A study on excess functions and thermodynamic parameters of some bromoform- containing binary mixtures1

SHRIKANT S. JOSHI A N D TEJRAJ M. AMINABHAVI'

Department of Chernistry, Knrrlatak UrliversiQ, Dhnrwnd, India 580 003

AND

SHYAM S. SHUKLA Depnrtrnent of Chernistry, Lnr~nr Universio~, Beaurnor~t, P.O. Box 10022, Texas 77710, USA

Received May 8, 1989

SHRIKANT S. JOSHI, TEJRAJ M. AMINABHAVI, and SHYAM S. SHUKLA. Can. J. Chem. 68, 251 (1990). Densities and viscosities have been determined for six binary mixtures of bromoform, aniline, n-hexane, benzonitrile,

butyronitrile, and benzylnitrile at different mole fractions and temperatures. The excess volumes vE, apparent excess values of viscosity Sq, excess Gibbs energy of activation of flow A G * ~ , and partial molar volumes V,, have been calculated from the experimental data. Furthermore, attempts were made to calculate theoretically the excess isobaric thermal expansion coefficient Sa, of the mixtures using the refractive index mixture rules. These results are in good agreement with the experimental data obtained from densities. Various excess functions and thermodynamic parameters have been used in the discussion of results to understand the nature and type of interactions in binary mixtures.

Key rvords: excess volume, refractive index mixture rules, interactions, bromoform, density, viscosity.

SHRIKANT S. JOSHI, TEJRAJ M. AMINABHAVI et SHYAM S. SHUKLA. Can. J. Chem. 68, 251 (1990). On a dttermine les densitts et les viscosites de six mtlanges binaires du bromoforme, de I'aniline, du n-hexane, du

benzo-nitrile, du butyronitrile et du phCnylacCtonitrile, a diverses fractions molaires et i diverses temperatures. En se basant sur ces donnCes experimentales, on a calculC les volumes en exces, v", les valeurs des excks apparents de la viscositC, 67, 1'Cnergie d'activation d'tcoulement de Gibbs en excts, AG*€, ainsi que les volumes molaires partiels, Vi. De plus, utilisant les rkgles de mtlange des indices de refraction, on a essay6 de calculer d'une f a ~ o n thtorique le coefficient d'expansion thermique isobare, Sa, des melanges. Ces rtsultats sont en bon accord avec les donnees experimentales obtenues l'aide des densitts. On a utilise diverses fonctions en excks et divers parametres thermodynamiques pour discuter les resultats, dans le but de comprendre la nature et le type d'interactions presentes dans les mClanges binaires.

Mots cle's : volume en excks, rkgles de mClange des indices de refraction, interactions, bromoforme, densitt, viscosite. [Traduit par la revue]

Introduction Solution properties of binary mixtures of bromoform with a

I number of organic solvents have been the subject of intensive research in view of their importance as media to study preferential adsorption of polymers in mixed solvents (1). Thermodynamic properties of a number of bromoform contain- ing mixtures have been studied earlier in our laboratories (2-5).

I To the best of our knowledge, extensive thermodynamic data on mixtures of bromoform with aniline, benzonitrile, benzylnit- rile, butyronitrile, and n-hexane have not been made. Such mixtures are of considerable interest from the viewpoint of the existence of intermolecular interactions between the mixing components.

In this paper, we report the density and viscosity data for five binary mixtures containing bromoform at different mole frac- tions and at 298.15, 303.15, 308.15, and 313.15K. From the experimental results the excess volumes vE , apparent excess values of the viscosity 6 q , excess Gibbs energy of activation of flow AG*E, and partial molar volumes V,, have been computed using the appropriate relations. From a temperature dependence of viscosity, enthalpy AH* and entropy AS*, of activation of flow have also been estimated using the theory of Eyring and co-workers (6). Furthermore, attempts have been made to compute the isobaric thermal expansion coefficient a,,,, of the

I mixture using the available refractive index mixture rules.

