Fluid Phase Equilibria, 4 (1980) 229-255 229 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

THERMODYNAMICS OF ACETONE--CHLOROFORM MIXTURES

ALEXANDER APELBLAT *, ABRAHAM TAMIR and MOSHE WAGNER

Department of Chemical Engineering, Ben Gurion University of the Negeu, Beer Sheva (Israel)

(Received November 26th, 1979; accepted in revised form February 7th, 1980)

ABSTRACT

Apelblat, A., Tamir, A. and Wagner, M., 1980. Thermodynamics of acetone-chloro. form mixtures. Fluid Phase Equilibria, 4: 229-255.

The excess thermodynamic functions GE, HE, SE, C, and VE and the vapourliquid equilibria at constant temperature, at constant pressure and azeotropic behaviour are satisfactorily described for the acetone + chloroform system using the ideal association model of the type A + B + AB + ABg. Existing data in the literature for the system were supplemented by determination of vapour pressures at 25.0 and 35.17%, excess volumes of mixing at 35OC and excess heat capacities at 30C.

INTRODUCTION

The acetone + chloroform system has been widely investigated since Dolezalek (1908) showed that the negative deviations from Raoults law, first observed by v. Zawidzki (1900) at 35.17C, can be attributed to com- plex formation between unlike molecules.

The successful reproduction of the pressure-composition curve, using a simple ideal associated solution model of the type A + B + AB,,had a stimul- ating effect on forthcoming investigations and it can probably be supposed that our knowledge about this system is greater than about any other mixture of nonelectrolytes.

The experimental data available on the system include the total and partial pressures determined by v. Zawidzki (1900) at 35.17C; Beckmann and Faust (1914) at 28.15, 40.40 and 55.1OC; Schulze (1919) at 30, 70 and 90C; Schmidt (1921) at O, 20, 40 and 55C; Briegleb and Scholze (1954) at 10 and 20C; Severns et al. (1955) at 50C; R&k and Schrijder (1957) at 15, 20, 30, 35, 40, 50 and 55C; Mueller and Keams (1958)

* To whom correspondence should be addressed.

230

at 25, 35 and 50C: Kudriavcev and Susarev (1963) at 35 and 55C; Campbell et al. (1966) at 25C and Campbell and Musbally (1970) at loo, 150, 160 and 180C.

Calorimetric measurements in the acetone-chloroform system, initiated by Hirobe (1926) at 25C were performed at the same temperature by Campbell and Kartzmark (1960), Matsui et al. (1973), Handa and Fenby (1975). At other temperatures, heats of mixing were determined by Schmidt (1926) at 14C, Onken (1962) at 35C, Morcom and Travers (1965) at 0, 25C, 37, 60 and 7OC, Sabinin et al. (1967) at lo, 25 and 4OC, and Morris et al. (1975) at 50C.

Heat capacities, isothermal compressibilities and coefficients of expan- sion in the 20-50C temperature range were determined by Staveley et al. (1955). Adiabatic compressibilities and ultrasonic velocities were measured at 27.5C by Parshad (1942). Densities and excess molar volumes were determined at25C by Hubbard (1910), Anisimov (1953), Campbell et al. (1966) and by Staveley et al. (1955) also at 50C. The solid-liquid phase diagram was determined by Korinek and Schneider (1957) and by Campbell and Kartzmark (1960) and heats of vaporization by Sabinin et al. (1967).

The deuterium isotope effect was considered by Rabinovich and Nikolaev (1960), Kagarise (1963), Morcom and Travers (1965) and Duer and Bertrand (1974). Handa et al. (1975) studied this effect in the (CH,),CO + CDCl,, (CD&CO + CHCl, and (CD&Z0 + CDCl, systems.

Association in the acetone + chloroform mixtures or in pure components was investigated by spectral methods (IR, UV and NMR) in a number of works (Nikuradse and Ulbrich (1954), Huggins et al. (1955), Korinek and Schneider (1957), Reeves and Schneider (1957), Denisov (1961), Creswell and Allred (1962) and Kagarise (1963)).

Dipole moments and.dielectric constants were determined by Fischer and Fessler (1953), Campbell et al. (1961) and Shakhparonov and Vakalov (1964).

The negative deviations from Raoults law and the negative heat of mixing HE are explained by assuming that the hydrogen-bonded complex AB

exists in the solution. Korinek and Schneider (1957) and Campbell and Kartzmark (1960) showed that the equimolar compound is stable in the solid state (m.p. 106C) but is highly dissociated in the molten state. Camp- bell and Kartzmark evaluated the energy of hydrogen bonding in the acet- one-chloroform system as -11.3 kJ mol-l. This value is close to that of Huggins et al. (1955), -10.45 kJ mol-l, deduced from NMR measurements, which indicate a specific interaction involving the proton of chloroform. Complex formation in the acetone + chloroform system was only rejected by Shakhparonov and Vakalov (1964) who, on the basis of measurable

231

dielectric properties, concluded that for all concentrations the mutual orien- tation of the molecules in the solution is random.

