Density, viscosity, isothermal (vapour + liquid) equilibrium, excess molar volume, viscosity deviation, and their correlations for chloroform + methyl isobutyl ketone binary system

J. Chem. Thermodynamics 39 (2007) 261–267 www.elsevier.com/locate/jct

Density, viscosity, isothermal (vapour + liquid) equilibrium, excess molar volume, viscosity deviation, and their correlations for chloroform + methyl isobutyl ketone binary system Rene´ A. Clara´, Ana C. Go´mez Marigliano, Horacio N. So´limo

*

Departamento de Fı´sica – Facultad de Ciencias Exactas y Tecnologı´a, Universidad Nacional de Tucuma´n, Av. Independencia 1800, 4000 San Miguel de Tucuma´n, Argentina Received 10 May 2006; received in revised form 6 July 2006; accepted 8 July 2006 Available online 26 July 2006

Abstract Density and viscosity measurements for pure chloroform and methyl isobutyl ketone at T = (283.15, 293.15, 303.15, and 313.15) K as well as for the binary system {x1 chloroform + (1  x1) methyl isobutyl ketone} at the same temperatures were made over the whole concentration range. The experimental results were fitted to empirical equations, which permit the calculation of these properties over the whole concentration and temperature ranges studied. Data of the binary mixture were further used to calculate the excess molar volume and viscosity deviation. The (vapour + liquid) equilibrium (VLE) at T = 303.15 K for this binary system was also measured in order to calculate the activity coefficients and the excess molar Gibbs energy. This binary system shows no azeotrope and negative deviations from ideal behaviour. The excess or deviation properties were fitted to the Redlich–Kister polynomial relation to obtain their coefficients and standard deviations. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Density; Viscosity; Excess functions; (Vapour + liquid) equilibrium; Empirical correlations

1. Introduction Excess thermodynamic functions and deviations of nonthermodynamic ones for binary liquid mixtures are fundamental for understanding of interactions between molecules, particularly when polar components are involved. These functions have also been used as a qualitative and quantitative guide to predict the extent of complex formation [1–3]. In this paper we report density q and viscosity g data for pure chloroform and methyl isobutyl ketone (MIK) as well as for the binary system constituted by these two chemicals in the whole mole fraction range at T = (283.15, 293.15, 303.15, and 313.15) K. The VLE data are also reported at T = 303.15 K. From these experimental results, excess *

Corresponding author. Fax: 54 381 4363004. E-mail address: [email protected] (H.N. So´limo).

0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.07.004

molar volume VE, viscosity deviation from the ideal behaviour Dg, activity coefficients ci, and excess molar Gibbs energy GE were calculated. Empirical equations for the density and viscosity of pure components as a function of the temperature as well as for the binary system as a function of temperature and composition were developed. These equations are useful for interpolation within the studied temperature range. The excess and deviation properties were fitted to a Redlich–Kistertype [4] equation using least squares to obtain their dependencies on concentration and temperature. Isobaric VLE data at atmospheric pressure have been previously measured for this binary system [5]. Density, refractive index, and viscosity at T = 298 K have been reported by Karr et al. [6], while Rama Varma et al. [7] reported molar excess volume determined dilatometrically at T = 308 K, whose values disagree with ours because they are more negative than those at T = 313.15 K reported in

R.A. Clara´ et al. / J. Chem. Thermodynamics 39 (2007) 261–267

262

this work. Furthermore, Shen et al. [8] give excess enthalpies at T = 323.15 K. However, as far as we know, neither isothermal VLE data nor excess molar or deviation properties at temperatures other than those stated above are available in the literature for this binary system.

Chloroform (analytical reagent) and methyl isobutyl ketone (analytical reagent) were supplied by Sintorgan (Argentina). They were used as received because no impurity was detected by gas chromatography using a HP 6890 gas chromatograph with a FID detector. The pure components were stored over 0.3 nm molecular sieves to prevent water absorption, and their water content was periodically checked by Karl Fischer titration using an automatic Mettler DL18 Karl Fischer titrator.

