(Solid + liquid) phase equilibria of binary mixtures containing N-methyl-2-pyrrolidinone and long-chain n-alkanols at atmospheric pressure

(Solid + liquid) phase equilibria of binary mixtures containing N-methyl-2-pyrrolidinone and long-chain n-alkanols at atmospheric pressure

Fluid Phase Equilibria 198 (2002) 1–14 (Solid + liquid) phase equilibria of binary mixtures containing N-methyl-2-pyrrolidinone and long-chain n-alka...

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Fluid Phase Equilibria 198 (2002) 1–14

(Solid + liquid) phase equilibria of binary mixtures containing N-methyl-2-pyrrolidinone and long-chain n-alkanols at atmospheric pressure U. Doma´nska∗ , J. Łachwa Faculty of Chemistry, Physical Chemistry Division, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland Received 6 April 2001

Abstract The (solid + liquid) equilibria for N-methyl-2-pyrrolidinone + n-alkanols (1-hexanol, or 1-heptanol, or 1-octanol, or 1-decanol, or 1-undecanol, or 1-dodecanol, or 1-tetradecanol) systems have been measured by a dynamic method for the whole concentration region x1 = 0–1. The experimental results have been correlated by four equations: Wilson, UNIQUAC ASM and two modified NRTL. The relative standard deviations of the solubility temperature correlation for all measured data vary from 0.1 to 1.4 K and depend on the particular equation used. In the calculations, the existence of two solid–solid first-order phase transitions in 1-tetradecanol has been taken into consideration. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Experimental; Solid–liquid equilibria; NMP; 1-Alkanols; Correlation; Wilson; UNIQUAC ASM; NRTL1; NRTL2

1. Introduction N-methyl-2-pyrrolidinone (NMP) is an aprotic and dipolar solvent of high selectivity. It has been used to extract aromatic hydrocarbons from coal tar [1] and petroleum [2,3] feedstocks. NMP is an electron donor and forms hydrogen bond association with the proton of the alkanol. The polymorphism, the melting and solid transition temperatures, and the associated enthalpy changes of the long-chain, normal primary alkanols have been a source of controversy for many decades. The solid–solid transformations for long-chain compounds are often slow, and the different solid phases can coexist for hours and longer. These substances are very hygroscopic. It was observed by Kuchhal et al. [4] that the transition temperature is lowered significantly in the presence of water and the melting point is increased compared with that of the corresponding anhydrous alkanols. Even small amounts of organic impurity tend to kinetic and/or thermodynamic stabilisation of phases that are thermodynamically unstable ∗

Corresponding author. Tel.: +48-22-6213115; fax: +48-22-6282741. E-mail address: [email protected] (U. Doma´nska). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 1 ) 0 0 7 5 2 - X

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in the pure compound. Through X-ray diffraction investigations, the observations of cooling curves and the values of dielectric constants, as well as differential scanning calorimetry (DSC) studies, at least three crystal forms for higher normal alkanols have been discovered. These include two forms (␤ and ␥) which are stable or metastable at lower temperatures and a waxy phase (α), which is stable till to the melting point. Meyer and Reid [5] studies dimorphism in alcohols C10 –C18 . Hoffman and Smyth [6] observed transitions in a number of n-alcohols (C12 , C14 , C18 and C22 ) during dielectric and thermal studies, with emphasis on the status of molecular rotation about the long axis. The transition points of even alcohols from C12 to C34 have been obtained by Watanabe [7] by thermal and X-ray studies. The solubilities of NMP in various solvents (e.g. aromatic hydrocarbons, chlorohydrocarbons, and alcohols) have been reported in the literature [8–17]. The present work forms the next part of a study into the physicochemical properties of binary mixtures involving N-methyl-2-pyrrolidinone [17,18]. Here, we continue our experimental work extending the available database on systems with NMP with solid–liquid equilibria measurements for mixtures containing NMP and long-chain n-alkanols (1-hexanol, 1-heptanol, 1-octanol, 1-decanol, 1-undecanol, 1-dodecanol and 1-tetradecanol). In this work, the results of the correlation of the solubility of NMP in various solvents with respect to the solid–solid phase transition in 1-tetradecanol are given in terms of Wilson equation [19], UNIQUAC associated-solution model (ASM) [20] and two modification of NRTL equation: NRTL1 and NRTL2 [21], utilising parameters taken from solid–liquid equilibrium.

