Indian Journal o f C hemistry Vol. 43A, January 2004. pp. 28-34

Prediction of excess heat capacity from internal pressure data for n-alkoxyethanol + water mixtures at 298.15 K

Amalendu Pal* & Harsh Kumar

Depart ment o f C he mistry, Kuru kshetra Uni versity, Kurukshetra 136 11 9

E-ma il : pa lche m @sify.co m

Received 10 April 2003; revised 3 Novell/bel' 2003

Excess heat capac iti es (C/) have been dete rm ined at 298. 15 K fo r nine bin ary liquid mi xtures of a lko~yethano l s wi th water both fro m the Pri gogine-Flory theory and the inte rnal pressure data. Inte rnal pressure va lues have been computed on

the basis of the stati stica l thermodynam ic theory due to Flory. Values o f deviatio n in inte rnal pressure ("'Pin') have al so been obtai ned from the da ta of pure compone nts.

Extensive work has been carried out on measurements o f excess mol ar vo lume, vi scosity, and ultrasonic speed of (amphiphile+water) mi xtures l

•4 in o ur

laborato ry and is still in progress . These parameters have been used in understanding the nature and type of intermolecul ar interactio ns between the component molecules.

In recent years, internal pressure and free vo lume in solution thermodynamics have been found to be important parameters in the study of several che mical reactions and in the in vesti gatio ns of molecul ar interactions. In a conti nuing effort to co llect other thermodynamic quanti ti es in order to extend the ava il able database and have a be tte r thermodynamic desc ripti on for (amphiphile+ wate r) mi xtures, we report here theoret ica ll y derived excess heat capac ities (e p

E) and dev iatio n in intern al pressure

(6.Pin,) .

The internal pressure in liquids and liquid mi xtures can be evaluated with the he lp of v iscos ity and ultrasonic speed or from direct and/o r indirect measurements of thermal coeffic ient of ex pansio n and isothermal compress ibility . Free volume, viscosity and thermal conducti vity data can also be used to evaluate this parameter5

.

In the present work the internal pressures were evaluated with the help o f viscos ity, ultrasonic speed and density relatio nship as g iven by Suryanarayana6

.7

.

An attempt has been made to evaluate the inte rnal pressure and its excess counterpart f ro m Flory's stati sti cal theory.

Excess heat capac it ies have been deduced fro m inte rnal pressure data obtained with the he lp of the

above two approaches . Furthermore, these va lues have been compared with the values obtained from the Prigogine-Flo ry theorl whi ch takes in to account o f the free-volume effect. The excess heat capac ity values obtained employing three d ifferent approaches are fo und to be quite analomous. Su itable expl anati ons have been g iven.

Working Equations Thermodynamic equation of sta le may be used to

calcul ate inte rnal pressure:

where U is the inte rnal energy, V is the vo lume and T is the temperature . For most o f the liquids, the term (d P/dT)v known as thermal pressure coeffi c ient, when multipl ied by the temperature, has a magnitude becomes thousand times the magnitude of P, and the atmospheric pressure P becomes negli gibl e by compari son9

. Hence Eq . (1 ) takes the fo rm:

. . . (2)

Making use of coeffi c ient of the rmal ex pansio n, a and isothermal compress i bility, KT, internal pressure can be ex pressed as lO

:

... (3)

At zero pressure

P i lll = a T/Kr . . . (4)

PAL el al.: PREDICTION OF EXCESS HEAT CAPACITY FOR I/-ALKOXYETHANOL+WATER MIXTURES 29

For multicomponent system the ideal values of Pint are given by additivity of internal pressures of pure components in the mole fraction scale:

(Pint)idl = Lxi (Pint)i i=1

... (5)

where Xi, and (Pint)i are the mole fraction and internal pressure of the ith component, respectively.

The deviation in internal pressure of liquid mixture is given byll:

... (6)

where (Pilll)mix is internal pressure of mixtures that includes all types of interactions.

In our previous thermodynamic studies we evaluated l2 Pint with the help of density p, viscosity 1')

and ultrasonic speed Ll as given by Suryanarayana6.7.

