28
—
0.1852
1.0279
1.6468
36.98
0.4216
1.0196
1.3674
36.12
0.5305
1.0113
1.0954
34.92
0.8861
0.3384
1.0309
1.6127
35.53
0.4529
1.0228
1.3692
34.57
0.6030
1.0139
1.1265
33.59
0.9093
0.4672
1.0334
1.5613
34.19
0.4753
1.0250
1.3465
33.14
0.6565
1.0161
1.1242
32.27
0.9515
0.5770
1.0357
1.4993
32.83
0.4912
1.0269
1.3048
31.84
0.6984
1.0179
1.1006
31.00
1.0064
0.6717
1.0374
1.4329
31.62
0.5028
1.0284
1.2511
30.66
0.7329
1.0192
1.0622
29.77
1.0707
0.7542
1.0393
1.3662
30.55
0.5111
1.0299
1.1908
29.60
0.7616
1.0205
1.0136
28.59
1.1427
0.8268
1.0406
1.3014
29.41
0.5166
1.0306
1.1282
28.63
0.7860
1.0215
0.9577
27.68
1.2224
0.8911
1.0419
1.2403
28.52
0.5206
1.0317
1.0659
27.76
0.8071
1.0221
0.8969
26.74
1.3091
0.9485
1.0432
1.1834
27.81
0.5239
1.0324
1.0057
26.96
0.8245
1.0217
0.8328
25.95
1.4040
1.0000
1.0437
1.1310
27.10
—
1.0325
0.9487
26.10
—
1.0213
0.7667
25.11
—
(e)
System: propanoic acid (1) + acetophenone (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
x
1
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
0.0000
1.0241
1.6589
38.74
—
1. 0156
1.3469
37.67
—
1.0069
1.0082
36.28
—
0.1485
1.0234
1.6616
37.55
0.5718
1.0155
1.4078
36.60
0.8421
1.0071
1.1222
35.46
1.2083
0.2818
1.0211
1.6244
35.95
0.5591
1.0132
1.4109
35.05
0.8131
1.0047
1.1734
33.93
1.1780
0.4022
1.0184
1.5657
34.23
0.5559
1.0102
1.3815
33.32
0.8065
1.0016
1.1826
32.18
1.1781
0.5113
1.0155
1.4956
32.61
0.5594
1.0070
1.3330
31.60
0.8161
0.9982
1.1627
30.45
1.2000
0.6108
1.0123
1.4199
30.97
0.5689
1.0036
1.2730
29.94
0.8395
0.9947
1.1217
28.82
1.2302
0.7019
1.0087
1.3417
29.52
0.5831
0.9999
1.2053
28.48
0.8748
0.9908
1.0651
27.40
1.2044
0.7855
1.0046
1.2630
28.20
0.6014
0.9956
1.1318
27.23
0.9211
0.9862
0.9965
26.22
1.3648
0.8626
0.9999
1.1846
27.10
0.6236
0.9905
1.0538
26.05
0.9795
0.9808
0.9184
25.14
1.4520
0.9339
0.9945
1.1069
26.09
0.6494
0.9845
0.9718
25.05
1.0520
0.9743
0.8326
24.13
1.5548
1.0000
0.9882
1.0305
25.13
—
0.9774
0.8858
24.07
—
0.9666
0.7412
23.10
—
(f)
System:  butanoic acid (1) + acetophenone (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
x
1
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
10−3 ρ, kg m−3
η, mPa s
103 σ, N m−1
d
0.0000
1.0241
1.6589
38.74
—
1.0156
1.3469
37.67
—
1.0069
1.0082
36.28
—
0.1238
1.0192
1.6809
37.21
0.2147
1.0114
1.4359
36.20
0.6827
1.0029
1.1843
34.89
1.5446
0.2412
1.0135
1.6949
35.81
0.2254
1.0057
1.4832
34.82
0.6336
0.9975
1.2710
33.55
1.3354
0.3528
1.0073
1.6994
34.47
0.2323
0.9993
1.5199
33.48
0.6545
0.9912
1.3134
32.28
1.2401
0.4588
1.0007
1.6943
33.19
0.2364
0.9925
1.5224
32.20
0.6429
0.9844
1.3145
31.04
1.1663
0.5598
0.9937
1.6803
31.90
0.2382
0.9855
1.5164
30.93
0.6650
0.9772
1.2913
29.83
1.1244
0.6561
0.9864
1.6587
30.63
0.2379
0.9781
1.4854
29.67
0.6693
0.9696
1.2499
28.60
1.1067
0.7480
0.9788
1.6311
29.36
0.2358
0.9703
1.4423
28.40
0.6845
0.9616
1.1897
27.34
1.0885
0.8357
0.9708
1.5991
28.08
0.2318
0.9621
1.3868
27.13
0.7058
0.9529
1.1232
26.10
1.1087
0.9197
0.9623
1.5644
26.79
0.2269
0.9531
1.3154
25.81
0.6884
0.9436
1.0526
24.80
1.2427
1.0000
0.9533
1.5283
25.31
—
0.9434
1.2421
24.33
—
0.9335
0.9562
23.35
—Table 3
Coefficients and standard deviation (SD) of (3).
