Prediction of excess molar volumes of binary mixtures of organic

Chemical Papers 62 (3) 302–312 (2008) DOI: 10.2478/s11696-008-0027-x

ORIGINAL PAPER

Prediction of excess molar volumes of binary mixtures of organic compounds from refractive indices‡ Ivona R. Radovi´ c, Mirjana Lj. Kijevčanin*, Marijan Z. Gabrijel, Slobodan P. Šerbanovi´ c, Bojan D. Djordjevi´ c Department of Chemical Engineering, Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11120 Belgrade, Serbia Received 30 March 2007; Revised 31 August 2007; Accepted 10 October 2007

The excess molar volumes of 51 binary mixtures containing diverse groups of organic compounds: alcohols (methanol, ethanol, propan-1-ol, butan-1-ol, pentan-1-ol, hexan-1-ol, and heptan-1-ol), (cyclo-) alkanes (hexane, heptane, octane, nonane, decane, undecane, dodecane, and cyclohexane), esters (diethyl carbonate and ethyl chloroacetate), aromatics (o-xylene, m-xylene, p-xylene, and ethylbenzene), ketones (acetone), and ethers (anisole), were predicted from the refractive index data, using three types of equations coupled with several different mixing rules for refractive index calculations: the Lorentz–Lorenz, Dale–Gladstone, Eykman, Arago–Biot, Newton, and the Oster. These systems were chosen since they belong to different classes of organic species forming molecular interactions and intermolecular forces during mixing resulting in positive or negative, smaller or larger deviations from ideal behaviour. The obtained results were analysed in terms of the applied equation and mixing rule, the nature of compounds of the mixtures and the influence of alkyl chain length of the alkane or alcohol molecule. c 2008 Institute of Chemistry, Slovak Academy of Sciences Keywords: excess molar volume, refractive index, prediction, binary systems

Introduction The knowledge of thermophysical properties (volumetric properties, refractive index, viscosity, etc.) of pure organic compounds and their mixtures is very important. It is required for a full understanding of non-ideal behaviour of mixtures, caused by molecular interactions and intermolecular forces occurring when two or more components are mixed, as well as for the design of processes and process equipment. Many papers on experimental data of densities and refractive indices of binary mixtures have appeared in the last years. Due to the fact that the experimental technique for refractive indices determination, in a wide range of temperatures, is relatively simple, refractive indices of liquids are frequently interrelated

using various empirical relationships with other properties, e.g. density, static relative permittivity, surface tension, internal pressure, transport properties, etc. (Brocos & Amigo, 2005). Besides, several mixing rules (Heller, 1965; Pi˜ neiro et al., 1999) allow a relatively accurate prediction of excess molar volume from refractive indices or prediction of refractive indices from the density of multicomponent mixtures (Nakata & Sakurai, 1987; Arancibia & Katz, 1993; Pi˜ neiro et al., 2000; Fontao & Iglesias, 2002; Brocos et al., 2003; Tasić et al., 1999). A possibility to predict the excess molar volume (V E ) from the refractive index (n) data at 298.15 K and atmospheric pressure was investigated for a set of 51 binary mixtures. The binary systems containing alcohols (methanol, ethanol, propan-1-ol, butan-1-

*Corresponding author, e-mail: [email protected] ‡ Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.

303

I. R. Radović et al./Chemical Papers 62 (3) 302–312 (2008)

ol, pentan-1-ol, hexan-1-ol, heptan-1-ol), (cyclo-) alkanes (hexane, heptane, octane, nonane, decane, undecane, dodecane, cyclohexane), esters (diethyl carbonate, ethyl chloroacetate), aromatics (o-xylene, mxylene, p-xylene and ethylbenzene), ketones (acetone), and ethers (anisole) were chosen, due to their: i) structural variety causing non-ideal behaviour in mixtures (mixtures exhibiting positive, negative, and S-shaped V E vs. composition curves), ii) industrial importance. For the prediction of V E from n data, three types of equations were tested: i) equation proposed by Nakata and Sakurai (1987), based on the use of mass-fractionbased mixing functions, first time applied in the work of Arancibia and Katz (1993) (Eq. I), ii) equation obtained by the first order expansion of Eq. I (Nakata & Sakurai, 1987) (Eq. II), and iii) a particular case of Eq. II developed for iso-refractive mixtures (Nakata & Sakurai, 1987) (Eq. III), coupled with different mixing rules for the refractive indices: the Lorentz–Lorenz, Dale–Gladstone, Eykman, Arago–Biot, Newton, and the Oster (Pi˜ neiro et al., 1999).