The Pint values, thus obtained, have been used to calculate the excess heat capacity .

The theoretical values of Pint for mixtures were calculated from Flory ' s theory as reported 13. The reduced volume v of the liquid is defined as:

v = VIV* = [(I + 4/3aD/(I + aD]3 ... (7)

where V and V* are the molar volume and the characteristic volume of the liquid.

Excess functions like excess molar volume 0, excess enthalpy HE, and excess isothermal compressibility K/ can be used to calculate the reduced volume of the mixture v. When determined on the basis of 0, the reduced volume of the mixutre l4 can be given by the expression:

.. . (8)

where <PI and <P2 are segment fractions of components and vE is reduced excess volume of mixture given by:

... (9)

In the present study the value of thermal expansion coefficient a for the mixture was determined from v values of the mixture using the reduced equation of state 13

:

aT=3(vJl}-I)/[I-3(v I/3 -1)] ... (10)

The theoretical values of Pint were then calculated from Eq. (4) . The derived Pint values have been used to calculate the excess heat capacity.

Excess heat capacity Cp E can be calculated from the internal pressure values with the following ex pression8.15.16:

Cp E = to. ( aPint V)

= amix(Pint)mix Vmix - Lxi ai (Pint)i Vi ... (II)

The Prigogine-Flory theory8.15 gives expression for C E

p

CpE

= (XISI * + x2S2*)Cp(D-xISI * Cp(TI)-X2S2*Cp(T2) ... (12)

where

Cp = (4/3\1·1 /3 - I) ... (13)

S* = P*V*/P .. . (1 4)

vand V* can be calculated from Eqs (7-9)

T= TIP = (v1/3 _ 1)lv4/3 ... ( IS )

... (16)

Results and Discussion The nine binary liquid mixtures taken for the

present investigation are: ethylene glycol monomethyl ether (EGMME) + ; ethylene glycol monoethyl ether (EGMEE) +; ethylene glycol monobutyl ether (EGMBE) +; diethylene glycol monomethyl ether (DEGMME) +; diethylene glycol monoethyl ether (DEGMEE) +; diethylene glycol monobutyl ether (DEGMBE) +; triethylene glycol monomethyl ether (tri-EGMME) +; triethylene glycol monoethyl ether (tri-EGMEE) +; triethylene glycol monobutyl ether (tri-EGMBE) + water. Density p, ultrasonic speed u and other thermodynamic parameter e.g. thermal expansion coefficient a, heat capacity Cp and isothermal expansion compressibility KT of pure liquid components J.3.4· 17.26 at 298.15 K are recorded in Table I. Table 1 also reports the characteristic parameters from Flory's theory. Internal pressure values Pint for all the liquid-liquid mixtures were calculated from Eq. (4). The thermal coefficients of expansion a were derived from Eq. (10). The theoretical values of Cp of binary mixtures were evaluated from the theoreticalll ·15 derived values of Cp E from Eq. (12) as given in Table 2. The isothermal compressibilities Kr were evaluated from the Lt, p and Cp relationship. The ultrasonic speed and densi ty values were taken from the measurements previously

30 INDIAN J CHEM, SEC A, JANUARY 2004

Table I- Prigogine-Flory and other related parameters for pure components at 298. 15 K

Component p x 10-3 /.l ex Cp KT Pin. II

(kg m-3) (m S- I) (kK- I) (JK- Imol - I) (TPa- l) (atm)

H2O 0.99704817 1496.687' 8 0.257 17 75.292 19 452.47 1671.33 1.0731 CH3OC2H4OH 0.9600220 1339.8920 0.9198" 176.421 693.54 3902.47 1.2312 C2HsOC2H4OH 0.9250220 1300.4020 0.9750" 210.321 770.59 3722.98 1.2426 C4H9OC2H4OH 0.89581 20 1304.4020 0.94 19" 270.621 784.93 3529.45 1.2356 CH3(OC2H4h OH 1.01764 1423.1 3 0 .849b 271.1 22 578.83 4315.93 1.2159 C2H5(OC2H4)20H 0.98394 1385.23 0 .84623 298.1 23 627.3 1 3968.32 1.2153 C4H9(OC2H4h OH 0.94794 1356.43 0.84323 358.423 674.59 3677.10 1.2147 CH3(OC2H4h OH 1.04304 1456.5 1 0.82824 358.024 541.84 4496.53 1.2098 C2H5(OC2H4h OH 1.016 14 1417.3 1 0.85625 389.025 588.45 4280.38 1.2175