(a)
System: ethanoic acid (1) + benzene (2)
Property
a
0
a
1
b
0
b
1
b
2
b
3
SD
10−3 ρ, kg m−3
0.0119
−0.0023
127.7241
25.6751
1.5885
26.0451
0.0005
η, mPa s
59.5012
−0.0292
38.0928
15.3389
−91.5172
162.0792
0.0098
103 σ, N m−1
152.321
−0.0092
78.8979
−6.4061
5.4754
−3.1067
0.0787
(b)
System: propanoic acid (1) + benzene (2)
Property
a
0
a
1
b
0
b
1
b
2
b
3
SD
10−3 ρ, kg m−3
0.0646
−0.0023
23.8828
4.1347
2.0768
0.2422
0.0004
η, mPa s
8.5892
−0.0253
84.0671
−51.2057
289.9852
−91.7128
0.0121
103 σ, N m−1
67.3803
−0.0098
218.9691
−50.9015
14.4385
−5.0172
0.0531
(c)
System: butanoic acid (1) + benzene (2)
Property
a
0
a
1
b
0
b
1
b
2
b
3
SD
10−3 ρ, kg m−3
0.0075
−0.0022
197.7351
31.0052
5.3648
0.0082
0.0004
η, mPa s
1.1224
−0.0039
0.9317
0.9135
1.0511
0.9013
0.1174
103 σ, N m−1
40.7458
−0.0097
345.5491
−83.2693
35.6763
−12.5341
0.0789
(d)
System: ethanoic acid (1) + acetophenone (2)
Property
a
0
a
1
b
0
b
1
b
2
b
3
SD
10−3 ρ, kg m−3
0.0133
−0.0018
135.4120
5.3912
0.5035
−1.2567
0.0008
η, mPa s
5.5360
−0.0078
1.0852
0.8055
0.1232
0.6509
0.3807
103 σ, N m−1
19.8974
−0.0061
466.4421
−181.1751
−103.1812
43.4471
0.0814
(e)
System: propanoic acid (1) + acetophenone (2)
Property
a
0
a
1
b
0
b
1
b
2
b
3
SD
10−3 ρ, kg m−3
0.0247
−0.0018
72.3523
−1.2922
−0.0496
−3.9453
0.0011
η, mPa s
478.863
−0.0308
51.9435
32.5293
−96.0902
33.3408
0.0217
103 σ, N m−1
82.6053
−0.0066
129.2180
−39.9785
−99.9945
64.4734
0.0998
(f)
System: butanoic acid (1) + acetophenone (2)
Property
a
0
a
1
b
0
b
1
b
2
b
3
SD
10−3 ρ, kg m−3
0.0219
−0.0017
80.5712
−5.6413
−4.3236
−1.0553
0.0005
η, mPa s
406.2351
−0.0313
70.2532
69.7560
−96.7418
16.7550
0.0271
103 σ, N m−1
71.4271
−0.0067
156.1280
−99.6785
26.3214
−17.0516
0.0658From the experimental data, excess molar properties, namely;VE, ηE, GE, and σE were calculated [12] from the following expressions:
(5)VE(cm3mol-1)=x1M1[1ρmix-1ρ1]+x2M2[1ρmix-1ρ2],log10(1η0)=x1log10(1η1)+x2log10(1η2),(6)ηE(mPas)=ηmix-η0,(7)GERT(Jmol-1)=[lnηmixVmix-(x1lnη1V1+x2lnη2V2)],(8)σE(mNm-1)=σmix-[x1σ1+x2σ2],
where M1 and ρ1 are the molecular weight and density of the carboxylic acids. The same symbols with subscript 2 refer to BEN or ACT, respectively. V1, V2, and Vmix are the molar volumes and σ1, σ2, and σmix are the surface tension of the 1st, and 2nd components and mixture, respectively.Graphical representations ofVE, ηE, GE, and σE as a function of the mole fraction (x1) of CA are given in Figures 1–8, respectively. Each of these functions, F=VE, ηE, GE and σE, has been fitted to the Redlich-Kister relation [13]:
(9)F=x1x2∑1nAj-1(2x1-1)j-1,
where Ao, A1, and A2 are adjustable parameters and have been evaluated by the method of least squares. The value of these parameters along with standard deviation is reported in Table 4. Consider
(10)SD=∑(observed-calculated)2N-1,
where N is the total number of experimental points.Table 4
Coefficients of (9) and standard deviation (SD) determined by the method of least squares.