2. Experimental 2.1. Materials The origins of the chemicals (in parentheses Chemical Abstracts registry number) are NMP (Aldrich, 99, 5% anhydrous), 1-hexanol (Reachim), 1-heptanol (Reachim), 1-octanol (Reachim), 1-decanol (Reachim), 1-undecanol (FLUKA AG) 1-dodecanol (FLUKA AG) and 1-tetradecanol (FLUKA AG). All liquid compounds were fractionally distilled under atmospheric pressure after prolonged reflux over different drying reagents and were stored over freshly activated molecular sieves of type 4A (Union Carbide). The solid chemicals were recrystallised repeatedly from n-hexane. The physical properties of the pure compounds are listed in Table 1. 2.2. Apparatus and procedure The solid–liquid equilibrium temperatures were determined using a dynamic method described in detail previously [32]. The appropriate mixtures of the solute and solvent were heated very slowly (at less than 2 K h−1 near the equilibrium temperature) with continuous stirring inside Pyrex glass cell, which was placed in a glass thermostat filled with acetone and dry ice. Increasing temperature was controlled as a step by step procedure. The weight of the sample was changing from point to point with the addition of the solvent. The weight of solute was constant and the amount of solute was about 0.5 × 10−3 kg. The temperature at which the last crystals disappeared was taken as the temperature of the (solid + liquid) equilibrium. The crystal disappearance temperatures, detected visually, were measured with a platinum resistance thermometer, Gallenkamp Autotherm II, produced by Sanyo Gallenkamp PLC, Leicester, UK.

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Table 1 Physical constants of pure compounds: V, molar volumes; Tf , melting temperature; Hf , enthalpy of fusion; Cp f , heat capacity change between the solid and liquid at the melting point; K, association constant and hA , enthalpy of hydrogen-bonding formation Component NMP 1-Hexanol 1-Heptanol 1-Octanol 1-Decanol 1-Undecanol 1-Dodecanol 1-Tetradecanol

V298.15 (cm3 mol−1 ) 96.43b 125.30g 141.90g 158.50g 191.60g 208.10g 224.70g 257.80g

expt

Tflit (K)

Tf

250.09c , 249.68d , 248.70e 225.80h 240.40i 258.35j 280.15l 284.15m 296.95l 311.15l

249.68

12f

226.55 238.62 258.90 279.82 289.54 297.89 311.86

15.38h 18.17i 23.70j 28.79l 33.61k 38.42l 20.14n

(K)

Hf (kJ mol−1 )

Cp f (J mol−1 K−1 ) 35.0d 43.28h 55.66i 68.75k 101.20k 119.00k 139.30k 184.25k

K323.15a – 59.60 49.80 41.20 25.30 19.50k 14.30k 8.90k

hA a (kJ mol−1 ) – −22.40 −22.10 −21.90 −21.80 −21.80k −21.80k −21.70k

a

[22]. [23]. c [8]. d [17]. e [9]. f [24]. g [25]. h [26]. i [27]. j [28]. k From interpolation of data for odd-, or even-numbered n-alkanols. l [29]. m [30]. n [31]. b

