lUlm ELSEVIER Fluid Phase Equilibria 123 (1996) 271-281

Excess enthalpies and volumes of mixing of 1-propanol or 2-propanol + cyclohexane at 298.15 and 308.15 K

K.C. Singh *, K.C. Kalra, Sanjeev Maken, Vibha Gupta Department of Chemistry, M aharshi Dayanand University, R ohtak-12 4001, India

Received 25 January 1995; accepted 11 January 1996

Abstract

Excess molar enthalpies and excess molar volumes at 298.15 and 308.15K are reported for 1-propanol or 2-propanol with cyclohexane. The analysis in terms of Mecke-Kempter association model with a Flory contribution term and generalized quasi-lattice model by Barker is described.

Keywords: Excess volume; Excess enthalpy; Mecke-Kempter model; Barker theory; Association

I. In troduct ion

The interpretation of the thermodynamic properties of solutions of alcohols in non-polar solvents has generally been made in terms of association of alcohol molecules through hydrogen bonding (Savini et al., 1965; Renon and Prausnitz, 1967; Van Ness et al., 1967; Stokes and Burfitt, 1973; Marsh and Burfitt, 1975) and of complex formation (Fletcher and Heller, 1967;Fletcher, 1969; Stokes and Marsh, 1976) between alcohol and solvent molecules. Lattice model theories of associated mixtures (Nath and Bender, 1981; Brandani, 1983; Treszczanowicz and Benson, 1985; Brandani and Evangelista, 1987) have been attempted to describe their behaviour. It has been found that the excess properties of mixtures formed from an alkanol with alkane could be correlated quite well by an association model of Mecke-Kempter (MK) type with an added Flory contribution term (Treszc- zanowicz and Benson, 1985). The use of generalized quasi-lattice theory described by Barker (Barker, 1952) to calculate the thermodynamic properties of mixing of associated solution has also been successful (Goates et al., 1962; Nigam et al., 1980).

In the present work we report the experimental results of H E and V E of 1-propanol or 2-propanol + cyclohexane at 298.15 and 308.15 K and their interpretation in terms of a n M K type of association model (Treszczanowicz and Benson, 1985) and quasi-lattice theory by Barker (Barker, 1952).

* Corresponding author.

0378-3812/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 3 8 1 2 ( 9 6 ) 0 3 0 1 6 - 6

272 K.C. Singh et al. / Fluid Phase Equilibria 123 (1996) 271-281

2. Experimental

1-propanol, 2-propanol and cyclohexane (Ranbaxy, AR grade) were purified by standard proce- dures (Vogel, 1978). The purities of final samples were checked by density determination at 298.15 ___ 0.01 K; densities agreed to within +5 × 10 -5 g cm -3 with the corresponding literature value (Brown and Smith, 1962; Aicart et al., 1980). The excess molar volumes, V E as a function of composition were measured dilatometrically as described by Singh and Sharma (Singh and Sharma, 1985). The temperature of the water bath was controlled to + 0.01 K. A continuous flow calorimeter (LKB-2107, Bromma, .Sweden) was used in the manner described by Monk and Wadso (Monk and Wadso, 1968) to measure the excess molar enthalpies H E. The estimated uncertainties in the measured V E and H E values are 0.5% and 1%, respectively.

Table 1 Molar excess volumes V E, parameters A, B, C, D and standard deviation (r for various (1 + 2 ) mixtures

X I V E (cm 3 mol -1 ) xl V E (cm 3 m o l - 1 ) xl V E (cm 3 m o l - t )

1-Propanol (1) + cyclohexane (2) Temperature 298.15 K 0.0937 0.226 0.4591 0.425 0.7859 0.273 0.1629 0.323 0.5162 0.418 0.8592 0.195 0.2738 0.400 0.5827 0.400 0.8952 0.151 0.3396 0.421 0.6339 0.378 0.9336 0.101 0.4268 0.426 0.7123 0.334 A = 1.6834; B ~ -0 .3480 ; C ~ 0.6706; D ~ -0 .4287 ; tr ~ 0.0015 Temperature 308.15 K 0.0689 0.223 0.4129 0.653 0.7771 0.48 1 0.1792 0.460 0.4562 0.660 0.8368 0.392 0.2589 0.562 0.5669 0.645 0.9025 0.265 0.3661 0.637 0.6592 0.598 0.9599 0. ! 20 0.3924 0.646 0.7123 0.555 A = 2.6354; B ~ - 0 . 1 9 2 3 ; C ~ 0.8417; D ~ - 0 . 0 5 1 0 ; o - ~ 0.0013

