Excess molar volumes and viscosities of binary mixtures of some n -alkoxyethanols with propylamine...

Excess molar volumes and viscosities of binarymixtures of some polyethers with propylamineat 298.15 K

Amalendu Pal and Rakesh Kumar Bhardwaj

Abstract: Excess molar volumes (V mE ) and dynamic viscosities (h) have been measured as a function of composition

for binary liquid mixtures of propylamine with 2,5-dioxahexane, 2,5,8-trioxanonane, 2,5,8,11-tetraoxadodecane, 3,6,9-trioxaundecane, and 5,8,11-trioxapentadecane at 298.15 K. The excess volumes are positive over the entire range ofcomposition for the systems propylamine + 2,5-dioxahexane, and + 3,6,9-trioxaundecane, negative for the systemspropylamine + 2,5,8,11-tetraoxadodecane, and + 5,8,11-trioxapentadecane, and change sign from positive to negativefor the remaining system propylamine + 2,5,8-trioxanonane. From the experimental data, deviations in the viscosity(D ln h) and excess energies of activation for viscous flow (DG*E) have been derived. These values are positive for allmixtures with the exception of propylamine + 2,5-dioxahexane.

Key words: excess volume, viscosity, binary mixtures.

Résumé: On a mesuré les volumes molaires en excès (V mE ) et les viscosités dynamiques (h) en fonction de la compo-

sition pour des mélanges liquides binaires de propylamine avec du 2,5-dioxahexane, du 2,5,8-trioxanonane, du 2,5,8,11-tétraoxadodécane, du 3,6,9-trioxoaundécane et du 5,8,11-trioxapentadécane, à 298,15 K. Les volumes en excès sont po-sitifs sur toute la plage de compositions pour les systèmes propylamine + 2,5-dioxahexane et + 3,6,9-trioxoaundécane,ils sont négatifs pour les systèmes propylamine + 2,5,8,11-tétraoxadodécane et + 5,8,11-trioxapentadécane et ils chan-gent de signe, de positif à négatif, pour le dernier système, celui de la propylamine + 2,5,8-trioxanonane. Utilisant lesdonnées expérimentales, on a dérivé les déviations dans la viscosité (D ln h) et dans les énergies d’activation en excèspour l’écoulement visqueux (DG*E). Ces valeurs sont positives pour tous les mélanges, excepté celui de la propylamine +2,5-dioxahexane.

Mots clés: volume en excès, viscosité, mélanges binaires.

[Traduit par la Rédaction] Pal and Bhardwaj 475

Introduction

In recent years, we have been actively engaged in a sys-tematic study of the thermodynamic, acoustic, and transportproperties of some binary mixtures of polyethers with or-ganic solvents (1–4), especially in terms of evaluation ofvarious thermodynamic properties and functions that give abetter understanding of the molecular interactions. Previ-ously (5), we reported excess molar volumes and viscositiesfor binary mixtures of some alkoxyethanols with propy-lamine. From these results it was observed that there existspecific interactions between amine and alkoxyethanol, in-cluding the self association of both the amine and alkoxy-ethanol molecules, which influence the properties of themixtures. As an extension of our studies and to understandthe molecular interactions between amines and polyethers,here we report new experimental data for the excess molar

volumes (V mE ) and viscosities (h) of binary solvent mixtures

containing 2,5-dioxahexane, 2,5,8-tetraoxanonane, 2,5,8,11-tetraoxadodecane, 3,6,9-trioxaundecane, and 5,8,11-triox-apentadecane with propylamine over the whole compositionrange at 298.15 K and atmospheric pressure. A survey of theliterature reveals that binary mixtures of alkoxyethanols oramines with alkanol (6–11) and different amines withstraight chain ethers (12) have mainly been studied. Re-cently, a few studies involving excess volumes and excessheat capacities of (polyethers + alkane or esters) (13–15),excess volumes and excess enthalpies of (alkanol +polyethers) (16–18) and excess volumes of (1–propanol,n-hexanol, or branched alkanols + polyethers) (19–21) havebeen reported. There is, however, no systematic study on thebehavior of propylamine with polyethers.

Experimental

MaterialsPropylamine, 3,6,9-trioxaundecane, and 5,8,11- trioxapen-

tadecane were Merck–Schuchardt products with statedpurities of 99, 98, and 98 mol%, respectively. 2,5-Dioxa-hexane, and 2,5,8-tetraoxanonane, Acros products with statedpurities of 99 and 99 mol%, respectively, were dried andfractionally distilled (22, 23). 2,5,8,11-Tetraoxapentadecane

Can. J. Chem.80: 467–475 (2002) DOI: 10.1139/V02-045 © 2002 NRC Canada

467

Received 17 October 2001. Published on the NRC ResearchPress Web site at http://canjchem.nrc.ca on 8 May 2002.

A. Pal1 and R.K. Bhardwaj.2 Department of Chemistry,Kurukshetra University, Kurukshetra 136 119, India.

1Corresponding author (e-mail: [email protected]).2Present address: Department of Chemistry, Dyal SinghCollege, Karnal 132 001, India.