The thermometer was calibrated on ITS-90. The accuracy of the temperature measurements was ±0.01 K and the reproducibility was ±0.1 K. Mixtures were prepared by mass and the error in the mole fraction did not exceed δx1 = 0.0005. 3. Results and discussion Tables 2 and 3 list the direct experimental results of the solid–liquid equilibrium temperatures, T versus x2 , the mole fraction and γ 2 activity coefficient of the NMP, or γ 1 , activity coefficient of the n-alkanols for the investigated systems. The solubility of a solid 1 in a liquid may be expressed in a very general manner by the equation       Cpf1 1 Tf1 Hf1 1 T −ln(x1 ) = − − 1 + ln(γ1 ), − + (1) ln R T Tf1 Tf1 T R were x1 , γ 1 , Hf1 , Cpf1 , Tf1 and T stand for mole fraction, the activity coefficient, the enthalpy of fusion, the difference in solute heat capacity between the solid and the liquid at the melting point, the melting temperature of the solute and the equilibrium temperature, respectively.

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Table 2 Experimental solid–liquid equilibrium temperatures (T) for n-alkanols (1) + N -methyl-2-pyrrolidinone (2)a γ 2b

x2

T (K)

249.68 248.92 247.67 246.51 244.89 243.40 242.24 241.01 239.66 238.51 237.09 235.73 234.57 233.51 231.88 230.70

1.000 1.031 1.045 1.052 1.058 1.061 1.062 1.062 1.062 1.061 1.000 1.031 1.060 1.059 1.058 1.056

0.6085 0.5885 0.5734 0.5513 0.5244 0.5047 0.4672 0.4328 0.3655 0.3156 0.2566 0.2085 0.2085 0.1636 0.0635 0.0000

229.30 228.16 227.09 225.52 223.43 221.95 219.21 216.11 215.40 217.38 219.82 221.77 221.82 223.15 225.61 226.55

1-Heptanol 1.0000 0.9482 0.9212 0.8690 0.8114 0.7855 0.7438 0.7183 0.6939 0.6698 0.3954 0.3720 0.3510 0.3181 0.2845 0.6495 0.6355

249.68 248.33 246.87 244.61 242.36 241.04 238.71 237.14 235.72 234.62 225.53 226.68 228.10 229.65 231.07 233.39 231.82

1.000 1.035 1.047 1.060 1.066 1.066 1.065 1.063 1.061 1.059

0.6206 0.6045 0.5738 0.5411 0.5206 0.4939 0.4487 0.4245 0.3954 0.3720 0.3510 0.3181 0.2845 0.2488 0.2082 0.1576 0.1053 0.0000

230.83 229.51 227.20 224.96 223.38 222.07 223.15 224.65 225.53 226.68 228.10 229.65 231.07 232.80 234.53 236.27 237.73 238.62

1-Octanol 1.0000 0.8623 0.8366 0.8143 0.7916 0.5497 0.5173 0.4872 0.4623

249.68 246.50 245.38 244.29 243.17 239.30 241.27 242.65 244.15

0.7636 0.7368 0.7083 0.6598 0.5830 0.3205 0.2634 0.2027 0.1444

241.92 240.67 239.38 237.15 238.10 249.55 251.87 253.89 256.28

x2

T (K)

1-Hexanol 1.0000 0.9547 0.9218 0.8957 0.8652 0.8385 0.8132 0.7892 0.7669 0.7453 0.7263 0.7045 0.6867 0.6706 0.6458 0.6301

γ 1b

0.947 0.955 0.962 0.970 0.978 1.056 1.055

1.000 1.080 1.087 1.092 1.097 0.956 0.961 0.966 0.969

γ 1b

γ 2b 1.054 1.053 1.051 1.050 1.048 1.046 1.044 1.043

1.065 1.063 1.063 1.062 1.062 1.058 1.032 1.000 1.053 1.051 1.047 1.042 1.039 1.035 0.924 0.935 0.947 0.955 0.961 0.970 0.977 0.984 0.989 0.994 0.998 1.000 1.101 1.103 1.105 1.106 0.950 0.986 0.991 0.995 0.998

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Table 2 (Continued ) T (K)