400 viscometer with appropriate Ubbelohde capillary viscometers calibrated by the manufacturer, respectively. The accuracies were of ±0.1 kg Æ m3 for density and ±0.001 mPa Æ s for viscosity. A Schott CT 1450 thermostatically controlled water bath, uncertain by ±0.01 K, was used for viscosity measurements. An equilibrium still, which was described by Boublik and Benson [9], was used to obtain isothermal VLE data. The equilibrium temperatures were measured with a Hart Scientific 1502A platinum resistance thermometer (certified by the National Institute of Standards and Technology; NIST) with an imprecision of ±0.007 K. All temperatures are reported in terms of ITS-90, whereas total pressures in the still were measured with an Edwards pressure transducer, Datametrics Controller 1501B, attached through a vacuum line with a precision of 13 Pa. Compositions of both conjugated phases were determined by density measurements at T = 303.15 K, being their estimated uncertainty in mole fractions lower than ±1 Æ 103.

2.2. Apparatus and procedure

3. Results and discussion

For density and viscosity measurements, liquid mixtures were prepared by mass in airtight stoppered bottles, keeping in mind the vapour pressures of the components when establishing the filling sequence. Each mixture was immediately used after it was well mixed by shaking. All the weightings were performed on an electronic balance (Mettler Toledo AG-245) accurate to 0.1 mg. The uncertainty in the mole fractions for these mixtures is estimated to be lower than ±1 Æ 104. Density and viscosity were measured with a vibratingtube densimeter KEM DA-300 with a built-in thermostatic unit accurate to 0.01 K, which allows working in the range T = (277 to 363) K using degassed bidistilled water and dry air as the calibrating substances, and a Schott-Gera¨te AVS

Experimental results for refractive index, density, and viscosity of pure compounds at several temperatures, and saturated vapour pressures at T = 303.15 K are summarized in table 1. For comparison, existing values found in the literature are also included. From experimental results reported in table 1, we conclude that the viscosity of the pure components does not have a linear behaviour with temperature, as commonly happens with non-ideal systems, while density has a linear plot. Experimental results for the density and viscosity corresponding to temperatures over the range (283.15 to 313.15) K for the system {x1 chloroform + (1  x1) methyl isobutyl ketone} are listed in table 2.

2. Experimental 2.1. Materials

TABLE 1 Density q, refractive index nD, and viscosity g values of pure components at several temperatures, and saturated vapour pressure P sat at T = 303.15 K i T/K

q/kg Æ m3 Experimental

Chloroform 283.15 1507.3 293.15 1488.4 303.15 313.15

1469.4 1450.0

MIK 283.15 293.15 303.15 313.15

809.8 800.7 791.6 782.2

a

From reference [10]. From reference [11]. c From reference [12]. d From reference [13]. e From reference [14]. f From reference [15]. b

nD Literature

b

1489.11

1470.60b

801.0b 792.0f

Experimental 1.45189 1.44589

Literature

b

1.4459

1.43987 1.43386

1.40061 1.39591 1.39122 1.38648

P sat i =kPa

g/mPa Æ s Experimental

Literature

0.629 0.573

0.625a 0.58c 0.563d 0.514b 0.464d

0.516 0.468

1.39576b 1.39145f

0.655 0.576 0.511 0.460

0.5848b 0.49751b

Experimental

Literature

32.19

32.395e

3.89

R.A. Clara´ et al. / J. Chem. Thermodynamics 39 (2007) 261–267

263

TABLE 2 Experimental density q and viscosity g values for {x1 chloroform + (1  x1) methyl isobutyl ketone} at several temperatures q/(kg Æ m3)

x1a 0.0000 0.0847 0.1841 0.2760 0.3529 0.4467 0.5060 0.6079 0.6959 0.8213 0.9067 1.0000 a