C4H9(OC2H4)30H 0.98684 1398.826 0.84825 450.025 617.52 4040.76 1.2158

Component T Cp P* X 10-6 V* X 106 T* S* (J m-3) (m3 mol- I) (K) (JK- Imol- I)

H2O 0.02 17 3.3075

CH3OC2H4OH 0.0544 4.0979

C2H5OC2H4OH 0.0562 4. 1630

C4H9OC2H4OH 0.0551 4.1229

CHJCOC2H4h OH 0.0519 4.0 125

C2Hs(OC2H4h OH 0.0518 4.0092

C4H9(OC2H4h OH 0.05 17 4.0059

CH3(OC2H4)30H 0.0508 3 .9790

C2Hs(OC2H4hOH 0.0522 4.0213

C4H9(OC2H4hOH 0.0519 4.01 19

"From ref 20 bCalculated from our measured densi ties

. d . h ' I b 1-4 16 h 20 carne out elt er In our a oratory .- or ot ers . Thus we obtained two sets of P i lll values of liquid­liquid mixtures; first from Eq . (4) and the second one from ultrasonic speed, density and viscosity relationship6.7 as reported in our earlier paperl 2. From the derived values of P i lll with two sets of data, the C/ values were calculated using Eq . (II). The calculated values are recorded in Table 2. Due to lack of experimental data on viscosi ty at 298.15 K we are unable to calculate (Pint)mix for the mixtures of ethylene glycol monoethyl ether and ethylene glycol monobutyl ether with water. The deviations in internal pressures I1Pillt calculated using Eqs (4) and (6) are given in Table 2.

An examination of Table 2 shows that for all mixtures the minima of I1Pint are shifted towards the water-rich region of the mixture as the polar head group as well as the alkyl chain length of the amphiphile increase and the values are positive over the whole concentration range. Further it shows that, with the addition of water to amphiphile, deviations from ideality in internal pressure are observed, which

195 16.8377 13739 0.2390

599 64.3797 548 1 7.0358

582 78.4059 5305 8.601 7

546 106.7666 5411 10.7733

647 97 .1054 5745 10.9360

554 112.21 17 5756 10.8001

550 140.8955 5778 13.4117

66 1 130.1 306 5869 14.6560

643 144.0694 5712 16.2179

605 171.9375 5745 18.1066

are maximum in the water-rich region. It has been established that the sign and magnitude of excess function give good est imate of the trength of the unlike interactions in binary mixtures. We can thus make an assumption that strong intermolecular interactions between amphiphile and water are predominant at lower concentrations of water. Further, positive values of I1Pillt decrease with the increase of the alkyl chain length of the amphiphile. It means that (Pillt)mix is more cohesive than the corresponding ideal mixture (Pint)idl. suggesting that ' non-chemical interaction' is less than the ' chemical interaction' in the binary mixtures. Th is behaviour is opposite to the change in the polar head group of the amphiphile.

The excess heat capacity Cp E value ') so obtained are compared in Table 2 with the Prigogine-Flory rheory and those obtained from Pillt data on the basis of Flory's theory and Suryanarayana' s method. However, calculated values of Cp E from the Prigogine-Flory theory and from the internal pressure data (derived from Flory 's theory) are negative and

PAL el al.: PREDICTION OF EXCESS HEAT CAPACITY FOR I1-ALKOXYETHANOL+WATER M IXTURES 31

Table 2-Deviation in internal pressures and excess heat capacities for (Il-alkoxyethanol + water) mixtures at 298. 15 K