I:\cjc\cjc80\cjc-05\V02-045.vpMonday, May 06, 2002 2:53:46 PM

Color profile: Generic CMYK printer profileComposite Default screen

(Acros, 99 mol%) was used without further purification.Prior to measurements, however, all liquids were degassedand stored over with molecular sieves. The purities of theliquids were checked by measuring and comparing the den-sities and viscosities at 298.15 K with their correspondingliterature values (24–30) as shown in Table 1. Densities (r)of pure solvents were measured with a bicapillarypycnometer. The pycnometer was calibrated at 298.15 Kwith doubly distilled water. The sensitivity of thepycnometer corresponded to a precision in density, 1 ×10–2 kg m–3. The reproducibility of the density estimates wasfound to be within 1 × 10–1 kg m–3. The mol fraction of eachmixture was obtained with an uncertainty of 1 × 10–4 fromthe measured masses of the components. All masses werecorrected for buoyancy.

The excess molar volumes were measured using a contin-uous-dilution dilatometer similar to that described byDickinson et al. (31). The details pertaining to calibration,experimental set-up, and measuring procedure have beenpreviously described (32). The measured excess molar vol-umes were reproducible to ±0.003 × 10–6 m3 mol–1. Eachrun covered just over half of the range of the ether mol frac-tion (x1) so as to give an overlap between two runs.

Kinematic viscositiesn (= h/r) of the pure liquids and themixtures were measured at 298.15 K with a calibratedUbbelohde suspended-level viscometer. The detailed proce-dure has been previously reported (33, 34). The viscometeris filled with liquid or liquid mixtures, and its limbs areclosed with Teflon caps, taking precautions to minimizeevaporation losses. The flow-time measurements were madewith an electronic stopwatch having a readability of ±0.01 s.Four- or five-flow times were averaged to evaluate the vis-cosity at each composition. The caps of the limbs are re-moved during the measurement of flow times. The measuredkinematic viscosities were converted to dynamic viscosities(h) by multiplication with the density. The reproducibility ofthe viscosity was within ±0.003 mPa s. All measurementswere carried out in a well-stirred water bath at a temperaturecontrolled to ±0.01 K.

Results

Tables 2 and 3 give the experimental results of the excessmolar volumes and viscosities at 298.15 K at various molfractions. The plots of excess molar volumes (V m

E ) and vis-cosities (h) against the mol fraction of the polyether aregiven in Figs. 1 and 2. For compact and smooth representa-tion of the results, the measured viscosities were fitted to apolynomial of type

[1] h ==

å a xii

i

n

10

by the method of least squares with each point equallyweighted. The values of coefficientsai and standard devia-tionss are listed in Table 4a.

From the measured values of the excess molar volumes,the densities of liquid mixtures were computed using theequation

[2] r = (x1M1 + x2M2)/(V mE + x1V 1

* + x2V 2* )

whereM1 andM2 represent molar masses. The accuracy inrdue to the estimated accuracy in excess molar volume(±0.003 × 10–6 m3 mol–1) is 1 × 10–1 kg m–3.

The deviation of the viscosity has been calculated fromthe following relationship (35, 36):

[3] Dln h = ln h – (x1 ln h1 + x2 ln h2)

wherex1 andx2 are the mol fractions,h is the dynamic vis-cosity of the mixture, andh1 and h2 are the viscosities ofcomponents 1 and 2, respectively.

The excess energies of activation for viscous flow wereobtained with the following expression:

[4] DG*E = RT [ln (hV) – x1 ln (h1V 1* )

– x2 ln (h2V 2* )]

whereV, V 1* , and V 2

* are the molar volumes of the mixtureand of the pure components 1 and 2, respectively. R andTare the gas constant and temperature, respectively. The

© 2002 NRC Canada

468 Can. J. Chem. Vol. 80, 2002

r × 10–3 (kg m–3) h (mPa s)

Component Expt. Lit. Expt. Lit.

Propylamine 0.7122 0.7121 (22) 0.356 0.353 (22)

2,5 Dioxahexane 0.8626 0.86262 (24) 0.417 0.424 (25)0.86132 (25) 0.432 (26)

2,5,8-Trioxanonane 0.9391 0.93905 (27) 0.992 0.989 (22)0.93873 (14) 0.991 (28)0.93875 (19)

2,5,8,11-Tetraoxadodecane 0.9807 0.98067 (14) 1.960 1.960 (29)0.98065 (19)0.98058 (27)

3,6,9-Trioxaundecane 0.9035 0.90281 (19) 1.2680.90390 (27)0.9033 (30)

5,8,11-Trioxapentadecane 0.8785 0.87830 (19) 2.160

Table 1. Densities and viscosities of the pure components at 298.15 K.



