Thermodynamics of associated solutions containing aniline and methanol

Fluid Phase Equilibria, 72 (1992) 147-162

147

Elsevier Science Publishers B.V.. Amsterdam

Thermodynamics and methanol

of associated solutions containing aniline

Isamu Nagata ’ and Masato Sano Department of Chemistry and Chemical Engineering, Division of Physical Sciences, Kanazawa University, Kodatsuno 2-40-20, Kanazawa, Zshikawa 920 (Japan)

(Received August 6, 1991; accepted in final form September 25, 1991)

ABSTRACT Nagata, I. and Sano, M., 1992. Thermodynamics of associated solutions containing and methanol. Fluid Phase Equilibria, 72: 147-162.

aniline

Excess molar. enthalpies of aniline-methanol-benzene mixtures were measured with an isothermal dilution calorimeter at 25°C. Experimental results for three binary mixtures constituting the ternary mixture are well correlated by use of the UNIQUAC associatedsolution model. The ternary experimental results are in close agreement with predicted values obtained from the model having binary parameters. The model is able to satisfactorily predict ternary liquid-liquid equilibria for aniline-methanol-n-hexane and anilinemethanol-n-heptane mixtures using binary information.

INTRODUCTION

The thermodynamic properties of binary and ternary mixtures containing an associating component such as an alcohol and aniline have been well correlated with the UNIQUAC associated-solution model (Nagata, 1985; Nagata and Ohtsubo, 1986a). Furthermore, the model has been extended to cover mixtures involving two alcohols (Nagata and Ohtsubo, 1986b; Nagata and Gotoh, 1986; Nagata et al., 1986). It is interesting for us to study the thermodynamic properties of binary and ternary mixtures of aniline and an alcohol by use of the UNIQUAC associated-solution model. We present here the experimental excess molar enthalpies of anilinemethanol-benzene and compare these measured results and the ternary

’ Author to whom correspondence 0378-3812/92/$05.00

should be addressed.

0 1992 Elsevier Science Publishers B.V. All rights reserved

x2

- 169.8 - 70.6 37.4 174.1 329.5 449.1 546.4 614.1 682.7 744.7 780.8 808.7 822.0 820.2 811.1 803.3 776.8 747.5 717.7

(J mol-‘)

f-f,”

4.2 5.7 9.8 13.7 13.5 9.0 5.7 8.5 7.6 7.5 7.5 6.6 6.0 3.4 1.5 1.2 0.6 1.2 3.1

AHEb (J mol-‘)

x2

x; = 0.4997 0.4869 0.0257 0.4664 0.0666 0.4373 0.1250 0.4048 0.1901 0.2720 0.3638 0.3263 0.3471 0.2990 0.4016 0.2869 0.4259 0.2511 0.4974 0.2216 0.5566 0.1979 0.6039 0.1797 0.6404 0.1649 0.6701 0.1509 0.6981 0.1285 0.7429 0.1117 0.7765 0.1002 0.7995 0.0906 0.8188

x1

- 88.6 29.9 186.3 339.8 508.4 635.9 712.0 739.7 807.1 842.3 857.6 860.7 857.2 848.8 823.2 793.0 765.9 738.9

H,” (J mol-‘) -4.6 -5.1 - 2.1 -4.6 - 10.2 - 14.3 - 14.3 - 15.1 - 12.4 - 10.8 -9.9 - 10.0 - 10.7 -11.2 -11.9 -11.1 -9.6 - 7.5

AH,E (J mot-‘) x2

(3) a

x; = 0.7504 0.7201 0.0403 0.6846 0.0876 0.6399 0.1472 0.5915 0.2117 0.5400 0.2803 0.4801 0.3602 0.4245 0.4343 0.3857 0.4860 0.3645 0.5143 0.3156 0.5795 0.2752 0.6332 0.2432 0.6760 0.2160 0.7122 0.1821 0.7574 0.1559 0.7922 0.1367 0.8178

Xl

H,"at 25°C for aniline (l&methanol @-benzene

a Obtained by mixing pure benzene with xi aniline + (1 - x;)methanol. b A indicates experimental value minus calculated value.

