Indian Journal of Chemistry Vol. 38A. March 1999. pp.2 19-229

Molar excess free energy of mixing of 1-propanol or 2-propanol + aromatic hydrocarbons at 308.15 K in terms of an association model

with a Flory contribution term

_ Sanjeev Maken* Department of Applied Sciences

C.R. State College of Engineering. Murthal Sonepat '133039, India

and Vibha Gupta, K C Kalra & K C Singh

Department of Chemistry, Maharshi Dayanand University, Rohtak 124001, India

Received 23 August 1996; revised 9 February 1998

Excess molar Gibbs free energy of mixing for I -propanol or 2-propanol + benzene, + toluene, + 0-, m-and p­xylenes at 308.15 K are calculated by Barker's method from vapour pressure data measured by a static method. The free energy of mixing for these binary systems are also predicted in terms of Mecke-Kempter type of association model with Flory contribution term using two interaction parameters. The predicted value agrees reasonably well with the experimental values .

The thermodynamic properties of binary mixtures of alkanol with polar or non-polar solvents have been described by a number of workt~rsl -5 in terms of lattice model theories . In our earlier work6

-9 we have

analysed the molar excess volumes and molar excess enthalpies data of I -propanol or 2-propanol + cyc1ohexane, benzene, toluene, 0-, m- and p-xylenes and molar excess Gibbs free energies of I-propanol or 2-propanol + cyc10hexane at 298.15 and 308.1 5 K in terms of an association model proposed by Treszczanowicz and Benson5

. In this paper Gibbs free energy of mixing for] -propanol or 2-propanol + aromatic hydrocarbons at 308.15 K calculated using Barker's methodlO and their interpretation in terms of Mccke-Kempter (MK) type of association model combined with a Flory contribution term is presented.

Materials and Methods I-Propanol, 2-propanol, benzene, toluene, 0-, m­

and p-xylenes (E. Merck) were purified by standard procedures. The p,urities of final samples were checked by measuring their densities at 298 .15 ± 0.01 K; these agree to within ± 5 x 10.5 g cm·3

with their corresponding literature values. Total . vapour pressure of I-propanol or 2-propanol (1) +

benzene, + toluene, +0- ,+m and +p-xylene (2) mixtures were measured as a function of liquid phase mole fraction X I at 308.15 ± 0.01 K by a static method ll

. The height of mercury column in the manometer was read up to ± 0.001 em USIng cathetometer (OSA W, India). All the vapour pressure measurements were reproducible to better than ± 0.02 torr. Our experimental values for the vapour pressure for all the pure compounds compared well with the literature values.

The composition of the liquid phase was determined by measuring its refractive index at 308.15 K using Abbe refractometer (OSA W, India), which could read up to ± 0.001 in the manner described by Struble et al l2

• The uncertainties in the liquid phase composition were about 0.01 mol%.

Results and Discussion The excess Gibbs free energy of mixing GE

, for the present I-propanol or 2-propanol (1) + aromatic

220 INDIAN 1 CHEM, SEC. A, MARCH 1999

Table I - Measured total vapour pressure (P), parti al pressure (PI and P2

, activi ty coefficients (YI and Y2), residual vapour pressure (Ra = P" I'II · PG,k)' and Gibbs free energy of mix ing (GE) fo r various ( I +2) binary systems as functions of mole

fraction of alkanol (XI) at 308, 15 K; also inc luded are the a,h,c parameters

x P PI P2 YI Y2

R GE I ..

(Torr) (Torr) (Torr) (Torr) (J mol'l )

1-Propanol(1)+Benzene(2)

0.0000 149.89

0.0511 152 . 21 11.44 142.57 5.5824 1. 0093 -2.30 247 . 64 d.1432 156.03 19.04 137.02. 3.3165 1. 0665 - 0.03 581 .15 0.2301 156 . 52 21. 20 133.81 2.2995 1.1590 1.48 78 2 .15 0 . 3092 154.64 22.23 131. 50 1. 7844 1.2696 0 . 89 885 . 60 0.4544 147.13 24.26 124.34 1 . 3324 1. 5208 -1.47 920 . 11 0.5505 ~39. 31 26.31 115 . 14 1 . 1850 1.7103 -1. 97 857 . 53 0.6192 132 .2 27 . 74 105 . 67 1.1190 1.8535 -1.19 780 . 51 0.6821 123.01 29.39 94 . 65 1. 0770 1. 9901 -1.04 691..19 0.7672 107 . 05 31.86 76 . 08 1 . 0389 2.1870 -0 . 90 54 1 . 92 0.8151 95 . 62 33.35 63.72 1.0243 2 . 3078 -1.45 446. 27 0.8802 75.02 35.48 44.49 1.0103 2 . 4913 -4.96 303. 2 4 0.9542 52.33 38 . 08 18 . 71 1. 0016 2 . 7434 -4.46 1 22 . 25 1.000 39 . 82

a = 3590.50; b = - 1283.660; c = 4 51.95

1-Propanol(1) + Toluene(2 )