Theoretical Equation establishing the relation between V E and n data of mixtures, based on the use of a massfraction-based mixing function for the specific refraction f (n)/ρ, and the definition of excess molar volume (Eq. I) could be written as 2

f (n) f (ni ) = wi ρ ρi i=1 VE =

2 i=1

(f (ni ) − f (n))

(1) xi Vi f (n)

(2)

where wi , ρi , ni and xi are the mass fraction, density, refractive index, and mole fraction of component i, respectively, f (ni ) and f (n) represent functions of the refractive index of pure component i and of a mixture and Vi is the pre-mixing molar volume of component i. Typical f (n) equations are (Pi˜ neiro et al., 1999) the Lorentz–Lorenz (L-L, n2 − 1 / n2 + 2 ), Dale– Gladstone (D-G, n − 1), Eykman (Eyk, n2 − 1 / 2 (n + 0.4)), Arago–Biot (A-B, Newton n), 2 (New, n − 2 2 1), and Oster (Os, (n − 1) 2n + 1 /n ) ones. Considering V E in Eq. (2) as a function of n and expanding to the first order (Nakata & Sakurai, 1987) at nφ = n1 φ1 + n2 φ2 , affords Eq. II for the excess molar volume calculation 2 f (ni ) E −1 − V = xi Vi f (nφ ) i=1 2 f (nφ ) xi Vi f (ni ) (3) − ∆φ n 2 f (nφ ) i=1

where f (nφ ) is the function of the refractive index of a mixture as in Eq. (2), f (nφ ) denotes the value of the first derivative of f (nφ ) and ∆φ n represents the deviation of the refractive index values of a binary mixture from ideal binary mixture ∆φ n = n − (n1 φ1 + n2 φ2 )

(4)

where n1 and n2 are the refractive indices, and φ1 and φ2 are the components volume fractions based on the molar volumes of pure components. Furthermore, for iso-refractive mixtures, when n1 = n2 , Eq. (3) is reduced to (Nakata & Sakurai, 1987) 2 f (n1 ) E (5) xi Vi V = −∆φ n f (n1 ) i=1 where f (n1 ) represents the function of the refractive index and f (n1 ) denotes the value of the f (n1 ) derivative as in the above equations. In further text Eq. (5) is assigned as Eq. III for calculation of the mixture excess molar volume.

Results and discussion The prediction of V E from n data at 298.15 K and atmospheric pressure was carried out for 51 binary systems for which experimental data were taken from literature (Touri˜ no et al., 2004; Orge et al., 1997; Casas et al., 2002; Rodriguez et al., 2001, 2003; Nayak et al., 2001; Diaz et al., 2001; Al-Jimaz et al., 2005; Iglesias et al., 2000), using the three chosen model Eqs. I, II, and III with incorporated L-L, D-G, Eyk, A-B, New, and Os mixing rules for refractive indices determination. The results of V E calculation were assessed by the absolute maximum percentage average deviation PDmax

N E E

− Vcal 100

Vexp

PDmax = (6)

E

Vexp

N max

i=1

i

E E where Vexp and Vcal represent the experimental and E calculated V values, respectively, EN is the number of experimental data points, while Vexp denotes the max absolute maximum value of experimental VE . The second criterion for V E prediction quality was the rootmean-square deviation σ, defined as

⎛ N

⎜ i=1 σ=⎜ ⎝

E Vexp,i

−

N

E Vcal,i

1/2 2 ⎞

⎟ ⎟ ⎠

(7)

The results and literature sources are summarised in Table 1 and graphically presented in Figs. 1–6. Analysis of the results was carried out for seven groups of binary systems.

304


Table 1. Absolute maximum percentage average deviation, PDmax , and root-mean-square deviations, σ, from the prediction results of the investigated binary mixtures for different equations Model System

Reference

Equation

Error L-L

D-G

Eyk

A-B

New

Os

25.9 0.029 42.0 0.079 60.2 0.158 38.4 0.166 13.4 0.064 13.5 0.065 12.6 0.063

HVa 26.7 0.030 43.4 0.082 62.7 0.165 41.3 0.179 12.8 0.065 12.9 0.065 16.8 0.079

25.2 0.029 41.5 0.078 60.0 0.158 38.8 0.168 12.3 0.062 12.4 0.062 14.2 0.069

37.7 0.045 30.8 0.059 25.6 0.075 32.3 0.153 46.0 0.202 46.0 0.202 45.7 0.201

28.6 0.033 46.9 0.088 67.4 0.178 46.2 0.201 14.0 0.073 14.1 0.073 25.4 0.119

25.2 0.029 41.9 0.079 61.3 0.162 25.9 0.117 12.8 0.066 15.6 0.075 12.0 0.061

PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ

33.3 0.165 32.6 0.161 35.2 0.184 8.5 0.046 8.2 0.046 8.2 0.044 12.0 0.059 11.9 0.059 13.4 0.054 33.2 0.105 33.2 0.105 30.3 0.115

39.2 0.209 38.5 0.204 41.0 0.224 11.2 0.060 10.9 0.058 12.8 0.070 16.3 0.065 16.0 0.064 17.7 0.067 29.5 0.107 29.4 0.106 31.1 0.127

36.2 0.186 35.5 0.182 37.5 0.202 9.8 0.047 9.5 0.046 10.1 0.055 14.0 0.058 13.8 0.058 15.4 0.059 30.3 0.104 30.3 0.104 30.2 0.120