x; = 0.2500 0.2452 0.0192 0.2365 0.0540 0.2265 0.0939 0.2129 0.1485 0.1955 0.2180 0.1800 0.2798 0.1657 0.3371 0.1550 0.3798 0.1415 0.4340 0.1259 0.4962 0.1138 0.5446 0.0998 0.6007 0.0867 0.6530 0.0764 0.6945 0.0680 0.7281 0.0634 0.7465 0.0535 0.7859 0.0462 0.8152 0.0404 0.8385

Xl

Experimental ternary excess molar enthalpies

TABLE 1

69.5 192.5 331.7 465.3 588.7 708.1 788.9 831.2 846.2 867.7 866.7 852.3 830.1 785.7 738.2 694.7

(J mol-‘)

H,”

- 8.2 -5.3 - 3.8 -5.1 -7.1 -5.1 -2.6 2.6 3.3 7.3 8.6 8.2 7.6 5.5 4.8 4.7

AH,” (J mol-‘)

Aniline -methanol Aniline -benzene Methanol-benzene

System (l-2)

3003.51 4.0086

- 665.86

AI

623.99

- 721.57 2.4777

-42

447.94 - 0.2986

423.36

4

Coefficients A, of eqns. (1) and (2) and standard deviation IT

TABLE 2

- 333.36 0.4673

- 20.621

- 0.0729

- 20.62

0.0560

0.5949

k

1.3

5.0

(J mol-‘)

f7

150

liquid-liquid equilibria (LLE) of aniline-methanol-n-hexane or n-heptane (Nagata, 1991) with those calculated from the UNIQUAC associated-solution model (Nagata and Ohtsubo, 1986b; Nagata et al., 1986). Excess molar enthalpies H,f at 25°C vapor-liquid equilibria (VLE) and mutual solubilities (MS) for the binary systems which constitute the ternary systems have E for aniline-methanol by Nakanishi and Touhara been reported: H,,,, (1986), for aniline-benzene by Nagata and Tamura (1992), and for methanol-benzene by Mrazek and Van Ness (1961); vapor-liquid equilibria (VLE) for aniline-methanol at 20°C by Maher and Smith (1980); mutual solubilities (MS), for aniline-n-hexane or n-heptane at 25°C by Nagata (1991), and for methanol-n-hexane or n-heptane by Nagata (1987).

EXPERIMENTAL

Aniline (Special Grade: Nacalai Tesque. Inc.) was used directly. Methanol (First Grade: Wako Pure Chemical Industries Ltd.) was fractionally distilled after shaking with calcium oxide and Benzene (First Grade: Kanto Chemical Co., Inc.) was subjected to repeated fractional crystallization. The densities of the chemicals, measured with an Anton-Paar densimeter (DMA40), agreed closely with literature values (Riddick et al., 1986). The ternary excess molar enthalpies were measured by use of an isothermal dilution calorimeter at 25°C (Nagata and Tamura, 1988). The error of the measured Hz values was less than 0.5% of the observed values.

RESULTS

Table 1 gives the ternary Hz values for the aniline-methanol-benzene system at 25°C. The binary HE data for aniline-methanol and aniline-benzene were fitted to eqn. (1). H&j =xixj

F A,&

-n,)“-‘/[l

-k(q

-xi)]

n=l

The corresponding Hz values for methanol-benzene (2) by Mrazek and Van Ness (1961). H&j = 104x,x,/

2 A,@, --xJ~-~ n=l

(1)

were fitted to eqn.

(2)

Table 2 lists the coefficients of eqns. (1) and (2) and the standard deviations (T. Figure 1 shows the experimental and calculated values for the

151

I

I 0.2

I

I

I

I 0 4

I 0. 6

I 0. 8

1 0

MOLE FRACTION OF 1ST COMPONENT

Fig. 1. Experimental excess molar enthalpies for three binary systems at 25°C: 1, 0, aniline (l&methanol (21, (Nakanishi and Touhara, 1986); 2, A, aniline (O-benzene (2) (Nagata and Tamura, 1991); 3, n , methanol (&benzene (2) (Mrazek and Van Ness, 1961). -, calculated from smoothing equations or the UNIQUAC associated-solution model.

three binary systems. The ternary experimental with eqn. (3).