The correctness of Dolezaleks theory has been discussed by Hildebrand and Scott (1964) who showed that the experimental P-x data can, with practically the same accuracy, be represented by the chemical A + B + AB model as well as the physical model. The asymmetry of the excess thermo- dynamic functions (GE, HE and TSE) was interpreted by Kearns (1961) as a result of the simultaneous formation of AB and AB, complexes (B -- chloro- form)

CH3 >C=O...H -XCl...H-Ll

Cl Cl (II)

CHs

Kearns used the ideal association model of the type A + B + AB + ABz, original- ly developed by McGlashan and Rastogi (1958) for the dioxane + chloroform system. From the van t Hoff equation he estimated the standard heats of formation of the complexes AI-I& = -10.1 kJ mol-l and Afloat = -13.8 kJ mol-, while Morcom and Travers (1965) and Matsui et al. (1973) deduced that AH& = -10.3 kJ mol-l and AffABZ = -13.0 kJ mol- at 25C.

The self-association of pure chloroform reported by Nikuradse and Ulbrich (1954) and Cresswell and Allred (1962), and the fact that the conditions AH&,/2 = AH& is not satisfied l , supports the nonequivalence of two hydrogen bonds in the ABz complex, i.e. the structure (II). However, the complex with two equivalent bonds

CH3

> c=o::: H-CC&

(III) CH3 H-CCL

was also proposed (Fisher and Fessler (1953) and Morcom and Travers (1965)). Maffiolo et al. (1972) analyzed the acetone-chloroform system within the framework of the three-parameter model, which includes the formation of AB and Bs complexes and the residual contribution resulting from the physical term. A quite different approach was suggested by Maron et al. (1960) who used the theory of polymer solutions to the system under consideration.

Our interest in the acetone-chloroform mixture was, at first, very limited. We wanted only to use, inter alia, the v. Zawidzki partial pressure at 35.17C for examination of the pressures obtained in our modified isoteniscope. Con- trary to other cases (e.g. measurements in the ethanol+enzene system at 45C and the acetone + chloroform + methanol system at 5OC), some dis- agreement was observed between v. Zawidzkis data and ours. It was there- fore decided to perform measurements at 26 C and results in complete

l Evidently the same can be expected if some hindrance exists in the AB2 complex.

232

agreement with Mueller and Keams (1958) data were obtained. Finally, the vapour pressures were supplemented by the excess molar volumes VE and the excess heat capacities, C,. In addition, a detailed thermodynamic analysis of the system is presented when we have limited ourselves to a two- parameter model. Taking into consideration that non-specific interactions and the existence of the chloroform dimer are neglected, it is evident that the ideal associated solution model of the type A + B + AB + ABz, used for description of the system, is only an approximation. The existence of the AB complex was confirmed in the NMR and IR investigations but there is no direct evidence (except from the dielectric relaxation experiments of Fischer and Fessler (1953)) for formation of the AB, complex. However, it should be emphasized that a remarkably good description of thermodynamic properties of the system is obtainable if the A + B + AB + ABs model is used.

EXPERIMENTAL

Materials

Analytical chloroform and acetone were supplied by Frutarom Laboratory Chemicals, Haifa and by Merck. Chloroform was purified by washing with water, dried and freshly redistilled. The middle fractions of it and of acetone were used in the experiments. The physical parameters of chloroform: (d = 1.4799 g cm*, ng5 = 1.4421) and of acetone: (d = 0.7862 g cms3, ng5 = 1.3560) are in satisfactory agreement with other investigations, especially for chloroform. There is much disagreement in the literature concerning the density of acetone. The vapour pressures of the pure components will be discussed later.

Procedure

Vapour pressures were measured by the isoteniscopic method described elsewhere (Apelblat et al. (1973)). In order to analyze the vapour phase, the gas chromatographic technique was used and the isoteniscope modified ac- cordingly. Details about this modified version will be published separately. Density measurements were performed with an Anton Paar model DMA 02D densitometer, which was calibrated with n-hexane and cyclohexane. Heat capacities of solutions were measured with an LKB 8700 Precision Calori- metry System using the procedure described by Grethe et al. (1973). The calibration curve was prepared with acetone, using the Staveley et al. (1955) value of CG = 129.7 J K-l mol- at 30C.

