Viscosities of binary liquid mixtures of some n ... - NOPR

Indian Journal of ChemistryVol. 46A, November 2007, pp. 1763-1771

Viscosities of binary liquid mixtures of some n-alkoxypropanolswith n-alkanols at 298.15 K

Department of Chemistry, Kurukshetra University, Kurukshetra 136 119, India

Email: [email protected]

The viscosities (11) in binary liquid mixtures of (Il-alkoxypropanols + methanol, ethanol, or I-propanol) have beenmeasured as a function of composition using an Ubbelohde viscometer at 298.15 K and atmospheric pressure over the fullrange of composition. The Il-alkoxypropanols are propylene glycol monomethyl ether (l-methoxy-2-propanol).CH30CHzCHzCHzOH, propylene glycol monoethyl ether (l-ethoxy-2-propanol), CzHsOCH2CHzCHzOH, propylene glycolmonopropyl ether (l-propoxy-2-propanol), C3H70CHzCHzCHzOH, propylene glycol monobutyl ether (l-butoxy-2-propanol), C4HgOCH2CHzCHzOH propylene glycol rerr-butyl ether (l-rerr-butoxy-2-propanol), CI-I3CHOHCH30C(C.HghThe 11 values for each of the mixture studied are positive over the whole mole fraction range. For all the cases. exceptpropylene glycolrerr-butyl ether, 11 increases in a positive direction with increase in chain length of Il-alkoxypropanols. Thevalues of Lill, which refers to the deviation of the experimental values of the dynamic viscosities of the mixtures from themole fraction mixture law values, are found to be positive for all the mixtures. Further, the excess free energies of activation(LiC'E) for viscous flow have been calculated from the experimental data. The results for 11, Li11, and LiC'E are discussed interms of interactions between the components of the mixtures. Equations such as Heric's, Auslaender's, and MeAllister'sfour-body interaction model have been used to cOll'elate the kinematic viscosities,

Systematic studies of thermodynamic, transport, andacoustic properties of mixtures containing alkoxy-propanols with n-alkylamines 1,2, or n-alkanols3

-8 have

been carried out in our laboratory with the aim tohave a better understanding of molecular interactionsof the amine or alcohol and the ether at 298.15 K. Theaim of the present studies is to improve ourunderstanding of the molecular interactions forcharacterizing the physico-chemical behavior ofliquid mixtures. The viscosities at 298,15 K forpropylene glycol monomethyl ether (PGMME),propylene glycol monoethyl ether (PGMEE), andpropylene glycol tert-butyl ether (PG t-BE) withI-propanol have been reported in our earlier paper8

,

Tu et al.9 have reported excess molar volume andviscosities of propylene glycol mono methyl ether(PGMME), propylene glycol monopropyl ether(PGMPE), or propylene glycol monobutyl ether(PGMBE) + ethanol at different temperatures. It is feltthat the study will be useful in developing a betterunderstanding of molecular interactions of the presentmixtures by extending the measurements to some

other alkoxypropanols or n-alkanols. In our presentinvestigations, we report new experimental data forviscosity of binary solvent mixtures containingmethanol, ethanol or I-propanol with propyleneglycol monomethyl ether (PGMME), propyleneglycol monoethyl ether (PGMEE), propylene glycolmonopropyl ether (PGMPE), propylene glycolmonobutyl ether (PGMBE), and propylene glycoltert-butyl ether (PG t-BE) over the whole compositionrange at 298.15 K and atmospheric pressure. Densitiesof these mixtures, reported by us as excess molarvolumeslO

, have been used in this work to calculatethe dynamic viscosities,

Materials and MethodsHPLC grade methanol, ethanol, and I-propanol

(S.D, Fine Chemicals, Mumbai) were dried byrefluxing over fused calcium oxide for 5 h and thenfractionally distilled 2-3 timesll

.12

. Propyleneglycol monomethyl ether (Merck-Schuchardt.FRG), propylene glycol monoethyl ether (Acros.U.S.A.), and propylene glycol tert-butyl ether (Fluka.

purum) were the same as those used in our earlierstudio Propylene glycol monopropyl ether andpropylene glycol monobutyl ether were obtainedfrom Aldrich and used without further purification.All samples were stored and protected fromatmospheric moisture and CO2, Before measurements,the samples were dried over 0.4 nm molecularsieve (Fluka, AG) and were partially degassedunder vacuum. The purities of liquids werechecked by measuring and comparing the densities at298.15 ± 0.01 K and atmospheric pressure with this

d· I' 191?-19 I .correspon mg Iterature va ues ' - , as s lown mTable 1.