43.5 0.203 43.6 0.203 43.2 0.201 46.9 0.227 46.6 0.227 46.2 0.225 44.5 0.167 44.5 0.167 44.2 0.166 53.9 0.152 53.9 0.152 53.4 0.150

50.8 0.282 49.9 0.277 51.5 0.289 22.0 0.122 21.5 0.119 22.6 0.119 27.4 0.108 27.0 0.106 24.5 0.096 35.9 0.130 35.8 0.129 36.7 0.150

41.8 0.228 41.0 0.223 43.3 0.238 13.7 0.076 13.3 0.074 14.7 0.081 19.7 0.075 19.4 0.074 19.3 0.072 31.3 0.112 31.1 0.111 32.1 0.132

PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ

25.6 0.081 25.5 0.081 25.5 0.113 18.5 0.051 18.5 0.051 13.9 0.039

23.3 0.096 23.2 0.096 26.2 0.130 15.1 0.046 15.1 0.046 18.2 0.049

24.0 0.088 24.0 0.088 25.5 0.121 16.5 0.045 16.4 0.045 15.9 0.043

35.6 0.098 35.6 0.098 35.0 0.096 41.4 0.116 41.4 0.116 40.7 0.114

29.9 0.129 29.8 0.128 32.7 0.159 25.4 0.071 25.3 0.071 25.3 0.070

24.8 0.106 23.4 0.087 25.4 0.089 16.6 0.052 13.3 0.039 12.6 0.037

Alkane + alkane Hexane(1) + heptane(2) Hexane(1) + octane(2)b

II

Hexane(1) + nonane(2)b

II

Hexane(1) + decane(2)b Hexane(1) + undecane(2)b

Touri˜ no et al. (2004)

II II

Hexane(1) + dodecane(2)

I II III

PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ Alcohol + alkane

Methanol(1) + pentane(2)

I II III

Methanol(1) + hexane(2)

I II III

Methanol(1) + heptane(2)

Orge et al. (1997)

I II III

Methanol(1) + octane(2)

I II III

Methanol(1) + nonane(2)

I II III

Methanol(1) + decane(2)

I II III

305


Table 1. (continued) Model System

Methanol(1) + undecane(2)

Reference

Casas et al. (2002)

Equation

I II III

Methanol(1) + dodecane(2)

I II III

Ethanol(1) + pentane(2)

I II III

Ethanol(1) + hexane(2)

I II III

Ethanol(1) + heptane (2)

Orge et al. (1997)

I II III

Ethanol(1) + octane(2)

I II III

Propan-1-ol(1) + pentane(2)

I II III

Propan-1-ol(1) + hexane(2)

I II III

Propan-1-ol(1) + heptane(2)

Orge et al. (1997)

I II III

Propan-1-ol(1) + octane(2)

I II III

Error L-L

D-G

Eyk

A-B

New

Os

PDmax σ PDmax σ PDmax RMSD PDmax σ PDmax σ PDmax σ

55.3 0.169 55.4 0.169 53.2 0.176 20.0 0.045 20.0 0.045 14.4 0.032

51.7 0.167 51.7 0.167 54.7 0.182 16.4 0.036 16.4 0.036 16.9 0.033

52.0 0.166 52.0 0.166 53.9 0.179 16.8 0.039 16.8 0.039 15.5 0.032

54.9 0.141 55.0 0.141 55.1 0.142 36.8 0.066 36.8 0.066 36.4 0.065

56.0 0.169 56.0 0.169 58.5 0.194 23.5 0.040 23.5 0.039 21.1 0.036

52.1 0.165 49.0 0.158 52.9 0.165 17.8 0.035 13.9 0.033 14.0 0.035


20.8 0.069 20.9 0.069 21.4 0.071 5.2 0.030 5.5 0.030 3.8 0.025 8.3 0.053 8.6 0.053 5.3 0.040 5.0 0.029 5.1 0.030 7.9 0.046

15.8 0.052 15.9 0.053 16.4 0.054 6.5 0.031 6.3 0.030 7.1 0.035 8.1 0.044 7.8 0.043 9.7 0.049 11.1 0.062 10.7 0.060 16.1 0.088

18.4 0.061 18.5 0.061 18.9 0.063 4.2 0.025 4.0 0.025 4.9 0.025 5.5 0.042 5.5 0.042 7.0 0.041 6.9 0.038 6.6 0.037 11.7 0.065

53.9 0.178 54.0 0.178 54.0 0.178 47.0 0.217 47.0 0.217 46.9 0.217 51.0 0.252 51.0 0.252 50.7 0.251 47.9 0.255 47.9 0.255 47.5 0.253

8.3 0.030 8.4 0.030 9.0 0.032 14.8 0.076 14.4 0.074 15.2 0.079 17.6 0.093 17.3 0.092 17.5 0.096 28.0 0.149 27.6 0.146 29.0 0.155