RESULTS AND DISCUSSION

The total vapour pressure, P, and the composition of the liquid and vapour phases, x and y are presented in Tables 1 and 2. Comparing the

233

TABLE 1

Vapour-liquid equilibrium in the acetone(l)-chloroform(2) system at 25%

Xl Yl P Wa)

Yl Y2 GE (J mol-l)

0.000 0.000 26.46 0.517 1.000 0 0.094 0.064 24.60 0.546 0.960 -233 0.216 0.162 22.82 0.559 0.922 -469 0.293 0.245 22.12 0.602 0.893 -567 0.363 0.327 21.64 0.653 0.851 -615 0.405 0.405 21.52 0.701 0.813 -662 0.480 0.545 22.46 0.831 0.744 -601 0.593 0.682 23.74 0.889 0.702 -530 0.666 0.758 25.06 0.928 0.687 -434 0.707 0.798 25.64 0.942 0.669 -397 0.822 0.888 27.48 0.966 0.654 -258 0.895 0.944 28.72 0.986 0.580 -173 0.951 0.976 29.81 0.996 0.553 -81 1.000 1.000 30.73 1.000 0.543 0

PYC, y data of v. Zawidzki (1900) and our results at 35_17C, shows that there is a good agreement between x and y values, but the v. Zawidzki pressures are systematically lower than ours (Figure 1). Since the pressures measured by v. Zawidzki at 35.17C are lower than corresponding values at a lower temperature, 35.OC (Rock and Schroder, 1957), Mueller and Keams (1958), Kudriavcev and Susarev (1963), Fig. l), it is clear that the

TABLE 2

Vapour-liquid equilibrium in the acetone(l)-chloroform(2) system at 35.17%

Xl

0.000 0.000 39.93 0.406 1.000 0 0.128 0.079 37.22 0.491 0.985 -272 0.160 0.105 35.97 0.504 0.960 -369 0.250 0.187 34.88 0.557 0.947 -480 0.378 0.378 34.09 0.728 0.854 -559 0.456 0.501 34.30 0.805 0.788 -586 0.578 0.671 35.93 0.890 0.702 -555 0.706 0.807 38.77 0.946 0.638 -439 0.749 0.850 39.64 0.960 0.594 -413 0.755 0.855 39.93 0.965 0.592 -398 0.827 0.907 41.57 0.973 0.560 -315 1.000 1.000 46.85 1.000 0.497 0

Yl P Wa)

Yl Y2 GE (J mol-l)

234

kPa

39

33

0 0.2 0.4 0.6 OF3 LO xr

Fig. 1. Vapour pressures in kPa, in the acetone(l) + chloroform (2) system at Rijck and Schrijder (1957); 2, Kudriavcev and Susarev (1963); 3, Mueller and (1958); and at 35.17C, 4, v. Zawidzki (1900); 5, this work).

TABLE 3

Vapour pressure of acetone(l) and chloroform(2) at 35.0 and 35.17OC

35.OC Kearns

(1,

pl Wa)

35.0 35.17O

pz WV

35.0 35.17O

R&k and Schrader (1957) 43.36 39.53 Mueller and Kearns (1958) 45.88 39.62 Kudriavcev and Susarev (1963) 46.46 39.33 Eqn. (1) or (2) 46.21 46.52 39.72 39.99 v. Zawidzki (1900) 45.93 39.08 This work 46.85 39.93

235

v. Zawidzki results have a systematic error. The same is observed when the vapour pressure of pure components, pp, i = 1,2, is considered (Table 3). Once again pp values at 3O.OC from different sources are higher than v. Zawidzkis pressures at 35.17C.

Using the pressure of pure components from works mentioned in this paper and from Timmermans compilation (1950), the Antoine equation was re-evaluated for the 0-100C range, for acetone:

logIo@;/Torr) = 7.26528 - 1281.6921237.5 + t

and for chloroform:

(1)

log,,@;/Torr) = 6.98448 - 1181.722/227 + t (2)

The constants in eqns. (1) and (2) differ slightly from those proposed by Hala et al. (1968).

The vapour pressures obtained were used for evaluation of the activity coefficients at temperature T:

ln y. = ln yip + @ii - CltP -PP) + 6 I

xiPi RT lZ~$t~ -Yi12 (3)

i=l,2 612 = =312--B11--22

and they are presented in Tables 1 and 2. The second virial coefficients Bii, i, j = 1,2 were estimated by the method proposed by Tsonopoulos (1974).