2-Propanol (1) + cyclohexane (2) Temperature 298.15 K 0.0879 0.292 0.4114 0.593 0.7259 0.427 0.1348 0.391 0.4526 0.590 0.8396 0.271 0.2692 0.550 0.5123 0.579 0.8999 0.175 0.3129 0.573 0.5869 0.545 0.9526 0.083 0.3962 0.592 0.6565 0.494 A ~ 2.3322; B = -0 .5504 ; C ~ 0.6219; D = 0.7188; o" = 0.0014 Temperature 308.15 K 0.1038 0.526 0.3299 0.949 0.7369 0.768 0.1635 0.714 0.3889 0.970 0.7912 0.675 0.2259 0.814 0.4727 0.969 0.8368 0.575 0.2738 0.905 0.5331 0.950 0.9498 0.224 0.2956 0.925 0.6120 0.904 A ~ 3.8516; B = 0.6307; C ~ 1.9097; D = - 0 . 2 0 7 6 ; o" = 0.0014

A, B, C, D and cr are in cm 3 mol-~.

K.C. Singh et a l . / Fluid Phase Equilibria 123 (1996) 271-281 273

3. Results

The V E and H E data for the binary mixtures of 1-propanol or 2-propanol with cyclohexane as a function of composition at 298.15 and 308.15 K are recorded in Tables 1 and 2. The measured data were expressed by

XE(X = V o r H ) = x l ( 1 - xl) [ a + B ( 2 x 1 - 1)+ C ( 2 x I - 1) 2 + D ( 2 x I - 1) 3] (1)

where x~ is the mole fraction of alcohol in various binary mixture and A, B, C, D are the adjustable parameters and evaluated by fitting Eq. (1) to Xe/x~(1 -x~) data by the method of least squares. These parameters are recorded together with the standard deviation in Tables 1 and 2. The V E and H z data in terms of Eq. (1) are represented in Figs. 1-4.

Table 2 Molar excess enthalpies H E, parameters A, B, C, D and standard deviation tr for various (1 + 2) mixtures

x I H E (J mol - i) xt H z (J m o l - l) xl H E (J m o l - i)

1-Propanol( l ) + cyclohexane(2) Temperature298.15K 0.0548 245 0.3791 0.1213 430 0.4359 0.1969 540 0.5128 0.2594 585 0.5979 0.3133 603 0.6551 A = 2305.60; B = -779 .10 ; C = 9 7 3 . 0 5 ; D ~ - Temperature308.15 K 0.0666 356 0.3219 0.1010 490 0.3727 0.1324 588 0.4343 0.1917 720 0.5010 0.2567 802 0.5794

605 595 570 525 480

1289.22; ~ ~ 1.92

834 834 813 765 695

A = 3073.53; B = - 1 5 7 6 . 5 9 ; C ~ 1366.73; D ~ - 390.95; ~ ~ 1.70

2-Propanol(1) + cyclohexane(2) Temperature298.15 K 0.0721 308 0.3809 762 0.1417 508 0.4572 759 0.2039 623 0.5112 744 0.2543 691 0.6074 671 0.3281 798 0.6715 601 A = 2986.02; B ~ - 873.89; C = 554.33; D = -730 .20 ; ~ ~ 2.00 Temperature308.15K 0.0909 531 0.3925 1033 0.1526 746 0.4678 1032 0.1918 843 0.5117 1018 0.2663 951 0.5891 973 0.3448 1017 0.6674 886 A = 4095.51; B ~ -709 .70 ; C = 1602.36; D = - 1206.93; o" = 1.67

0.7024 431 0.7613 362 0.8427 242 0.9125 125

0.6234 648 0.7111 539 0.8080 391 0.8927 238

0.7239 529 0.8148 370 0.8897 226 0.9406 122

0.7227 800 0.8012 634 0.8673 453 0.9381 224

A, B, C, D and (~ are in J mol-1 .