g/mPa Æ s

T/K = 283.15

293.15

303.15

313.15

283.15

293.15

303.15

313.15

809.8 849.0 898.2 947.2 991.1 1048.8 1087.7 1159.3 1226.7 1332.6 1412.3 1507.3

800.7 839.4 888.1 936.6 980.1 1037.0 1075.3 1146.0 1212.4 1316.7 1395.0 1488.4

791.6 829.9 878.0 925.8 968.7 1025.0 1062.8 1132.5 1197.9 1300.6 1377.7 1469.4

782.2 820.0 867.5 914.9 957.1 1012.6 1050.0 1118.7 1183.2 1284.1 1359.8 1450.0

0.655 0.685 0.719 0.755 0.780 0.808 0.812 0.814 0.798 0.746 0.689 0.629

0.576 0.598 0.630 0.659 0.678 0.696 0.703 0.704 0.696 0.664 0.629 0.573

0.511 0.531 0.558 0.577 0.596 0.616 0.620 0.623 0.619 0.592 0.560 0.516

0.460 0.472 0.493 0.513 0.526 0.542 0.551 0.557 0.554 0.533 0.503 0.468

Mole fraction of chloroform.

To obtain empirical correlations for pure compounds with temperature, the following functional relationships for density and viscosity were used: q ¼ a1 þ b1  ðT =KÞ;

ð1Þ 2

g ¼ a2 þ b2  ðT =KÞ þ c2  ðT =KÞ ;

ð2Þ

where a1, b1, a2, b2, and c2 are constants, given in table 3 together with the standard deviations. These equations were fitted using least squares with all points equally weighted, which allows evaluation of all constants. The appropriate number of significant digits was selected taking into account the above reported experimental errors for density, viscosity, and temperature. Calculated values from these equations compare well with experimental data within the standard deviations reported in table 3. Polynomial equations were used to correlate the same properties for {x1 chloroform + (1  x1) methyl isobutyl ketone}, as follows: q=kg  m3 ðx1 ; ðT =KÞÞ ¼ a1 ðT =KÞ þ b1 ðT =KÞ  x1 þ c1 ðT =KÞ  x21 ;

ð3Þ g=mPa  s ðx1 ; ðT =KÞÞ ¼ a2 ðT =KÞ þ b2 ðT =KÞ  x1 þ c2 ðT =KÞ  x21 ;

ð4Þ

where ai, bi, and ci are constants, given in table 4 within their corresponding equations. To obtain their respective dependences on composition, density or viscosity of the mixture was plotted against the mole fraction of chloroform at each temperature, as shown in figure 1 for the density of {x1 chloroform + (1  x1) methyl isobutyl ketone}, which was taken as an example to indicate the calculation methodology. Equations (3) and (4) were fitted using a non-linear regression method based on the Levenberg-

Marquardt algorithm [16]. This fit shows quadratic behaviour with composition for the two properties studied. The constants of equation (3) obtained from this fit were plotted against temperature, as can be seen in figure 2. In this way, the dependence on temperature and composition of each property was obtained. The appropriate number of significant digits was selected taking into account the experimental errors for density, viscosity, and temperature reported above. The resulting equations for the density and viscosity of this binary system are collected in table 4 together with their standard deviations r. Equations (5) and (6) (included in table 4) make it possible to predict the density and viscosity of the binary system at any composition as well as temperature over the temperature range (283.15 to 313.15) K, respectively, within its respective standard deviation r. Values calculated with these equations compare well with experimental data, and the standard deviations are similar to those obtained in previous works [17,18]. On the other hand, the excess molar volume VE, viscosity deviation Dg, and excess molar Gibbs energy GE were calculated using the following equations:   M1 M2 ; V E =m3  mol1 ¼ ½ðx1 M 1 þ ð1  x1 ÞM 2 Þ=q  x1 þ x2 q1 q2 ð7Þ ð8Þ Dg=mPa  s ¼ g  exp½x1 ln g1 þ ð1  x1 Þ ln g2 ; GE =J  mol1 ¼ RT ½x1 ln c1 þ ð1  x1 Þ ln c2 ;

ð9Þ

where x1 is the mole fraction of chloroform; M1 and M2 are the molar masses of chloroform and methyl isobutyl ketone; q and g are the density and viscosity of the mixture; q1, q2, g1, and g2 are the densities and viscosities of the pure

TABLE 3 Coefficients and standard deviations of equations (1) and (2) Compound

Chloroform MIK

q/kg Æ m3

g/mPa Æ s

a1

b1

r/kg Æ m

2047.7 1069.9

1.909 0.919

0.2 0.1

3

a2

103b2

105c2

r/mPa Æ s

3.929 8.695

17.32 48.22

2 7

2 Æ 103 1 Æ 104

x21

a

x1: mole fraction of chloroform.