Thermodynamic consistency in the acetone + chloroform system has been considered by Rock and Schrijder (1957), Mueller and Kearns (1958) and Kearns (1961) using the Redlich-Kister test (1948) in the form:

JT=RT ln(r, h2kh 0

(4)

The isothermal vapour+iquid equilibrium data are considered practically consistent if IJrl

236

TABLE 4

Thermodynamic consistency tests, eqns. (4) and (5), for the acetone-chloroform system tern

JT JT D .(J mol-l) =

Briegleb and Scholze (1954) Rock and SchrSder (1957)

Briegleb and Scholze (1954) Rock and Schrijder (1957)

Mueller and Kearns (1958) Campbell et al. (1966) This work

Beckmann and Fast (1914)

Schulze (1919) Rock and SchrSder (1957)

Rock and SchrSder (1957) Mueller and Kearns (1958) Kudriavcev and Susarev (1963)

v. Zawidzki (1900) This work

Rock and Schrijder (1957)

Beckmann and Faust (1914)

Kudriavcev and Susarev (1963)

Severns et al. (1954) Rock et Schrijder (1957) Mueller and Kearns (1957)

Rock and Schriider (1957) Kurdriavcev and Susarev (1968)

Beckmann and Faust (1914)

Schulze (1919)

Schulze (1919)

10.0 15.0

20.0

25.0

28.15

30.0

35.0

35.17

40.0

40.4

45.0

50.0

55.0

55.1

70.0

90.0

+18.8 +o.ooa 0.0158 -11.5 -0.0048 0.009

-153 4.0628 0.123 -38.1 4.0156 0.030

-77.4 -0.0312 0.0160 +68.5 +0.0277 0.0702 -8.4 -0.0034 0.0087

-21.3 -0.0085 0.0167

+18.0 +0.0071 0.0132 -35.5 -0.0141 0.030

-33.9 -0.0132 0.0255 -36.9 -0.0144 0.0143 +44.2 +0.0173 0.0386

-109.0 -0.044 0.100 -12.6 -0.0049 0.011

-5.9 -0.0023 0.0054

-5.0 -0.0019 0.0043

+7.6 +0.0029 0.0066

+64.0 +0.0238 0.0626 +4.2 +0.0016 0.0043

-87.9 -0.033 0.0895

-6.3 -0.0023 0.0064 +2.5 +0.0009 0.0022

+9.6 +0.0035 0.0091

-58.6 -0.0205 0.0061

-11.6 -0.0038 0.0160

237

The excess free energy of mixing:

GE = RT(xl In y1 + 3celn 7s) (3)

was calculated using eqn. (3) and are presented in Tables 1 and 2. From the activity data, the appropriate association model is deduced in the following way. For the A + B + AB type of association one has:

KAB = XABIXAXB

XA+XB+XAB=~ (7)

where A and B denote the monomeric molecules of acetone and chloroform and 1 and 2 in the following equations denote nominal components, acetone- (1) and chloroform(2). Assuming that the mixture is ideal, i.e.,

al =xlyl =aA=xA

a2 =x2y2 =aB=xB (8)

the following expression for evaluating the equilibrium constant, KAs, can be derived :

F,=(l-aI - aZ)/a2 = Karl (9)

The activities in eqn. (9) are calculated from the experimental data using eqns. (3) and (8). The corresponding expression for the A + B + AB + AB, type of association is (McGlashan and Rastogi, (1958)):

F2 = (1 - aI - a2)/a1a2 = K, + K2a2

where

(10)

K, = KAB = XABtXAXB

K2 = KAB~ = xAB2 /XAXi (11)

XA+XB+XAB+XAB~= 1

Verification of the chosen model and determination of the equilibrium con- stants are easily performed graphically by plotting F1 vs. al, or Fs vs. a2, because the functions F1 and F2 express straight lines. Typical behaviour of Fl and F2 at 25 and 35C is presented in Figs. 2 and 3. As can be seen, the A + B + AR + AB2 model is superior to the A + B + AB model, which is only valid for dilute solutions of acetone in chloroform.

Using the literature data at different temperatures, from slopes and inter- cepts of F1 and F2, the equilibrium constants and the standard heats of formation of AB and AB2 complexes were evaluated from the van t Hoff

238

. .

Fig. 2. Verification of the models A + B + AB + ABz, (1) and A + B + AB, (2) at 26.OC i;;sn;n19c) and (10)). Data: 1, C ampbell et al. (1966); 2, Mueller and Kearns (1958); 3,

I I I 8 I I

/ / 4A

0.6 _

PA 43 ,sA

a- ._, 2 v-3

0.2 t-4 _ o- 5

239

Fig. 4. Temperature dependence of the equilibrium constants. Models: A + B + AB, (1: KAB) and A + B + AB + AB2, (2: Km,; 3: KABJ.

relationship :

( 1 aln K1 AS

aT p=E?F i=AB,AB2

AIP&AB=WAB-RA--PB (12)

AHY+.I32 = fcOAB2 - H* - 2 % where x denotes the molar enthalpy of the ith component in solution. The ln K vs. l/T plot is linear over a wide temperature range (Figure 4) and there- fore the integral form of eqn. (12) is:

ln K1 = (1240/T) - 4.021

In K2 = (2421/T) - 8.237 (13)

240

TABLE 5

Standard heats of formation of AB and AB2 complexes

fW --aHAB (kJ mol-l)