13.9 0.046 14.0 0.047 14.5 0.048 8.6 0.042 8.3 0.040 8.9 0.045 11.0 0.055 10.7 0.054 11.7 0.060 16.5 0.089 16.1 0.088 19.4 0.106


116.1 0.151 116.4 0.151 103.8 0.134 19.2 0.052 19.2 0.052 19.7 0.053 4.8 0.018 4.9 0.018 4.7 0.018 7.2 0.032 7.1 0.031 8.9 0.040

120.7 0.159 121.1 0.159 116.9 0.153 13.6 0.041 13.6 0.041 14.5 0.043 6.9 0.025 6.8 0.025 7.0 0.026 15.4 0.069 15.2 0.068 16.9 0.076

117.3 0.153 117.7 0.154 110.5 0.143 16.2 0.046 16.3 0.046 17.1 0.047 4.1 0.017 4.0 0.016 4.2 0.017 11.2 0.050 11.0 0.049 12.8 0.058

40.2 0.058 40.2 0.058 40.2 0.058 48.8 0.131 48.8 0.131 48.9 0.131 47.3 0.170 47.3 0.170 47.3 0.170 45.7 0.185 45.7 0.185 45.6 0.184

128.4 0.173 128.9 0.173 136.1 0.181 11.6 0.036 11.6 0.036 11.7 0.036 16.6 0.064 16.4 0.063 16.6 0.064 29.7 0.127 29.4 0.125 30.6 0.131

120.8 0.160 121.2 0.160 122.4 0.161 12.5 0.038 12.5 0.038 12.9 0.040 9.5 0.036 9.4 0.035 9.6 0.036 19.6 0.086 19.3 0.085 20.7 0.091

306



Reference

Equation

Error L-L

D-G

Eyk

A-B

New

Os


5.9 0.038 5.7 0.037 5.3 0.035 6.6 0.055 6.9 0.057 6.6 0.055 4.4 0.058 4.6 0.059 3.9 0.049 10.2 0.144 9.4 0.133 16.4 0.221

13.6 0.080 13.4 0.079 12.3 0.073 3.8 0.033 3.7 0.031 3.7 0.032 7.0 0.070 6.7 0.067 7.3 0.075 22.6 0.291 21.7 0.279 26.7 0.341

9.8 0.059 9.5 0.057 8.6 0.053 3.4 0.033 3.5 0.034 3.4 0.033 5.1 0.051 4.9 0.050 5.1 0.051 16.8 0.224 16.0 0.212 21.6 0.282

37.6 0.231 37.6 0.231 37.7 0.231 47.3 0.389 47.3 0.390 47.3 0.389 45.2 0.437 45.2 0.438 45.1 0.437 41.5 0.478 41.6 0.479 41.2 0.474

25.2 0.148 24.9 0.146 23.4 0.137 11.4 0.109 11.1 0.105 11.3 0.107 16.2 0.171 15.8 0.166 16.6 0.174 40.8 0.505 39.7 0.490 41.8 0.519

16.9 0.099 16.7 0.098 15.5 0.091 4.8 0.050 4.6 0.047 4.7 0.049 9.4 0.097 9.0 0.094 9.8 0.101 28.7 0.363 27.8 0.350 31.0 0.392

PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ

13.6 0.055 27.6 0.178 15.1 0.152 15.2 0.153 16.4 0.162 7.3 0.090 7.2 0.088 7.6 0.090 15.4 0.173 15.4 0.173 15.7 0.180 9.1 0.129 9.4 0.133 9.5 0.134

21.3 0.074 42.4 0.256 15.9 0.140 15.8 0.140 16.0 0.144 15.5 0.166 15.0 0.161 12.8 0.147 15.8 0.169 15.7 0.167 16.0 0.169 6.1 0.115 5.9 0.111 6.0 0.111

14.0 0.058 35.0 0.220 14.8 0.139 14.6 0.139 15.3 0.148 10.3 0.125 9.8 0.121 8.5 0.113 15.6 0.164 15.5 0.163 15.9 0.167 6.3 0.103 6.4 0.103 6.5 0.104

40.5 0.129 36.8 0.236 54.9 0.447 55.0 0.448 55.2 0.450 47.5 0.481 47.5 0.481 47.7 0.483 55.3 0.547 55.3 0.547 55.4 0.548 51.1 0.698 51.1 0.698 51.1 0.698

51.2 0.154 65.7 0.377 23.0 0.203 22.6 0.200 20.1 0.179 31.4 0.311 30.8 0.304 27.8 0.278 23.6 0.247 23.2 0.242 22.5 0.233 18.2 0.256 17.6 0.248 17.4 0.246

22.8 0.077 35.5 0.226 17.1 0.154 15.3 0.144 15.3 0.147 20.6 0.211 9.4 0.121 8.8 0.117 18.1 0.187 15.8 0.166 15.9 0.167 9.0 0.151 6.3 0.103 6.3 0.103