0 . 0000 48.03 0.0551 62.21 17 . 04 46.07 7.7441 1. 0138 -0 . 87 32 2. 06

0 .1421 66.49 23 . 70 44.71 4 . 2105 1. 0821 - 1. 93 693. 69

0.2191 68.82 24 . 39 44.48 2.7911 1 . 1835 -0.05 91 3. 50

0 . 2843 69.19 24.37 44.49 2 . 1489 1 . 2918 0 . 32 1 026 .62

0.3112 69.32 24.63 44 . 25 1.6632 1. 4622 0 . 44 10 9 5 .95

0.4521 68 . 60 25.40 43.27 1 . 4089 1 . 6410 0 . 12 1 0 9 ~!. 41

0.5414 67 . 54 26 . 24 41. 94 1.2433 1. 8551 -0.24 1028 .10

0 . 6012 66 . 00 28.09 38.53 1.1715 2.0076 -0 . 61 955 .95

0.6432 64.48 29.07 36.39 1.1332 2.1205 ..,.0 . 98 893 .21

0.7001 62 . 60 34.49 32.95 1. 0925 2.2848 -0 . 86 7 93. 66

0.7922 58 . 41 33 . 02 25.96 1 . 0457 2 . 5991 -0 . 58 5 99. 19

0.8 713 52 . 85 35 . 37 18.27 1. 0188 2 . 9572 -0 . 81 3 9 9 .21

0 . 9402 46.83 37 . 6 1 9' .74 1 .0044 3 . 3949 -0 . 54 197 .97

a = 4259.72 ; b= -1498.13 ; c = 748.90

Contd .. ",

MAKEN et al. : MOLAR EXCESS FREE ENERGY OF MIXING

Table I - Measured total vapour pressure (P), partial pressure (P I and P2

, acti vity coefficients (YI

and Y1

), residual vapour pressure (Ro = Pcxptl- P<;,IC)' and Gibbs free energy of mixing (GE) for various ( I +2) binary systems as functions of mole

fraction of alkanol (XI) at 308.15 K; also included are the a,h,c parameters (Contd ..... )

0.0000 0.0514 0.0982 0.1773 0.2692 0.3554 0.4202 0.4621 0.5432 0.6160 0.6752 0.7141 0.8532 0.9413 1.0000

0.0000 0.0811 0.1112 0.1454 0.1952 0 . 2444 0.3321 0.4133 0.5050 0.6111 0.6832 0.7392 0.8203 0.9312 1.0000

0 . 0000 0.0592 0.1242 0.1811 0.2463 0.3510 0.4322

P (Torr)

12.68 32.01 34.95 37.14 38.89 39 . 91 40.40 40.64 41. 01 41. 31 41. 50 41. 50 40.92 40.40 39.82

14.10 34.82 37.62 39.64 41. 32 42.69 44.59 45.50 45.79 45.30 44.71 44.05 42.81 41.10 39.82

15.47 37.25 40 . 51 41. 68 42.46 43.05 43.14

PI (Torr)

19.84 25.80 27.72 27.38 27.37 27.81 28.29 29.52 30.84 31. 98 39.74 35.58 37.81

P2

(Torr)

12.18 11. 95 11.83 11. 89 11.88 11 . 77 11. 59 11.12 10.45

9.78 9.28 6.75 3.75

R" (Torr)

1-Propanol(1)+ o-Xylene(2)

9 . 7234 6.5974 3 . 9269 2.5542 1.9341 1 . 6626 1.5376 1.3648 1.2571 1.1892 1.1512 1.0471 1.0087

1. 0132 1. 0452 1.1345 1.2829 1. 4530 1. 5986 1. 7001 1. 9170 2.1466 2.3751 2.5576 2.6300 5.0655

-0.06 -2.79 -2.42 -0.37

0.65 0 . 82 0.74 0.38

· 0.01 -0.27 -0.60 -1. 42 -1.18

331. 38 576.91 887.28

1111.83 1217.75 1244.18 1240.77 1194.46 1112 . 72 1019.72

945.51 585.59 264.83

a = 4901.26; b = -1109.38; c = 1117.84

20.56 24.44 27.42 29.99 31. 28 32.06 32.' 08 32.04 32.30 32.80 33.41 34.10 37.41

1-Propanol(1) + m-Xylene(2)