The densities (p) were measured with a single stempycnometer with an accuracy of ± 3 x 10-3 kg m,3.The kinematic viscosities of both the pureliquids and liquid mixtures were measured at298.15 K and atmospheric pressure using aUbbelohde suspended level viscometer2o

-22

. Theviscometer was filled with liquid or liquidmixtures, and its limbs were closed with Tefloncaps, taking due precaution to minimize evaporationlosses. The flow times measurement were made usingan electronic stop-watch with a precision of ± 0.01 s.An average of four or five sets of flow timeswas taken for each liquid mixture. The capsof the limbs were removed during the measurementsof flow times. The measured values of kinematicviscosities (v) were converted to dynamic viscosity(Y]) after multiplication by the density. Thereproducibility of dynamic viscosity results was foundto be within ± 0.003 mPa s. A thermostaticallycontrolled, well-stirred water bath, whose temperaturewas controlled to ± 0.01K, was used for all themeasurements.

Results and DiscussionResults obtained experimentally for viscosity of all

binary mixtures over a range of mole fraction at298.15 K and atmospheric pressure are given inTable 2. The measured viscosities were fitted to apolynomial of the type Eq. (1):

k~ i-IY] = £.J ({iXI

i=1

by the method of least-squares with each pointweighted equally. The values of coefficient ({i andstandard deviations () are summarized in Table 3.

The deviation of viscosity (L111) from a lineardependence on the average mole fraction has beencalculated from the relationship Eq. (2):

where Y],Y]1,and 112 are the viscosities of the mixturesand components 1 and 2, respectively. The variationsof L1Y]with mole fraction of ether at 298.15 K areshown in Figs 1 and 2.

The excess energies of activation (L1C*E) forVISCOUS flow were obtained from the expressionEq. (3).

L1C*E=RT{ In(Y]v)-x, in(Y]Iv,)-X2In(112v2)} ... (3)

where v is the molar volume of mixture, Rand T havetheir usual meaning. Data on derived densities.viscosities and excess energies of acti vation forviscous flow for the different binary mixtures at298.15 K are given in Table 2.

The values of L111, and L1G*Efor each mixture werecorrelated to the Redlich-Kister polynomial equationEq. (4).

Table 1- Observed and literature values or densities (p *) andviscosities (11) of pure liquid components at 298.15 K and

atmospheric pressure.X 10.3P 11

(kg m·3) (mPa s)

Expt. Lit Expl. Lit

0.91639 0.9165" 1.67 1.69'+"0.91650h 1674'

0.89241 1.905

088128 0.8813" 2.396 2.389"

0.87463 08848" 2.876 2.855"

0.86973 3.246

0.78645 0.78637" 0.546 0.5513'0.786433d 0.545"

0.7856 0.78551 1095 1.0969d

0.7854g 1.099g

0.79961 0.79960" 1954 19'+30'0.7996i'

Propylene glycolIllonomethyl ether

Propylene glycolmonoethyl ether

Propylene glycolmono propyl ether

Propylene glycolmonobutyl ether

Propylene glycolterr-butyl ether

Methanol

"ref.9; href.14; "ref. 12; dref.15; "ref. 16: Irel".l7: gref.18: hrel".l9:iref.13

PAL & GABA: VISCOSITIES OF BINARY LIQUID MIXTURES OF SOME n-ALKOXYPROPANOLS 1765

Table 2 - Densities (p), viscosities (11), deviation in viscosities (~11), and excess energies of activation (~G'E) for viscous !low of (n-alkoxypropanol + n-alkanol) systems at298.15 K

XI p' X 10'3 11 ~11 ~G'E XI p' X 10'3 11 ~11 ~G'E

(kg m'3) (mPa s) (mPa s) (J morl) (kg m") (mPa s) (mPa s) (J mol'l)

Propylene glvcol/llOnomelhyl elher (J) + Inel!twlOl (2) Propylene glycol/llOnoelhyl elher (J) + /llelhanol (2) - Conld.