© 2002 NRC Canada

Pal and Bhardwaj 469

x1 V mE × 106 x1 V m

E × 106 x1 V mE × 106

2,5-Dioxahexane (1) + propylamine (2)0.0086 0.012 0.3870 0.289 0.5887 0.3190.0292 0.026 0.4035 0.294 0.6011 0.3200.0657 0.059 0.4162 0.301 0.6151 0.3160.1153 0.100 0.4426 0.304 0.6460 0.3070.1601 0.139 0.4570 0.309 0.6507 0.3040.2149 0.176 0.4755 0.310 0.6808 0.2960.2474 0.199 0.4981 0.316 0.7406 0.2590.2904 0.231 0.4985 0.314 0.7872 0.2260.3328 0.261 0.5314 0.319 0.8330 0.1920.3416 0.264 0.5393 0.317 0.8921 0.1320.3653 0.280 0.5614 0.320 0.9308 0.0870.3737 0.276 0.5725 0.319 0.9706 0.0432,5,8-Trioxanonane (1) + propylamine (2)0.0071 0.003 0.2593 0.017 0.4409 0.0020.0146 0.004 0.2688 0.018 0.4705 –0.0020.0323 0.006 0.2904 0.016 0.4776 –0.0030.0520 0.008 0.2982 0.016 0.5058 –0.0090.0812 0.010 0.3170 0.016 0.5651 –0.0160.1141 0.014 0.3352 0.015 0.6018 –0.0200.1397 0.014 0.3570 0.013 0.6484 –0.0280.1724 0.015 0.3693 0.012 0.7080 –0.0350.2026 0.015 0.3865 0.011 0.7835 –0.0370.2137 0.016 0.3951 0.008 0.8458 –0.0360.2279 0.015 0.4122 0.006 0.9073 –0.0270.2472 0.018 0.4260 0.002 0.9569 –0.0162,5,8,11-Tetraoxadodecane (1) + propylamine (2)0.0073 –0.002 0.2647 –0.052 0.4608 –0.0580.0326 –0.012 0.2922 –0.054 0.5223 –0.0570.0625 –0.016 0.2957 –0.052 0.5935 –0.0530.1367 –0.034 0.3275 –0.056 0.6598 –0.0470.1775 –0.039 0.3290 –0.057 0.7590 –0.0390.1913 –0.043 0.3614 –0.058 0.8244 –0.0310.2169 –0.046 0.3822 –0.060 0.9055 –0.0200.2459 –0.050 0.4069 –0.059 0.9783 –0.0060.2536 –0.049 0.4205 –0.0583,6,9-Trioxaundecane (1) + propylamine (2)0.0079 0.002 0.2798 0.022 0.4692 0.0310.0310 0.006 0.2918 0.024 0.4953 0.0300.0511 0.010 0.3001 0.024 0.5560 0.0320.1037 0.016 0.3272 0.025 0.6550 0.0310.1446 0.018 0.3439 0.026 0.7715 0.0280.2012 0.020 0.3663 0.026 0.8359 0.0240.2101 0.016 0.4018 0.028 0.8952 0.0150.2276 0.018 0.4113 0.028 0.9473 0.0050.2504 0.023 0.4229 0.0290.2582 0.020 0.4514 0.0305,8,11-Trioxapentadecane (1) + propylamine (2)0.0098 –0.002 0.2589 –0.033 0.4805 –0.0390.0407 –0.006 0.2702 –0.035 0.5520 –0.0400.0839 –0.015 0.2847 –0.035 0.6220 –0.0390.1298 –0.020 0.3153 –0.037 0.6608 –0.0370.1683 –0.025 0.3182 –0.037 0.7210 –0.0350.1798 –0.023 0.3310 –0.038 0.8293 –0.0280.1939 –0.025 0.3627 –0.039 0.8904 –0.0200.2117 –0.027 0.4127 –0.042 0.9451 –0.0100.2251 –0.032 0.4176 –0.0400.2305 –0.031 0.4583 –0.042

Table 2. Excess molar volumes (V mE , m3 mol–1) for polyether + propylamine systems at 298.15 K.



© 2002 NRC Canada

470 Can. J. Chem. Vol. 80, 2002

x1

r × 10–3

(kg m–3)h

(mPa s)DG*E

(J mol–1) x1

r × 10–3

(kg m–3)h

(mPa s)DG*E

(J mol–1)