13.13 12.53 12.69 12.47 12.33 12 .2 12 . 21 12.12 12.09 11. 73 11. 20

9.75 5.39

6.3671 5.5174 4.7357 3.8594 3.2147 2.4232 1.9488 1. 5927 1. 3272 1. 2053 1. 1350 1. 0622 1.0090

1. 0181 1. 0037 1. 0572 1.1025 1.1607 1. 3012 1. 4807 1.7569 2.2111 2.6371 3.0593 3.8683 5.5597

1.13 0.29

-0.47 -1.15 -0.92

0.32 1. 20 1. 52 0.90 0 . 16

-0.58 -1. 66 -1. 69

426.91 562.15 701.18 876.67

1019.74 1203.58 1296.53 1316.93 1233.84 1114.33

987.03 749.73 323.83

a = 5272.25; b = -400.71; c = 171 . 92

23.36 29.72 30.03 28.90 27.10 26.53

1-Propanol(1)+p-Xylene(2)

14.83 14.52 14.50 14.66 15.07 15 . 27

9.8975 6.0035 4.1651 2.9462 1. 9388 1. 5417

1.0163 1 . 0686 1.1410 1.2531 1. 4951 1.7314

-0.91 386.80 -3.71 719.16 -2.86 938.80 -1.10 1117.57

0.88 1264.16 1.34 1275.56

Contu ..

22 1

222 INDIAN 1 CHEM, SEC. A, MARCH 1999

Table I - Measured total vapour pressure (P), parti al pressure (PI and P2

, activity coeffi cients (YI

and y), res idual vapour pressure (Ra = P

CX Pd" Peak)' and Gibbs free energy of mi xing (GE) for various ( I +2) binary systems as functions of mole

fraction of alkanol (x) at 308 .15 K; also included are the a,h,c parameters (Contd ..... )

XI P P I P2 YI Y2 R GE

" (Torr) (Torr) (Torr) (Torr) (J mol· l )

0.50n 42.52 26.72 15.15 1.3185 1 . 9-883 0.63 1225 . 08

0.5724 42.20 27.39 14.13 1.2012 2.2181 0.09 1141. 57 0.6513 41. 75 28.74 13.62 1.1078 2.5179- - 0.61 985 . 80 0.7494 42.24 31.13 11. 25 1. 0432 2.8928 -1.14 763 . 19 0.8162 40.75 33.14 8.94 1. 0187 3.1382 -1.35 579' .. 40 0.8943 41 . 11 35.80 5.59 1.0054 3.4068 -1.28 344 . 43 0.9543 39- . 90 38.02 2.55 1. 0009- 3.5980 -0.69 152 . 46 1.0000 39.82

a = 4937.13 b = -1941.03; c · = 381.49

2-propanol{ 1) + Benzene(2)

D..OOOO 149.89 0.0381 162.05 19.40 144.96 6.4229 1.0046 - 2.31 192 . 95 0.1192 172.82 39 . 11 137 . 87 4.t383 1. 0426 -4.16 527 . 88 0 . 2212 179.12 47.13 133 . 13 2.6872 1. 1382 -1.16 818 .. 43 0 . 3041 181. 02 49 . 55 130.86 2.0543 1. 2518 0.60 961 .. 20 0.3721 181. 43 50.92 129.07 J..7249 1.3684 1.44 1 02 4 . 30

0.5455 . 180.72 52.65 126.01 1.4610 1.5375 2.05 1042 . 67 0.5460 176.51 55 . 14 120 . 20 1.2735 1 . 7630 1.16 997 . 76 0 . 6162 170 . 05 57.53 113.16 1.1778 1 . 9643 -0.65 92 2. 23

0.6931 160.25 60.66 102.05 1 . 1048 2. 2170 -2.48 80 2 . 93 0.77 0 2 140.07 64.35 86 . 47 1. 0553 2.5107 -3.76 648 . 33 0.8433 132.52 68 . 26 67.18 1. 0255 2 . 8276 -2 . 92 476 . 90 0.9023 116.44 72.21 45.96 1 . 0095 3. 1 459- - 1. 53 308 . 79