0.0156 0.7919 0.567 0.004 68.62 0.5207 0.8722 1.465 0.214 1146.000.0334 0.7979 0.592 0.009 145.27 0.5819 0.8761 1.550 0.216 10783800500 0.8031 0.617 0.015 220.28

0.6406 0.8794 1.624 0.208 982:'\200768 0.8111 0.658 0.026 329.42

0.6980 0.8822 1.700 0.195 873060.1145 0.8213 0.712 0.037 449.36

01612 08326 0.781 0.054 582.800.7435 0.8842 1.713 0.171 75960

0.1932 0.8395 0.830 0.067 662.18 0.7753 0.8854 1.766 0.156 68001

0.2131 0.8436 0.858 0.073 701.22 0.8211 0.8871 1.781 0.128 55378

0.2435 0.8493 0.904 0.085 75996 0.8758 0.8889 1.821 0.086 3856-1-

02967 0.8584 0.980 0.101 83022 0.9013 0.8896 1.838 0067 30623

0.3394 0.8648 1042 0.114 872.73 0.9520 0.8911 1.880 0.035 153.730.3764 0.8699 1.087 0.118 880.22 Propylene glycolmonopropyl elher (J) + /llelha/lol (2)03957 08724 1.116 0.125 895.09

0.0120 0.7907 0.602 0.005 103.810.4445 0.8782 1.178 0.133 895.70

00281 0.7960 0.640 0.014 236990.5267 08867 1280 0.142 864.82

05663 0.8904 1.321 0.139 827.740.0572 0.8046 0.709 0.029 44763

0.6579 08978 1.421 0.136 729.18 0.0974 08149 0.809 0056 170530

0.7208 0.9022 1.486 0.129 640.52 0.1431 08246 0.929 0.091 949.1-1-

0.7397 09034 1.499 0.121 601.77 0.1913 0.8332 1.059 0.131 11:'\5.47

08046 0.9073 1.554 0.103 480.66 0.2228 0.8380 1.140 o 155 12:'\463

0.8774 0.9111 1.608 0075 323.29 0.2471 0.8413 1.202 0.172 1316.020.9115 0.9128 1.628 0.057 239.58 0.2598 0.8430 1.236 0182 1348020.9278 0.9135 1.634 0.045 193.99

0.2929 0.8469 1.317 0.202 1405 170.9549 09146 1649 0.030 124.27

0.3347 0.8513 1.429 0237 1472.25Propylene glycol/llOnoelhyl elher (J) + melhanol (2)

0.0131 0.7910 0.566 0.003 73.950.4121 0.8581 1.604 0269 149276

0.0328 0.7973 0.604 0.013 204.04 0.4613 0.8617 1.709 0.283 146954

0.0562 0.8043 0.647 0.025 339.86 0.5254 0.8656 1.839 0.296 140636

0.0868 0.8126 0.707 0.043 505.94 05657 0.8678 1.910 0.292 1339.47

0.1146 0.8193 0762 0.061 641.01 0.5921 0.8691 1.958 0291 129385

0.1507 0.8272 0827 0.077 769.35 0.6403 0.8712 2.035 0.279 1190550.1836 08335 0.889 0.094 874.07 0.6996 0.8735 2.117 0.252 1036790.2172 0.8393 0.950 0.109 958.28

0.7697 0.8758 2.213 0.218 839.450.2496 0.8443 1.015 0.121 1018.96

08094 0.8769 2.254 0.186 708.420.2713 0.8474 1.046 0.136 1068.46

0.3358 0.8556 1.160 0.161 1144.92 0.8579 0.8782 2.302 0.144 53983

0.3934 0.8616 1.268 0.189 1193.40 0.9063 0.8793 2.351 0.104 369.40

0.4537 0.8670 1.365 0.203 1184.99 09546 0.8803 2.390 0.054 184.22

0.4842 0.8695 1.430 0.212 1176.81 0.9759 0.8808 2.405 0.030 99.40

1766 INDIAN J CHEM, SEC A, NOVEMBER 2007

Table 2 - Densities (p), viscosities (11), deviation in viscosities (b.ll), and excess energies of activation (b.C*E) for viscous !low of(n-alkoxypropanol + n-alkanol) systems at 298.15 K - Con/d.