γ 1b

0.4264 0.3872 0.3627

245.82 247.18 248.20

0.975 0.980 0.982

1-Decanol 1.0000 0.9639 0.9364 0.9122 0.8911 0.7239 0.6839 0.6481 0.6149 0.5844 0.8703 0.8391 0.8195 0.7961 0.7710

249.68 249.28 248.19 247.37 246.75 255.54 257.36 258.90 260.17 261.63 247.22 249.25 251.00 252.06 253.20

1-Undecanol 1.0000 0.9884 0.9751 0.9740 0.9710 0.9696 0.9564 0.9474 0.9374 0.9135 0.8768 0.8440 0.4518 0.4276 0.4017 0.3735 0.3250 0.2784

249.68 249.05 248.76 248.59 248.40 248.22 247.99 249.64 251.92 253.83 256.75 259.89 278.70 279.40 280.69 281.45 282.69 284.58

1-Dodecanol 1.00000 0.98043 0.96669 0.95411 0.91914 0.90384 0.86927 0.84083

249.68 251.13 255.09 258.69 262.80 264.00 266.82 268.40

x2

γ 2b

x2

T (K)

γ 1b

0.0828 0.0000

258.16 258.90

0.999 1.000

1.000 1.023 1.035 1.042 1.045

0.7467 0.2899 0.2510 0.2106 0.1681 0.5566 0.5284 0.4955 0.4274 0.3782 0.3284 0.1284 0.0818 0.0000

254.45 272.46 273.76 275.01 276.50 262.75 264.10 265.24 267.88 269.29 271.27 277.79 278.87 279.82

1.209 1.004 1.002 1.001 1.001 1.045 1.036 1.027 1.015 1.009 1.006 1.000 1.000 1.000

1.000 1.011 1.030 1.032 1.036 1.039 1.062

0.8116 0.7860 0.7511 0.7147 0.6837 0.6535 0.6251 0.6026 0.5739 0.5409 0.5143 0.4817 0.2195 0.1645 0.1239 0.0826 0.0000

261.14 262.89 264.45 266.84 268.35 269.70 271.10 272.05 273.52 274.65 275.75 276.88 286.40 287.85 288.50 289.08 289.54

1.232 1.178 1.125 1.087 1.064 1.047 1.035 1.027 1.019 1.013 1.009 1.005 0.999 0.999 1.000 1.000 1.000

0.51854 0.50279 0.47120 0.56042 0.57922 0.63325 0.65826 0.66588

282.29 283.03 284.25 285.38 285.85 287.80 288.65 289.27

1.173 1.125 1.094 1.072 1.057 1.671 1.481 1.397 1.320 1.256

2.463 2.202 1.805 1.487 1.330 1.003 1.001 1.000 0.999 0.999 0.998

3.249 2.459 2.061 1.527 1.405 1.234 1.152

γ 2b

0.983 0.983 0.984 0.985 0.986 0.989 0.990 0.990

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Table 2 (Continued ) x2

γ 1b

T (K) 0.80772 0.79150 0.77513 0.73811 0.70270 0.68360 0.62911 0.57283 0.56419 a b

270.19 271.00 271.70 273.24 274.88 275.70 277.90 280.24 280.67

γ 2b

x2

T (K)

1.090 1.069 1.051 1.023 1.006 0.999 0.988 0.983 0.983

0.69000 0.71160 0.71635 0.76038 0.79780 0.84123 0.88467 0.90463 1.00000

289.77 290.66 290.74 292.62 294.01 294.44 295.63 295.97 297.89

γ 1b

γ 2b 0.992 0.993 0.993 0.995 0.996 0.998 0.999 0.999 1.000

The γ 1 and γ 2 are activity coefficient of n-alkanol and NMP, respectively. Calculated by Wilson equation.