' ~ a s e d on the Ph.D. thesis of S.S.J. submitted to Karnatak University, Dharwad.

'~u thor to whom correspondences should be addressed.

These data compare satisfactorily with the experimental data of a, and are further used to predict the apparent excess values of the expansion coefficient 6 a .

Experimental Bromoform (Thomas Baker, Bombay) was obtained in its highest

purity and was used as supplied. The remaining solvents were all purified by the standard procedures as described by Weissberger et nl. (7). Density of pure liquids and their mixtures was determined by a pycnometer with an accuracy of 20.0001 g cm-j. Viscosities were measured by using a Cannon-Fenske viscometer, size 100, and the accuracy was found to be k0.002 cP. Details of the procedures for these measurements have been given earlier (8). A thermostatically- controlled bath, constant to 20.02 K was used in all these measure- ments. The experimental densities and viscosities at 298.15, 303.15, 308.15, and 313.15 K have been measured for pure components and their mixtures over the entire range of mole fraction^.^ The observed data for pure liquids are in agreement with those available in the literature (7, 9).

Results The values of VE, 8 q , and A G * ~ were calculated from the

experimental data with the following equations (10).

[ l ] V E = V " , - C vix, i= 1

j ~ l l numerical data may be purchased from the Depository of Unpublished Data, CISTI, National Research Council of Canada, Ottawa, Ont., Canada K1A 0S2.

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CAN. J. CHEM. VOL. 68, 1990

TABLE 1. Computer evaluated parameters of eq. [7]

Temperature Function (K) Ao A I A2 A3 u

(i) Bromoform (1) + aniline (2)

p, cm3 mol-' 298.15 0.399 -0.127 0.176 0.485 0.006 303.15 0.434 -0.129 -0.089 0.310 0.009 308.15 0.434 -0.077 -0.053 0.061 0.006 313.15 0.477 -0.066 -0.072 0.176 0.006

69, CP 298.15 -0.347 -0.043 0.366 -0.827 0.004 303.15 -0.168 -0.022 0.521 -0.649 0.009 308.15 -0.060 -0.01 1 0.449 -0.495 0.006 313.15 0.040 0.01 1 0.324 -0.487 0.008

AG*E, J mol-' 298.15 64.31 -17.14 113.4 -203.9 0.856 303.15 66.92 -18.14 153.2 - 186.6 1.968 308.15 65.30 - 14.79 140.0 -158.6 1.431 313.15 75.20 -9.87 118.1 - 170.7 2.187

Vl , cm3 mol- 298.15 0.154 -0.284 0.037 -0.003 0.031 303.15 0.214 -0.268 0.037 -0.045 0.021 308.15 0.201 -0.256 0.034 -0.040 0.021 313.15 0.231 -0.268 0.055 -0.056 0.014

V2, cm3 mol-I 298.15 0.531 0.188 0.234 0.064 0.009 303.15 0.396 0.022 0.115 0.050 0.006 308.15 0.449 0.048 0.123 0.047 0.006 313.15 0.451 0.005 0.063 0.030 0.003

(ii) Bromoform (1) + n-hexane (2)

@, cm3 mol-I 298.15 -1.818 0.472 0.994 -0.295 0.020 303.15 -2.071 0.419 1.377 0.304 0.01 1 308.15 -2.553 0.639 1.900 -0.142 0.039 313.15 -2.771 0.871 2.051 -0.498 0.040

69, cp 298.15 - 1.585 0.581 -0.137 -0.020 0.004 303.15 - 1.470 0.531 -0.088 -0.078 0.004 308.15 - 1.396 0.515 -0.131 -0.057 0.002 313.15 - 1.243 0.458 -0.084 -0.093 0.004

A G * ~ , J mol-I 298.15 -187.5 -28.26 6.62 - 92.3 4.293 303.15 - 176.6 -32.43 21.88 - 98.1 3.604 308.15 - 166.7 - 10.70 8.34 - 117.8 2.715 313.15 -155.9 4.47 12.67 -154.5 3.638