XI p* X 10.3 11 b.ll b.C*E XI p*x 10'3 11 b.ll b.C*E

(kg m'3) (mPa s) (mPa s) (J morl) (kg m'3) (mPa s) (mPa s) (J morl)

Propylene glycol monobutyl ether (1) + methanol (2) Propylene glycol monoe/hyl ether (1) + e/hanol (2)

0.0176 0.7926 0.639 0.025 253.41 0.0119 0.7882 1.105 0.000 \3.86

00408 0.7999 0.716 0.048 509.24 0.0405 0.7944 1.144 0.016 7899

0.0760 0.8095 0.841 0.092 851.78 0.0966 0.8055 1.219 0.045 190.+7

0.\095 0.8\73 0.951 0.125 1093.80 0.1391 0.8\32 1.269 0.062 252.40

0.1498 0.8252 1.085 0.167 1326.84 0.1810 0.8203 1.322 0080 3\2.07

0.1901 0.8318 1.215 0.203 1498.71 0.2336 0.8284 1382 0.097 365630.2102 0.8348 1.276 0.220 1564.71 0.2940 0.8367 1.448 0.114 4121\0.2526 0.8402 1.408 0.253 1674.05 0.3411 0.8426 1.497 0.125 437390.3095 0.8463 1.580 0.294 1763.77 0.3618 0.8451 1.5\4 0.126 439.330.3551 0.8504 1.706 0.315 1784.92 0.4152 0.8510 1.562 0.131 448.450.4130 0.8548 1.867 0.342 1779.56 0.4677 0.8563 \.605 0.131 443750.4815 0.8591 2.047 0.365 1721.18 0.5209 0.8612 1.645 0.\28 428680.5503 0.8626 2.214 0.373 1611.41 0.5721 0.8656 1.689 0.\31 419.380.6345 0.8660 2.397 0.362 1416.82 0.6221 0.8696 1.723 0.124 392.370.6720 0.8673 2.467 0.346 1308.52 0.6935 0.8748 1.773 0.1\6 350.\20.7096 0.8685 2.541 0.333 1197.98 0.7272 0.8771 1.791 0.107 320.180.7568 0.8698 2.623 0.307 1042.79

0.7823 0.8806 \.826 0.098 278.080.8161 0.8712 2.709 0.257 821.99

0.8692 0.8856 1.871 0.072 189840.8697 0.8724 2.773 0.197 602.16

0.9\72 0.8882 1.892 0.055 133240.9081 0.8731 2.811 0.147 434.93

0.89060.9646 1.912 0.035 73.0409481 0.8738 2.845 0.088 251.93

Propylene glycol/en-butyl ether (1) + methanol (2)Propylene glycol/er/-bu/yl ether (1) + e/hanol (2)

0.0289 0.7920 1.165 0.008 118.620.0167 0.7925 0.630 0.014 223.33

0.0498 0.7963 1.218 0.0\6 \99950.0499 0.8029 0.720 0.016 506.29

0.0895 0.8130 0.836 0.025 796.050.0825 0.8026 1302 0030 3\563

0.1235 0.8202 0.940 0.038 1005.030.1135 0.8080 1.382 0.043 410.4\

0.1805 0.8299 1.126 0.072 1292.330.1607 0.8154 1.502 0.061 529.29

0.2083 0.8339 1.219 0.091 1401.41 0.2175 0.8231 1.649 0086 64526

0.2127 0.8344 1.231 0.091 1410.43 0.2795 0.8303 1.806 0.110 73251

0.250\ 0.8390 1.357 0.117 1523.75 0.3207 0.8354 1.911 0.126 773.55

0.3207 0.8459 1.597 0.167 1660.66 0.3574 0.8379 2.000 0.137 79575

0.3813 0.8506 1.798 0.207 1707.18 0.4089 0.8422 2.128 0.154 81564

0.4760 0.8562 2.089 0.245 1660.04 0.4494 0.8453 2.224 0.163 81608

0.5469 0.8595 2.283 0.250 1546.59 0.4827 0.8476 2.303 0.169 80885

0.5955 0.8613 2.408 0.244 1439.44 0.5429 0.8514 2.443 0.\81 78286

0.6361 0.8626 2.503 0.231 1331.93 0.6440 0.8568 2.665 0.185 69347

0.6810 0.8639 2.600 0.207 1196.05 0.7110 0.8598 2.802 0.177 60716

0.8005 0.8666 2.831 0.118 773.84 0.7674 0.8621 2.909 0.164 5\8.64

0.8516 08675 2.922 0.069 570.40 0.8417 08648 3.042 0.136 3833\

08708 0.8678 2.958 0.058 498.46 0.8830 0.8662 3.109 0.1\4 297.99

0.9341 0.8688 3.081 0.011 245.54 0.9235 0.8674 3.170 0089 207.92\

09532 0.8690 3.125 0.004 172.41 0.9621 0.8686 3.226 0.061 117.34

PAL & GABA: VISCOSITIES OF BINARY LIQUID MIXTURES OF SOME n-ALKOXYPROPANOLS 1767

Table 2 - Densities (p), viscosities (11), deviation in viscosities (L'.11), and excess energies of activation (L'.C·E) for viscous flow of(n-alkoxypropanol + n-alkanol) systems at 298.15 K - Contd.