(a)
System: ethanoic acid (1) + benzene (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
Coeff. of (9)
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
A
0
3.4057
−2036.7
−0.7083
−0.1438
3.3546
−2190.4
−0.6270
−0.1148
3.2885
−1582.1
−0.4091
−0.1021
A
1
0.1473
−570.94
−0.3870
0.1166
0.2460
−919.75
−0.3834
0.0811
0.3229
875.912
0.1482
0.0671
A
2
0.5936
1060.26
0.1385
0.0069
0.2239
2253.75
0.3941
−0.0229
0.0329
4602.96
1.0281
0.0052
SD
0.0046
0.9097
0.0004
0.0024
0.0066
15.0513
0.0029
0.0019
0.0106
20.9443
0.0006
0.0025
(b)
System: propanoic acid (1) + benzene (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
Coeff. of (9)
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
A
0
1.5593
−817.53
−0.2753
−0.3333
1.4645
−908.81
−0.2545
−0.2841
1.3824
−59.558
−0.0305
−0.2906
A
1
−0.1945
406.993
0.0821
0.1821
−0.2298
631.847
0.1348
0.1516
−0.2524
1926.95
0.4671
0.1026
A
2
−0.5306
1137.63
0.3751
−0.1745
−0.4702
1653.71
0.4651
−0.2454
−0.4703
1900.34
0.5546
−0.0278
SD
0.0025
4.9749
0.0002
0.0022
0.0033
7.6158
0.0001
0.0032
0.0035
13.9527
0.0011
0.0023
(c)
System: butanoic acid (1) + benzene (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
Coeff. of (9)
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
A
0
1.3265
−766.41
−0.2993
−0.6355
0.9972
−479.11
−0.1557
−0.5632
0.9699
1437.98
0.3753
−0.4996
A
1
−0.0839
352.158
0.0682
0.2170
−0.2319
723.101
0.2175
0.2762
−0.2740
538.149
0.2511
0.2161
A
2
0.2549
1271.88
0.5053
−0.2678
−0.2829
1144.88
0.4437
−0.2589
−0.4747
−1097.5
−0.2301
−0.1274
SD
0.0025
7.9049
0.0011
0.0037
0.0026
10.4486
0.0005
0.0045
0.0011
7.4136
0.0001
0.0019
(d)
System: ethanoic acid (1) + acetophenone (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
Coeff. of (9)
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
A
0
−1.1887
1773.18
0.6988
3.5069
−1.5271
2302.41
0.8237
3.4363
−1.7228
3144.69
0.9608
4.7515
A
1
−0.0156
318.334
−0.0168
−0.1138
0.0861
643.012
0.1139
−0.1918
0.0136
795.337
0.1274
−0.4302
A
2
−0.2739
−46.906
−0.0924
−2.4741
−0.2552
−51.471
−0.1390
1.1646
−0.9039
600.09
0.0699
0.4843
SD
0.0078
0.2584
0.0001
0.0368
0.0107
0.5067
0.0001
0.0249
0.0077
2.8808
0.0001
0.0421
(e)
System: propanoic acid (1) + acetophenone (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
Coeff. of (9)
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol-1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
A
0
−2.1586
1575.04
0.7842
3.2115
−2.5740
2266.12
0.9866
3.5476
−2.9319
3336.55
1.2061
3.6371
A
1
−0.4770
89.9121
−0.1441
−4.1671
−0.4158
224.961
−0.1081
−4.8025
−0.4622
412.138
−0.0243
−5.4345
A
2
−1.1862
159.141
0.0621
0.8986
−1.8773
440.569
0.1263
1.6488
−2.9319
636.631
0.0692
3.7051
SD
0.0057
0.4763
0.0001
0.0296
0.0046
1.7711
0.0001
0.0289
−0.4622
2.5552
0.0001
0.0371
(f)
System: butanoic acid (1) + acetophenone (2)
Temp.