Vl , cm3 mol-I 298.15 - 1.024 0.964 -0.216 0.350 0.074 303.15 - 1.227 1.037 -0.274 0.442 0.026 308.15 -1.514 1.290 -0.275 0.554 0.078 313.15 - 1.644 1.454 -0.285 0.592 0.120

V2, cm3 mol-' 298.15 -1.131 0.462 0.056 -0.106 0.016 303.15 - 1.079 0.778 0.388 -0.006 0.009 308.15 - 1.305 0.935 0.275 -0.120 0.023 313.15 - 1.395 0.955 0.147 -0.202 0.028

(iii) Bromoform (1) + benzonitrile (2)

p, cm3/mol-I 298.15 -0.21 1 0.31 0.12 -0.25 0.009 303.15 -2.176 35.87 - 17.45 -66.10 0.020 308.15 -0.108 0.18 0.11 0.48 0.007 313.15 -0.168 0.24 0.11 0.38 0.004

69, cp 298.15 0.971 -0.713 -0.082 0.324 0.012 303.15 0.814 -0.626 -0.116 0.331 0.019 308.15 0.708 -0.580 -0.141 0.330 0.013 313.15 0.582 -0.438 -0.024 0.102 0.01 1

AG*E, J mol-I 298.15 422.4 -159.0 -29.5 84.1 3.865 303.15 384.5 -83.2 -163.5 -336.6 1.992 308.15 377.7 - 155.1 -65.2 110.4 4.755 313.15 364.9 -121.6 -21.8 33.6 4.869

VI, cm3 mol-' 298.15 -0.153 0.15 -0.018 0.053 0.017 303.15 1.416 15.77 4.266 0.505 0.033 308.15 -1.124 0.09 -0.109 0.020 0.020 313.15 -0.158 0.14 -0.109 0.031 0.014

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TABLE 1 (concluded)

Temperature Function (K) Ao A I A2 A 3 u

VE, cm3 mol-'

ST, cp

AG*E, J mol-I

V,, cm3 mol-'

V2, cm3 mol-'

VE, cm3 moI-'

ST, cp

AG*E, J mol-'

V, , cm3 mol-'

V2, cm3 mol-I

-0.009 0.05 -4.248 19.06

0.213 0.23 0.169 0.21

(iv) Bromoform (1) + benzylnitrile (2)

0.552 0.289 0.523 0.234 0.625 0.326 0.557 0.264

1.110 -0.089 0.993 0.065 0.823 0.044 0.685 -0.075

357.9 25.08 352.1 25.22 318.9 24.69 305.3 17.93

0.247 -0.185 0.209 -0.207 0.271 -0.212 0.262 -0.188

0.611 -0.078 0.673 -0.037 0.724 -0.055 0.566 -0.115

(v) Bromoform (1) + butyronitrile (2)

-1.134 -0.149 -1.133 -0.070

0.906 - 1.363 - 1.300 -0.160

0.016 -0.173 0.002 -0.169

-0.063 -0.216 -0.062 -0.056

475.4 120.6 466.4 104.2 447.3 37.8 431.9 152.1

-0.578 0.483 -0.634 0.554

1.062 -0.262 -0.677 0.571

0.966 0.235 -0.748 0.335 - 1.679 -2.008 - 1.061 0.300

Z

[3] = RT[ln rlrnVm - 1 ( x i In T q ~ J ? ] Where p, is mixture density and M i represent the molecular r=l weight of component i in the mixture.

where xi, V: and '1: represent the mole fraction, molar The partial molar volumes, V 1 and V 2 , of components 1 and 2

volume, and viscosity of the ith pure component of the mixture; were calculated from (1 1 )

the subscript, m refers to the property of the mixture, and R T has [ 5 ] V I = V? + v E / x I + ~ ~ x ~ [ a ( v ~ / x , ) / a . ~ , ] the conventional meaning.