0.9654 93.62 76 ~ 31 18.25 1. 0012 3.5360 -0 . 96 114. 91

1. 0000 78 . 89 a = 4 113.42; b = -985.89; c = 282.09

2-Propanol(1)+Toluene(2) 0.000 0 48.03 0.0171 84.23 39.86 44.59 6.5562 1.0024 - 1.14 42 3 . 82

0 . 1362 91.05 49.22 44.45 4 . 5783 1 . 0669 - 2.63 67 4 . 27

0.2020 94.06 52.28 43.95 3.2779 1. 1417 - 2 . 17 885 . 31

0 . 2631 96.32 52 . 70 43.86 2 . 5375 1. 2335 -0.26 1023 . 84

0 . 3154 97.03 52.64 43.90 2 . 1132 1.3286 0.50 110 2 . 99

0 . 31 9 2 97.34 52.64 43 . 88 1. 7482 1. 4 648 0.71 115 5 . 38

0 .. 4291 97.35 52 . 9-5 43.70 1 . 5628 1.5864 0.68 1165 . 88

0 .4973 96.70 53.91 43. 02 1.3729 1.7735 -0.20 1141. 74

0.5552 9-6.15 55.23 41. 86 1.2599 1. 9507 -0.95 1090 . 07

0.6411 95.52 58 . 02 38.86 1 . 1462 2.2439 - 1. 36 96 7 . 36

0.73 0 3 94 . 04 61.89 33.67 1. 0733 2 . 5880 -1. 52 789 .. 42

0 . 8182 9L64 66.57 26.07 1.0306 2 . 9725 -0.99 57 0 . 6 3

0.9210 87 . 05 73.09 13 . 34 1. 0055 3 . 5009 0.63 266 . 48

1.000 0 a· = 4559.14; b = - 1357.65; c = 346.91

Conld .. ...

MAKEN et al.: MOLAR EXCESS FREE ENERGY OF MIXING

Table I - Measured total vapour pressure (P), parti al pressure (P I and P2, acti vity coefficients (YI and Y2), residual vapour pressure (Ra = P" PII- P,,,k)' and Gibbs free energy of mi xing (QE) for various ( I +2) binary systems as functions of mole

fract ion of alkanol (X I) at 308. 15 K; also included are the a,h,c parameters (Contd ..... )

0.0000 0.0291

0 . 832 0.1363 0.2012

0.2721 0.3514 0.3903 0.4860 0.5552 0.7273 0.8313 0.9072 1.0000

0.0000 0.0521 0.1252 0.1841 0.2372 0.3011 0.3852 0.4581 0.5292 0.5922 0.6713 0.7433 0 .. 8214 0.9253

.1.0000

P

(Torr)

12.65 40.07

56.54 63.03 67.24

70.05 73.14 73.92 76.82 78.41 82.03 82.25 81. 82 79.92

14.01 48.53 62.44 68.51 70.42 72.55 75.07 77.42 79.32 81.14 83.05 84 . 23 84.64 83 . 05 78 . 89

PI (Torr)

25.58

46.25 53.07 56.07

58.08 60.76 62.31 66.38 6·9.05 72.73 73.43 74.50

P2 Y\ Y2 R" (Torr) (Torr)

2-Propanol(1) + o-Xylene (2)

12.37

12.03 11. 84 11.72

11.60 11.38 11. 21 10.67 10.22

9.37 9.06 8.13

11.1711

7.0614 4.9410

3.5355

2.7079 2.1927 2 . 0243 1.7313 1.5766' 1.2747 1.1196 1.0408

1.0043

1.0316 1. 0777 1.1528

1.2513 1.3759 1.4422 1.6284 1.8029 2.6550 4.2124 6.8890

2.10 191.15

-1.78 489.83 -1. 90 723.46 -0.57 942.00

0.351112.63 1. 00 1237.15 0.40 1277.17

-0.22 1325.60 -0.87 1319.27 -0.09 1142.23 -0.25 862.15 -0.84 551.85

a = 5308.38; b = 114.27; c = 1739.14

35.17 50.'91 55.08 57.26 59.59 62.98 66.09 68.87 70.84 72.44 73.09 73.13 74.99

2-Propanol(1)+ffi-Xylene(2)

13.58 13 . 19 13.00 12.88 12.70 12.35 11. 92 11.45 11.06 10.66 10.43 10.26

8.56

8.5794 5.1585 3.7958 3 . 0622 2.5103 2.0735 1.8288 1.6497 1. 5163 1.3~76

1. 2462 1.1328 1.0272

1.0123 -0.27 31&.&1 1.0627 -1.66 662.66 1.1236 0.39 872.83 1.1896 0.25 1019.42 1.2794 0.23 1151.2& 1.4130 -0.26 1264.09 1.5479 -0.59 1315.16 1.7116 -1.01 1327.05 1.9065 -0.77 1305.85 2.2784 -0.05 1231.91 2.8564 0.70 1109.43 4.0378 0.94 901.17 8.0722 -0.53 463.40

a = 5306.58; b = 242.37; c = 164&.91

2-Propanol(1)+p-Xylene(2)