Hi results were correlated

(3) where A&RT

= n&B,(l

- 2x,)“-‘41

- Z(1 - 2x,)]

(4)

152

Methanol

02 Aniline

0.4 Mole

0.6 traction

08 Benzene

Fig. 2. Curves of constant excess molar enthalpies for the aniline W-methanol (2)-benzene calculated from eqns. (3) and (4); - - - - - -, calculated from the (3) system at 25°C: UNIQUAC associated-soktion model.

The coefficients of eqn. (4) were calculated using an unweighted leastsquares method: B, = 1.1514, B, = -0.3558,B, = 0.8826, B, = -3.7182, B, = 3.3263 and I = -0.10949; and the arithmetic-mean deviation AAD = 7.2 J mol-‘, the standard deviation (T= 8.6 J mol-’ and the relative-mean deviation is 2.5%. Figure 2 plots contours of the ternary HE.,,, calculated from eqns. (3) and (4).

DATA ANALYSIS

The UNIQUAC associated-solution model (Nagata and Ohtsubo, 1986b; Nagata et al., 1986) assumes that the linear association of aniline (A) and methanol (B) molecules and the multisolvation of polymers result in homopolymers (A, and Bi) and copolymers ((AiB,jk, AI(BjAkjl, (B,Ajjk and BI(AjB~G)I), and the resulting polymers and benzene (C) form other complexes: AC, B,C, (A,Bj),C, A,(B,A,),C, (B,Aj),C and B,(A,Bk)&. The subindices i, j, k and I go from one to infinity. The equilibrium constants are assumed to be independent of the degree of association and solvation.

153

The ternary HE based on the UNIQUAC (Nagata et al., 1986) is expressed by

associated-solution

u,“BxB’Bl +

Q

(2

-

rAYE3K&3~A,@BlUAUB)

+

u

A

@ A

53KBCXB rAKACxA

B

‘A

+

+ @‘cl rAKAB’B

rAKAC&xA@Al

hKAJ3’A

(2-rr

+ @A

A

B

I- uA

K*@ AB

Al

CDBl UU) A B

II

rBKBCUAUBXB%31 + UA%

+

(2 - rAr,K,&@A,@,,UAUB)

‘B:‘B1

+ uAzcA1

B rBKBC% +

+@a ‘AKAB@B

$

KBc8BxB@Bl

+

(2-r

@B

rAKACGBUAXA@Al + %@A

Ii

A

r B K*AB @Al @ Bl UU) A B

model

154

+

hAB

i(

XB -+-

XA

‘A%

‘B’A uBxB@Bl

QxA@Al

+2

@A

+

@B

+

Al

Q>Bl UU) A B

rBKBCUBXB~Bl

rAKAC%xA@A1

+2

AB

K AB

rB@A

‘A@,

+ @A

+

(l+rrK*@ A B

‘AKACxA

rBKBCxB

+@a

63

i

[

XA

uAxA@Al

hACrAKAC%l

‘A

‘AKAB’A

+

I

XB

43-%3~Bl +hBCrBKBC%l %

’

( 1 -

‘ArB

rAKAB’B

+

Kk3@Al@Bl~UB) I

rrK2@ A B AB ’

(I

-

Al

@ Bl UU A

rArBK.k@AI@BlUAu13)2

B

cG7IX, -

(5)

I

where the segment fraction @, the surface fraction 8, the sytibols u,, pa, U, and U,, the binary coefficients rJ, related to the energy parameter a,, the monomer segment fractions of pure aniline and methanol @i1 and @zl, and the symbols 02 and 0: are given by eqns. (61417). @?I“XYI/

c-55 J

(6)

0, =x,q,/

CxJqJ

(7)

J u,

= KA@Al/(l

uB

= KB@131/(1

uA

=

l/c1

-KA@AI)

(10)

uB

=

l/(1

-

(11)

rJI

=

ew(

-

-

W’d

-a,/T)

KA@A1)2

(8)

KB@,l)2

(9)

(12)

155

a, = C, + DJ,(T - 273.15)

(13)

@& = [ 1 + 2K, - (1 + 41Q0”] /2K;

(14)

@‘oB1 = [l + 2K, - (1 + 4K,)0.5]/2K;

(15)

Q = K*@&/( 1 - K*@‘jQ2

(16)

UB”= I&@,/(

(17)