The molar volume V , of the mixture was calculated from [6] V Z = v:+ V ~ / X ~ + X ~ X ~ [ ~ ( V ~ / X ~ ) / ~ X ~ ]

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254 CAN. J. CHEM. VOL. 68, 1990

The various quantities Y(VE, 6q , A G * ~ , V,, and V2) over the entire range of composition have been fitted to empirical equa- tion (12):

A nonlinear least-squares method (Marquardt algorithm) was used to estimate the coefficients, A;. In each case, the optimum number of coefficients was ascertained from an examination of the variation of the standard error (u) of the estimate with:

where n is the total number of data points and P is the number of coefficients considered ( P = 4 in the present calculation).

The last term of eqs. [5] and [6] was obtained by differentiat- ing eq. [7] for vE. Although this procedure is not adequate for small xi, the results obtained can be considered valid since the contribution of the last term of eqs. [5] and [6] to the partial molar volume is less than 0.5% over the entire mole fraction scale. All these results are summarized in Table 1.

The isobaric thermal expansion coefficients, a, of the mixture at a particular composition can be obtained either from the temperature variation of densities or by adding the contribu- tions of the expansivities of each component in the mixture. Application of the latter method gives the relation for a, of the mixture as:

wherev, is the average value of the molar volume of the mixture at each composition; pq and ciq are the average values of density and expansivity of pure components. Such average values are considered to be constant within the range of temperature used in this work. The values of 159 were computed from the application of refractive index mixture rules (13, 14) using the known values of (dn/dT); for ith liquid using the following relations:

For Gladstone-Dale (G-D) relation (15)

[lo] ciq (G-D) = -(1 I n i - l)(dn/dT);

For Lorenz-Lorentz (L-L) relation (16)

For Eykman (Eyk) relation (17)

For Oster (Ost) relation (18)

The values of (dn/dT); for pure components needed in the above relations viz., eqs. [lo]-[13], were either computed by extrapolation of the refractive index data over an interval of temperature or in some cases, these were directly obtained from the literature (9). On the other hand, experimentally, a,, can be obtained by using.

The excess isobaric thermal expansion coefficient a" of the mixture is a parameter which can be calculated from the

FIG. 1. Viscosity, qm versus mole fraction, x l for binary mixtures at 298.15 K for mixtures of bromoforrn with (0) n-hexane; (A) aniline; (0) benzonitrile; (a) butyronitrile; (A) benzylnitrile.

following considerations:

As a first approximation, Aa may be described by means of a constant aE according to:

Alternatively, aE can be expressed more generally, as a function of x l and x2 fitted to the experimental data by a polynomial. Thus,

2 3

[17] a, = 1 &?xi + x l i 2 1 A,(xl - x2)' i= 1 i= 1

Here, the values of ciq have been calculated from the mixture rules. The fitted values of a" are used to trace the plots of Figs. 7 and 8.

In view of the importance of enthalpy, AH*, and entropy, AS*, of activation of flow, we have calculated these quantities from the theory of Eyring et al. (6):

[18] q m = (NAh/Vm) exp (AH*/RT - AS*/R)

Where NA is Avogadro constant and h is Planck's constant. A plot of In (qmVm/NAh) versus 1 / T should be a straight line; the values of AH* and AS* were obtained from the slope and intercept, respectively.

To the best of our knowledge, there are no literature data on densities and viscosities of the studied mixtures with which the present results can be compared. Figures 1 and 2 show the dependence of viscosity and density of mixtures at 298.15 K.

However, the dependence of vE, 6 q , and AG*" on xl at

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JOSH1 ET AL. 255

j FIG. 2. Density, p, versus mole fraction, x , at 298.15K. All i ! mixtures and symbols have the same meaning as in Fig. 1.

FIG. 3. Excess molar volume, versus mole fraction, x , at 298.15 K. All mixtures and symbols have the same meaning as in Fig. 1.

FIG. 4. Apparent excess values of viscosity, 67 versus mole fraction, x , at 298.15 K. All mixtures and symbols have the same meaning as in Fig. 1.