1.19 -2.86 -2.97

394 . ~4

609.00 793.36

223

0.0000 0.0671 0.1132 0.1623 0.2182

15.47 55.81 60.05 63.25 66.07

39.84 48.36 51. 81 53.22

14.80 14.54 14.39 14.32

7.5312 5.4218 4.0511 3.0944

1.0201 1. 0536 1.1036 1.1754 -1.47 955.17 Contd .. .. .

224 INDIAN J CHEM. SEC. A. MARCH 1999

Table I - Measured total vapour pressure (P). partial pressure (PI and P2• activity coefficients (YI and y). residual vapour pressure (Ro = Pe' PII- P<"k)' and Gibbs free energy of mi xing (GE) for various ( I +2) binary systems as functions of mole

fraction of alkanol (XI) at 308. 15 K; also included are the a, b,c parameters (Contd ... .. )

0.2801

0.3514 0.4223 0.4812 0.5572 0.6254 0.6962 0.7191 0.8980 1. 0000

P (Torr)

68.32

70.51 72.30 73.35 74.50 75.53 76.42 77.23 78.05 78.89

PI (Torr)

54.04

55.22 56.93 58.73 61. 31 63.67 66.05 68.69 72.94

P2

(Torr)

14.24

14.11 13.83 13.49 12.87 12.19 11. 38 10.14

7.25

2.4473

1.9929 1.7097 1.5475 1. 3950 1. 2908 1.2026' 1.1176 1.0297

1. 2701

1.3956 1.5367 1. 6681 1. 8655 2.0872 2.3065 2.9488 4.5599

R GE

" (Torr) (J mol · l )

0.03 1083.23

1.18 1174.81 1. 52 1216.24 1.13 1218.40 0.31 1182.59

-0.34 11.15.27 - -1. 00 1009.45 -1.62 834.07 -2.15 468.85

a = 4853.87; .b = -664.86; c = 1167.03

-1 a,b and c are in Jmol

hydrocarbons (2) were calculated from their vapour­pressure data using Barker's method lO and recorded in T able 1. The fonn of function used for GE

foll owing Redlich and Kister.

where a, b and c are the adjustable parameters. These parameters are recorded in Table I. The second virial coefficients required in these calculations were obtained from the Berthelot ' s

. 21 equatIOn .

... (2)

and necessary critical constant data were taken from the literature l4

. The values of activity coefficients (YI

and Y2 ), partial pressure (PI , P2 ) , residual pressure (Ro) ( = PcxpII - P ealed) and excess Gibbs free energy (GE

) were recorded in Table I.

E We are unaware of any G ' values of the present I-propanol or 2-propanol + aromatic hydrocarbons at 308 .15 K wi th which to compare our results . GE values for all these systems are positive over the whole composition range. Plots of CE

versus XI are symmetrical for I-propanol or 2-propanol (l) + benzene, toluene and p-xylene (2) systems, while these are slightly skewed towards low mole fraction of alkano] for i-propanol or 2-propanol (1) + 0- and m~~ylene (2) systems. For an

equimolar mixture, GC value for I-propanol or 2-propanol (1) + an aromatic hydrocarbon (2) varies in the order: benzene < toluene <: p- xylene < a-xylene =:: m-xylene . The high positive value of CE for these systems indicates the dissociation of hydrogen bonding in I-propanol or 2-propanol by the addition of aromatic hydrocarbon.

Mecke-Kempter aSSOCIatwn model with a Flory contribution term

This modelS assumes that the mode of self­association of alkanols is of M ecke-Kempter (MK) type in which linear multimers Am are formed due to the consecutive association reaction

A[ + A,,,-[ ~AIII (m > 2) .. . (3)

The association constant, Km, mol , can be expressed in terms of standard association parameters mode of

(t1 h~ ,m_ 1 and 11 S; m- l) of H - bond formation .

In MK degree of association, these parameters are taken to be independent of m. Further it has been found

l5 that standard entropy of H-bond formation,

t1 S; .m_l for alkanol depends on the number of

segments rl in a molecule of monomer. Thus for all alkanol

.,.