Xl p'x 10-3 11 L'.11 L'.c·E Xl p' X 10-3 11 L'.11 L'.C·E

(kg m-3) (rnPa s) (mPa s) (J morl) (kg m-3) (rnPa s) (mPa s) (J morl)

Propylene glycollllonopropyl ether (I) + I-propanol Propylene glycolmonoblllyl ether (I) + I-propanol

0.0196 0.8026 1.973 0.010 23.17 0.0205 0.8029 1.998 0025 49.62

0.0242 0.8034 1.980 0.014 30.83 0.0532 0.8078 2.056 0052 110.44

00466 0.8065 2.000 0.025 54.74 0.0800 0.8116 2.107 0.079 161490.1134 0.8157 2.069 0.062 126.89 0.1279 0.8179 2.191 0.119 2374201743 0.8232 2.114 0.079 166.41

0.1898 0.8252 2.285 0.156 307.920.2245 0.8289 2.153 0.094 196.75

0.2679 0.8336 2.177 0.098 208.650.2443 0.8309 2.367 0.187 359.43

0.3142 0.8382 2.208 0.108 226.41 0.2875 0.8351 2.421 0.201 38376

0.3550 0.8420 2.229 0.109 231.61 0.3359 0.8394 2.482 0.218 407.86

0.3754 0.8438 2.240 0.111 234.62 0.3558 0.8410 2.505 0.222 41391

0.4325 0.8487 2.261 0.105 229.74 0.4490 0.8481 2.591 0.221 41217

0.4884 0.8530 2.286 0.104 227.40 0.5093 0.8522 2.640 0.215 398910.5407 0.8568 2.308 0.102 220.61 0.5539 0.8550 2.672 0.206 381.460.6041 0.8611 2.334 0.099 210.43

0.6081 0.8581 2.711 0.195 357.8406473 0.8638 2.347 0.092 195.38

0.6488 0.8602 2.737 0.182 333.920.6824 0.8659 2.362 0.090 187.30

0.7513 0.8697 0.0730.7040 0.8630 2.760 0155 28918

2.377 154.25

0.8071 0.8726 2.390 0.060 125.67 0.7365 0.8645 2.776 0.141 26341

08783 0.8760 2.403 0.040 83.61 0.7766 0.8663 2.796 0.124 23108

0.8993 0.8770 2.397 0.024 60.71 0.8505 08693 2.833 0.092 16694

09592 0.8796 2.408 0.007 21.98 0.9127 0.8717 2.853 0.055 99.88

09892 0.8806 2.414 0.002 8.70 0.9346 0.8724 2.858 0.040 . 7422

Table 3 - Coefficients aj of Eq. (I) and standard deviations (J of (n-alkoxypropanol + n-alkanol) systems at 298.15 K

al a2 a3 a4 a5 (J

Propylene glycolmonomethyl ether (I) + methanol (2)

11 (mPa s) 0.5414 1.5167 - 0.0366 - 0.3524 0002

Propylene glycoll1lonoethyl ether (I) + methanol (2)

11 (mPa s) 0.5467 1.7472 0.9449 - 2.1517 0.8010 0004

Propylene glycolmonopropyl ether (I) + methanol (2)

11 (mPa s) 0.5709 2.3624 1.6014 - 3.7078 1.6012 0.003

Propylene glycolmonobutyl ether (I) + methanol (2)

11 (mPa s) 0.5725 3.5569 - 1.0508 0.2253 - 0.4341 0.002

Propylene glycoltert-butyl ether (I) + methanol (2)

11 (mPa s) 0.5938 2.2903 5.0183 - 8.6996 4.0205 0003

Propylene glycol mono ethyl ether (I) + ethanol (2)