2,5-Dioxahexane (1) + propylamine (2)0.0057 0.7132 0.356 1 0.4707 0.7889 0.378 –140.0115 0.7142 0.357 1 0.5131 0.7953 0.380 –180.0320 0.7178 0.358 5 0.5662 0.8031 0.381 –280.0568 0.7222 0.360 13 0.6099 0.8095 0.383 –330.0815 0.7264 0.362 19 0.6466 0.8148 0.386 –330.1075 0.7309 0.364 24 0.7017 0.8226 0.390 –310.1552 0.7389 0.368 34 0.7400 0.8280 0.392 –310.1871 0.7442 0.369 31 0.8022 0.8366 0.397 –320.2467 0.7539 0.372 31 0.8330 0.8408 0.399 –290.2882 0.7606 0.373 23 0.8785 0.8468 0.403 –280.3386 0.7686 0.374 15 0.9167 0.8519 0.408 –170.3526 0.7708 0.374 5 0.9436 0.8554 0.411 –90.3761 0.7744 0.374 –1 0.9811 0.8602 0.415 –50.4134 0.7802 0.375 –72,5,8-Trioxanonane (1) + propylamine (2)0.0044 0.7139 0.359 13 03647 0.8252 0.613 5060.0179 0.7192 0.368 45 0.3683 0.8261 0.615 5080.0461 0.7298 0.385 95 0.4079 0.8355 0.644 5240.0659 0.7370 0.400 145 0.4628 0.8478 0.679 5160.0913 0.7459 0.417 192 0.5243 0.8608 0.721 5070.1293 0.7587 0.443 260 0.5823 0.8723 0.757 4780.1685 0.7712 0.472 327 0.6408 0.8833 0.796 4470.1892 0.7775 0.487 355 0.7358 0.8998 0.840 3250.2354 0.7911 0.518 404 0.7900 0.9086 0.873 2720.2682 0.8003 0.541 431 0.8565 0.9189 0.908 1840.2727 0.8015 0.544 437 0.8970 0.9248 0.935 1470.3150 0.8127 0.575 471 0.9375 0.9306 0.955 830.3201 0.8140 0.579 476 0.9887 0.9376 0.985 152,5,8,11-Tetraoxadodecane (1) + propylamine (2)0.0076 0.7166 0.366 42 0.3623 0.8614 0.864 8490.0166 0.7218 0.375 72 0.4044 0.8731 0.935 8720.0296 0.7291 0.393 149 0.4583 0.8870 1.022 8650.0659 0.7482 0.440 303 0.5139 0.9001 1.115 8410.0954 0.7627 0.480 419 0.5761 0.9136 1.225 8030.1298 0.7785 0.526 524 0.6483 0.9278 1.365 7490.1596 0.7913 0.567 600 0.6867 0.9347 1.435 7000.1909 0.8039 0.611 667 0.7450 0.9447 1.549 6220.2265 0.8174 0.659 720 0.8308 0.9581 1.720 4840.2351 0.8205 0.673 739 0.8787 0.9650 1.805 3790.2622 0.8300 0.711 768 0.9203 0.9706 1.862 2580.2681 0.8320 0.721 780 0.9618 0.9760 1.917 1320.3073 0.8448 0.782 8263,6,9-Trioxaundecane (1) + propylamine (2)0.0050 0.7143 0.361 24 0.3686 0.8187 0.709 7280.0106 0.7165 0.367 51 0.4053 0.8260 0.737 7100.0197 0.7202 0.379 110 0.4615 0.8263 0.786 6950.0413 0.7285 0.402 206 0.5261 0.8471 0.848 6730.0623 0.7362 0.423 286 0.5564 0.8518 0.875 6520.0897 0.7457 0.451 378 0.6025 0.8586 0.919 6180.1329 0.7597 0.498 515 0.6358 0.8633 0.951 5900.1762 0.7725 0.538 593 0.6749 0.8685 0.988 5520.2138 0.7829 0.572 645 0.7261 0.8750 1.038 4960.2434 0.7905 0.600 681 0.7852 0.8819 1.090 4090.2446 0.7908 0.603 689 0.8437 0.8883 1.152 3370.2849 0.8005 0.636 707 0.8917 0.8933 1.201 264

Table 3. Densities, viscosities, and excess energies of activation for viscous flow of polyether + propylamine systems at 298.15 K



derived densities, viscosities, and excess energies of activa-tion for viscous flow for the different binary mixtures at298.15 K are given in Table 3.

The values ofV mE , Dln h, andDG*E for all mixtures were

represented mathematically by the Redlich–Kister polyno-mial.

[5] Y(x) x x a x xii

i

n

= - -

=

å1 2 1 21

0

( )

Values of the coefficientsai and standard deviations aresummarized in Table 4b. For all mixtures,s (V m

E ) £ 0.003, inaccord with the precision attainable with the dilatometer

© 2002 NRC Canada


x1

r × 10–3

(kg m–3)h

(mPa s)DG*E

(J mol–1) x1

r × 10–3

(kg m–3)h

(mPa s)DG*E

(J mol–1)

0.2887 0.8014 0.640 710 0.9396 0.8979 1.235 1590.3251 0.8096 0.672 726 0.9698 0.9008 1.248 735,8,11-Trioxapentadecane (1) + propylamine (2)0.0095 0.7169 0.375 107 0.3977 0.8229 1.129 14500.0288 0.7258 0.417 321 0.4621 0.8322 1.240 13910.0455 0.7330 0.450 470 0.5160 0.8390 1.330 13120.0845 0.7483 0.529 760 0.5979 0.8482 1.489 11940.1266 0.7627 0.622 1030 0.6482 0.8532 1.579 10900.1754 0.7771 0.719 1225 0.6986 0.8577 1.689 10010.2172 0.7879 0.806 1357 0.7471 0.8617 1.774 8720.2531 0.7962 0.870 1408 0.7956 0.8655 1.869 7480.2660 0.7990 0.904 1453 0.8618 0.8701 2.010 5750.3172 0.8092 0.994 1479 0.9261 0.8742 2.093 3270.3559 0.8161 1.055 1465 0.9641 0.8765 2.143 178

Table 3 (Continued)

Fig. 1. Experimental excess molar volumes for propylamine (2) +2,5-dioxahexane (1) (s); 2,5,8-trioxanonane (1) (D); 2,5,8,11-tetraoxadodecane (1) (u); 3,6,9-trioxundecane (1) (d); 5,8,11-trioxapentadecane (1) (q). Continuous curves were calculatedfrom eq. [5].

Fig. 2. Experimental viscosities for propylamine (2) + 2,5-dioxahexane (1) (s); 2,5,8-trioxanonane (1) (D); 2,5,8,11-tetraoxadodecane (1) (u); 3,6,9-trioxaundecane (1) (d); 5,8,11-trioxapentadecane (1) (q). Continuous curves were calculatedfrom eq. [1].



used. Literature values forV mE or h for these mixture are not

available for comparison.