Table 3 Experimental solid–liquid equilibrium temperatures (T, phases ␣, ␤ and ␥, respectively) for 1-tetradecanol (1) + N -methyl-2-pyrrolidinone (2)a x2

T␣ (K)

1.0000 0.9672 0.9594 0.9155 0.8180 0.7499 0.6825 0.6304 0.6098 0.5342 0.4822 0.4163 0.3784 0.3431 0.3146 0.2910 0.2458 0.2351 0.2038 0.1754 0.1639 0.1473 0.1281 0.0981 0.0771 0.0737 0.0000

T␤ (K)

T␥ (K) 249.68 272.94 270.93 279.27 285.29 288.14 290.92 292.83 293.62 296.41 298.21 300.90 302.26 303.10 304.15 304.74 305.97 306.18

307.19 307.99 308.14 308.75 309.62 310.48 310.99 311.06 311.86

γ 1b 3.760 3.400 2.325 1.587 1.390 1.275 1.214 1.194 1.137 1.107 1.077 1.063 1.051 1.043 1.037 1.026 1.024 1.018 1.013 1.012 1.010 1.007 1.004 1.003 1.002 1.000

The Greek subscripts indicate the type of solid–solid phase transition of the 1-tetradecanol; γ 1 activity coefficient of 1-tetradecanol. b Calculated by Wilson equation. a

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If the solid–solid transitions occur before fusion, an additional terms must be added to the right-hand side of the Eq. (1). The solubility equation for temperatures below that of the phase transition must include the effects of the one or two transitions. The result for the two first-order transitions is:         Cpf1 Hf1 1 1 T Htr11 1 1 Tf1 −ln(x1 ) = − ln − −1 + − + R T Tf1 R Tf1 T R T Ttr11       Cptr11 T Htr21 1 1 Ttr11 − ln −1 + − + R R Ttr11 T T Ttr21     Cptr21 Ttr21 T − + (2) ln − 1 + ln(γ1 ), R Ttr21 T where Htr11 and Ttr11 stand for the enthalpy of first transition and the first transition temperature of the solute (1), and Htr21 and Ttr21 stand for the enthalpy of second transition and the second transition temperature of the solute, respectively. The values of Cptr11 and Cptr21 represent the difference in solute (1) heat capacity between the solid and the liquid at the transition temperature Ttr11 or Ttr21 and unfortunately is usually unknown. In our work Eq. (2) was used for 1-tetradecanol. In this study four methods are used to derive the solute activity coefficients γ 1 from the so-called correlation equations that describe the Gibbs excess free energy of mixing, (GE ): the Wilson [19], UNIQUAC ASM [20], NRTL1 and NRTL2 [21]. Parameter α 12 , a constant of proportionality similar to the non-randomness constant of the NRTL1 and NRTL2 equations was (α12 = α21 = 0.40). The Mecke–Kempter model of association [33] of n-alkanols has been used for calculations. The results are presented in Figs. 1–7. The association parameters: enthalpy of hydrogen-bonding formation, hA , and association constant K at the temperature 323.15 K for n-alkanols are listed in Table 1. The temperature dependence of the association constant K was calculated from the van’t Hoff relation assuming the enthalpy of hydrogen bond formation to be temperature independent. The parameters of the equations were found by an optimisation technique using Marquardt’s maximum neighbourhood method of minimisation [34]. The non-linear equations were solved using the secant method. The root-mean-square deviation of temperature (σ T defined by Eq. (3)) was used as a measure of the goodness-of-fit of the solubility curves.  n 1/2  (T calc − Ti )2 i σT = , (3) n−2 i=1 where Ticalc and Ti are the calculated and experimental temperatures of the ith point, respectively, n is the number of experimental points, which includes the melting point and 2 is the number of adjustable parameters. The calculated values of the equation parameters and corresponding root-mean-square deviations are presented in Table 4. The pure component structural parameter r (volume parameter) and q (surface parameter) in the UNIQUAC ASM and NRTL equations were obtained in accordance with the methods suggested by Vera et al. [35] and relationships from [36] ri = 0.029281Vi ,