0.0199 0.0398 0.0598 0.0797 0.0983 0.1303 0.1705 0.2203 0.2797 0.3393

0.0079 0.0 159 0.0249 0.0348 0.0505 0.0625 0.0748 0.0873 0.0999 0.1 196 0.1500 0.1796 0.2 195

0.003 1 0.0032 0.0065 0.0066 0.0099 0.0 100 0.0 132 0.0134 0.0159 0.0246 0.0334 0.0400 0.0500 0.0551 0.0741 0.0860 0.0949

0.0435 0.0495 0.06 18 0.0705 0.0817 0. 1063 0. 1226

188.3 1 370. 17 540.19 686.22 803.76 960. 11 1092.96 1182.08 1219.57 1218.07

12 1.47 23 1.89 342.79 452.08 603.01 701 .59 780.72 848.55 907.66 982.49 1067.9 1 11 33.74 1176.99

66.63 68.05 135.48 136.05 195.37 195.49 247.49 247.74 274. 13 333. 14 406.54 457.82 539.67 566.64 687.77 745.70 786.38

54 1.48 605.71 742.33 824.79 92 1.2 1 11 03.85 11 94.97

Eq.( 12) Eq.(4& 11 ) Eq.(l l )*

-0.02 -0.32 -0.04 -0.6 1 -0.05 -0.87 -0.07 -1.10 -0.08 - 1.30 -0. 11 -1.62 -0. 13 -1.95 - 0. 15 -2.28 - 0.17 - 2.53 -0.18 -2.6 1

-0.01 -0. 14 - 0.02 -0.29 -0.03 -0.45 -0.04 -0.63 -0.06 -0.9 1 -0.07 - 1. 11 - 0.09 - 1.32 -0. 10 -1.5 1 -0.1 1 -1.70 -0. 13 -1.96 -0.15 -2.29 - 0.1 7 - 2.52 -0. 19 -2.77

-0.0 1 -0.06 -0.0 1 - 0.07 - 0.0 1 -0. 13 -0.0 1 - 0. 14 - 0.02 -0.22 -0.02 -0.22 - 0.02 -0.29 -0.02 -0.29 - 0.Q2 -0.36 -0.04 -0.56 - 0.05 -0.72 -0.05 -0.83 -0.06 -0.98 - 0.07 - 1.00 -0.09 - 1.30 -0.09 -1 .44 -0. 10 - 1.53

- 0.05 -1.07 -0.06 -1.20 -0.08 -1.42 -0.09 - 1.58 -0. 10 -1.77 -0. 12 -2. 12 -0. 13 - 2.33

CH,OC1 H40H (1) + H20 (2) 1.68 0.3977 1176.08 3.35 4.74 6.04 6.96 8.87 10.83 12.99 14.86 15.89

0.4590 0.5167 0.5798 0.6393 0.6999 0.7599 0.8205 0.8732 0.9259

1110. 16 1024.29 9 13.29 797.78 672.0 1 541.86 4 12.23 294.41 180.24

C2HsOC2H40H (1) + H20 (2) 0.2703 120 1.48 0.3293 1183.38 0.40 14 0.4682 0.54 17 0.6 128 0.6698 0.73 19 0.7906 0.8506 0.90 14 0.9515

1096. 17 104 1.6 1 925.89 796.34 686. 14 560.55 44 1.24 316.26 208.46 100.62

C4H90C2H40H ( I ) + H20 (2) 0. 1152 862.25 0.1545 0. 175 1 0.2222 0.2562 0.2845 0.38 10 0.4572 0.5062 0.5816 0.6434 0.6755 0.7375 0.8226 0.8444 0.904 1 0.9806

CH,(OC1H4hOH (I) + H20 (2)

965.10 998.42 1039.94 105 1.59 1049.43 991.6 1 904.17 842. 10 73 1.63 63 1.88 576.09 473.09 319.60 28 1.66 157.55 31.68