Table 2 - Molar volume (V), isobaric thermal expansivity (a), isotherm al compressibility (KT

), viri.al coeffi cient ( ~) and vapour pressure (P i) for the pure components at 308. 15K

Component V a x 10'

(cm)mol·l ) (K" )

1-Propanol 75.910 1.070

2-Propanol 77.968 1.175

Benzene 90.468 1. 252

Toluene 108.031 1. 085

o-Xylene 122.402 0.995

m-Xylene 124 . 725 1. 055

p-Xylene 125 . 203 1.060

. .. (4)

and

... (5)

These assumptions indicate that

... (6)

where

KH = exp [-(Ll h~- TLls~) / RT] .. (7)

is a constant for a homologous series of self-

KT X 10" ~ p i (Torr)

(cm)]-') (cm)mol")

715.05 -1044.64 39.82

863.16 - 955 . 36 78.89

1082.30 - 1265.10 149.89

993.83 -1753.81 48.03

886.06 -2477 .43 12 . 65

939.95 -2390.60 14 . 10

980.96 -2434.84 15 . 47

where ~* is the characteristic molar vo lume of

alkanol and 17.12 cm3 mor t is the van der Waals molar volume for methane16.

According to Treszczanowicz and Benson5 the excess free energy of mixing GE is composed of three type of contributions combinatorial contribution described by Flory-Huggins theory, chemical (MK type of association of alkanot) contribution and a physical contribution described by Flory theory17·18.

... (9)

associated components and Combinatorial contribution is given by the relation

'i = ~. / 17.12 .. . (8) .. . (10)

226 INDIAN J CHEM, SEC. A, MARCH 1999

Table 3 - Values of association parameters (tJJ1H' " !:J. SH 0, !:J. VH 0) of Mecke-Kempter association

model and Flory interaction parameters (xiland Q'l) for the various (1+2) binary

systems at 308.1 5 K

Systems !:J.hHo !:J. SilO !:J. V

Ho Q'l X' i

(J mol' l) (JK,I mol 'l) (cm) mol'l) (J cm') (J cm)

1-Propanol+ -24400 -33.00 -10 0.1530 60.5611

Cyclohexane

1-Propanol+ -23646 -32.77 -5 0.0555 22.3630 Benzene

1-Propanol+ -19772 -33.92 -5 -0 . 1209 -24.9299 Toluene

1-Propanol+ -20532 -38.96 -5 -0 . 2104 -40.4364 o-Xylene

1-Propanol+ -18510 -27.61 -5 -0.1392 -20 .5376

1-Propanol+ -19071 -13.67 -5 -0 . 1532 -28 . 4744 p-Xyl ene

2-Propanol+ -24400 -33.00 -10 0. 1405 63.24 2 6 Cyclohexane

2-Propanol+ -21222 -29 . 58 -5 0 . 0339 29.3 9 17 Benzene

2-Pro panol+ -19593 -32 . 80 -5 -0 . 1083 -15.30 06 Toluene

2"";Propanol+ -21849 -:44.73 -5 -0.1939 -3 1.1442 o-Xylene

2-Propanol+ -19423 -33.89 -5 -0 . 1426 - 16 . 0 796 m-Xylene

2-Propanol+ -19820 -35.84 -5 -0.1352 -20.391 7 p-Xylene

MAKEN e/ al.: MOLAR EXCESS FREE ENERGY OF MIXING 227

where

S!mb =-R[xi In(¢1 I XI ) + X2 In (¢2 I X2 )]

... (11)

The chemical (MK) contribution is given by

G!K =(x I RTIK¢¢I)[¢I(1+K¢)

In (1+K¢)-(1+K¢ ¢I) In (l+K¢ I¢I)]

.. ,( 12)

where ~ = 1 + In ' (KH / rl ) ... (13)'

In these equations R is the gas constant, T is the temperature, XI . the mole fraction of alkanol and ¢ 2

and ¢ I = 1- ¢ 2 are segment volume fraction

and defined by

... (14)

where r21 = V:; I VI' is the size ratio parameter

obtained by dividing the characteristic (hard core) molar volume of the components.