(4)

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Fig. 1. Solid–liquid phase diagram for the {1-hexanol (1)+NMP (2)}: 䊊, points experimental values; doted lines, ideal solubility; solid line calculated by the Wilson equation.

qi =

(Z − 2) 2 ri + (1 − li ), Z Z

(5)

where Vi is the molar volume of pure component i at 298.15 K; Z is the coordination number, assumed to equal 10 and li is the bulk factor: it was accepted that li = 0 for alkanol as a linear compound and li = 1 for NMP as a cyclic compound [36]. The molar volumes of the alcohols at 298.15 K were taken from the literature and are shown in Table 1. General the results for the correlation of experimental points in binary systems of NMP in n-alkanols are similar for all equations. The best descriptions of solid–liquid equilibrium were obtained for systems containing the short chain alkanol (σ¯ T < 1 K). The worst results (σ¯ T > 1 K) were obtained for a long-chain n-alkanol, especially for 1-tetradecanol, exhibiting the solid–solid phase transitions. The comparison of the correlation by four equations is given in Table 4 in the form of parameters of the equations and the corresponding root-mean-square deviations. Solid–liquid equilibrium of mixtures investigated in this work are characterised mainly by the following: (1) the solubility (x1 ) of n-alkanols in NMP decreases with increasing number of the carbon atoms, what is presented in Fig. 7; (2) the solubility of NMP (x2 ) is lower than the ideal solubility (positive deviations from Raoult’s low γ2 > 1) for all of the systems; (3) the negative deviations from Raoult’s low are found for 1-heptanol and partly for 1-octanol as a solute at low concentration of NMP (γ1 < 1); (4) the temperature of eutectic point increases with increasing number of the n-alkanol carbon atoms and it moves to the higher concentration of NMP (see Fig. 7).

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Fig. 2. Solid–liquid phase diagram for the {1-heptanol (1) + NMP (2)}: 䊊, points experimental values; doted lines, ideal solubility; solid line calculated by the Wilson equation.

Fig. 3. Solid–liquid phase diagram for the {1-octanol (1)+NMP (2)}: 䊊, points experimental values; doted lines, ideal solubility; solid line calculated by the Wilson equation.

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Fig. 4. Solid–liquid phase diagram for the {1-decanol (1)+NMP (2)}: 䊊, points experimental values; doted lines, ideal solubility; solid line calculated by the Wilson equation.

Fig. 5. Solid–liquid phase diagram for the {1-undecanol (1) + NMP (2)}: 䊊, points experimental values; doted lines, ideal solubility; solid line calculated by the Wilson equation.

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Fig. 6. Solid–liquid phase diagram for the {1-tetradecanol (1) + NMP (2)}: 䊊, points experimental values; doted lines, ideal solubility; solid line calculated by the Wilson equation.

Fig. 7. Solid–liquid phase diagram for the (n-alkanols + NMP): 䊊, 1-hexanol; 䉬, 1-heptanol; ×, 1-octanol; 䉫, 1-decanol; 䊏, 1-undecanol; , 1-dodecanol and 䊐, 1-tetradecanol. Solid lines calculated by the Wilson equation.

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Table 4 Correlation of the solubility data of n-alcohols (1) + N -methyl-2-pyrrolidinone (2) by means of the Wilson, UNIQUAC ASM, NRTL1 and NRTL2 equations: values of parameters and measures of deviations System

NMP + 1-hexanol NMP + 1-heptanol NMP + 1-octanol NMP + 1-decanol NMP + 1-undecanol NMP + 1-dodecanol NMP + 1-tetradecanol

Parameters Wilson

UNIQUAC ASM

NRTL1a

NRTL2a

λ12 − λ11 (λ12 − λ22 ) (J mol−1 )

u12 (u21 ) (J mol−1 )

u12 (u21 ) (J mol−1 )

u12 (u21 ) (J mol−1 )