GE ¼ x1 ð1  x1 Þ½3965 þ 563  ð1  2x1 Þ

(16)

(15)

Dg ¼ x1 ð1  x1 Þf19:878  0:12092  ðT =KÞ þ 1:8708  104  ðT =KÞ2 þ

½12:627 þ 0:08192  ðT =KÞ  1:3479  104  ðT =KÞ2   ð1  2x1 Þg

(14)

60/J Æ mol1

0.005/mPa Æ s

1 Æ 108/m3 Æ mol1

0.007/mPa Æ s

0.7/kg Æ m3 (5) (6)

r

No.

V E ¼ x1 ð1  x1 Þf3:26  106  1:370  108  ðT =KÞ þ ½1:9  107 þ 2:59  109  ðT =KÞ  ð1  2x1 Þg

½10:685 þ 0:03224  ðT =KÞ  x31 þ ½4:279  0:01325  ðT =KÞ  x41 g

gðx1 ; T Þ ¼ f9:197  0:05154  ðT =KÞ þ 7:551  105  ðT =KÞ2 þ ½1:386  0:00397  ðT =KÞ  x1 þ ½4:748  0:01413  ðT =KÞ  x21 þ

qðx1 ; ðT =KÞÞ ¼ 1078:1  0:9334  ðT =KÞ þ ½476:9  0:3038  ðT =KÞ  x1 þ ½481:4  0:6470  ðT =KÞ 

Equations

TABLE 4 Equations for density, viscosity, excess molar volume, and viscosity deviation as functions of temperature and composition, and excess molar Gibbs energy as function of composition for {x1 chloroform + (1  x1) methyl isobutyl ketone}a

264 R.A. Clara´ et al. / J. Chem. Thermodynamics 39 (2007) 261–267

R.A. Clara´ et al. / J. Chem. Thermodynamics 39 (2007) 261–267

TABLE 5 Experimental results for the mole fraction of chloroform in the liquid x1 and vapour y1 equilibrium phases, total pressure P, and calculated activity coefficients ci for {x1 chloroform + (1  x1) methyl isobutyl ketone} at T = 303.15 K

1600

1400

-3

/(kg·m )

265

1200

1000

800 0.0

0.2

0.6

0.4

0.8

1.0

x1 FIGURE 1. Plot of density against mole fraction x1 for {x1 chloroform + (1  x1) methyl isobutyl ketone}: T = 283.15 K, j; 293.15 K, d; 303.15 K, m; 313.15 K, ..

x1

y1

P/kPa

c1

c2

0.0000 0.0959 0.1852 0.2468 0.3514 0.4459 0.5575 0.6019 0.6279 0.6603 0.6989 0.7328 0.7538 0.8285 0.9402 1.0000

0.0000 0.2872 0.4873 0.6183 0.7758 0.8747 0.9280 0.9530 0.9599 0.9670 0.9744 0.9853 0.9868 0.9952 0.9994 1.0000

3.89 4.68 5.68 6.56 8.54 11.00 14.89 16.74 17.70 19.03 20.70 22.39 23.33 26.52 30.87 32.19

0.343a 0.435 0.464 0.510 0.586 0.670 0.770 0.832 0.841 0.866 0.897 0.935 0.949 0.990 1.019 1.000a

1.000a 0.948 0.918 0.854 0.759 0.639 0.623 0.508 0.490 0.475 0.453 0.317 0.322 0.191 0.069 0.037a

a

Extrapolated to infinite dilution.