Comparison of experimental results with severalempirical laws of mixing

Several relations have been proposed to evaluate the dy-namic viscosity (h) of liquid mixtures by using severalchemical laws of mixing representative of the viscosity ofbinary mixtures with an adjustable empirical parameter. Theliterature contains many laws of mixing, which can be de-fined according to the number of adjustable parameters usedto account for the deviation from an ideal mixture. Thus,there are laws based on parameters of zero, one, two, three,and so forth

The equation of Kendall and Monroe (37), which has noadjustable parameters, is expressed as

[6] h = (x1h11/3 + x2h2

1/3)3

The equations of Grunberg–Nissan (38), Tamura andKurata (39), Hind (40), and Katti and Chaudhry (41) haveone adjustable parameter. The single-parameterGrunberg–Nissan equation (38) reads

[7] ln h = x1 ln h1 + x2 ln h2 + x1x2G12

whereG12 is a parameter proportional to the interchange en-ergy. Tamura and Kurata (39) developed the following ex-pression for the viscosity of binary mixtures:

[8] h = x1f1h1 + x2f2h2 + 2(x1x2f1f2)1/2T12

whereT12 is the interaction parameter andf1 andf2 are thevolume fractions. Hind et al. (40) proposed the followingequation:

[9] h = x12h1 + x 2

2h2 + 2x1x2H12

whereH12 is attributed to unlike-pair interactions. Katti andChaudhry (41) derived the following equation:

[10] ln (hV) = x1 ln (h1V 1* ) + x2 ln (h1V 1

* )

+ x1x2Wvis/RT

where Wvis is an adjustable parameter. The two-parameterHeric and Brewer equation (42) is of the form

[11] ln n = x1 ln n1 + x2 ln n2 + x1 ln M1 + x2 ln M2

+ ln (x1M1 + x2M2) + x1x2[a12 + a21(x1 – x2)]

wherea12 anda21 are adjustable parameters andni is the ki-nematic viscosity of pure componenti. The two-parameter

© 2002 NRC Canada

472 Can. J. Chem. Vol. 80, 2002

Propylamine (2) + a1 a2 a3 a4 a5 s

2,5-Dioxhexane (1)V m

E x 106 (m3 mol–1) 1.2709 0.2650 –0.1631 0.003Dln h (mPa s) –0.0678 –0.1234 0.0664 0.0108 0.002DG*E (J mol–1) –81.7 –316.1 363.7 8.5 –339.6 3

2,5,8-Trioxanonane (1)V m

E x 106 (m3 mol–1) –0.0233 –0.2887 –0.1161 0.001Dln h (mPa s) 0.6828 –0.1820 –0.1121 –0.0169 0.003DG*E (J mol–1) 2053.7 –508.0 –271.9 –45.6 7

2,5,8,11-Tetraoxadodecane (1)V m

E × 106 (m3 mol–1) –0.2308 0.0517 –0.0366 0.001Dln h (mPa s) 1.0709 –0.2273 0.4500 0.0013 0.003DG*E (J mol–1) 3391.8 –751.5 1172.5 –11.7 6

3,6,9-Trioxaundecane (1)V m

E × 106 (m3 mol–1) 0.1206 0.0329 0.0521 0.002Dln h (mPa s) 0.8095 –0.3671 0.5484 –0.0986 0.003DG*E (J mol–1) 2729.7 1088.9 1411.9 –263.2 7

5,8,11-Trioxapentadecane (1)V m

E × 106 (m3 mol–1) –0.1655 –0.0066 –0.0352 0.001Dln h (mPa s) 1.5924 –0.9230 1.1101 –0.1503 0.004DG*E (J mol–1) 5365.5 –2771.4 2953.8 –460.7 10

Table 4b. Coefficientsai of eq. [5] and standard deviations.

Propylamine (2) + a1 a2 a3 a4 a5 s

2,5-Dioxhexane (1) 0.3560 0.0850 –0.1305 0.1082 0.0012,5,8-Trioxanonane (1) 0.3574 0.5917 0.6318 –1.1192 0.5306 0.0022,5,8,11-Tetraoxadodecane (1) 0.3507 1.4376 –0.8066 2.5938 –1.6026 0.0053,6,9-Trioxaundecane (1) 0.3529 1.2533 –1.4676 2.2305 –1.0946 0.0035,8,11-Trioxapentadecane (1) 0.3407 2.5957 –2.9613 4.3557 –2.1337 0.010

Table 4a. Coefficientsai of eq. [1] for viscosityh (mPa s) and standard deviationss



McAllister equation (43), based on Eyring’s theory of abso-lute reaction rates (44), and the three-body interaction modelis

[12] ln n = x13 ln n1 + 3x1

2x2 ln Z12 + 3x1x 22 ln Z21

+ x 23 ln n2 – ln [x1 + x2(M2/M1)]

+ 3x12x2 ln [(2 + M2/M1)/3]

+ 3x1x 22 ln [(1 + 2M2/M1)/3] + x 2

3 ln (M2/M1)

The four-body model gives

[13] ln n = x14 ln n1 + 4x1

3x2 ln Z1112

+ 6x12x 2

2 ln Z1122 + 4x1x 23 ln Z2221 + x 2

4 ln n2

– ln [x1 + x2(M2/M1)] + 4x13x2 ln [(3 + M2/M1)/4]

+ 6x122x 2

2 ln [(1 + M2/M1)/2]

+ 4x1x 23 ln [(1 + 3M2/M1)/4] + x 2

4 ln (M2/M1)

whereZ12, Z21, Z1112, Z1122, andZ2221 are interaction parame-ters andMi is the molecular mass of pure componenti. Thethree-parameter Auslaender eq. [45] is of the form

[14] n1(x1 + B12x2)(n – n1) + A21x2(B21x2 + x2)(n – n2) = 0

whereB12, A21, and B21 are the parameters representing bi-nary 1 – 2 interactions. The correlating capability ofeqs. [6]–[14] was tested by calculating the standard percent-age deviation (s%) between the experimental and the calcu-lated viscosity using the following relation:

[15] s(%) = [1/(p – k) S (100(hexp – hcal)/hexp)2]1/2

wherep represents the number of experimental points andkthe number of numerical coefficients in the respective equa-tions.