16.9 0.223 17.3 0.228

8.3 0.126 8.6 0.129

11.8 0.166 12.2 0.170

51.5 0.659 51.6 0.659

10.6 0.142 10.2 0.136

7.2 0.102 13.3 0.177

Ester + alkane Diethyl carbonate(1) + hexane(2)

I II III

Diethyl carbonate(1) + heptane(2)

I II III

Diethyl carbonate(1) + octane(2)

Rodriguez et al. (2003)

I II III

Diethyl carbonate(1) + cyclohexane(2)

I II III

Ethyl chloroacetate(1) + hexane(2)b Ethyl chloroacetate(1) + heptane(2) Ethyl chloroacetate(1) + octane(2)

II II I II III

Ethyl chloroacetate(1) + nonane(2)

I II Nayak et al. (2001)

Ethyl chloroacetate(1) + decane(2)

III I II III

Ethyl chloroacetate(1) + dodecane(2)

I II III

Ketone + alkane Acetone(1) + nonane(2)

I II

PDmax σ PDmax σ

307



Reference

Equation

III Acetone(1) + decane(2)

I II III

Acetone(1) + undecane(2)

Casas et al. (2002)

I II III

Acetone(1) + dodecane(2)

I II III

Error

PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ

L-L

D-G

Eyk

A-B

New

Os

9.4 0.133 25.2 0.336 25.5 0.340 17.2 0.229 27.6 0.365 27.9 0.369 18.6 0.247 39.9 0.619 40.0 0.620 31.8 0.514

5.9 0.085 16.1 0.222 16.4 0.226 11.6 0.162 18.0 0.247 18.3 0.251 13.2 0.187 31.5 0.518 31.6 0.519 28.6 0.478

6.7 0.103 20.1 0.271 20.4 0.275 14.4 0.196 22.2 0.296 22.5 0.300 16.0 0.217 34.9 0.558 35.0 0.559 30.1 0.496

51.2 0.654 53.1 0.703 53.1 0.703 52.8 0.698 53.3 0.711 53.3 0.711 52.9 0.706 56.7 0.792 56.7 0.793 56.4 0.789

10.1 0.139 7.1 0.108 7.0 0.108 5.4 0.093 9.9 0.144 9.8 0.144 8.2 0.133 24.0 0.395 24.0 0.396 25.7 0.429

14.3 0.187 11.7 0.170 19.9 0.264 21.3 0.282 13.0 0.194 20.7 0.274 22.6 0.296 27.2 0.464 31.9 0.510 34.4 0.543

15.6 0.023 15.6 0.023 13.5 0.020 16.7 0.048 16.8 0.048 16.7 0.048 23.2 0.074 23.3 0.074 21.4 0.069

13.0 0.022 13.0 0.022 13.1 0.022 11.0 0.033 11.1 0.034 11.1 0.034 16.3 0.057 16.4 0.057 15.5 0.055

13.5 0.021 13.5 0.021 13.2 0.021 13.7 0.040 13.8 0.041 13.8 0.040 19.5 0.064 19.6 0.064 18.4 0.061

41.6 0.060 41.7 0.060 41.7 0.060 49.6 0.130 49.6 0.130 49.6 0.130 54.5 0.169 54.5 0.169 54.5 0.169

22.0 0.035 21.9 0.035 17.3 0.030 5.6 0.016 5.7 0.016 5.7 0.016 11.9 0.043 11.9 0.043 11.8 0.043

14.1 0.025 14.1 0.025 13.6 0.024 9.1 0.028 9.2 0.028 9.1 0.028 13.1 0.050 13.2 0.050 13.1 0.050

8.2 0.060 8.0 0.058 13.3 0.090 21.5 0.186 21.6 0.187 17.8 0.160 13.8 0.100 13.4 0.098 20.3 0.136

7.4 0.050 7.5 0.051 8.4 0.061 27.0 0.223 27.2 0.224 20.1 0.176 7.8 0.058 7.6 0.056 15.1 0.103

46.7 0.308 46.7 0.3079 46.0 0.303 58.3 0.429 58.3 0.429 57.9 0.426 43.0 0.296 43.0 0.296 42.4 0.292

39.1 0.256 38.6 0.253 28.1 0.182 17.7 0.140 17.6 0.139 15.2 0.131 43.3 0.290 42.8 0.287 35.9 0.238

21.4 0.145 21.1 0.142 18.1 0.119 16.4 0.140 16.5 0.140 16.4 0.147 26.9 0.183 26.5 0.180 25.4 0.169

Ester + alcohols Diethyl carbonate(1) + ethanol(2)

I II III

Diethyl carbonate(1) + propan-1-ol(2)

I Rodriguez et al. (2001)

II III

Diethyl carbonate(1) + butan-1-ol(2)

I II III

PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ

Cyclohexane + aromatic hydrocarbon Cyclohexane(1) + o-xylene(2)

I II III

Cyclohexane(1) + m-xylene(2)

I II III

Cyclohexane(1) + p-xylene(2)