The physical contribution is given by Flory theoryl7,18

G E H E _ T.'SE F = F F ... (15)

where

2

= Xi (1 2 (VI' / \I) XI2 + L [ Xi P;" v; ' (\I-I V - I)] i; 1

... (16)

and 2

S J. = X I e 2 VI' Q 12 - 3 I, [( Xi P; ' Vi' IT;' ) i=1

In [9; - 113 - 1 ]) I ( V; -1 /3 - 1 ) ] ] ... ( 17)

where 82 is the contact surface fraction of component 2 and defined by

... ( 18)

The reduced pressure, volume and temperature

( j5, V, f ) are obtained by dividing pressure,

volume and temperature by the corresponding ,

characteristics values (P, V, T). These defining

relations together with the equations

,,;1/3 = 1 + a i T I [3 (1 + a iT) ]

.. . (19)

(,,113 -1) fV; 4/3 ... (20)

and

... (2 1)

serve to determine the characteristics and reduced quantities for the components, a and KT are the isobaric expansivity and isothermal compressibility of the pure components (recorded in Table 2) were taken from the literature and KT values for 1-propanol and 2-propanol were evaluated using the following relation l9 (22).

= a; TIKT .. . (22)

where 8 is the solubility parameter and taken from the literature 14.

The values of association parameters

( ~ h~ , ~ s;J and ~ v~) for alkanol + alkane

systems are reported5 to be -24.4 kJ mor l , -33 J mor l and -10 cm3 morl respectively where only the association of alkanols are taken into consideration, As aromatic hydrocarbons are potential electron donor20

, the electron donor­acceptor type interactions are expected between the hydroxyl hydrogen of alkanol and TC-electron of aromatic ring. Therefore, it is not justified to use the same values of association parameters as those of alkanol + alkane systems. Further it has been observed by Stokes et aZ20

.22

. from thermodynamic, spectroscopic and dielectric measurements studies of ethanol + benzene and + p-xylene mixtures that the specific interactions between alkanolic hydroxyl group and the aromatic TC-electron systems may be treated as a solvation of the alkanol molecule and thus reduces the effective strength of each ,hydrogen bond. So the association parameters for these binaries, calculated in our earlier work8 as suggested by Treszczanawicz and Benson5

, also takes indirectly into consideration the effect of interactions of alkanol and aromatic hydrocarbons.

It can be observed from ~ h~ values that these

are less than -24.4 kJ morl , showing that the effective strength of H-bonding is reduced due to the specific interactions of alkanol and TC-electron of

228 DIAN J CHEM, SEC. A, MARCH 1999

14 00' - ----------- --

12 00

, 1000 -0 E ...,

o E

'" w

lD

-, o E ...,

U. lD

o

/

/

/ /

/' ....

"-

/ p- XylenCl

m- XylQne

" Toluene

Benzene

0.4 0 .6

- xl --+-

" " ,

, ,

, , \ \

\ \

\ \ \

', -~ ~ ~ ~

"

" 1200

1000

800 , 600 0

E ..., 4 00 w~

lD

200

1000

800 , "0 E ..., w~

l')

200

0

Fi g. - Molar excess Gihhs f ree energy, GE, o f 1-propanol( I )+a rom alic hydro carbol1s(2) al 298 . 15 K : __ GE(ex pll ); ---- -- GE (caled)

aromatic hydrocarbons. The strength of specific interactions is more for xylene systems than that fo~'

benzene or toluene systems as the values of 6,. h~

for xylenes are less than those of benzene or toluene. The most suitable value fo r the molar volume of

association, 6,. v~ , that reproduces HE and vE data

close to experimental values is found to be -5 cm-3

mor l . This value is les ' than the values -10 cm-3

mOrl and -7.5 cm' mOr l calcul ated by Treszczanowicz and Benson5 and Stokes2:l

respectively, for alkanol + alkane systems but is in agreement with the values reported by Liu et al

24 '.

From these values of association parameters

6,. h;~ , f!:.. '<1 and l1 v~ (Table 3), ~ was

calcul ated from Eg. (1 3). Usi llg this value of ~ ,

G~K was computed from Eg. (12). Calculation of

, -0 E ...,

UJ~ l')

o E ....,

o E ....,

UJ l')

1400

1200

1000

800

600

400

2 0~ ~

~

/ /

I I

I I

I

/ ~ / // p-XylenCl

X l ~

-;--0 E ....,

UJ l')

, o E

w l')

Fig . 2 M ol ar excess Gihhs free ene rgy. G E• of 1-

propa l1 o l ( I )+aI'o l1l :ll i c hydro (;,rhoI15(2) al 29X.15 K : __ G" (expll ): ---- -- GI' (ca.J ed)

physical contribut ion G;:' from Eq. (15) regUlres

two unknown interaction parameters Xl2 and Q1 2.