2 7 4 K.C. Singh et al . / Fluid Phase Equilibria 123 (1996) 271-281

4 . D i s c u s s i o n

H E data for l-propanol or 2-propanol (1) + cyclohexane (2) at 298.15 and 308.15 K have been reported in the literature (Vesely et al., 1979). Our H E values at 308.15K are higher by 60-80 J mol-~ at mole fraction 0.3 < x~ < 0.5 while at 298.15 K these values are lower by 20 J mol- l and 60 J mol -~ for 1-propanol (1) + cyclohexane (2) and for 2-propanol (1) + cyclohexane (2), respectively, at mole fraction 0.3 < x I < 0.5. The plots of V E and H E against x~ are slightly skewed towards low mole fraction of alcohol. Both V E and H E for all these mixtures are positive over the whole composition range with positive temperature coefficient. The positive and high magnitude of V E and H E values for these systems can be attributed to the breaking of three-dimensional hydrogen network of alcohol with the addition of cyclohexane. The higher magnitude of V E and H E in the 2-propanol + cyclohexane mixture than in the 1-propanol + cyclohexane mixture may be due to the branching of the propyl group, causing more steric hindrence to cyclohexane molecules to adjust in the hydrogen bonded network. It has been shown by Treszczanowicz and Benson (Treszczanowicz and Benson, 1985) that V E and H E of n-alkanol + n-alkanes mixtures could be represented by an MK type of association with an added Flory contribution term. The model assumes that H E and V E are composed of a chemical (MK) term and a physical contribution described by Flory theory (Flory, 1965; Abe and Flory, 1965).

x E ( x = V o r H ) =X~K + X ~ (2)

The chemical term is

HEK = Ah°xlh(K~,dpl) (3)

VEK = Av 0 Xlh ( Ke~,dpl ) (4)

where

h( K't',dp, ) = [ 4 h l n ( 1 + K4',cbI ) I /K 4' qb, (5)

0.$1

l O.E

o

,,., O.i E

taJ > .

I 0.~

.. ""_"-'_.a •

"," / / . \ . / \ \

i / I ".\ \ \

. l / ' / ' ~ - ~ ~ ~ "'` ,

I I I I " ~ 0.~. 0.4. 0.6 0.8 !.0

X 1

- - V E (exptl) Fig. 1. Molar excess volumes, V E, of 1-propanol (1) + cyclohexane (2): , V E (expti) at 298.15 K; --, - V E (MK model) at 298.15K; V E (MK model) at 308.15K. at 308.15 K; . . . . , . . . . . . . ,

K.C. Singh et a l . / Fluid Phase Equilibria 123 (1996) 271-281 275

I.o I / ~"-'--':: '~.\ / / / " " \ \ \

°t /7 ',', I I/" ' \ \ \

-" o.6~- i.. ..

/ f f ~ '~ / / i / / "% \ ~

lJ ./' \ ,', 1i9'

o,~1.4.//" \,,\\

0 0.2 0 . ; 0.6 0 .8 1.0

X 1 )

- - V E (exptl) Fig. 2. Mola r exces s vo lume, V E of 2-propanol (1) + cyc lohexane (2): , V E (exptl) at 298.15 K; - - ,

V E ( M K mode l ) at 2 9 8 . 1 5 K ; • V e ( M K model ) at 308 .15K. at 308.15 K; . . . . . , . . . . . . ,

r !

0

E l--m

ILl "r"

i

1400 ° o ~ oo f ~ -°

\

'\ °

\

o

/ a,

i .o

I

: I \ . ! \

/ / g/ \

ii \ • ~ ~

I l I 0 0,2 0.~

X I ~-

\ \ \

\ \ -,

\ \ \.\ \

\\ \ \

0.6 0.8 I. 0

m , H E Fig. 3. Mola r excess enthalpies , H z o f l -p ropanol (1) + cyc lohexane (2): H E (exptl) at 298 .15K; - - , H E ( M K mode l ) at 308 .15K; O , H E (Barker) at H E ( M K mode l ) at 298 .15K; . . . . . . . , (exptl) at 308.15 K; . . . . . ,

298 .15K; 0 , H E (Barker) at 308 .15K.

276 K.C. Singh et al. / Fluid Phase Equilibria 123 (1996) 271-281

I 80o

I

0 E

60(] LU

"z-

~o(~

/ - N \

/ ".

/" \ • ' \

/

; I / . .~ \ / / / ~, "

200

0 0.2 0.~ 0.6 0 .6 1.0 X 1

Fig. 4. Molar excess enthalpies, H E of 2-propanol (1) + cyclohexane (2): - - , H E (exptl) at 298.15K; -- , H z (exptl) at 308.15K; . . . . . , H E (MK model) at 298.15K; . . . . . . . , H E (MK model) at 308.15K; O, H E (Barker) at 298.15K; O, H E (Barker) at 308.15K.

and

In K s = 1 - ( a h ° - T a s ° ) / l l T - ln (Vl* /17 .12cm3mol - ' ) (6)

In these equations, R 6 is the gas constant, T is the temperature and x~, ~b~ and V~ are the mole fraction, segment volume fraction and hard-core molar volume of the associating component, respectively. +2 and +~ ( = 1 - ~b z) are segment volume fractions defined by