FIG. 5. Excess Gibb's energy of activation of flow, A P E versus mole fraction, x , at 298.15 K. All mixtures and symbols have the same meaning as in Fig. 1.

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256 CAN. J. CHEM. VOL. 68. 1990

FIG. 6. Dependence of partial molar volumes, VI and V2, on mole fraction, x , at 298.15 K for mixtures of bromoform with benzylnitrile (0) for Vl and (m) for V2; butyronitrile (A) for V1 and (A) for V2; benzonitrile ( 0 ) for VI and ( 0 ) for V2.

298.15 K for all the mixtures is shown in Figs. 3, 4 , and 5. In Fig. 6, the dependence of V, and V2 for a few typical mixtures is presented. 'The computed aE values from the mixture rules, i.e., eqs. [ lo] to [I31 and those of experimental aE are presented in Figs. 7 and 8 for only a few typical mixtures.

Discussion From a linear dependence of q,, on x , , as shown in Fig. 1, it is

found that the mixture, bromoform (1) + butyronitrile (2) exhibits an ideal behavior; this is due to their identical molar volumes (i.e., -88cm3 mol-' at 298.15 K). This is further confirmed by the linear variation of p, with x , (Fig. 2). However, a large negative deviation as observed for bromoform (1) + n-hexane (2) in both viscosity and density profiles is attributed to their large differences in molar volumes (e.g., for bromoform, Vy = 87.8cm3 mol-I; for 11-hexane Vq = 13 1.2 cm3 mol-' at 298.15 K). Similarly, mixtures of bromo- form with benzylnitrile and benzonitrile show significant devia- tions from linearity. On the other hand, for bromoform (1) + aniline (2), a slight deviation from linearity is prevalent for both p, and q,. This is because the molar volume of aniline (v; = 91.44cm3 mol-' at 298.15 K) is somewhat close to that of bromoform. The same dependencies are observed at higher temperatures. However, to avoid overcrowding, these curves are not drawn.

Figure 3 shows the variation of excess molar volumes of the binaries at 298.15 K. For all mixtures, it is noticed that V" tend to increase with an increase in temperature; this increase is somewhat insignificant for the chosen systems in the temperat- ure interval of 298.15 to 313.15 K and thus, only the room temperature data are plotted. A close inspection of the VE plots reveals ~osit ive VE values for mixtures of bromoform with benzylnitrile and aniline; no sharp maxima are observed in both cases. The molecular interactions in these mixtures are thus

FIG. 7 . Dependence of a" on .x, for bromoform + aniline mixture at 298.15 K. ( 0 ) Gladstone-Dale relation, (A) Lorenz-Lorentz relation, (0) Eykman relation, ((3) Oster relation, ( 0 ) density.

characterized by dispersion type forces. Replacement of NH2 group as in aniline by a more bulkier group like -CH,CN as in benzylnitrile increases their steric repulsions with bromine atoms of bromoform. This wolild mean that benzylnitrile (due to its increased electron-donating capacity) will be attracted to the bromine atoms of bromoform leading to increased repulsion. Since VE reflects the packing of the components of a binary mixture, it should be more positive for bulkier groups. This explains the observed higher V" values of bromoform (1) + bebzylnitrile (2) mixture as compared to bromoform (1) + aniline (2). Such observations can also be found in the literature (19).

A small but negative vE as observed for bromoform (1) + " ~,

benzonitrile (2) mixture may be due to the fact that benzonitrile (dipole moment, p = 4.05 D at 303.15 K) is more polar than bromoform ( p = 0.99 D at 303.15 K) . Thus, there is an induced dipole-dipole interaction leading to negative V" (20). Similar- ly, mixtures of bromoform with 11-hexane and butyronitrile suggest the existence of specific interactions as evidenced by large but negative values of VE; sharp minima are observed around middle of the composition scale for both the mixtures. However, the highest negative VE shown by bromoform (1) + n-hexane (2) mixture is attributed to a large difference in their molar volumes. In general, the trend in the variation vE followed the sequence:

benzylnitrile > aniline > benzonitrile > butyronitrile > n-hexane

Figure 4 shows the dependence of Sq on x l ; mixtures of bromoform with aniline or with n-hexane exhibit negative 6-q. On the other hand, mixtures of bromoform with benzylnitrile or benzonitrile exhibit positive 6-q with maxima or minima occurring .around the middle of the composition scale. Surpris- ingly, the system bromoform (1) + butyronitrile (2) exhibits an entirely different behavior i.e., both positive and negative 6-q