In order to calcu late interchange in terac tion

parameter in Flory theory X 12 ,V/ at equimole

fraction is calculated from the relation

VE- VE VE F - exprl - .11K .. . (23)

where

... (24)

and h ( K¢ ,¢) =[¢ I In ( 1 + K¢ ) -

In (l -,- K ) ~)l)J / K;' ¢ .. . (25)

f V E Thi<; value 0 F was then used t caiculatc Flory

...

MAKEN el al. : MOLAR EXCESS FREE E ERGY OF MIX II G 229

interaction parameter Xl 2 using the following set of . 171 8 equatIOns . .

.. . (26)

f =. (V 1/3 -1) V 4/3 ... (27) 2 2 __

X 12 = [L ¢; P/ - L (¢; P;* r; / T ) e 2 ¢ I ;=1 ;=1

.. . (28)

The other Flory interaction parameter QI 2 was calculated by assuming that at an eguimole fraction

G E GG E G E and E F = expll - comb - MK usmg qs.

(I S) (17). The values of XI 2 and QI 2

aiongwith association parameters and

!J. v~ for all the present systems were recorded in

Table 3. CE at other mol e fraction for all these (1+2) binary systems were calculated from Eg. (9) and graphically shown in Fig. I and Fig. 2. It has

been observed from the plots of G~IlCd and GE cxp II

against XI (Figs 1 and 2) that G~llcti are 111

reasonabl y good agreement with the G !PII .

Thus it may be concluded that the CE values for 1-propanol or 2-propanol (1) + benzene, toluene, +0- , + /11,- and + p-xylenes (2) at 308 .15 K may be represented by MK type association model with a Flory contribution term5 using two interaction

parameters Xl2 and Q12.

Acknowledgement This work was supported by the CSTR and the

UGC, New Delhi .

References Brandani Y. Fiuid Phase Equilibria. 12 (1983) 87.

2 Brandani Y & Evangeli sta V. Fluid Phase Equilibria . 17 (1984) 281.

3 Nath A & Bender E. Fluid PhQ.\ e Eqlliilbras, 7 (1981), 275.

,. uranaam v 6l tvangel1sta t, Illd Hllg Chern Res., 26 (1987) 2423.

5 Treszezanowicz A J & Benson G C, Fluid Phase Equilibria, 23 (1985) 117 .

6 Singh K C, Kalra K C, Maken S & Gupta V , Fluid Phase Equilibria , 123 (1996) 271.

7 Singh K C, Kalra K C, Maken S & Gupta V, Thennochim Acla, 276 (1996) 271.

8 Singh K C, Kalra K C, Maken S & Gupta V, Fluid Phase Eqllilibria, I J 9 (1996) J 75 .

9 Gupta V, Maken S, Kalra K C & Singh K C, Fluid Phase Equilibria, 120 (1996) 195.

10 Barker J A, Ausi. 1. Chem., 6 (1953) 207.

Il Taha A A, Gridsby R D, Johnson J R, Christi an S D & Affrsprung 1-1 E, .! chern Edllc , 43 ( 1966) 432.

12 Strubl K, Svoboda V. Holub R & Pick J, Collect Czech Chem COlllllllln , 35 (1970) 3004.

lJ Scatehard A & Ticknor L B, J Am chelll Soc, 74 ( 1952) 3724.

14 Weast R C (Ed), Hand book of chemistry and physics, 67th edn (CRC Press , Bo(;a Raton, FL) 1986/87.

15 Keh iaian H Y, Thermodynamic Review of Science, Vol I, Thermochemis try and Thermodynamics, edited by Skinner H I\. (Butterworths, London) 1972, Chap. 5.

16 Bondi A, Physical properties of molecular CI}'slals, liquids and glasses (Wiley, New York) 1968, pp-502.

17 Flory P J , J Am chern Soc, 87 ( 1965) 1833 .

18 Abe A & Flory PJ , .IAm chemSoc, 87( 1965) 1838.

19 Hildbrand J 1-1 , Prausn itz J M & Scott R L, Regll iar and related solutions (Van Nostrand , Reinhold , New York) 1970.

20 Stokes R H & Marsh K N, J chem thermodyn, 8 (1976), 1709.

2 1 Stokes R H & Burfitt C J , J chem tlzermodyn, 5 (1973) 623.

22 Stokes R H & Adamson M J, J chern Soc Faraday Trans I , 7 1 (1975) 1707.

23 Stokes R H, .I chetn Soc Faraday Trans I, 73 (1977) 1140.

24 Liu A, Kohl!:' r P, Karrer L, Gaube /\ & Spellu cc i R, Pure appl Chelll , 61 (1989) 1441.