1 - K,@Q2

The monomer segment fractions (PAI, a,, calculated from eqns. (HI--(20). QA = (1 + rAK,,@c,)SA

rAKA8AsB

+ (I-

QB =

and Qcl are simultaneously

r*r13K3*SB)2

x (2+rBK4BsA(2 - r.453GsAsl3) + c4KArJE3 +%[(r*K,c + 5343c)+ ?4rBK*BK*Cs‘4 x (2- c4MG3s*sl3) + r,wY4BKecsBl) rBKABsA% (1 + rBK,,@,,)S, +

(18)

(1 - r*rBKx4SB)2

x (2 + r,K,,S,(2 + @‘cl [ wL,

- r.4r,K3*S,) + b&,,)

x (2 - L43&A&)

+ ?453~AB~&3 + c44L*~*CSAl)

1 + r,KAcS,

Qc = acl

+ r,K,,S,

i X

K AC

-+

I ‘BKAF3

+ rBKABSA

K BC

+ K,,S,

+

(19)

rAQ3~cGBsAsB (1 - r*r,K%4Sr3)

+ K,,S,

(20)

rAKAB

where the sums sA, s,, S, and S, are defined by eqns. (2%(24). s,=~Al/(1-KA~Al~2

(21)

SE3 = @'sl/(l

(22)

-&@Ed2

sA=@Al/(l-KA'Al)

(23)

Sk3 =%/(l

(24)

-wbl)

156 TABLE Values

3 of the pure-component

Component

structural

r

Aniline Methanol Benzene

2.98 1.15 2.56

parameters

4

Component

r

9

2.38 1.12 2.05

n-Hexane n-Heptane

3.61 4.15

3.09 3.52

The association parameters of pure components are: for aniline, KA = 15 at 50°C and h, = - 15.4 kJ mole1 (Nagata and Ohtsubo, 1986a); for methanol, K, = 173.9 at 50°C (Brandani, 1983) and h, = -23.2 kJ mol-’ (Stokes and Burfitt, 1973). The solvation parameters are: for anilinemethanol, KAB = 25 at 25°C and h,, = -20.7 kJ mol-‘; for aniline-benzene, K,, = 1 at 50°C and h,, = - 10.8 kJ mol-’ (Nagata and Ohtsubo, 1986a); for methanol-benzene, K,, = 4 at 50°C and h,, = -8.3 kJ mol-’ (Nagata, 1985). Th e pure component structural parameters r and 4 were estimated from the method of Vera et al. (1977) and are given in Table 3. All standard enthalpies were assumed to be independent of temperature and fix the temperature dependence of the equilibrium constants through the van? Hoff relation. Table 4 gives the coefficients of eqn. (171, C,, and D,,, and the absolute arithmetic-mean and standard deviations between the calculated and experimental values. A simplex method (Nelder and Mead, 1965) was used to obtain C, and DJI by minimizing the sum of the squares of deviations in HE for all data points. The absolute arithmetic-mean deviation (AAD), root-mean-square deviation (RMSD) and average relative deviation CARD) between the fifty-two experimental Hz and predicted values from the UNIQUAC association model are AAD = 11.1 J mall’, RMSD = 12.2 J

TABLE

4

Parameters System (l-2)

Aniline -methanol Aniline -benzene Methanol -benzene

C,, and D,, for binary systems Number of data points

16

at 25°C

Parameters C

Deviation D21

340.2

0.3662

14

- 188.1

519.5

- 1.073

10

1260.7

- 190.3

2.174

a AAD = absolute

u (J mol-‘)

4.0

5.0

-2.111

4.5

9.0

- 0.3827

1.7

2.6

D12

(I$ - 36.86

arithmetic-mean

deviation,

(T = standard

a

AAD (J mol-‘)

0.3748

deviation.

157

mol-’ and ARD = 2.7%. These values are similar to those for ternary mixtures containing alcohols and one hydrocarbon (Nagata and Tamura, 1988). Binary VLE for aniline-methanol and ternary LLE for anilinemethanol-n-hexane and aniline-methanol-n-heptane were successfully correlated with the UNIQUAC associated-solution model. The activity coefficients of aniline (A) and the saturated hydrocarbon (C) (Nagata and Ohtsubo, 1986a) are described as

@A 0‘4 -1

K

In z

In yc = In

I

i

C

(26)

•t

where the true molar volume of the aniline mixture v and that of pure aniline Vj are expressed by eqns. (27) and (28).