6.23 0.2342 1490.12 7. 14 8.7 1 9.79 10.99 13.77 15.43

0.2830 0.3367 0.4449 0.5842 0.6670 0.749 1

1492.72 1461.96 1305.38 10 13.99 823.20 327.29

Eq. (12) Eq.(4& 11) Eq. (l I)*

-0. 18 - 0.18 -0. 17 - 0.16 -0.1 5 -0. 13 -0. 11 - 0.08 -0.06 -0.03

-0.20 -0.2 1 -0.2 1 -0.20 - 0. 19 -0. 17 -0. 15 -0.1 3 - 0.10 -0.08 -0.05 -0.03

-0. 11 -0.13 - 0. 14 -0. 16 - 0.16 -0. 17 -0. 17 -0.17 -0. 16 -0.1 4 -0. 13 - 0. 12 -0. 10 - 0.07 -0.06 -0.04 -0.0 1

-0. 18 -0. 19 -0.20 -0. 19 -0. 16 -0. 14 -0. 11

-2.60 -2.47 - 2.3 1 -2. 10 -1.87 - 1.60 - 1.33 - 0.95 -0.66 - 0.28

- 2.94 -3.02 -3.04 -2.77 - 2.49 -2.2 1 -1.93 -1.62 - 1.28 -0.90 - 0.63 -0.0 1

- 1.7 1 - 1.99 - 2. 11 -2.3 1 -2.38 - 2.42 -2.4 1 - 2.33 -2. 18 - 1.91 -1 .70 - 1.59 - 1.26 -0.9 1 -0.78 -0.65 -0. 10

- 3.09 -3.23 -3.2 1 -3.00 -2.51 -2.1 1 - 1.62

16.94 16.82 16.33 14.91 13.92 12.25 9.84 6.87 5.25 3.2 1

24.96 27.39 29.67 28.06 24.01 20.73 15.42

COllld···-

32 INDIAN J CHEM, SEC A, JANUAR Y 2004

Table 2-Deviation in internal pressures and excess heat capac ities for (II-alkoxyethanol + water) mixtures at 298 .15 K-Colltd

0.1460 0.1791

0.0430 0.0521 0.0653 0.0805 0.1008 0.1210 0.1354 0.1531 0.1695

0.0016 0.0020 0.0057 0.0091 0.0107 0.0144 0.0168 0.0191 0.0209 0.0232 0.0340 0.0398 0.0408 0.0477 0.0588

0.0010 0.0025 0.0040 0.0082 0.0147 0.0380 0.0514 0.0609 0.0711 0.0854 0.1098 0.12 17 0.1415 0.1640 0.1852 0.2063 0.2565

0.0004 0.0016 0.021

1304.85 1408.64

609.84 716.1 6 844.30 965.39 1088.3 1 1180.76 1225.26 1268. 15 1301.84

59.52 71.49 182.03 278.76 327.37 410.95 459.69 499.98 520.60 553.00 663.21 715.30 725.38 776.37 861.41

23.73 57.59 79.17 169. 19 291.61 701.76 893.28 1012.50 1126.56 1261.80 1427.93 1483.52 1558.66 1610.68 1649.28 1660.2 1 1659.02

13.1 2 39.83 52.31

Eq.( 12) Eq.(4&11) Eq.(II)*

-0. 15 -2.56 -0. 17 -2.82

-0.06 -1.07 -0.07 -1.25 -0.08 -1.50 -0.09 -1.76 -0. 11 -2.08 -0. 12 -2.33 -0. 13 -2.50 -0.14 -2.69 -0. 15 -2.82

-0.002 -0.03 -0.003 -0.04 -0.0 1 - 0.11 -0.0 1 -0.17 -0.02 -0.19 -0.02 -0.26 -0.03 -0.31 -0.03 -0.35 - 0.03 -0.39 -0.03 -0.43 -0.05 -0.65 -0.05 -0.76 -0.06 -0.78 -0.06 -0.9 1 -0.07 - 1.08