T = 298.15, K
T = 308.15, K
T = 318.15, K
Coeff. of (9)
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
V
E, cm3 mol−1
G
E, J mol−1
η
E, mPa s
σ
E, dyne cm−1
A
0
−2.1062
609.099
0.3895
2.5197
−2.5541
1683.49
0.9184
2.7061
−3.0827
3014.95
1.2999
2.9131
A
1
−0.1445
19.8592
0.0009
1.9580
−0.1158
82.0211
0.0129
1.8902
−0.1071
−644.28
−0.3272
1.8747
A
2
−0.4769
−78.407
−0.0556
0.6841
−1.1813
104.424
−0.0028
0.9832
−1.0573
860.142
0.2081
0.8359
SD
0.0019
0.0827
0.0001
0.0267
0.0049
5.0118
0.0029
0.0194
0.0031
8.1692
0.0031
0.0183Figure 1
Plot ofVE versus x1 for EA + BEN (■ 298.15 K, ▴ 308.15 K, ◆ 318.15 K); PA + BEN (□ 298.15 K, △ 308.15 K, ◊ 318.5 K); II BA+BEN (⬤ 298.15 K, × 308.15 K, + 318.15 K) III calculated from (5).Figure 2
Plot ofVE versus x1 for EA + ACT (■ 298.15 K, ▴ 308.15 K, ◆ 318.15 K) IV; PA + ACT (□ 298.15 K, △ 308.15 K, ◊ 318.15 K) V; BA + ACT (⬤ 298.15 K, × 308.15 K, + 318.15 K) VI calculated from (5).Figure 3
Plot ofηE versus x1 for EA + BEN (■ 298.15 K, ▴ 308.15 K, ◆ 318.15 K) I; PA + BEN (□ 298.15 K, △ 308.15 K, ◊ 318.15 K) II; BA + BEN (⬤ 298.15 K, × 308.15 K, + 318.15 K) III calculated from (6).Figure 4
Plot ofηE versus x1 for EA + ACT (■ 298.15 K, ▴ 308.15 K, ◆ 318.15 K) IV; PA + ACT (□ 298.15 K, △ 308.15 K, ◊ 318.15 K) V; BA + ACT (⬤ 298.15 K, × 308.15 K, + 318.15 K) VI calculated from (6).Figure 5
Plot ofGE versus x1 for EA + BEN (■ 298.15 K, ▴ 308.15 K, ◆ 318.15 K) I; PA + BEN (□ 298.15 K, △ 308.15 K, ◊ 318.15 K) II; BA + BEN (⬤ 298.15 K, × 308.15 K, + 318.15 K) III calculated from (7).Figure 6
Plot ofGE versus x1 for EA + ACT (■ 298.15 K, ▴ 308.15 K, ◆ 318.15 K) IV; PA + ACT (□ 298.15 K, △ 308.15 K, ◊ 318.15 K) V; BA + ACT (⬤ 298.15 K, × 308.15 K, + 318.15 K) VI calculated from (7).Figure 7
Plot ofσE versus x1 for EA + BEN (■ 298.15 K, ▴ 308.15 K, ◆ 318.15 K) I; PA +BEN (□ 298.15 K, △ 308.15 K, ◊ 318.15 K) V; BA + BEN (⬤ 298.15 K, × 308.15 K, + 318.15 K) VI calculated from (8).Figure 8
Plot ofσE versus x1 for EA + ACT (■ 298.15 K, ▴ 308.15 K, ◆ 318.15 K) I; PA + ACT (□ 298.15 K, △ 308.15 K, ◊ 318.15 K) V; BA + ACT (⬤ 298.15 K, × 308.15 K, + 318.15 K) VI calculated from (8).Stevanovic et al. [14] have recently compared the available correlation models for liquid mixture viscosities of organic compounds. Amongst the available correlations for predicting the binary liquid mixture viscosity, the present experimental binary viscosity data was fitted to the following five correlations.McAllister's [15] model:
(11)lnηmix=x13lnη1+x23lnη2+3x12x2lnη12+3x1x22lnη21-ln[x1+x22(M2M1)]+x12x2ln[23+(M23M1)]+3x1x22ln[13+(2M23M1)]+x23ln(M2M1),
where η12 and η21 are interaction parameters.Heric [16] model:
(12)lnηmix=x1lnη1+x2lnη2+x1lnM1+x2lnM2-ln(x1lnM1+x1lnM2)+β12,
where β12 is a deviation function given by
(13)β12=x1x2[δ12+δ21(x1-x2)].