1

x4

--+-+ vr*

SB Yu

l

2

r‘&K~rS

+-

CD Cl rC

(27) (28)

The activity coefficient of methanol is obtained by changing the subscript A in eqns. (25) and (28) to B. The monomer segment fractions QAl and @nl are obtained from eqns. (18) and (19) by setting K,, = K,, =0 and acl = Qc for anilinemethanol-saturated hydrocarbon, since there are no complexes formed with a saturated hydrocarbon. Binary VLE data for aniline-methanol were reduced using a computer program as described by Prausnitz et al. (1980), and considering vapor-phase non-ideality and the Poynting correction, and are compared with calculated results in Fig. 3. Table 5 presents the results of binary phase equilibrium data reduction. Mutual solubilities were used to obtain the energy parame-

158

3: c ._ & 8 x f E 2

, 0

I

0.2

0.4

Mole

fraction

I 0 6

I 0 .a

of Amline

Fig. 3. Vapor-liquid equilibrium for the aniline-methanol system at 20°C; 0, experimental calculated from the UNIQUAC associated-soludata of Maher and Smith (1980); -, tion model.

TABLE

5

Binary parameters of the UNIQUAC vapor-liquid equilibrium data reduction System (l-2)

Aniline -methanol Aniline - n-hexane Aniline - n-heptane Methanol -n-hexane Methanol -n-heptane a MS = mutual

associated-solution

model

and

results

Temperature (“Cl

Number of data points

Root-mean-square deviations Parameters 8F 6T 6x (Tort-) (K> (x 103) FG 1031 $1

20

13

1.50

25

MS a

200.8

25

MS

176.8

25

MS

25

MS

solubility.

0.00

0.0

- 195.4

25.89 1.965

of binary

a21

(K) 197.1 9.744 16.80 57.89 89.43

159

ters for partially miscible systems by solving the following relation for both components: (Wx

= (WY

(29)

Methanol

Aniline

Mole

fractton

n-Hexane

(a)

Methanol

Andine

Mole

fraction

n-Heptane

b)

Fig. 4. Ternary liquid-liquid equilibria at 25°C: l ----0, experimental tie-line data of Nagata (1991); (a), aniline-methanol-n-hexane; (b), aniline-methanol-n-heptane; -, calculated from the UNIQUAC associated-solution model.

160

Figure 4 shows the ternary experimental and predicted LLE results at 25°C for aniline-methanol-n-hexane and aniline-methanol-n-heptane, indicating that agreement is good.

CONCLUSION

The ternary excess molar enthalpies and liquid-liquid equilibria of mixtures containing aniline, methanol and one hydrocarbon have been very well predicted by means of the UNIQUAC associated-solution model with only binary parameters.

LIST OF SYMBOLS

A B, C

a,, Ai, Bi

A&C A,C

An

*?I B,C

hAB, hA0 hBC

k KA,

KAB, I

P 41 rI

KB KAC,

KBC

aniline, alcohol and hydrocarbon binary interaction parameter i-mers of aniline and alcohol complex containing i molecules of aniline, j molecules of alcohol and one molecule of hydrocarbon complex containing i molecules of aniline and one molecule of hydrocarbon constants of eqns. (1) and (21 constants of eqn. (4) complex containing i molecules of alcohol and one molecule of hydrocarbon coefficients of eqn. (13) enthalpies of hydrogen-bond formation of aniline and alcohol enthalpies of complex formation between unlike molecules excess molar enthalpy excess molar enthalpies of binary mixtures 1-2, l-3 and 2-3 constant of eqn. (1) association constants of aniline and alcohol solvation constants between unlike molecules constant of eqn. (4) total pressure molecular geometric area parameter of pure component I molecular geometric volume parameter of pure component I

161

universal gas constant sums as defined by eqns. (21) and (22) sums as defined by eqns. (23) and (24) absolute temperature quantities as defined by eqns. (8) and (9) quantities as defined by eqns. (10) and (11) true molar volume of aniline mixture given by eqn. (27) true molar volumes of pure aniline and alcohol given by eqn. (28) liquid mole fraction of component I liquid mole fraction of component I in a binary mixture lattice coordination number equal to 10