-0.002 -0.03 -0.005 -0.08 -0.007 -0.15 -0.0 1 -0.29 -0.03 -0.5 1 -0.06 -1.20 -0.08 -1.55 -0.Q9 -1.77 -0. 11 -1.99 -0. 12 -2.27 -0.14 -2.69 -0.16 -2.89 -0. 17 -3. 15 -0. 18 -3.42 -0.20 -3.60 -0.20 -3.79 -0.22 -4.03

-0.0 1 -0.01 -0.0 1 -0.06 -0.0 1 -0.08

17.74 20.55

0.8389 0.9582

410. 18 109.38

C2H,(OC2H4)20H ( I) + H20 (2) 8.20 0.1913 1334.93 9.39 11.42 13.76 16.07 18.74 20.56 22.89 24.50

0.2485 0.3116 0.3975 0.5108 0.6 172 0.7235 0.7818 0.8860

1387.27 1335.34 1234.78 1042.60 829.29 601.42 473. 11 247 .62

C4H9(OC2H4hOH ( I) + H20 (2) l.l 3 0.0778 969.11 1.32 2.75 3.95 4.45 5.68 6.46 7.20 7.86 8.58 12.00 13.86 14.35 16.5 1 19.28

0.1025 0.1352 0.1713 0.2244 0.2695 0.3081 0.4136 0.4994 0.5582 0.6696 0.7403 0.8806 0.9321

CH .1 (OC2H4hO H ( I) + H20 (2)

1072.60 11 49.57 1196.9 1 1208.33 11 86.76 11 93.29 1033.13 908.73 820.06 621.78 789.88 215.07 11 8.09

-3.44 0.2890 1633.45 - 2.50 - 1.80 0.23 2.58 9.26 12.23 14.3 1 16.40 19.5 1 22.65 25.23 27 .37 30.22 33.06 34.66 39.03

0.3194 0.3583 0.4019 0.4415 0.4719 0.5787 0.5754 0.5898 0.6561 0.7082 0.7359 0.7820 0.8142 0.8802 0.9349 0.9739

1601.43 1545.0 1 1471.20 1392. 17 1320.22 11 47.94 1087.83 1052.92 885.44 749.33 675.78 550.72 468.51 29 1.42 147.67 42.74

C2H\(OC2H4h OH ( I) + H20 (2) -3.67 0.2463 1648.80 -2.87 0.2778 1628. [3 -2.48 0.3082 1579. 17

C/ /(1 K -I mol- I ) Eq . (12) Eq . (4&1 1) Eq.(II)*

-0.07 -0.0

-0.1 6 -0. 17 -0. 18 -0. 18 -0. 16 -0. 14 -0. 11 -0.09 -0.05

-0.09 -0. 11 -0. 13 -0. 14 -0. 16 -0. 17 -0. [7 -0.17 -0. 16 -0. 14 -0.11 -0.09 -0.05 -0.04

-0.22 -0.22 - 0.22 -0.21 -0.2 1 -0.20 -0. 17 -0. 17 -0. 16 -0. 14 -0. 13 -0. 12 -0. 10 -0.09 -0.06 -0.03 -0.0 1

-0.24 -0.24 -0.24

- 1 02 -0. 18

-2.96 -3 .14 -3.26 -3 13 -2.77 -2 35 -189 -1.58 -0.91

-1 .35 -164 -1.98 -226 -2.58 -275 -2 .69 -2 84 -2.60 -2.28 - 1 81 -1 .54 - l.J 3 -0 .82

-4 .12 -4.13 -4 .10 -3 .99 -3 .87 -3.79 - 3.62 -3 .3 [ -3 .24 -2.93 -2.71 -2 .59 -2.43 -2.17 -182 -137 -1 .09

-3.92 -3 .94 -3.97

13.14 5.30

25.80 30.88 32.4 1 33.28 28.79 23.45 18.51 15.25 6.14

23.51 28.30 34.29 37.84 41.28 43.45 43.46 39.21 34.73 28.89 22.92 18.90 7.27 0.64

39.76 40.93 42.41 39.87 40.29 39.69 28.47 28.59 29.51 27.37 23 .37 17.68 19.29 6.65 7.73 0.96