11 (mPa s) 1.0877 1.4233 - 0.7384 0.1558 0002

Propylene glycoltert-blllyl ether (I) + ethanol (2)

11 (mPa s) 1.09 I3 2.5411 0.2172 - 0.5744 0001Propylene glycolmonopropyl ether (I) + I-propanol (2)

11 (mPa s) 1.9515 1.1559 - 1.4528 1.2876 - 0.5323 0003Propylene glycolmonobutyl ether (I) + I-propanol (2)

11 (mPa s) 1.9521 2.0848 - 1.7313 0.5778 0.003

X'I

Fig, I - Experimental viscosity deviations (1'>.11) for n-alkoxy-propanols (I) [a; I-melhoxy -2-propanol( 0); b; l-ethoxy-2-propanol (C); e; l-propoxy-2-propanol (1'>.); d; l-buloxy-2-propanol (0); e; l-tert-buloxy-2-propanol (.)] + melhanol (2)mixtures al 298,15 K, The solid curves have been derived fromEq, (4),

x 1

Fig, 2 - Experimental viscosity deviations (1'>.11) for n-alkoxy-propanol (I) + n-alkanol (2) al 298,15 K. [a, l-elhoxy-2-propanol(I) + ethanol (2) (C); b, l-terl-butoxy-2-propanol (I) + ethanol (2)(.); e, l-propoxy-2-propanol (I) + I-propanol (2) (1'>.):d, l-buloxy-2-propanol (I) (0) + I-propanol (2), The solid curveshave been derived from Eq, (4).

Table 4 - CoelTieients ai of Eq. (4) and standard deviations (cr) of (n-alkoxypropanol + n-alkanol) systems at 298.15 Ka I a2 a3 a4 as cr

Propylene glycollllOno/llethyl ether (J) + /IIethanol (2)

1'>.11 (mPa s) 0.5571 0.1592 - 0.0419 0.0743 0002I'>.C'E (J marl) 3517.5240 - 968.1860 343.3720 4

Propylene glycol/llonoethyl ether (J) + /IIethanol (2)

1'>.11 (mPa s) 0.8526 02960 - 0.2850 - 0.2413 0003I'>.C'E (J mOrl) 46526030 - 1371.9520 341.3332 - 5896103 7

Propylene glycol/llonopropyl ether (J) + /lIethanol (2)

1'>.11 (mPa s) 11675 0.2344 - 0.3756 0.1812 0.002I'>.C'E (J marl) 5746.6250 - 22942450 703.6607 4

Propylene glycol/llonobll/yl ether (I) + /IIethanol (2)

1'>.11 (mPa s) 14685 03184 0.0996 - 00372 0.002I'>.C'E (J mOrl) 6787.1380 - 2817.2140 1633.2670 - 1677.4710 1312.5690 6

Propylene glycoltert-blltyl ether (I) + /IIethanol (2)

1'>.11 (mPa s) 0.9977 0.3371 - 1.0943 - 04968 0.1511 0004I'>.C'E (J mOrl) 6523.5740 - 27654860 112.8932 - 1027.9390 921.9525 13

Propylene glycolmonoethyl ether (J) + ethanol (2)

1'>.11 (mPa s) 0.5272 - 0.0670 0.1091 0.3119 0.003I'>.C'E (J marl) 1758.3870 - 503.7724 2844699 410.1269 5

Propylene glycolterl-blltyl ether (J) + ethanol (2)

1'>.11 (mPa s) 0.6875 0.3105 0.1442 0.2724 0004I'>.C'E (J marl) 3216.9700 - 812.0545 321.7064 115.3384 222.0332 3

Propylene glycolmonopropyl ether (J) + J -propanol (2)

1'>.11 (mPa s) 04]87 - 0.0950 0.2740' - 0.1246 - 0.3668 0003I'>.C'E (J marl) 9082722 - 227.7369 336.9378 - 158.6350 - 374.0950 3

Propylene glycollllOnoblltyl ether (J) + J -propanol (2)

1'>.11 (mPa s) 08710 - 0.3035 00018 0.1100 0.003I'>.C'E (J mOrl) 1611.3440 - 574.4738 146.7540 3

kY (x) = (XI X2)L aj (XI-X2)i-1

i=1

Values of coefficients aj and the standard deviation0" are summarized in Table 4.