-M2 (kJ mol-l)

Huggins et al. (1954) 28 10.5

Kearns (1958) 25 10.1 13.8 35 10.2 15.6 50 10.3 18.1

Campbell and Kartzmark (1960) 25 11.3

Morcom and Travers (1965) 25 10.3 13.0 50 11.2 14.7

Matsui et al. (1973) 25 10.3 13.0

This work 10-90 12.7 10.3 20.1

for the A + B + AB + ABs model, while

In KAB = (1528/T) - 4.569 (14)

for the A + B + AB model. From eqns. (12), (13) and (14), the standard heats of formation of the AB

and AB, complexes (AH, = AwAB, AH, = AN,,, for the A + B + AB + ABa and AHAB for the A + B + AB model) were evaluated and they are presented together with the literature data in Table 5. As can be seen, if the A + B + AB + AB, model is considered, there is excellent agreement between W1 val- ues and significant scattering between mz values. The standard heat of for- mation of the AB, complex reported in this work AE& = -20.1 kJ mol- is the highest one. Its value is almost twice that of the standard heat of forma- tion of the AB complex, Hi = -10.3 kJ mol- and this fact supports the existence of the structure (III) -having two equivalent hydrogen bonds if there is no steric hindrance in the complex.

The values of AWAB (Table 5) are in reasonable agreement with each other. Knowing the K1(T), K,(T), AH, and AH, values, the excess thermodynamic functions can be calculated and compared with the experimental results. The activity coefficients of the nominal components are given by:

71 =xA/xl (15)

72 =xBtx2

where the mole fraction of monomeric A and B are obtained from eqn. (11)

241

Fig. 5. Excess thermodynamic functions in J mol-, . m the acetone-chloroform system at 35%. Full line - calculated for the A + B + AB + AB2 model. Experimental data: 1, Zawidzki (1900); 2, Rijck and Schriider (1967); 3, Mueller and Kearns (1968); 4, this work; 5, Hirobe (1926); 6, Keams (1961).

with

XA+XAB+lCAB2

"'=I +XAB+sXAB2 (16)

x2 = l-x1

Introducing eqn. (15) into eqn. (6) the values of GE were calculated and the excess enthalpies and entropies of mixing were evaluated from:

(17)

GE =HE_-sE

The evaluated values of GE, HE and TSE and the experimental results, GE and HE at 35, 40, 50 and 70C are presented in Figs. 5,6,7 and 8. Because we deduced the A + B + AB + AB2 model from the activity data, the agree-

242

0 -3

Fig. 6. Excess thermodynamic functions in J mol-l, in the acetone-chloroform system at 40%. Full line - calculated for the A + B + AB + AB2 model. Experimental data: 1, Beckmann and Faust (1914); 2, Rijck and Schrijder (1957); 3, Sabinin et al. (1967).

ment between theoretical and experimental GE values is not surprizing. Based on the iYE data, the chosen model behaves reasonably well in the 35-50C interval.(Figs. 5, 6 and 7). Outside this interval, in both directions, deviations increase between the predicted and experimental HE values, and, at 70C for example, the symmetrical A + B + AB model should be preferred (Fig. 8). However, it is worthwhile to note that only one set of the HE data at 70C exists in the literature and therefore it is difficult to decide if the experiments performed at elevated temperatures are sufficiently ,accurate.

The acetone + chloroform system is characterized by the existence of an azeotrope with minimum pressure (Fig. 1). Because the determination of azeotropic points is difficult, they are usually estimated, not especially accurately, by interpolation between the experimental points. In this paper, the pressure, Pa,, and the composition of the liquid phase at the azeotropic point, x:2 = 1 - xzaz, in the 0-100X interval are deduced from the A + B + AB + ABz model.

243

I I 1 I , I 0 0.2 0.4 0.6 08 I.0

x, Fig. 7. Excess thermodynamic functions in J mol-l, in the acetone-chloroform system at 50C. Full line-calculated for the A + B + AB + AB2 model. Experimental data: 1, Severns et al. (1955); 2, R&k and SchrGder (1957), 3, Mueller and Kearns (1958); 4, Morris et al. (1975); 5, Morcom and Travers (1965).

I 1 I I I 0 0.2 O-4 x, 0.6 0.8 1.0

Fig. 8.. Excess thermodynamic functions in J mol-l, in the acetone-chloroform system at 70C. Full line - calculated for the A + B + AB + AB2 model, dashed line - calculated for the A + B + AB model. Experimental data: 1, Schulxe (1919); 2, Staveley et al. (1955).