Discussion

From Fig. 1, it can be seen thatV mE is large and positive

for the 2,5-dioxahexane + propylamine mixtures at 298.15 Kover the entire range of composition. For the same value ofx1, the magnitude of theV m

E decreases with each additional -OC2H4- group in the parent molecule 2,5-dioxahexane. Thebehavior is similar to that ofV m

E for 2-methoxyethanol orpropylamine withn-alkoxyethanol (5, 7, 46, 47), ethyl ace-tate with (mono and poly) ethers (14), and alkanols withpolyethers (19, 27, 48), whereV m

E decreases with the in-creasing number of oxygen atoms in the ether chain. InFig. 1, it can also be observed thatV m

E increases in the se-quence 5,8,11-trioxapentadecane > 3,6,9-trioxundecane >2,5,8- trioxanonane. This behavior may be compared withthat of V m

E for 2-(2-methoxyethoxy)ethanol, 2-(2-ethoxy-ethoxy)ethanol, or 2-(2-butoxyethoxy)ethanol with propyl-amine (5). The behavior of these mixtures is very complexand the overall values ofV m

E are attributable to the result ofseveral opposing and diverse effects (49, 50): (i) a disruptionof liquid order on mixing and unfavorable interactions be-tween unlike molecules, which contribute positively toV m

E ;(ii ) a volume decrease caused by the differences in molecu-lar volumes and free volumes and possible interstitial ac-commodation of propylamine within larger molecules. Uponincreasing the size of the polar-head group of the polyether,the interactions between unlike molecules become more im-portant;V m

E decreases and becomes more negative for the

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Fig. 3. Experimental viscosity deviations for propylamine (2) +2,5-dioxahexane (1) (s) ; 2,5,8-trioxanonane (1) (D); 2,5,8,11-tetraoxadodecane (1) (u); 3,6,9-trioxaundecane (1) (d); 5,8,11-trioxapentadecane (1) (q). Continuous curves were calculatedfrom eq. [5].

Fig. 4. Experimental excess energies of activation for viscousflow for propylamine (2) + 2,5-dioxahexane (1) (s); 2,5,8-trioxanonane (1) (D); 2,5,8,11-tetraoxadodecane (1) (u); 3,6,9-trioxaundecane (1) (d); 5,8,11–trioxapentadecane (1) (q). Con-tinuous curves were calculated from eq. [5].



larger polyethers. In the same homologous series, the alge-braic values of V m

E at x1 > 0.8 for the three binary systemswith propylamine vary in the following order: 5,8,11-trioxapentadecane < 2,5,8-trioxanonane < 3,6,9-trioxaundecane.The negative contribution to V m

E for the 5,8,11-trioxapenta-decane systems is caused by stronger interactions betweenunlike molecules giving higher negative values comparedwith those of the other two mixtures.

Figure 2 shows that � increases with the ether mol frac-tion (x1) for all of the mixtures studied. The deviation in theviscosity (�ln �) and the excess energies of activation forviscous flow (�G*E) are represented in Figs. 3 and 4. All ofthe mixtures show positive deviations from mol fraction lin-earity, except for the 2,5-dioxahexane + propylamine systemat low ether mol fractions. Similar behavior is observed for�G*E. The magnitude of �, �ln �, and �G*E increase with in-creasing size of the polar-head group and with increasingalkyl chain length of polyether. The positive values of �G*E

are attributed to the large size and cohesive-energy differ-ence between the two unlike molecules. The positive �ln �

and �G*E values are an indication of specific interactions(51, 52). Indeed, we observe positive deviations in the vis-cosity that regularly increase as the size or viscosity of thepolyether is increased. This reveals that the strength of spe-cific interaction is not the only factor influencing the viscos-ity deviation of liquid mixtures. The molecular size andshape of the components also play important roles.

The results of the correlating eqs. [6]–[14] are compiledin Tables 5 and 6. The fitting precision of eq. [6] (no adjust-able parameters) and eqs. [7]–[10] (one adjustable parame-ter) are presented in Table 5. Table 6 gives the fitting resultsfor the two-parameter Heric–Brewer equation (eq. [11]), theMcAllister three-body model (eq. [12]), the three-parameterMcAllister four-body model (eq. [13]), and the Auslaenderequation (eq. [14]). The values of the different fittings pa-rameters in eqs. [7]–[14] and the percentage standard devia-tion listed in Tables 5 and 6 were obtained from the

experimental viscosity data using least squares with equalweights assigned to each point.