492 = x 2 r 2 , / ( x , + r2, x2) (7)

where

r21 = V2*/VI* (8)

is the size ratio parameter obtained by dividing the characteristic (hard core) molar volumes, V i * of the components. The detail of the Flory term ( H ~ and V~) and the method for calculating association parameters (Ah ° , Av ° and As ° have been described by Treszczanowicz and Benson (Treszczano- wicz and Benson, 1985). The values of physical constants like a (coefficient of volume expansion), K T (isothermal compressibility) of cyclohexane were taken from the literature (Singh et al., 1968) and K v values for 1-propanol and 2-propanol are evaluated using the following relation (Hildbrand et al., 1970)

2 = ot T / K T (9)

K.C. Singh et al . / Fluid Phase Equilibria 123 (1996) 271-281 277

Table 3 Molar volume V, isobaric thermal expansivity ot and isothermal compressibility K T for the component liquids: characteristic values of pressure P *, molar volume V * and temperature T* obtained from Flory theory

Component Temperature V (cm 3 mol-J) ot X 10 3 K- r X 10 6 P * (J cm - 3 ) V * (cm 3 mol- l) T" (K) (K) (K- l ) (cm 3 j - 1 )

1-Propanol 298.15 75.164 0.9964 644.00 717.28 60.28 5239.90 308.15 75.910 1.0704 7 1 5 . 0 5 742.96 59.81 5121.20

2-Propanol 298.15 76.953 1.1167 795.83 676.01 60.54 4928.10 308.15 77.968 1.1747 863.16 697.89 60.44 4884.58

Cyclohexane 298.15 104.378 1.217 968.58 623.96 80.88 4717.56 308.15 110.061 1.248 1 2 6 8 . 6 9 515.65 84.38 4742.89

where ~ is the solubility paramete r and is taken f rom the literature (Weast , 1986). In order to calculated the H E and V E from Eq. (2), HM~K and VMEK were first calculated using the same value of

association parameters ( A h ° , As ° and Av ° ) as calculated by Treszczanowicz and Benson (Treszc- zanowicz and Benson, 1985). The V z at equimolar composi t ion was obtained f rom relation

= voL,,- v & (lO)

This value of V E was than used to calculate the Flory interaction parameter (Xl2) f rom the fol lowing set o f equations as described by Flory theory (Flory, 1965; Abe and Flory, 1965). ( 2 )

v¢= v* ,2- Eg6, i = 1

~ = (~1/3 -- 1)/~k74/3

(11)

(12)

The values o f various parameters of pure components and association parameters o f the M K model for various alkanol (1) + cyc lohexane (2) systems have been reported in Tables 3 and 4. The calculated and experimental values are compared in Figs. 1 -4 . It can be seen that the model reproduces well the V E values but the same is not true for H E data. H~ca is a lways higher than

Table 4 Values of various parameters of the Mecke-Kempter model for various alkanol (1) + cyclohexane (2)

System Temperature K '1' X~2 (J cm-3) Ah o As o Av o (K) (Jmol - l ) (JK - l mol - I ) (cm 3 mol - j )

l-Propanol(1) + 298.15 274.57 44.2802 -24400 -33 - 10 cyclohexane(2) 308.15 201.04 60.5611 -24400 -33 - 10

2-Propanol(2) + 298.15 279.39 44.1280 - 24400 - 33 - 10 cyclohexane(2) 308.15 198.16 63.5411 -24400 -33 - 10

278 K.C. Singh et al. / Fluid Phase Equilibria 123 (1996) 271-281

HEptl. But the general shape and the sign of the HElca curves are the same. HElca can be made to agree with E H~xpt I if we adopt the lower value of Ah ° or Flory's interaction parameter (X12). This adjustment also lowers the V E calculated values. Moreover, we have no justification for doing so, because the heat of association A h ° , of propanol will be the same whether it is calculated by one method or the other.