−2823.29 (7977.22) 12255.28 (−3986.69) 44539.87 (−2275.45) 850.68 (−332.99) 35.66 (−32.49) 317.32 (−227.81) −3002.13 (3777.35)

4218.86 (−2108.49) −2713.35 (11833.55) −1312.34 (952.32) −55.87 (59.46) −501.53 (547.95) −852.17 (995.54) 1478.36 (−780.25)

6539.73 (−3796.57) −3196.98 (2092.48) −1950.91 (1855.93) −396.56 (980.08) −69.44 (75.64) −254.80 (359.50) 3068.34 (−3020.59)

4541.69 (−2649.11) −2095.83 (1729.20) −1819.19 (1896.57) −61.18 (64.73) −445.02 (466.48) −925.57 (1051.72) 1552.41 (−877.22)

σ T (K)

σ T (K)

σ T (K)

σ T (K)

0.10 0.42 0.26 0.42 1.11 1.19 1.36

0.23 0.42 0.26 0.43 1.10 1.19 1.42

0.27 0.42 0.26 0.42 1.10 1.19 1.41

0.33 0.43 0.26 0.43 1.10 1.19 1.43

Deviationsb

NMP + 1-hexanol NMP + 1-heptanol NMP + 1-octanol NMP + 1-decanol NMP + 1-undecanol NMP + 1-dodecanol NMP + 1-tetradecanol a b

Calculated with the third non-randomness parameter, α12 = 0.40. According to the Eq. (3) in the text.

Table 5 The literature data of transition point; molar heat of transition (␣ → ␤) and (␤ → ␥), Htr11 and Htr21 ; the values of eutectic point and transitions temperatures (this work), Ttr11 and Ttr21 in binary systems System

x2eu

Teu (K)

Ttr11 (␣ → ␤) (K)

Htr11 (␣ → ␤) (kJ mol−1 )

Ttr21 (␤ → ␥) (K)

Htr21 (␤ → ␥) (kJ mol−1 )

NMP + 1-hexanol NMP + 1-heptanol NMP + 1-octanol NMP + 1-decanol NMP + 1-undecanol NMP + 1-dodecanol NMP + 1-tetradecanol

– 0.4856 0.6345 0.8920 0.9564 – –

– 220.78 235.40 246.72 247.99 – –

– – – – – – 308.17

– – – – – – 17.50a

– – – – – – 306.43

– – – – – – 2.13a

a

[31].

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4. Conclusions The results for the correlation of experimental points in binary systems of NMP in n-alkanols are generally similar for all equations. The worst results for the correlation of experimental points were obtained for systems containing longer chain n-alkanol. The reason is that the association of higher alcohols is weaker and the intermolecular interaction solute–solvent predominates the alcohol–alcohol interaction which is taken into account in correlations with the UNIQUAC ASM, NRTL1 and NRTL2. The values of the eutectic points and values of transition points are listed in Table 5. List of symbols Cpf molar heat capacity change during the melting process hA enthalpy of hydrogen-bonding formation Hf molar enthalpy of fusion of pure compound Htr1 molar enthalpy of first transition of pure compound Htr2 molar enthalpy of second transition of pure compound K association constant n number of carbon atoms in the n-alkanol q relative molecular area r relative molecular volume R gas constant (8.314472 J mol−1 K−1 ) T temperature Tf melting temperature Ttr1 first solid–solid phase transition temperature Ttr2 second solid–solid phase transition temperature x mole fraction Z coordination number Greek letters α molecular surface fraction, or solid phase of the n-alkanol β solid phase of the n-alkanol ∆ absolute mean deviation γ solid phase of the n-alkanol γi activity coefficient of substance i σT standard deviation of temperature σ¯ T average standard deviation of temperature Superscripts calc calculated value exp experimental value Subscript i type of molecule (component)

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Acknowledgements A support from the Polish Committee for Scientific Research (Grant no. 7 T09B 09521) is acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]

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