800

of Van Ness et al. [19], as modified by Fredenslund et al. [20], since the average absolute deviation between yi (exp) and yi (calc) is equal to 0.015 using a four-parameter Legendre polynomial, while the average absolute deviation in pressure is DP = 0.1 kPa. The excess molar volume, excess molar Gibbs energy, and viscosity deviation were fitted by means of a Redlich– Kister-type equation [4] with the same fitting procedure as indicated above: n X Y E ¼ x1 ð1  x1 Þ aj ð1  2x1 Þj ; ð11Þ

a1, b1, or c1

700 600 500 400 300 200 280

285

290

295

300

305

310

E

T /K FIGURE 2. Plot of constants j, a1(T/K); d, b1(T/K); and m, c1(T/K) in equation (3) against temperature for {chloroform (1) + methyl isobutyl ketone (2)}. Units: a1(T/K), kg Æ m3; b1(T/K), kg Æ m3 Æ K1; and c1(T/ K), kg Æ m3 Æ K2.

components; whereas c1 and c2 are activity coefficients of chloroform and methyl isobutyl ketone, which, in the liquid phase, are related to VLE by: Y i ¼ y i P =xi P oi :

j¼0

315

ð10Þ

Here, xi and yi are the mole fractions in the liquid and vapour phases of component i, while P and P oi are the total pressure and the pure component vapour pressure, respectively. In equation (10), the vapour phase is assumed to be an ideal gas, and the pressure dependence of the liquidphase fugacity is neglected. This equation was selected to calculate activity coefficients because the low pressures observed in the present VLE data make this simplification reasonable. The VLE data reported in table 5 for {x1 chloroform + (1  x1) methyl isobutyl ketone} were found to be thermodynamically consistent according to the point-to-point test

where Y represents either VE, GE, or Dg. Since the coefficients aj are functions of the temperature, they were plotted against this variable in order to obtain equations that represent each property over the temperature range studied. We propose the following dependence with temperature for these coefficients: m X i aj ¼ aji  ðT =KÞ : ð12Þ i¼0

Using this temperature dependence, equation (11) can be rewritten as follows: n X m X aji T i ð1  2x1 Þj : ð13Þ Y E ¼ x1 ð1  x1 Þ j¼0

i¼0

The equations arising from this fit are also summarized in table 4 (reported as equations (14), (15) and (16), respectively), together with their standard deviations r, defined as: hX i1=2 2 r¼ ðY Eexp:  Y Ecalc: Þ =ðN  pÞ ; ð17Þ where N and p are the numbers of experimental points and parameters, respectively. The choice of the appropriate

R.A. Clara´ et al. / J. Chem. Thermodynamics 39 (2007) 261–267 0

-200

-400 -1

-600

E

number of constants in equation (13) was based on the variation with n and m of the standard error of the estimated value. Their significant digits were determined taking into account each experimental error. Figures 3 and 4 show the excess molar volume and viscosity deviation, plotted against the mole fraction of chloroform for {x1 chloroform + (1  x1) methyl isobutyl ketone} at several temperatures, while figure 5 shows a similar plot for the excess molar Gibbs energy at T = 303.15 K. The total pressure P, liquid-phase x1, and vapour-phase y1 mole fraction measurements at T = 303.15 K are reported in table 5 and plotted in figure 6.

G /(J·mol )

266

-800

-1000 0.0

0

0.2

0.4

0.6

0.8

1.0

x1 -5 FIGURE 5. Plot of excess molar Gibbs energy against mole fraction x1 for {x1 chloroform + (1  x1) methyl isobutyl ketone} at T = 303.15 K. Solid line corresponds to the least-squares fit using equation (11).

V E108 /(m3·mol -1 )

-10 -15

35

-20

30

-25

25

P / ( k Pa

(

-30 0.0

0.2

0.4

0.6

0.8

1.0

20 15

x1 FIGURE 3. Plot of excess molar volume against mole fraction x1 for {x1 chloroform + (1  x1) methyl isobutyl ketone}: T = 283.15 K, j; 293.15 K, d; 303.15 K, m; 313.15 K, .. Solid lines correspond to the least-squares fit using equation (11).