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JOSH1 ET AL. 257

FIG. 8. Same as in Fig. 7 for bromoform + n-hexane mixture at 298.15 K. Symbols have the same meaning as in Fig. 7.

values are observed. Values of 6q increase with increase in temperature. This indicates that in these binary mixtures, the forces between pairs of unlike molecules are somewhat less than the forces between pairs of like molecules and that is why the mixture is less viscous (10).

Bromoform is less polar as compared to the three nitriles used here. Thus, in mixtures, it is expected that highly polar nitriles induce a dipole moment on somewhat less polar molecule like bromoform leading to the rupture of the molecular order as evidenced by the positive excess free energy of flow (Fig. 5). However, small but positive A G * ~ for brornoform (1) + aniline (2) system is due to the less polar nature of the aniline (p = 1.5 1 and E = 6.9). The negative AG*E for bromoform (1) + n-hexane (2) mixture indicates the absence of dipole-dipole type interactions because the dipole moment of n-hexane is smaller than bromoform. For all mixtures, except bromoform (1) + aniline (2), the A G * ~ profiles are highly symmetric over the entire x l scale and the maxima or minima occurred for values of x, between 0.4 to 0.6.

The trend in the variation of 6q and that of AG*E, vary respectively, in the following sequence: 6q: benzylnitrile > benzonitrile > butyronitrile > aniline > n-hexane; AGeE: butyronitrile > benzonitrile > benzylnitrile > aniline > n-hexane.

Thus, on the whole, it appears that there are strong specific interactions between bromoform and n-hexane in solution.

Figure 6 shows the variation of Vl and V2 with x1 for some representative mixtures viz., nitriles with bromoform. It is seen that the convex shapes are observed for V2 in case of mixtures of bromoform with benzonitrile and benzylnitrile whereas a reverse tendency is seen for the dependence of V1. Similar

observations are seen with other mixtures of bromoform except bromoform (1) + butyronitrile (2) wherein VI showed convex behavior and V2 the concave shape.

Following the approach developed by Eyring and co-workers (6), the values of AH* and AS* are estimated for the mixtures considered here. It is found that in all cases, AS* values are negative and small. Nitriles when mixed with bromoform produced almost identical AS* values and vary generally in the range -42 to 59 J mol-I K-I. However, no systematic variation of AS* is seen with x l for many mixtures, except bromoform (1) + aniline (2), wherein -AS* values increased systematic-

lth an increase in bromoform ally from -27 to 52 J mol-I K-' w' content of the mixture. In general, the negative AS* values confirm the formation of activated weak molecular complexes leading to increased order as result of flow. For all the mixtures, the positive AH* which range from -5 to 2 kJ mol-I K-I suggest the endothermic nature of the mixing process.

The variation of at on xl for the system, bromoform (1) + aniline (2) at 298.15 K is shown in Fig. 7. It is found that Eykman relation agrees somewhat closer to the experimental a" than the other mixture rules. Similar observations are also seen for the bromoform (1) + n-hexane (2) mixture (see Fig. 8) and other mixtures of bromoform with nitriles.

Acknowledgements We thank the University Grants Commission, New Delhi,

India, for major financial support (F. 12-55/88-SR-111) and to the Robert A . Welch Foundation for partial support. We thank Dr. Keith Hansen, Chairman of Chemistry, and Dr. John Idoux, Dean, Lamar University, for their interest in this research.

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