The values of � are in the range from 1.3 to 20.3% foreq. [6] (no adjustable parameters); from 0.9 to 9.2% for thesingle-parameter fitting eqs. [7]–[10]; from 0.2 to 3.5% forthe two-parameter eqs. [11] and [12]; and from 0.2 to 3.5%for the three-parameter eqs. (13] and [14]. Table 5 showsthat, because of lower values of �%, the equations ofTamura and Kurata (eq. [8]), and Hind et al. (eq. [9]), thebehavior of the binary mixture satisfactorily compares withthe equations of Grunberg–Nissan (eq. [7]) and Katti andChaudhary (eq. [10]). The equations of Kendall and Monroe(eq. [6], with no adjustable parameters) has higher values of�% than those of the single-parameter eqs. [7]–[10]. Use ofthe two-parameter eqs. [11] and [12] significantly reducesthe �% values below that of the single-parameter eqs. [8]and [9], except with 3,6,9-trioxaundecane and 5,8,11-trioxapentadecane. For all of the systems studied here, thethree-parameter equation of McAllister (eq. [13]) gives verygood results. The values of �% are in the range of only0.2–0.4%. Use of the three-parameter equation ofAuslaender (eq. [14]), however, gives higher �% values thanthat of the three-parameter equation of McAllister (eq. [13]).

From this study it can be concluded that all of the corre-lating equations considered are effective in the empirical fit-ting of viscosity data for (polyether + propylamine)mixtures. This is not surprising in view of the number of ad-justable parameters in each equation, where a very largevariability of the experimental measurements with composi-tion of the solvent mixtures is observed. Thus it becomevery difficult to suggest any general rule in establishing theeffectiveness of one fitting over the other. The comparisonsare, however, more suitable with the same number of adjust-able parameters. Thus the equations having one adjustableparameter (Tamura and Kurata, and Hind et al.) show a goodcorrelating ability over the equation of Grunberg–Nissan andKatti and Chaudhry.

© 2002 NRC Canada

474 Can. J. Chem. Vol. 80, 2002

eq. [6] eq. [7] eq. [8] eq. [9] eq. [10]

Propylamine (2) + �% G12 �% T12 �% H12 �% Wvis/RT �%

2,5-Dioxhexane (1) 1.32 0.06 0.85 0.37 0.93 0.37 0.88 –0.01 0.892,5,8-Trioxanonane (1) 8.39 0.69 1.29 0.65 0.97 0.72 0.78 0.84 1.442,5,8,11-Tetraoxadodecane (1) 10.94 1.17 2.26 0.79 1.46 1.01 1.93 1.49 2.763,6,9-Trioxaundecane (1) 10.84 0.89 3.36 0.74 0.94 0.86 1.09 1.19 3.865,8,11-Trioxapentadecane (1) 20.31 1.64 8.06 1.06 1.58 1.41 1.38 2.44 9.23

Table 5. Values of the parameters in eqs. [7]–[10] and standard percentage deviations in eqs. [6]–[10] for polyether + propylamine sys-tems.

eq. [11] eq. [12] eq. [13] eq. [14]

Propylamine (2) + �12 �21 �% Z12 Z21 �% Z1112 Z1122 Z2221 �% B12 B21 A21 �%

2,5-Dioxhexane (1) –1.17 6.67 0.22 0.46 0.50 0.25 0.47 0.56 0.51 0.16 1.21 1.29 1.33 0.292,5,8-Trioxanonane (1) 1.17 –0.71 0.49 0.94 0.83 0.38 0.94 1.27 0.71 0.24 –0.69 0.10 –0.54 0.542,5,8,11-Tetraoxadodecane (1) 1.84 –0.42 1.41 1.62 1.25 1.31 1.89 1.75 1.06 0.20 0.01 0.07 0.13 3.503,6,9-Trioxaundecane (1) 1.19 –0.52 1.54 1.13 1.10 1.54 1.35 1.30 0.99 0.27 –0.95 0.11 –0.75 1.525,8,11-Trioxapentadecane (1) 2.35 –1.23 3.25 1.79 2.29 3.47 2.52 1.96 1.92 0.42 –1.81 0.07 –1.3 1.71

Table 6. Values of the parameters in eqs. [11]–[14] and standard percentage deviations in correlating viscosities of polyethers +propylamine systems.

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© 2002 NRC Canada


With respect to the three-parameter equations, it should benoted that the McAllister equation (eq. [13]) gives the bestfit of the experimental values. Furthermore, the reproduc-ibility of the experimental point is similar to those obtainedby applying the two-parameter equations of Heric-Brewerand McAllister (eq. [11] and 12]).

Acknowledgment

RKB gratefully acknowledges the University Grants Com-mission (UGC), New Delhi, for awarding teacher fellowship(No. F.3–(TF 13)/98(NR)) and financial assistance for thisstudy.

References

1. A. Pal and R. K. Bhardwaj. Int. J. Thermophysics,22, 769(2001).

2. A. Pal and H. Kumar. Fluid Phase Equilib.181, 17 (2001).3. A. Pal and G. Das. Can. J. Chem.78, 444 (2000).4. A. Pal and S. Sharma. J. Chem. Thermodyn.31, 273 (1999).5. A. Pal, S. Sharma, and H. Kumar. Can. J. Chem.78, 427

(2000).6. T. M. Aminabhavi and B. Gopalakrishna. J. Chem. Eng. Data,

40, 402 (1993).7. J.C. Cobos, C. Casanova, J. Garcia, G. Roux–Desgranges, and

J.-P.E. Grolier. Thermochim. Acta,131,73 (1988).8. J.C. Cobos and C. Casanova. Fluid Phase Equilib.20, 155

(1985).9. S.L. Oswal and H.S. Desai. Fluid Phase Equilib.149, 359

(1998).10. I. Farnandez, M.I. Paz–Andrade, M. Pintos, F. Sarmiento, and

R. Bravo. J. Chem. Thermodyn.15, 581 (1983).11. D. Papaionnou and C. Panayiotou. J. Chem. Eng. Data,40,

202 (1995).12. T.M. Letcher and U. Domanska. J. Chem. Thermodyn.26, 553

(1994); 26, 1241 (1994).13. C.A. Tovar, E. Carballo, C.A. Cerdeirina, J.L. Legido and L.