44 .97 45.51 46.88

COII/d. -

PAL et al.: PREDICTION OF EXCESS HEAT CAPACITY FOR Il-ALKOXYETHANOL+WATER MIXTURES 33

Table 2-Deviation in internal pressures and excess heat capacities for (n-alkoxyethanol + water) mixtures at 298. 15 K-Contd

Eq.(l2) Eq.(4&11) Eq.(II)* Eq.(12) Eq.(4&11) Eq.(lI)*

0.0041 0.0066 0.0099 0.0144 0.0215 0.0337 0.0418 0.0525 0.0613 0.0714 0.0827 0.0914 0.1127 0.1437 0.1746 0.2059

90.64 147.24 220.25 312.15 454.95 686.60 812.63 968.35 1075.28 1183.67 1269.89 1337.5 1 1449.99 1550.58 1610.37 1636.87

-0.01 -0.01 -0.02 -0.03 -0.04 -0.07 -0.08 -0.10 -0.11 -0.12 -0.14 -0.15 -0.17 -0.20 -0.21 -0.23

-0.17 -0.26 -0.38 -0.56 -0.81 -1.19 -1.44 -1.72 -1.94 -2.17 -2.43 -2.59 -2.96 -3.39 -3.67 -3.85

-1.29 -0.01 1.55 3.35 5.76 9.34 11.71 14.29 16.44 18.89 21.35 23.17 27.37 33.73 37.20 41.14

0.3551 0.4041 0.4405 0.4693 0.5172 0.5556 0.6038 0.6420 0.6811 0.7486 0.7756 0.8113 0.8352 0.8804 0.9549 0.9740

1514.58 1400.05 1355.81 1295.23 1191.80 1102.72 987.58 899.26 804.14 637.61 569.46 474.32 414.68 301.81 114.48 64.47

C4H9(OC2H4hOH (I) + H20 (2) 0.0045 172.83 -0.01 -0.14 0.73 0.3062 1414.08 0.0099 359.73 -0.02 -0.29 3.96 0.3418 1367.96 0.0134 464.85 -0.03 -0.39 5.73 0.4033 1271.53 0.0177 579.93 -0.04 -0.50 7.98 0.4651 1162.52 0.0207 640.91 -0.04 -0.59 9.62 0.4965 1106.38 0.0247 706.56 -0.05 -0.70 11.29 0.5465 1008.22 0.0316 807.30 -0.06 -0.90 14.46 0.5766 947.61 0.0432 951.91 -0.08 -1.18 19.06 0.6303 835.01 0.0573 1093.67 -0.10 -1.49 24.53 0.6961 689.86 0.0684 1178.63 -0. 11 -1.70 28.10 0.7515 567.16 0.0839 1276.54 -0.12 -1.97 32.45 0.7845 488.72 0.1079 1375.23 -0.15 -2.34 38.31 0.8367 365.59 0.1420 1458.32 -0.17 -2.74 45.53 0.8824 262.38 0.1845 1493.24 -0. 19 -3.14 49.87 0.9209 173.30 0.2152 1491.44 -0.20 -3.33 53.79 0.9518 101.34 0.2686 1458.58 -0.21 -3.53 54.46 0.9713 60.99

*Intemal pressure values 12 calculated using Suryanarayana equation6.7

•

-0.24 -0.23 -0.22 -0.21 -0.20 -0.19 -0.17 -0.16 -0.15 -0.12 -0.11 -0.09 -0.08 -0.06 -0.02 -0.01

-0.21 -0.21 -0.20 -0.19 -0.18 -0.17 -0.16 -0.14 -0.12 -0.10 -0.09 -0.08 -0.06 -0.05 -0.03 -0.02

-3.84 - 3.69 -3.54 - 3.40 -3.15 -2.94 -2.73 -2.47 -2.20 -1.78 -1.63 - 1.45 -1.28 -0.94 -0.32 -0.21

-3.61 -3.60 -3.47 -3.22 -3.03 -2.73 -2.54 -2. 19 -1.90 -1 .59 -1 .53 -1.44 -1.17 -1.00 -0.76 -0.43