Here, δ12 and δ21 are interaction parameters.Auslander [17] model:
(14)x1(x1+B12x2)(ηmix-η1)+A21x2(B21x1+x2)(ηmix-η2)=0,
where B12, A21, and B21 are parameters representing binary interactions.Teja and Rice [18] model:
(15)ln(ηmixεmix)=x1ln(η1ε1)+x2ln(η2ε2),
where εi=Vci2/3/(TciMi)1/2 for i=1 or 2 component or the mixture
(16)VCmix=18[x12VC1+x22VC2+2x1x2(VC11/3+VC21/3)],Tcmix=1Vcmix[(Tc1Vc1Tc2VC2)1/2x12Tc1Vc1+x22Tc2Vc2+2x1x2φ12(Tc1Vc1Tc2VC2)1/2];η1 must be evaluated at a temperature T(Tc1/Tcmix) and η2 at a temperature T(Tc2/Tcmix). T is the system temperature and φ12 is an adjustable interaction parameter having a value unity. The interaction parameter has been shown to be independent of temperature and composition [19, 20]. The subscript c indicates a reduced quantity.Kubendran et al. model [21]:
(17)lnηmix=x1lnη1+x2lnη2+x1lnM1+x2lnM2-ln[x1M1+x2M2]-2.303x1x2[B12+C12(x1-x2)+D12(x1-x2)2],
where B12,  C12, and D12 are binary interaction constants.The observed data on surface tension of binary mixtures was fitted to the following models available in the literature.Zihao and Jufu model [22]:
(18)σmix=x1σ1x1+γ12x2+x2σ2x2+γ21x1,
where γ12 and γ21 are interaction parameters.Rice and Teja model [23]:
(19)σmixΦmix=x1σ1Φ1+x2σ2Φ2,
where Φi=Vci2/3/Tci for i=1 or 2 component or the mixture
(20)VCmix=18[x12VC1+x22VC2+2x1x2(VC11/3+VC21/3)],Tcmix=1Vcmix[(Tc1Vc1Tc2VC2)1/2x12Tc1Vc1+x22Tc2Vc2+2x1x2φ12(Tc1Vc1Tc2VC2)1/2].Here,σ1 is to be evaluated at a temperature = T(Tc1/Tcmix) and σ2 at a temperature = T(Tc2/Tcmix).  T is the system temperature and φ12 is an adjustable interaction parameter having a value around unity. The interaction parameter has been shown to be independent of temperature and composition [19, 20]. The subscript c indicates a reduced quantity.Empirical two-constant model [24]:
(21)σmix=x1σ1+x2σ2+x1x2[A′+B′(x1-x2)],
where A′ and B′ are binary interaction parameters.The model parameters of (11), and (13)–(21) were determined using nonlinear regression technique and the estimated values are reported in Table 5.Table 5
Interaction parameter/parameters for various models and standard deviation (SD) determined by least square method.