Rodriguez et al. (2001)

I II III

PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ PDmax σ

18.8 0.132 19.1 0.134 5.0 0.036 38.3 0.295 38.5 0.296 23.6 0.197 10.2 0.078 10.5 0.080 9.1 0.067

308



Reference

Cyclohexane(1) + ethylbenzene(2)

Equation

I II III

Error

PDmax σ PDmax σ PDmax σ

L-L

D-G

Eyk

A-B

New

Os

28.4 0.165 28.6 0.166 11.9 0.071

8.5 0.055 8.7 0.056 5.6 0.046

15.4 0.092 15.6 0.093 8.4 0.054

48.5 0.282 48.5 0.283 48.0 0.280

23.6 0.128 23.3 0.126 12.3 0.076

8.3 0.053 8.1 0.052 4.8 0.048

a) Excessively high errors for V E values; b) Results for Eqs. I and III were omitted due to excessively high errors for V E values.

Alkane + alkane systems In this group, 6 mixtures of hexane with alkanes (heptane, octane, nonane, decane, undecane, and dodecane) were investigated. For all systems, changes of refractive indices (∆n) were positive while excess molar volumes were negative in the whole composition range at 298.15 K, with exception of the system containing heptane which has very small positive V E values (Touri˜ no et al., 2004). These small V E values and the fact that changes of refractive indices and excess molar volumes have the opposite sign could explain the very high and unsatisfactory predicted V E values, which are not included in Table 1. For the remaining systems, as the chain length of the alkane molecule was increasing, absolute V E values became higher (Touri˜ no et al., 2004). Eq. II is the most successful equation in describing the variation of V E on basis of the refractive index while neither one mixing rule can be distinguished as the most superior. The possible explanation of the best results achieved for the system with dodecane might be the largest negative V E values and the most symmetric V E − x1 curve (Touri˜ no et al., 2004). Alkohol + alkane systems In this group of binary mixtures, three subgroups were examined: 8 systems containing methanol and alkane (pentane, hexane, heptane, octane, nonane, decane, undecane, and dodecane), 4 systems containing ethanol and alkane (pentane, hexane, heptane, and octane), and 4 systems containing propan-1-ol and alkane (pentane, hexane, heptane, and octane). For the investigated systems, the following observations of V E behaviour can be pointed out (Orge et al., 1997; Casas et al., 2002): i) for all three subgroups of the systems, V E values at 298.15 K were rising as the alkyl chain length was increasing and they were positive, except for the propan-1-ol + pentane system, for which the V E − x1 curve was S-shaped and negative at higher alcohol mole fractions and positive at low propan-1-ol content, ii) as the alcohol chain length increased (from methanol to propan-1-ol), the V E values were decreasing (comparison of the systems contain-

ing alcohol and pentane, or hexane, or heptane, or octane). Systems of methanol + alkanes (except the system with pentane) is characterised by partial miscibility (Orge et al., 1997; Casas et al., 2002) caused by the high difference of polarity and molecular volume and shape of the mixture components (Casas et al., 2002). This effect increases with the chain length in an alkane molecule. For these systems it was observed (Table 1) that the mixing rule influences the result quality more than the chosen excess molar volume equation: for lower alkanes (from pentane to heptane), the Lorentz– Lorenz mixing rule offers the most accurate results, while the Dale–Gladstone, Eykman, and Oster mixing rules gave the best and relatively similar results for the systems with the remaining alkanes. However, the results for all systems were considered unsatisfactory, and no general relation could be derived between the results quality and the alkyl chain length. Two additional groups of alcohol + alkane systems are typically miscible in the entire composition range. This could be the explanation of better results obtained for these groups of binary systems compared to those containing methanol. Table 1 shows that the poorest results were achieved for the systems alcohol + pentane. In case of the system comprising ethanol, this observation could be explained by the most asymmetric V E − x1 curve in comparison to the remaining ethanol + alkane systems and the opposite sign of the V E value and changes of the refractive index values (Orge et al., 1997). Considering the propan-1-ol + pentane system, the probable reason of the unsatisfactory fit of experimental data is the sigmoid shape of the V E − x1 curve (Orge et al., 1997). It is interesting that satisfactory results were obtained for the system propan-1-ol + octane employing Eq. II coupled with the L-L model, in spite of the fact that the ∆n − x1 curve has the sigmoid shape, changing the value from a negative to a positive one, while the V E −x1 curve is positive and almost symmetric. In almost all cases, the noticeable inferiority of the Arago–Biot mixing rule can be emphasized, which is also evident from Fig. 1, where the V E − x1 curves at 298.15 K are shown for the system ethanol + hexane using Eq. II coupled with all mixing rules.