244

At a given temperature, the condition for appearance of the azeotrope is:

(18)

Using K1(T) and Kz(2) from eqn. (13) and the ratio pi/pi from eqns. (1) and (2) and combining eqn. (11) with (18), xtZ and xg are evaluated from the simultaneous solution of the following equations:

P'; _ x31 -xz)2(K, + 2x82) az z? - x2(x2 - xB) 1 (19) xz =

[

X*(1 + KI + &x,(2 - xs)) 1 *= 1 + 2x&, -x2,(& + Ks(2xs - 3)) and the azeotropic pressure:

In Table 6 are presented values of P,, and ~2 from eqns. (19) and (20). Taking into account the scattering of experimental results (Table 6), the estimated values can be considered as very reliable.

Without introducing new data, boiling and condensation curves can be predicted from the ideal associated solution A + B + AB + AB2 model, by assuming that the vapour phase is a perfect gaseous mixture. The vapour- liquid equilibrium at constant pressure, can be expressed by (Prigogine and Defay (1965)):

i=l,2 (21)

where Aflap is the heat of vaporization of ith component and E is its boiling point. Taking into consideration that :

d In pp _ AHiVaP --z----s- (2-w

from eqns. (1) (2) and (22) one has

AH-p = B$tfP/(Ci + T)2 I

w&r&?, = 2965.0, C1 = -35.65, B2 = 2721.0 and C2 = -46.15.

(23)

Comparison between the experimental values of Aflap in the lo--40C temperature range, measured by Sabinin et al. (1967) and those estimated from eqn. (23) is satisfactory, the differences not exceeding 3% (Table 7).

245

TABLE 6

Estimated from the A + B + AB + AB2 model azeotropic pressures, Paz and composition of the liquid phase, x(iz, in the acetone-chloroform system.

CtW Xl= PaZ WW Xl aZ* pSZ*

Wa)

0 0.392 5.998

10 0.3,90 10.37 0.395 10.57

15 0.389 13.40

20 0.337 17.11 0.395 17.28

25 0.385 21.65 0.405 21.52 0.409 21.54 0.35 21.66

30 0.382 27.13

35 0.379 33.69 0.386 33.54 35.17 0.437 33.12

0.378 34.09

40 0.376 41.41

45 0.372 50.59

50 0.368 61.25 0.314 60.68

l Experimental data from the literature and this work.

TABLE 7

Molar heats of vaporization of acetone( 1) and chloroform( 2) system --~ ~-~~

m (kJ mol-l)

10C 25C 40C

i = 1 Sabinin et al. (1967) 32.20 31.34 30.42 Eqn. (23) 32.26 31.80 31.39

B;f +%&tin et al. (1967) 32.22 32.29 31.46 31.66 30.69 31.12

246

Introducing eqn. (23) into (21) one obtains:

l&L- =-_B .-..L--_-_- 1 Xl% ( T+C1 T1 +c1 =--x,(T)

InY2=Jj 1 1 X2Y2

T",+--~ =h2CO

orusingy,=l-y2andx1=1--x2:

x2= =pGb I- 71

72=x0, +X2)-71

(24)

(25)

y2 = r2902 1 [ew(Xl) - YI 1 72ewOb + A21 -71

For a given temperature T, the values of X1 and A2 are calculated from eqn. (24) and the activity coefficients rl and r2, knowing K1 (T) and K2 (T) from eqn. (13). Using eqns. (11) and (16):

l-xs xA = 1+ x&K1 + XaKs) (26)

X XB+XAXB(K1+2X&2)

2 = 1 + X~xz(Ki + 2x&s)

the value of xa, which corresponds to x2 and y2 at the boiling and condensa- tion curves respectively, can be evaluated by equating x2 from eqns. (25) and (26):

l---B exp(X1)[l -xB exp(X2)l = 1 + xB(K1 + xBK2) (27)

Finally, introducing xB from eqn. (27) into (26), x2 is calculated and y2 from:

Y2 =XBexdh2) cm

It is evident that at the azeotropic point, yy = xy, hence it follows that:

+&+wCMTaz)l = 1 (29)

where xi=, xzZ and T,, are evaluated by the simultaneous solution of eqns. (26) (27) and (29). Introducing the boiling temperature of acetone, tl = 56.2C, and of chloroform t20 = 61.2C into eqn. (24), the vapour-liquid equilibrium at atmospheric pressure was evaluated according to the above procedure and the results of calculations are presented in Table 8.