(a)
Model
Constants
Ethanoic acid (1) + benzene (2)
Propanoic acid (1) + benzene (2)
Butanoic acid (1) + benzene (2)
298.15 K
308.15 K
318.15 K
298.15 K
308.15 K
318.15 K
298.15 K
308.15 K
318.15 K
McAllister (11)
η
12
0.6336
0.5291
0.6408
0.8286
0.7390
0.8245
1.0808
0.9825
0.9409
η
21
0.5943
0.5347
0.3980
0.6163
0.5221
0.4268
0.7227
0.6129
0.6406
SD
0.0092
0.0161
0.0289
0.0105
0.0128
0.0128
0.0146
0.0108
0.0088
Heric (13)
δ
12
−0.8692
−0.8380
−0.4591
−0.2946
−0.2916
0.0521
−0.2445
−0.1271
0.4815
δ
21
−0.2173
−0.3069
0.4582
0.1763
0.2640
0.7480
0.1390
0.2814
0.2095
SD
0.1357
0.2015
0.3185
0.1524
0.2269
0.3356
0.3258
0.2169
0.2614
Krishnan and Laddha (17)
B
12
0.9275
0.9606
0.7031
0.3620
0.3859
0.0528
0.3173
0.1913
−0.5399
C
12
0.2536
0.3832
−0.3062
−0.1643
−0.2472
−0.7294
−0.1430
−0.2849
−0.2063
D
12
−0.4145
−0.8715
−1.7348
−0.4654
−0.6512
−0.7241
−0.5103
−0.4499
0.4099
SD
0.1468
0.1225
0.0701
0.0559
0.0502
0.0629
0.0595
0.0378
0.1101
Auslander (14)
B
12
−0.0168
−0.0901
0.0523
1.8404
1.4898
1.9109
3.9322
2.5479
0.1292
A
21
6.4585
8.2007
7.3214
6.5731
6.5502
5.6764
9.9261
6.0937
0.2803
B
21
0.4409
0.2966
−0.0996
0.0997
0.0271
−0.2735
0.0896
0.0999
1.7186
SD
0.0041
0.0116
0.0121
0.0043
0.0051
0.0038
0.0074
0.0048
0.0010
Teja and Rice (15)
φ
12
1
1
1
1
1
1
1
1
1
SD
0.0306
0.0224
0.0132
0.0101
0.0083
0.0131
0.0056
0.0139
0.0279
Zihao and Jufu (18)
γ
12
0.9377
0.9099
0.8985
0.9431
0.9413
0.9016
0.9343
0.8178
0.8038
γ
21
1.0684
1.1008
1.1162
1.0624
1.0636
1.1114
1.0709
1.2259
1.2473
SD
0.0081
0.0055
0.0049
0.0252
0.0256
0.0071
0.0858
0.0193
0.0111
Two-parameter model (21)
A
′
0.0302
0.0304
0.0305
−0.0053
−0.0056
−0.0069
−0.0121
−0.0118
0.0079
B
′
0.0072
0.0061
0.0057
0.0061
0.0052
0.0038
0.0067
0.0096
0.0079
SD
0.0023
0.0019
0.0024
0.0055
0.0079
0.0023
0.0088
0.0088
0.0041
Rice and Teja (19)
φ
12
1
1
1
1
1
1
1
1
1
SD
0.0643
0.0128
0.0039
0.1423
0.1183
0.1183
0.2210
0.1862
0.1874
(b)
Model
Constants
Ethanoic acid (1) + acetophenone (2)
Propanoic acid (1) + acetophenone (2)
Butanoic acid (1) + acetophenone (2)
298.15 K
308.15 K
318.15 K
298.15 K
308.15 K
318.15 K
298.15 K
308.15 K
318.15 K
McAllister (11)
η
12
1.6072
1.4795
1.3403
1.5061
1.4196
1.3377
1.7139
1.6209
1.3511
η
21
1.6910
1.4186
1.1794
1.7024
1.5097
1.3028
1.7471
1.6208
1.5934
SD
0.0006
0.0006
0.0069
0.0034
0.0071
0.0082
0.0013
0.0034
0.0120
Heric (13)
δ
12
0.7141
0.9027
1.2314
0.6855
0.9560
1.3476
0.2817
0.7089
1.2371
δ
21
0.1271
0.2502
0.3406
0.0584
0.1214
0.1976
0.0134
0.0417
−0.2198
SD
0.3671
0.1578
0.2654
0.3963
0.1814
02120
0.6821
0.3761
0.0201
Krishnan and Laddha (17)
B
12
−0.7161
−0.9048
−1.1986
−0.6742
−0.9286
−1.3101
−0.2854
−0.7014
−1.1893
C
12
−0.1293
−0.2525
−0.3052
−0.0511
−0.1036
−0.1733
−0.0147
−0.0392
0.2360
D
12
0.0149
0.0160
−0.2399
−0.0803
−0.1955
−0.2679
0.0262
−0.0528
−0.3361
SD
0.3071
0.3478
0.4162
0.2904
0.3731
0.4819
0.1301
0.3097
0.4936
Auslander (14)
B
12
−0.0265
−0.8582
−3.1960
−0.1986
−0.9382
−3.3948
−1.9043
−7.8002
−21.0019
A
21
1.5819
2.0665
1.2531
0.5603
0.6151
0.9108
1.2163
1.0309
0.5851
B
21
1.2206
1.3443
4.5532
3.3567
4.7933
6.0789
2.8998
9.5205
39.1308
SD
0.0002
0.0008
0.002
0.0002
0.0005
0.0001
0.0001
0.0026
0.0029
Teja and Rice (15)
φ
12
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
SD
0.0284
0.0070
0.0146
0.0029
0.0324
0.0411
0.0826
0.0137
0.0178
Zihao and Jufu (18)
γ
12
0.8333
0.9319
0.8198
0.4586
0.4317
0.3288
1.2367
1.2653