We have determined 11 and calculated 611 at298.15 K. The absolute values of 1( for mixtures ofmethanol molecules at 298.15 K vary in the order:PGMME < POMEE <POMPE< PGMBE < PO t-BE.Our results for 11 and those from Tu et al.9 andPal et al.8

, show that 11 decreases with I-propanol +lower ethers and increases for all other higher etherswith increasing mole fraction XI of alkoxypropanol.Again, there is a very obvious increase in themagnitudes of the viscosity as the alkyl chain lengthof the alkoxypropanol increases.

The values of 611, presented in Figs. 1 and 2 arepositive for all the mixtures over the entirecomposition range at 298.15 K. In fact, strongpositive deviations in the viscosity for the propy-lene glycol tert-butyl ether + ethanol at higheralkoxypropanol rich region and for the propyleneglycol monobutyl ether + I-propanol at loweralkoxypropanol rich region are observed. For eachether, the magnitude of the positive deviationdecreases as the alkyl chain length or viscosity of 1-alkanol increases. There is a very obviousincrease in the magnitude of 61( with the alkylchain end length increase in the alkoxypropanolmolecules, as is evident from Fig. 1. Figure 1 alsoshows that the values of 61( for propylene glycoltert-butyl ether + methanol become progressivelymore positive than those for propylene glycolmonobutyl ether + methanol. The positive 61(

suggests the specific interaction present in themixtures. The strong positive deviation in theviscosity for alkoxypropanol - lower l-alkanolsystems will imply that (i) the mixture is moreviscous than the corresponding ideal mixtureand (ii) the specified interactions, result in thenegative VmE (ref. 10) and positive excessenergies of activation 6C*E for viscous flowshown in Table 2. The magnitude of 6C*E increasesfrom propylene glycol monomethyl ether topropylene glycol monobutyl ether. They areattributed to large size and cohesive energydifference between the two unlike components.

Positive values of 6C*E parameter may be consideredas reliable guide to the presence of interaction2

)

between molecules. The higher values of 11, 61(.and 6C*E suggests that strength of speci ficinteraction is not the only factor, <Jnd that themolecular sizes and shapes of the components areequally important factors.

Assuming a four-body interaction model.McAllister proposed the following relations for theviscosity of mixtures:

where v (= 1(/p) refers to the kinematic viscosity ofthe mixture, VI and V2 are the kinematic viscosities ofthe pure components 1 and 2, respectively, and 21 [12,

21122, 22221 are interaction parameter that arecharacteristic of the binary system and can beevaluated by the least-square procedure.

Heric proposed the following relation forcorrelating the kinematic viscosities of binarymixtures:

where A, B, and C are the best fit coefficients of theHeric equation and represent the interactions betweenunlike molecules, and MI and M2 are molecularweights of components 1 and 2, respectively.

Auslaender developed the following expression(Eq. 7) for kinematic viscosities of binary mixtures:

where B12• A21, and B21 are the adjustable parametersrepresenting binary 12 interactions. To perform anumerical comparison of the correlating capabilitiesof Eqs (5-7), we have calculated the standardpercentage deviation 0" (%) between the experimentaland calculated viscosities using the relation:

Table 5 - Values of the parameters and standard percentage deviation in Eqs. (5), (6) and (7) in correlating viscosities ofdifferent mixtures

Mixtures Eq. (5) Eq. (6) Eq. (7)

Zll12 ZI122 Z2221 a (%) A B C a (%) BI2 B21 A21 a('fr)Methanol (2) +

Propylene glycol 0.57 0.79 0.26 0.16 1.43 - 0.41 0.18 0.15 1.53 3.25 03.+ 023mono methyl etherPropylene glycol 0.72 1.03 0.43 0.39 1.88 - 0.64 0.15 0.40 0.39 0.85 038 052monoethyl etherPropylene glycol 2.35 1.26 0.55 0.24 233 - 0.89 0.34 0.25 0.96 2.84 0.70 052monopropyl etherPropylene glycol 268 1.26 I. I I 1.18 2.72 - 1.37 0.98 1.09 2.68 17.53 167 058monobutyl etherPropylene glycol 2.59 1.54 0.90 0.79 2.62 -1.26 024 0.79 2.43 5. I I 204 281ter/-butyl ether

Ethanol (2) +Propylene glycol 0.77 0.99 0.61 0.48 0.71 - 0.15 0.1 I 021 1.27 2.90 0.76 OAOmonopropyl etherPropylene glycol 1.28 1.46 0.90 0.15 1.30 -0.31 0.18 0.13 2. I I 5. I I 0.40 0.21ter/-butyl ether

I-Propanol (2) +Propylene glycol 1.04 1.27 1.02 0.18 0.39 -0.08 0.1 I 0.24 2.64 -1.78 088 03.+monopropyl etherPropylene glycol 1.19 1.48 1.14 0.08 0.68 -0.16 0.16 0.31 0.47 086 020 017monobutyl ether

where 11 represents the number of experimental dataand k the number of numerical coefficients in therespective equations.