Romani. Int. J. Thermophysics,18, 761 (1997).14. C.A. Tovar, E. Carballo, C.A. Cerdeirina, and L. Romani. J.

Chem. Eng. Data,40, 1085 (1997).15. J. Peleterio, C.A. Tovar, E. Carballo, J.L. Legido, and L.

Romani. Can. J. Chem.72, 454, (1994).16. J.C. Cobos, I. Garcia, J.A. Gonzalez, and C. Casanova. J.

Chem. Thermodyn.22, 383 (1990).17. J.C. Cobos, M.A. Villamanan, and C. Casanova. J. Chem.

Thermodyn.16, 861 (1984).18. S. Mohren and A. Heintz. Fluid Phase Equilib.133, 247 (1997).19. A. Serna, I. Garcia de la Fuente, J.A. Gonzalez, and J.C.

Cobos. Fluid Phase Equilib.133, 187 (1997).20. A. Serna, J.C. Cobos, I. Garcia de la Fuente, J.A. Gonzalez,

and C. Casanova. The proceedings of the 13th IUPAC confer-ence on chemical thermodynamics. Clermont, Ferrand, France.1994. p. 80.

21. T.M. Aminabhavi and B Gopalakrishna. J. Chem. Eng. Data,39, 865 (1994).

22. J.A. Riddick, W.B. Bunger, and T.K. Sakano. Organic sol-vents: physical proprerties and method of purifications. 4th ed.Wiley Interscience, New York. 1986.

23. T.M. Letcher. J. Chem. Thermodyn.4, 159 (1972).24. G. Douheret, M.I. Davis, M.E. Hernandez, and H. Flores. J.

Indian Chem. Soc.70, 395 (1993).25. P.K. Muhuri and D.K. Hazara. J. Chem. Eng. Data,39, 375

(1994).26. W.J. Wallace and A.L. Methews. J. Chem. Eng. Data,8, 496

(1963).27. F.J. Carmona, F.J. Arroyo, I. Garcia de la Fuente, J.A. Gonza-

lez, and J.C. Cobos. Can. J. Chem.77, 1608 (1999).28. T.M. Aminabhavi and B. Gopalakrishna. J. Chem. Eng. Data,

40, 462 (1995).29. W.J. Wallace, C.S. Shephard, and C. Underwood. J. Chem.

Eng. Data,13, 11 (1968).30. G. Roux, G. Perron, and J.E. Desnoyers. Can. J. Chem.56,

2808 (1978).31. E. Dickinson, D.C. Hunt, and I.A. McLure. J. Chem.

Thermodyn.7, 731 (1975).32. A. Pal and Y.P. Singh. J. Chem. Thermodyn.26, 1063 (1994).33. A. Pal and W. Singh. J. Chem. Eng. Data,42, 234 (1997).34. A. Pal and A. Kumar. J. Chem. Eng. Data,43, 143 (1998).35. A. Aucejo, M.C. Burguet, R. Munoz, and M. Sanchotello. J.

Chem. Eng. Data,41, 508 (1996).36. R.S. Ramadevi, P. Venkatesu, and M.V.P. Rao. J. Chem. Eng.

Data,41, 479 (1996).37. J. Kendall and K.P. Monroe. J. Am. Chem. Soc.39, 1787

(1917).38. L. Grunberg and A.H. Nissan. Nature (London),164, 799 (1949).39. M. Tamura and M. Kurata. Bull. Chem. Soc. Jpn.25, 32 (1952).40. R.K. Hind, E. McLaughlin, and U.R. Ubbelohde. Trans. Fara-

day Soc.56, 328 (1960).41. P.K. Katti and M.M. Chaudhry. J. Chem. Eng. Data,9, 442

(1964).42. E.L. Heric and J.C. Brewer. J. Chem. Eng. Data,12, 574

(1967).43. R.A. McAllister. AIChE J.6, 427 (1960).44. S. Glasstone, K.J. Laidler, and H. Eyring. The theory of rate

processes. McGraw–Hill, New York. 1941.45. G. Auslaender. Br. Chem. Eng.10, 196 (1965).46. A. Pal and W. Singh. J. Chem. Thermodyn.28, 227 (1996).47. A. Pal and W. Singh. J. Chem. Eng. Data,41, 888 (1996).48. A. Pal and A. Kumar. Fluid Phase Equlib.161, 153 (1999).49. S.N. Vinogradov and R.H. Linell. Hydrogen bonding.

Van–Nostrand, Reinhold, New York. 1971. p. 136.50. G.C. Benson, C.J. Halpin, and A.J. Treszczanowicz. J. Chem.

Thermodyn.13, 1175 (1981).51. R.J. Fort and W.R. Moore. Trans. Faraday. Soc.62, 1112 (1996).52. R. Palepu, J. Oliver, and B. Mackinnon. Can. J. Chem.63,

1024 (1985).



Excess molar volumes and viscosities of binary mixtures of some n -alkoxyethanols with propylamine...

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