1.3189
γ
21
1.0468
0.9544
1.0082
1.5047
1.5256
0.4304
0.8074
0.7899
0.7593
SD
0.0779
0.0395
0.0405
0.0474
0.0465
0.2786
0.1261
0.1209
0.1292
Two-parameter model (21)
A
′
0.3968
0.4167
0.4557
0.3096
0.3329
0.3509
0.2215
0.2365
0.2478
B
′
0.0643
0.0865
0.0764
−0.0738
−0.0893
−0.1025
0.0989
0.1033
0.1075
SD
0.0666
0.0599
0.0402
0.0298
0.0403
0.0983
0.0493
0.0557
0.0513
Rice and Teja (19)
φ
12
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
SD
0.1802
0.1131
0.0764
0.2090
0.1756
0.1678
0.1604
0.1024
0.1126


## 4. Discussion

The values ofVE as illustrated in Figures 1 and 2 are positive for the entire concentration range at all the three temperatures for the systems EA + BEN, PA + BEN, and BA + BEN and negative for the remaining three systems. About 5% more negative or less positive VE values at higher temperatures for all the systems may be due to increased population of acid monomers to enter into the hetero-intermolecular interactions.The positive and negativeVE values may be explained by considering the following three steps equilibria accompanying the mixing process as proposed by Lark and Banipal [2]:
(22)D-M⟺D+M,(23)D⟺2M,(24)M+II⟺M—IIndcomponent(BENorACT),
where D and M denote a dimer and a monomer of the acid under question. The first process is accompanied with a large volume increase in the right direction; the second is isochoric; that is, the volume of the dimer is assumed to be equal to twice the value of the monomer [4, 5]; the third step is accompanied with large contraction in case of ACT and expansion in case of BEN. So the addition of ACT or BEN to anyone of the acids first creates monomers by the first two steps resulting in expansion. In the third step, stronger heteromolecular dipole-dipole interactions result in the observed negative VE in case of CA + ACT and positive VE values in the case of CA + BEN system due to induced dipole-dipole interactions. Therefore, the third step is accompanied with contraction in volume in case of ACT and expansion in case of BEN.ThepKa values of EA, PA, and BA are 4.76, 4.88, and 4.82, respectively. It is expected that the order of dimerization constants of various acids would increase in the same order. The increasing dimerization constant would lead to a smaller number of available monomers and thus to a smaller volume increase as described by (22).However, the observed order ofVE for the CA + BEN system is as follows: BA > PA > EA (Table 6). This shows that in case of BEN there are strong acid-solvent interactions which govern the magnitude and sign of VE, which increases as the inductive effect of alkyl chain of the acid as is also observed by Lark et al. [25]. Similar results were also obtained by  Venkateswarlu and Raman [26] as the positive excess volumes of 1,2-dichloroethane and 1,2-dibromoethane with three acids observe the following order: BA > PA > EA, which is the same as discussed above; that is, the increase in chain length of acid contributes to the decrease in excess volume. The large negative VE values in the case of CA + ACT mixture arise due to depolymerization of acid accompanied with strong hydrogen-bonded heterocomplex formation. However, in CA + ACT system, the VE values follow the order PA > BA > EA as was also observed by Lark et al. [25] in CA + MEOH system.Table 6
Comparison of excess volumeVE cm3 mol−1 of equimolar mixture at 298.15 K.