4.1. Barker's quasi-lattice model

This model (Barker, 1952) assumed a different type of contact site on a molecule and energies for all possible interactions of these sites. For alcohol molecules three types of sites - - hydrocarbon- (designated as type I), hydroxyl hydrogen- (H) and oxygen- (O) type sites were recognized and for the cyclohexane molecule only 'S' type sites were specified. The number of sites present on the alcohol molecules was calculated on the assumption that each carbon and each oxygen atom occupied one position in a fourfold coordinated lattice. Some of the four nearest neighbours of each carbon or oxygen atom are atoms within the same molecule. The remainder, the number of those sites available for contact with another molecule, are designated by the letter Q, with a superscript 1 for alcohol and 2 for cyclohexane. Subscripts to Q (H,O,I and S) refer to the type of site. The number of contact sites for both the alcohols and cyclohexane were deduced directly from the structural formulae of the compounds and are given below

CH3-CH2-CH2-OH CH3-CH-CH 3 I OH

C6H12

Qh 1 2 7 -

1 2 7 -

12

In the present systems, four types of sites are present, resulting in the following ten interactions: H - H , H - O , H- I , H-S , O-O , O-I , O-S , I - I , I -S and S-S. The energy of interaction of the H - H , O-O , I - I and S -S sites is zero by definition. Of the remaining six interactions, two ( H - O and I -S) were considered significant, because H - O interactions have high energy values and the number of I -S interactions is large compared with other interactions. The energy terms for the remaining four interactions were set equal to zero. Since both H and O might be expected to be preferentially involved in the more energetic interaction (H-O). The interaction energy for hydrogen bond formation Uo_ n was taken equal to - 24.4 kJ mol- l and Ul_ s equals 100 or 150 J mol- 1. In order to calculate H E, the following set of four quadratic equations were solved for X functions as given by Barker.

XH(X H 4- X 1 + Xo~o_ H -t- Xs) = Q~H x~/2

Xi(X H --I- X 1 d- X O --[- Xsnl_ s) = Q~x,/2

Xo(Xn~/o_ H + X , + X o + X s ) = Q~)x,/2

Xs(X n + X,rl,_s + X o + X s ) = a 2 x 2 / 2 )

(14)

(15) (16)

(17)

K.C. Singh et al./ Fluid Phase Equilibria 123 (1996) 271-281 279

In the above equations r~ = e -U/Rr. All calculations were performed manually. The X values were adjusted so that the difference between the right-hand side and left-hand side was less than 5% of the right:hand side. H E at different mole fractions x 1 (0.1, 0.3, 0.5, 0.7 and 0.9) were calculated for all systems from Eq. (18) and are shown in Figs. 3 and 4.

H E - - - 2RT[( X o X H - - XlX~)XH)r/o_ H In r/o_ n + XiXsr/i_ s In r/i_s] (18)

where X~ and X n are the values of X function when xl = 1. It can be observed that the calculated and experimental values agree reasonably well except the value at x~ = 0.1. It is found that Uo_ H interactions are important in determining the extent of asymmetry of the heat of mixing curves and UI_ s interactions effect the height of the curve. The values U~_ s equals 100 J mol -~ and 150 J mol- were chosen for the 1-propanol and 2-propanol systems, respectively, because these values produced the nearest fit of the experimental curve.

5. Conclusion

It can be concluded that the generalized quasi-lattice model is useful for interpreting heat of mixing data of alcohol-cyclohexane systems. By assigning values to the lattice parameters that are based solely on the geometry of the molecules and making only rough estimates of reasonable values of energy parameters, one can obtain qualitative information about the height and shape of H E vs. composition curves.

6. List of symbols

A , B , C , D

h(gc ' ,qbl ) H E

K* Kv P i , Pi*

C , 0. 2 r21 R T

T

V E

,vi* V

x i

Xi(i = I,O,S,H)

adjustable parameters of Eq. (1) function of K ~' and dpl defined by Eq. (5) molar excess enthalpy equilibrium constant defined by Eq. (6) isothermal compressibility reduced and characteristic pressure of compound i number of contact sites of components 1 and 2 size ratio parameters gas constant thermodynamic temperature characteristic and reduced temperatures of the component i, respectively reduced temperature of the mixture energy of interaction between various contact sites of the components of a binary mixture molar excess volume reduced and characteristic volumes of the component i, respectively reduced volume of mixture mole fraction of the component i Barker's adjustable parameters of Eqs. (14)-(18)

280 K.C. Singh et al . / Fluid Phase Equilibria 123 (1996) 271-281

7. Greek letters

ot

a h o

A s o Ao o

02

XI2

isobaric thermal expansivity solubility parameter solubility parameter standard molar enthalpy of H-bond formation standard molar entropy of H-bond formation standard molar volume of H-bond formation contact surface fraction segment fraction interchange interaction parameter in Flory theory

7.1. Subscripts

exptl F i MK

experimental value calculated from Flory theory component i (1 for alkanol, 2 for aromatic hydrocarbon) calculated from the Mecke-Kempter model

Acknowledgements

The authors (S.M. and V.G.) thank the Council of Scientific and Industrial Research and University Grant Commission, New Delhi for financial assistance.

References

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