10 5 0.0

0.1

0.2

0.3

0.4 0.5

0.6

0.7

0.8

0.9

1.0

x 1 , y1 FIGURE 6. Plot of total pressure P against liquid-phase mole fractions x1, d or vapour phase mole fractions y1, j for {x1 chloroform + (1  x1) methyl isobutyl ketone} at T = 303.15 K.

0.18 0.16 0.14

0.04

Figure 7 shows the logarithm of the activity coefficients against the mole fraction of chloroform for {x1 chloroform + (1  x1) methyl isobutyl ketone} at T = 303.15 K. The lines in figure 7 were obtained with a non-linear regression fit, which produces the following equations for the activity coefficients at infinite dilution of both components, as previously reported [21]:

0.02

c11 ¼ lim expðln c1 Þ ¼

/(mPa· s)

0.12 0.10 0.08 0.06

x1 !0

0.00 0.0

0.2

0.4

0.6

0.8

1.0

x1

lim expð1:071 þ 1:920  x1  0:804  x21 Þ;

x1 !0

ð19Þ

c21 ¼ lim expðln c2 Þ ¼ x1 !1

FIGURE 4. Plot of viscosity deviation against mole fraction x1 for {x1 chloroform + (1  x1) methyl isobutyl ketone}: j, T = 283.15 K; d, 293.15 K; m, 303.15 K; ., 313.15 K. Solid lines correspond to the leastsquares fit using equation (11).

lim expð0:054  2:016  x1 þ 5:996  x21  7:330  x31 Þ;

x1 !1

ð20Þ

R.A. Clara´ et al. / J. Chem. Thermodynamics 39 (2007) 261–267

with the conclusion reported by Fort and Moore [26] who proposed that positive values of this property are characteristic of systems where association forces predominate. Figure 4 also shows that as the temperature is increased, the Dg values become less positive due to the increase of the thermal energy that diminishes the chloroform-methyl isobutyl ketone hetero-association in the mixture.

0.4 0.0 -0.4

ln 1, ln

2

-0.8 -1.2 -1.6 -2.0

Acknowledgement

-2.4 -2.8 -3.2 0.0

267

0.2

0.4

0.6

0.8

1.0

Financial support from the Consejo de Investigaciones de la Universidad Nacional de Tucuma´n of Argentina (Grant No. 26/E338) is gratefully acknowledged.

x1 FIGURE 7. Plot of logarithm of the activity coefficients c1 (j) and c2 (d) against mole fraction x1 for {x1 chloroform + (1  x1) methyl isobutyl ketone} at T = 313.15 K. Solid lines correspond to the least-squares fit using equations (19) and (20).

where c11 and c21 are the activity coefficients of chloroform and methyl isobutyl ketone at infinite dilution, respectively, and x1 is the mole fraction of chloroform. Equations (19) and (20) lead to the values 0.343 and 0.037 for c11 and c21, respectively. These values show that the interactions between methyl isobutyl ketone (as solvent) and chloroform (as solute) are stronger than in the opposite situation. Furthermore, figures 6 and 7 indicate that this binary system shows no azeotrope and negative deviations from the ideal behaviour. Figure 3 shows that the excess molar volumes are always negative for all the studied temperatures and for any composition. This would indicate that interactions between different molecules are stronger than interactions between molecules in the pure liquids and that associative forces dominate the behaviour of the solution. Therefore, in this system, a compression in free volume is considered to occur, making the mixtures more compressible than the ideal mixture, which ultimately culminates into negative values of VE. From this plot, we can also conclude that as the temperature is increased, the VE values become more negative. We cannot find a reasonable explanation for this fact because the system appears less ideal when the temperature is increased. However, this behaviour is often observed for similar and dissimilar binary systems [22–24]. According to Kauzman and Eyring [25] the viscosity of a mixture strongly depends on the entropy of the mixture that in turn is related to the liquid’s structure and enthalpy. Therefore, the viscosity deviation depends on molecular interactions as well as on the size and shape of the molecules. As can be seen in figure 4, the viscosity deviations are positive for all studied temperatures over the whole composition range, which would correspond to binary systems that exhibit negative deviations from Raoult’s law as is the case for our work. The sign of Dg is also in agreement

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JCT 06-118