Component II
Component I
Ethanoic acid
Propanoic acid
Butanoic acid
Benzene
0.8514
0.3898
0.3316
Acetophenone
−0.2972
−0.5396
−0.5266The data presented in Figures3 and 4 reveal that excess viscosity (ηE) is positive for the systems EA + ACT, PA + ACT, and BA + ACT, and is negative for the systems EA + BEN, PA + BEN, and BA + BEN at 298.15 K. The algebraic positive values of ηE may be represented in the following order: PA + ACT > EA + ACT > BA + ACT > BA + BEN > PA + BEN > EA + BEN. The sign and magnitude of ηE depend on the combined effect of the factors such as molecular size, shape, and intermolecular forces. The positive value of ηE for the CA + ACT system suggests that the viscosity of the mixture is higher than that of the pure components and hence the fluidity of the mixture is low. This indicates the presence of a specific interaction such as the formation of charge-transfer complex between unlike molecules. The negative value of ηE in the systems EA + BEN, PA + BEN, and BA + BEN suggests the mutual loss of a specific interaction in like molecules that outweigh the specific interaction between unlike molecules. The positive values of ηE increase with the increase in temperature in all these systems. The GE values almost observe the similar trend as observed by ηE as shown in Figures 5 and 6.The variation of Grunberg and Nissan parameter “d” with composition of a particular mixture is not large. The values of “d” are negative for CA + BEN system and positive for CA + ACT system for most of the concentration range. The positive values of “d” for CA + ACT system show that CA forms an intermolecular complex with ACT in the liquid phase. The values of “d” increase with the increase in temperature in all the systems showing that the interactions between the components increase with the increase in temperature. Even the negative values of “d” for CA + BEN system change their sign from negative to positive with the increase in temperature from 298.15 to 318.15 K.According to Hildebrand [27], free volume is necessary for flow and then shrinkage on mixing (which would reduce the free volume) would be associated with increase in viscosity of the system. If H is defined as η/ηo, where η is the experimental viscosity of the mixture and ηo is the ideal viscosity, calculated using
(25)ηo=x1lnη1+x2lnη2,
then this quantity could be related to free volume (Vo) of the solution according to Stairs [28] by the following equation:
(26)H-1=1Vo(Vo+VE).According to (26), a plot of H-1 versus VE should be linear. However, when H-1 is plotted against VE, a nonlinear plot was obtained in the present study. However, when lnH is plotted against GE, a single straight line with a nonzero intercept was obtained in Figure 9. This type of result is not unexpected, because the expression for GE takes into account both viscosity and volume. Also, in all these systems, positive ηE and negative VE and vice versa have been observed for most of the concentration range. This behaviour was also observed by Palepu et al. [29] in binary mixtures o-chlorophenol with substituted anilines.Figure 9
Plot oflnH versus GE (■ EA + BEN, ◆ PA + BEN, ▴ BA+ BEN, × EA + ACT, ⬤ PA + ACT, + BA + ACT) at 298.15 K.From the literature, no clear cut theoretical basis has been proposed for the prediction of nonideal behaviour of the binary mixtures in terms of theirσE values. However, recently, Papaioannou and Panayiotou [30] have correlated the sign of σE values with ηE values and the deviations from Raoult's law. Their observation reveals the following.(1)
Corresponding to the positive enthalpies of mixing(HE), positive volume of mixing (VE) and positive deviations from Raoult's law, σE values, have been observed to be negative.(2)
Corresponding to the negative enthalpies of mixing(HE), negative volume of mixing (VE) and negative deviations from Raoult's law, σE values have, been observed to be positive. As shown in Figures 7 and 8, the excess surface tension (σE) values are negative for CA + BEN system and are positive for CA + ACT system. The positive values of excess surface tension (σE) increase with the rise in temperature in all systems. The negative value of σE in CA + BEN system is due to the predominance of the following factors: homopolymer complex formation and the tendency of the component with lower surface tension to be adsorbed at the interface. But in CA + ACT system complex formed are block copolymer [CA]n[ACT]m and also dipole-dipole interactions between carboxylic functional group of CA and carbonyl group of ACT in the bulk phase rather than in the interface.The interaction parameters of various models used can change with temperature but not with composition, but the interaction parameterφ12 in Rice and Teja and Teja and Rice models, based on the theory of corresponding states, has been shown to be independent of temperature and composition [19, 20]. It is observed that the models of McAllister, Auslander, and Teja and Rice fit  the experimental viscosity data very well as compared to the Heric and Krishnan and Laddha models. Surface tension data is well predicted by the empirical two-parameter model [21] as well as by Rice and Teja model. The Zihao & Jufu model, based on the work of Hildebrand & Scott [31], also predicts satisfactory results for the systems studied.



---

*Source: 612837-2013-08-27.xml*