Table 5 gives the result of the correlating Eqs (5-7).The values of the different fitting parameters inducedin Eqs (5-7) were determined for the systems using aleast squares method, with equal weights assigned toeach point. These values are reported in Table 5together with the percentage standard deviations (cr%)between the calculated and experimental values. Allthree correlative models are capable of representing,with a higher or lesser degree of accuracy, theviscometric behavior of the studied mixtures. Thevalues of the parameters for most of the models varyregularly while going from propylene glycolmonomethyl ether to propylene glycol mono-propyl ether with methanol. It is observed that theMcAllister and the Heric relations fit the experimentalvalues better as compared to the Auslaender modelbecause the cr% values for the latter are larger than theothers in all of the systems except with propyleneglycol monobutyl ether + methanol, and propyleneglycol monopropyl ether + ethanol, as evidenced by

small cr% values. But in the case of propylene glycolmonobutyl ether + l-propanol, the three parametersequations of McAllister (Eq. 5) and Auslaender(Eq. 7) give very good results.

AcknowledgementFinancial support for the project (Grant No.

SRiSI/PC-33/2003) by the Government of Indiathrough the Department of Science and Technology(DST), New Delhi is gratefully acknowledged.

ReferencesI Pal A, Kumar A & Kumar H, J Chelll Therlllodyn. 38 (2006)

1227.2 Pal A & Bhardwaj R K, Z Ph)'s ChOIl, 216 (2002) 1033.3 Pal A & Kumar H, J Chelll ThemlOdyn, 36 (200'+) 173.4 Pal A & Kumar A, Indian J Phys, 78 (2004) 1319.5 Pal A & Kumar H, J Sol Chelll, 30 (200 I) 4 I I.6 Pal A & Kumar H, Indian.! Phys, 75B (200 I) 4 I9.7 Pal A, Sharma S & Singh Y P, .! Chelll Eng Data. 42 (1997)

1157.8 Pal A, S Sharma & Singh Y P, Indian'! Chelll. 37A (1998)

434.9 Tu Chein-Hsiun , Ku Su-Chen & Peng I-Hung . .! Chelll Eng

Data, 46 (2001) 1392.10 Pal A & Gaba R,.! Mol Liq, 135 (2007) 146.1I Perin D D, Armarego W L F & Perrin D R. Purificatioll of

Laboratory Chelllicals, 3'J Edn, (Pergamon Press. Oxford.UK) 1980.

12 Riddick J A, Bunger W B & Sakano T K, Organic Solvents,Techniqlles of Chelllistry, Vol II, 4th Edn, (John Wiley, NewYork) 1986.

13 Lorenzo D L, Maurizo F & Goivanni T, J Chell1 Eng Data,41 (1996) I 121.

14 Ku SlI-Chen & Tu Chein- Hsiun, J Chelll Eng Data, 45(2000) 391.

15 Haraschla P, Heintz A, Lehmann J K & Peters A, J ChelllEng Data, 44 (1999) 932.

16 Bakshi M S & Kour G, J Chelll Eng Data, 42 (1997) 298.17 Aminabhavi T M, Patil V B & Banerjee K, J Chem Eng

Data, 44 (1999) 1291.

18 Aralagllppi M I, Jadar C V & Aminabhavi T M, .J Chelll EngData, 44 (1999) 216.

19 Segade L, Jimenez de Liano J, Dominguez-Perez M, Caheja0, Cabanas M & Jimenez E, J Cheln Eng Data, 48 (2003)1251.

20 Conclaves F A, Kestin J & Sengers J V, Int J Thennophrs.12 (I 99 I) 1013

21 Pal A & Singh W, J Chelll Eng Data, 42 (1997) 23422 Pal A & Singh Y P, J Chelll Eng Data, 41 (1996) 1008.Palepu R, Oliver J & Mackinnon B, Can J Chelll, 63 (1985)1024.