247

TABLES Vapour-liquid equilibriumatconstantpressure(P = 101.325 kPa) intheacetone(l)+ chloroform(2)system,estimated from the A+ B + AB + AB2model

Xl Yl t("C) 71 72

0.000 0.000 61.2 - 1.000 0.0226 0.0133 61.5 0.492 0.9996 0.0608 0.0386 62.0 0.522 0.997 0.101 0.107 63.0 0.589 0.984 0.194 0.156 63.5 0.632 0.971 0.252 0.235 64.0 0.691 0.946 0.384 0.397 64.2 0.792 0.887 0.435 0.468 64.0 0.830 0.859 0.502 0.560 63.5 0.874 0.820 0.550 0.623 63.0 0.901 0.791 0.592 0.673 62.5 0.921 0.766 0.629 0.716 62.0 0.937 0.745 0.664 0.754 61.5 0.950 0.725 0.697 0.787 61.0 0.961 0.706 0.729 0.818 60.5 0.970 0.689 0.760 0.845 60.0 0.977 0.672 0.972 0.871 59.5 0.983 0.656 0.823 0.894 59.0 0.988 0.641 0.854 0.916 58.5 0.992 0.626 0.885 0.937 58.0 0.995 0.612 0.916 0.956 57.5 0.998 0.598 0.948 0.974 57.0 0.999 0.584 0.980 0.990 56.5 0.9999 0.571 1.000 1.000 56.2 1.000 -

The phase diagram based on the A + B + AB + AB2 model is compared with experimental data compiled from different sources for the system (Hala et al. (1968)) in Fig. 9. As can be seen, the agreement is very satisfac- tory, except in the vicinity of the azeotrope, where the calculated values are lower than the experimental temperatures by about 0.2-0.3C.

By differentiation of the excess heat of mixing, HE, in eqn. (17) with respect to temperature, the excess molar heat capacity at constant pressure, Cz, for the A + B + AB + AB2 model is obtained:

CE =XAB(AC;)~B + XAB&C;)AB~ + CT aXAB(AH"AB(l + 2XAB2)-AwAB2XABz) P

1 +xAB+2xAB2 (l+XAB+ 2xAB2) +

(,) a* (WA,& + XAB)-~A~PA$AB) + (l+xAB+ 2XAB2)2

(30)

246

Fig. 9. Vapour-liquid phase diagram at atmospheric pressure in system. Full line - calculated for the A + B + AB + AB2 model. from H&la et al. (1968) compilation.

where the standard heat capacities of association are:

= (c;)*B - (G)* - (G)B P (31)

(AC,)ABZ = (a;?) p = (c;),, - (c;), - 2(Ci),

and (CG), denotes the molar heat capacity of the ith component. It is evident that m, i = AB, AB2, are weakly dependent on temperature (Fig. 4) but it is impossible to determine, with reasonable accuracy, (ACi)i values directly, and this problem will be considered further.

. . Takmg into account that AflAB is practically twice the value of AH&, eq. (30) is considerably simplified:

CE = XAB(AC;)AB + XAB@~;)AB~ Aw,, a%B+2aXAB2

aT aT ) P

1 + XAB + 2xAB2 + (1 + xAB + 2XAB2)2

The derivatives in eqn. (32) were evaluated using eqns. (11) and (16)

(32)

axAB% = GAB2 AwAB

aT L RT2 (33)

249

L = x.2 - XlXAB + (xlx*B - xg) XA + (I---2"2hABz 2xA+x2xAB

and

kAB _xAB (XA+(1-2r2tiAB2) axAB2 ~-__

aT XAB2 (2xA +XZXAB) aT (34)

In order to evaluate the standard heat capacities of association (ACg)i, eqn. (32) is written in the form:

Cz = C;(AC;) + C;(AH) (35)

where the second term in eqn. (35) can be calculated for any x1 because K1, K2 and AlP, values are known.

Using the experimental values of Cg (determined at 3OC, Table 9), the desired (AC;),, and (AC;),,, values were determined from the intercept and slope of the function:

Fa = K~(A~~)AB+K~(AC~)AB~XB

F

3 = CC:)- - C:(AH) (36)

and they are (AC,),, = -43.5 J K-l mol-l and (ACOp)~a2 = -247 J K- mol-l . In Fig. 11 are presented the calculated and experimental values of Cz. As can be seen, the agreement is reasonable, especially in acetone-rich mixtures. Using (Ci)A = 129.7 J K-l mol-l and (C,), = 114.9 J K-l mol-l (Staveley et al. (1955)), the values of (CX)Aa = 201 J K-l mol-l and (Cz)Ana = 112 J K-l mol-l may be deduced from eqn. (31). The evaluated molar heat

TABLE 9

Molar heat capacities, C,, and excess heat capacities, Cz at 303.15 K for the acetone-chloro- form system (in J K- mol-l)

Xl C, C% ___~ 0.0000 114.9 0.0723 117.6 1.7 0.1398 119.1 2.0 0.1896 120.2 2.5 0.2619 122.7 3.9 0.3202 124.8 5.2 0.5122 126.7 4.3 0.7667 128.1 1.9 0.9190 129.1 0.6 1.0000 129.7 -

250

+ac

C

-QC

0.C

vE

-0.1

-0.1

-aI

P-

)-

e

m-

IO -

4-

6 -

0

A-3

0.2 0.4 0.6 0.6 XI

1

Fig. 10. Excess molar volume of mixing, in cm3 molV1, in the acetone-chloroform system at 25OC and 35C. Curves: calculated for the A + B + AB + AB2 model. Experi- mental data at 25OC: 1, Hubbard (1910); 2, Anisimov (1953); and at 35OC: 3, this work.

capacity of the complex AB can be considered as reasonable if it is accepted that (Cp)*s =. Cc,), + (C,),, but in this case the value of (Cg)ABs is evidently too low. Taking into consideration that the accuracy of determined CE values is not especially high, it is preferable to regard (CP)*a and (c,),,, as adjustable parameters.