309


0.6

1.5 D-G

5

0.4

1.2

6

L-L

-1 3

0.2 4

0.6

0.2

0.4

0.6

L-L

0.3

0.1 0.0 0.0

0.9

E

3 E

3

1

0.3

V /(cm mol )

2

-1

V /(cm mol )

0.5

0.8

1.0

0.0 0.0

0.2

0.4

0.6

0.8

1.0

x1

x1

Fig. 1. Experimental (symbols, Orge et al., 1997) and predicted (lines) V E for the ethanol(1) + hexane(2) system at 298.15 K using Eq. II and the L-L (line 1), D-G (line 2), Eyk (line 3), A-B (line 4), New (line 5), and Os (line 6) mixing rules.

Fig. 3. Experimental (symbols, Nayak et al., 2001) and predicted (lines, Eq. II coupled with the L-L or D-G mixing rules) V E for the: ( ) ethyl chloroacetate(1) + hexane(2), () ethyl chloroacetate(1) + nonane(2), and () ethyl chloroacetate(1) + dodecane(2) systems at 298.15 K.

1.5

VE/(cm3mol-1)

1.2 0.9 0.6 0.3 0.0 0.0

0.2

0.4

0.6

0.8

1.0

x1

Fig. 2. Experimental (symbols, Rodriguez et al., 2003) and predicted (lines, Eq. III coupled with the L-L mixing rule) V E for the: ( ) diethyl carbonate(1) + hexane(2), ( ) diethyl carbonate(1) + heptane(2), () diethyl carbonate(1) + octane(2), and () diethyl carbonate(1) + cyclohexane(2) systems at 298.15 K.

•

Table 1 and Fig. 2 show a good fit of the experimental data for all systems containing diethyl carbonate and alkane. It is evident that the applied equation for V E does not influence the fit quality. Thus, the quality of the excess molar volume prediction is principally influenced by the applied mixing rule for n. All results obtained by the Arago–Biot and Newton equation were found unsatisfactory, while successful prediction of the V E values was achieved applying the Lorentz–Lorenz (all ester + alkane systems studied) and Eykman mixing rule (system ester + heptane). For the systems containing ethyl chloroacetate and alkane, slightly poorer results were obtained. The exception were the systems containing nonane and dodecane (Fig. 3) using Eq. II coupled with the L-L or D-G mixing rules to predict the V E data. For these systems, inferiority of the Arago–Biot mixing rule is obvious. Ketone + alkane systems

Ester + alkane systems To this group, the diethyl carbonate + alkane (hexane, heptane, and octane), diethyl carbonate + cyclohexane, and ethyl chloroacetate + alkane (hexane, heptane, octane, nonane, decane, and dodecane) systems were included. For all systems containing diethyl carbonate or ethyl chloroacetate, positive deviation of the V E − x1 and negative deviations of the ∆n − x1 curves are characteristic with the respective maximum or minimum slightly shifted towards the alkane-rich region (Rodriguez et al., 2003; Nayak et al., 2001) (Figs. 2 and 3). Positive V E values and absolute changes of the refractive index values increased with the alkyl chain length (Figs. 2 and 3). For the systems comprising ethyl chloroacetate asymmetry of the V E − x1 curves disappeared when higher alkanes were the second component of the binary mixture (Fig. 3).

Four systems of acetone and alkane (nonane, decane, undecane, and dodecane) were investigated. Both, changes of refractive indices and excess molar volumes data, were positive for all systems in the whole composition range (Casas et al., 2002). Changes of the refractive indices values increased significantly with the increase of the alkyl chain length, while the influence of the alkyl chain length on the excess molar volume was almost negligible (Casas et al., 2002) (Fig. 4). This group of binary systems is specific in comparison to the previous groups, since the applied equation influences the calculated V E values considerably. Namely, Eq. III coupled with all mixing rules except with the Oster one, gave the best fit of experimental data. On the other hand, Table 1 shows a noticeable increase of the PDmax and σ values (except for the Newton mixing rule) with the increasing

310

I. R. Radović et al./Chemical Papers 62 (3) 302–312 (2008) 1.5

1.0 New

1.2

0.8

V /(cm mol )

-1

0.6

3

3

-1

V /(cm mol )

D-G 0.9

0.4

E

E

0.6 0.3 0.0 0.0

0.2

0.2

0.4

0.6

0.8

0.0 0.0

1.0

0.2

0.4

Fig. 4. Experimental (symbols, Casas et al., 2002)and predicted (lines, Eq. III coupled with the D-G or New mixing rules) V E for the: ( , —) acetone(1) + nonane(2), ( , – –) acetone(1) + decane(2), (, · · ·) acetone(1) + undecane(2), and (, − · −) acetone(1) + dodecane(2) systems at 298.15 K.

•

0.6

0.8

1.0

x1

x1

Fig. 5. Experimental (symbols) and predicted (lines, Eq. III coupled with the D-G mixing rule) V E for the: ( ) diethyl carbonate(1) + heptane(2) (Rodriguez et al., 2003) and ( ) diethyl carbonate(1) + propan-1-ol(2) (Rodriguez et al., 2001) systems at 298.15 K.