XI

4 z Greek letters Yr

s h

123

01 u

activity coefficient of component I experimental value minus calculated value function as defined by eqn. (4) surface fraction of component I standard deviation coefficient as defined by exp( -a,,/T) segment fraction of component I monomer segment fraction of component I

Subscripts

A, B, C Al, Bl, Cl AB, AC, BC i, j, k 1 I, J, K

aniline, alcohol and hydrocarbon monomers of components A, B and C binary complexes i, j, k and I-mers of aniline and alcohols or indices components I, J and K

Superscripts ff7 P

0

conjugated liquid phases pure-liquid reference state

REFERENCES Brandani, V., 1983. A continuous linear association model for determining the enthalpy of hydrogen-bond formation and the equilibrium association constant for pure hydrogenbond liquids. Fluid Phase Equilibria, 12: 87-104.

162 Maher, P.J. and Smith, B.D., 1980. Vapor-liquid equilibrium data for binary systems of aniline with acetone, acetonitrile, chlorobenzene, methanol, and 1-pentene. J. Chem. Eng. Data, 25: 61-68. Mrazek, R.V. and Van Ness, H.C., 1961. Heats of mixing: alcohol-aromatic binary systems at 25”, 35”, and 45°C. AIChE J., 7: 190-195. Nagata, I., 1985. On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilibria, 19: 153-174. Nagata, I., 1987. Liquid-liquid equilibria for acetonitrile + methanol + saturated hydrocarbon and acetonitrile + 1-butanol + saturated hydrocarbon mixtures. Thermochim. Acta, 114: 227-238. Nagata, I., 1991. Ternary liquid-liquid equilibria for [(aniline + saturated hydrocarbon) + methanol or ethanol]. Thermochim. Acta, 186: 123-130. Nagata, I. and Gotoh, K., 1986. Thermodynamics of alcohol solutions. Excess molar enthalpies of liquid mixtures containing two alcohols. Thermochim. Acta, 102: 207-222. Nagata, I. and Ohtsubo, K., 1986a. Thermodynamics of associated solutions. Excess thermodynamic properties of mixtures of aniline with hydrocarbons. Thermochim. Acta, 97: 37-49. Nagata, I. and Ohtsubo, K., 1986b. Thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing two alcohols. Thermochim. Acta, 102: 185-205. Nagata, I. and Tamura, K., 1988. Excess molar enthalpies of binary and ternary mixtures formed by methanol, 2-butanol and benzene. Fluid Phase Equilibria, 41: 127-139. Nagata, I. and Tamura, K., 1992. Excess enthalpies of (aniline+acetonitrile or benzene) and (aniline + acetonitrile + benzene). J. Chem. Thermodyn., 24(5). Nagata, I., Tamura, K. and Gotoh, K., 1986. Thermodynamics of alcohol solutions. Excess molar enthalpies of ternary mixtures containing two alcohols and one active nonassociating component. Thermochim. Acta, 104: 227-238. Nakanishi, K. and Touhara, H., 1986. Excess molar enthalpies of (methanol +aniline), (methanol + N-methylaniline), and (methanol + N,N,-dimethylaniline). J. Chem. Thermodyn., 18: 657-660. Nelder, J.A. and Mead, R., 1965. A simplex method for minimization. Comput. J., 7: 308-313. Prausnitz, J.M., Anderson, T.F., Eckert, CA., Hsieh, R. and O’Connell, J.P., 1980. Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria. Prentice-Hall, Englewood Cliffs, NJ. Riddick, J.A., Bunger, W.B. and Sakano, T.K., 1986. Organic Solvents, 4th Edn. Wiley-Interscience, New York. Stokes, R.H. and Burfitt, C., 1973. Enthalpies of dilution and transfer of ethanol in non-polar solvents. J. Chem. Thermodyn., 5: 623-631. Vera, J.H., Sayegh, S.G. and Ratcliff, G.A., 1977. A quasi-lattice-local composition model for the excess Gibbs free energy of liquid mixtures. Fluid Phase Equilibria, 1: 113-135.