45.69 45.32 45.61 43.95 37.41 34.30 30.76 25.79 27.84 23.0) 15 .59 16.93 17.80 9.55 10.67 -0.09

56.35 55.13 49.77 45.10 41.22 37.82 31.50 35.07 28.88 20.73 22.03 11.65 12.82 -0.09 -0.06 -0.12

can be considered satisfactory . Both theories predict the sign and similar variation of C/ with the alkyl chain length as well as the polar head group of the amphiphile and gives a reasonable estimate of the value. The disagreement with Suryanarayana is more due to the inaccuracy of internal pressures. This may be attributed to the uncertainties in the experimental data of p, u and YJ .

2 Pal A & Singh Y P,.! Chelll Therlllodyn, 27 (1995) 1329. 3 Pal A & Singh Y P,.! Gem Thennodyn, 28 (1996) 143.

Acknowledgement Harsh Kumar thanks the CSIR, New Delhi for a

Senior Research Fellowship (Fellowship no. 9/105/107/2001IEMR-I) and financial assistance.

References 1 Pal A & Singh Y P,.! G elll Eng Dara, 42 (1997) 689.

4 Pal A & Singh Y P, Indial! J Chelll, 35A (1996) 11 20; 35A (1996) 137.

5 Suryanarayana C V & Kuppusami J, J Acoust Soc India , 4 (1976) 75.

6 Sliryanarayana C V, Indiall J Pure Appi Phys, 28 (1989) 757. 7 Suryanarayana C V, Indian J Chelll, 25A (1986) 538. 8 Prigogine I (with the collaboration of Mathet V & Bellemans

A) Th e Molecular Theory of Soillliol1s (North Holland Publishing Co., Amsterdam), 1957; Flory P J, DisCl/s Faraday Soc, 49 (1970) 7.

9 Dack M R J, Chem Soc Rev. 4 (1975) 211. 10 Renllncio JAR, Breedve1d G J F & Prallsnitz J M. J Phys

Gem, 81 (1977) 324. 11 Aminabhavi T M, Patil V B, Banerjee K & Balundgi R H,

Bull Chelll Soc Japan , 72 (1999) 1187. 12 Pal A & Kumar H, Phys Chelll Liq, 41 (2003) 405. 13 Flory P J, J Alii Chem Soc, 87 (1965) 1833. 14 Abe A & Flory P J, J Alii Gem Soc, 87 (1965) J 838.

34 INDIAN J CH EM, SEC A, JAN UARY 2004

15 Bhattacharyya S N & Patterson D, J Phys Chelll , 83 ( 1979) 2979.

16 Pandey J D, Dubey N, Dwi vedi D K & Dey R, Phys Chelll Liq, 39 (200 I ) 78 1.

17 Kell G S, J Chelll Ellg Data, 12 ( 1967) 66. 18 DelGrosso V A & Madar C W, J Acoust Soc Allier, 52 ( 1972)

1442 . 19 Ke ll G S, J Chelll Ellg Data , 20 ( 1975) 97. 20 Douheret G, Pal A & Dav is M I, J Chelll TherlllodYIl . 22

( 1990) 99. 2 1 Roux G, Perron G, & Desnoyers J E, J Solll Chelll , 7 ( 1978)

639.

22 Ridd ick J A, Bunger W B & Sakano T K, Orgall ic Solvellts: Physical Properties alld Method of Puri/icatioll . (Wiley Interscience, New York) 4 th Edn, 1986.

23 Douheret G, Salgado S, Davis M I & Loya J, Thenllochilll Acta, 207 ( 1992) 3 13.

24 Douheret G, Lajo ie P, Davis M I , Ratliff J L, U lloa J & Ho il and H, J Chelll Soc Faraday Trails, 9 1 ( 1995) 229 1.

25 Douheret G, Davis M I, Ulloa J , Ho iland H & Fjellanger J, J Chelll Soc Faraday Trails, 92 ( 1996) 2369.

26 Singh Y P, Ph D Doctoral Thesis, Kurukshetra Uni versity, Kurukshetra ( 1996).