•

0.8

0.6

Ether + alkane systems The prediction of V E from the refractive index data at 298.15 K was performed for 6 binary mixtures containing anisole and alkane (hexane, heptane, octane, nonane, decane, and dodecane). Experimental changes of the refractive indices were negative for all systems, while excess molar volume data were positive for systems with higher alkanes (from nonane to decane), negative for the system with hexane, and for the system anisole + heptane, V E was changing from positive to negative values as the content of anisole was increasing (Al-Jimaz et al., 2005). The prediction of V E from the refractive index data was unsatisfactory (in most cases were the PDmax values above 100 %). Therefore, results for this group are not presented in Table 1. Alkane or ester + alkohol systems Three systems of hexane + alcohol (pentan-1-ol, hexan-1-ol, and heptan-1-ol) were investigated showing an opposite behaviour of the refractive indices and excess molar volumes with the change of the alcohol carbon chain length (Iglesias et al., 2000). While the values of V E were decreasing (becoming more negative), the refractive index values were increasing from negative values for the system hexane + pentan-1ol to positive ones for the hexane + heptan-1-ol system. The opposite behaviour and sigmoid shape of the V E −x1 and n−x1 curves could explain the unsatisfactory prediction of V E from the refractive index data. Therefore, the results are not presented in Table 1.

0.4

E

3

-1

V /(cm mol )

alkane chain length. For all ketone + alkane systems, the Arago-Biot mixing rule performed unsatisfactory, while good result were achieved employing the DaleGladstone and Newton mixing rules as shown in Fig. 4.

0.2

0.0 0.0

0.2

0.4

x1

0.6

0.8

1.0

Fig. 6. Experimental (symbols, Diaz et al., 2001) and predicted (lines, Eq. III coupled with the L-L mixing rule) V E for the: ( , —) cyclohexane(1) + o-xylene(2), ( , – –) cyclohexane(1) + m-xylene(2) and (, · · ·) cyclohexane(1) + p-xylene(2) systems at 298.15 K.

•

Three systems containing diethyl carbonate and alcohols (ethanol, propan-1-ol and butan-1-ol) show positive V E values while increasing the alkyl chain length of alcohols (Rodriguez et al., 2001) with considerable lower maxima compared to the systems of diethyl carbonate with alkanes (Fig. 5), and noticeable larger errors (Table 1). The exception is the system with propan-1-ol, where the Newton mixing rule and all applied equations for V E calculation worked very well. Cyclohexane + aromatic hydrocarbon systems Systems containing cyclohexane with xylene isomers (o-xylene, m-xylene, and p-xylene) and ethyl benzene showed positive V E values and relatively symmetric V E − x1 curves (Diaz et al., 2001) (Fig. 6). Refractive indices of mixtures containing xylene isomers showed a negative deviation from ideality, while those of the cyclohexane + ethyl benzene system ex-


hibited small positive values. It is evident that position of the two methyl groups in the xylene molecule exerts a large influence on the excess molar volume of the mixtures of xylenes with cyclohexane. For the systems with o-xylene and p-xylene, a relatively good fit of experimental data was obtained using Eq. III coupled with the L-L mixing rule and Eq. II coupled with the Eyk mixing rule, respectively, while for the system with m-xylene, presenting the most asymmetric shape of the V E − x1 curve, the results were unsatisfactory irrespective of the excess molar volume equation and mixing rule applied. As shown in Fig. 6, the V E − x1 curves obtained by Eq. III coupled with the L-L mixing rule does not fit the experimental data of the system cyclohexane + m-xylene, while a considerably better fit was obtained in case of the binary systems containing the two remaining xylene isomers. In addition, for this group of binary systems, the selection of equation applied to the V E calculations is of a great importance. Eq. III could be distinguished as the superior, except for the system comprising p-xylene. In case of the cyclohexane + ethylbenzene system, the best fit of experimental data was achieved employing Eq. III coupled with the Oster mixing rule.

Conclusions Based on the results obtained for the investigated binary systems, it can be concluded that: i) unsatisfactory fit of experimental data was achieved for systems exhibiting negative or small absolute V E values (alkane + alkane systems) and for systems exhibiting asymmetric or S-shaped experimental V E vs. composition curves (ethanol or propan-1-ol + pentane, hexane + alcohol systems); ii) regarding systems with symmetric and positive V E vs. composition curves, reasonable or very good fit of experimental data was obtained; iii) for almost all systems, the equation for V E calculation applied does not significantly influence the fit quality, except for the acetone + alkane and cyclohexane + aromatic hydrocarbon systems, for which Eq. III gave the best fit of experimental data; iv) the mixing rule used for refractive index calculations is of a great influence when comparing the fit quality. Although, none of the relations considered can be generally emphasized as superior, the Arago–Biot mixing rule offered the worst experimental data fit for a number of investigated systems. Acknowledgements. The authors gratefully acknowledge the financial support received from the Research Fund of the Ministry of Science and Environmental Protection of Serbia and the Faculty of Technology and Metallurgy, University of Belgrade (project No 142064).

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