Finally, in the frame of the A + B + AB + ABa model, the excess molar volumes VE in the acetone + chloroform system is analyzed. In this case, the excess volume is given by:

AI& = vAB-vA-vB (37)

where the standard reaction volumes, AC, can be deduced from the experi-

251

4

5

4

3

2

I

0

I I 1 I I I

0

0 0.2 0.4 x, 0.6 0.8

Fig. 11. Excess molar heat capacity, in J K- mol -I, in the acetone-chloroform system at 3OC. Full line - calculated for the A + B + AB + AB2 model. Experimental data: 1, Stavely et al. (1955); 2, this work.

mental VE values and knowing the K1 and K2 constants. Using a similar procedure to that described previously for evaluation of (ACi)i, the standard reaction volumes are determined from the intercept and slope of the func- tion :

F4 = KIAV&, + KIAV&xe

$? = (VE)V + x*x&K1 + 2x&)) 4

XAXB

(33)

252

TABLE 10 Excessmolarvolume ofmixinginthe acetone-chloroform system at 35%

Xl

0.0 0.0972 0.1609 0.1695 0.1760 0.1943 0.2108 0.2779 0.3336 0.4139 0.4496 0.5316 0.7088 0.8728 0.9050 1.0000

dl2 (g ems)

1.45509 1.39531 1.35515 1.35050 1.34593 1.33453 1.32375 1.28055 1.24002 1.19020 0.16480 1.10980 0.98566 0.86489 0.84002 0.77409

VE ( cm3 mol-l)

0.0 -0.084 -0.123 -0.128 -0.131 -0.140 -0.146 -0.165 -0.170 -0.163 -0.156 -0.125 -0.042 +0.017 +0.020 0.0 ~~

The values of AV& and AvAB2 obtained in this way are: at 25OC: 0.42 cm3 mol- and -4.40 cm3 mol-; at 35C: 0.29 cm3 mol- and -3.20 cm3 mol-; and at 50C: 0.26 cm3 mol-l and -7.95 cm3 mol-l respectively. Using vd, = 75.02 cm3 mole1 and Vs = 82.05 cm3 mol- at 35C (Table lo), one obtains, from eqn. (37) VAB= 157.5 cm3 mol- and V&s = 235.9 cm3 mol-. In Fig. 10 are presented experimental and calculated values of VE at 25" and 35C. As can be seen, the agreement is very satisfactory, (the same behaviour is observed at 5OC), confirming once again the validity of the chosen A + B + AI3 + AB2 model.

SYMBOLS

a A B Bij Bi ci

% At?;

activity of component, eqn. (8) monomeric molecules of acetone monomeric molecules of chloroform virial coefficient; i, j = 1, 2, eqn. (3) constant, eqn. (23) constant. eqn. (23) molar heat capacity of component, eqn. (31) excess molar heat capacity; eqn. (31) standard heat capacity of association, eqn. (31)

CE(AC;) C&H?

defined in eqns. (32) and (35) defined in eqns. (32) and (35)

253

D Fl FZ F3

F4 GE H- HE AH AH-* JT K L

0

:: R SE t

> v VE Av x Y

defined in eqn. (5) function defined in eqn. (9) function defined in eqn. (10) function defined in eqn. (36) function defined in eqn. (38) excess free energy of mixing, eqn. (6) molar enthalpy of component, eqn. (12) excess enthalpy of mixing. eqn. (17) standard heat of formation. eqn. (12) molar heat of vaporization, eqn. (22) defined in eqn. (4) equilibrium constant, eqns. (7) and (11) defined in eqn. (33) vapour pressure of pure component total pressure gas constant excess entropy of mixing temperature in C temperature in K boiling point of pure component molar volume of component, eqn. (37) excess molar volume, eqn. (37) standard reaction volume, eqn. (37) mole fraction of component in the liquid phase mole fraction of component in the vapour phase

Greek letters

activity coefficient, eqn. (3) defined in eqn. (3)

h defined in eqn. (24)

Superscripts and subscripts

az azeotrope E excess ex experimental i nominal components, i = 1,2 i actual components, i = A, B, AB, ABs j =l, 2 0 pure component

F constant pressure constant temperature

254

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