Thermodynamics of Organic Mixtures Containing Amines. VII. Study of

Ind. Eng. Chem. Res. 2008, 47, 1729-1737

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Thermodynamics of Organic Mixtures Containing Amines. VII. Study of Systems Containing Pyridines in Terms of the Kirkwood-Buff Formalism Juan Antonio Gonza´ lez,* Isaıás Garcıá de la Fuente, Ismael Mozo, and Jose´ Carlos Cobos G.E.T.E.F. Dpto Termodina´ mica y Fı´sica Aplicada, Facultad de Ciencias, UniVersidad de Valladolid, Valladolid, 47071 Spain

Nicola´ s Riesco Department of Chemical Engineering, Loughborough UniVersity, Loughborough, LE113TU Leicestershire, United Kingdom

Mixtures formed by a pyridine base and alkane, benzene, or 1-alkanol have been investigated in the framework of the Kirkwood-Buff theory. In this work, the derivatives of the molar excess Gibbs energies (GE), relative to the mole fraction, needed for the determination of the Kirkwood-Buff integrals (Gij) and related quantities were calculated using the DISQUAC group contribution model. Systems with alkanes are characterized by interactions between similar molecules (G12 < 0). Mixtures with pyridine or 4-methylpyridine show Gii curves with a maximum at high amine concentrations, which indicates that amine-amine interactions are stronger than in solutions with dimethyl or trimethylpyridines. For solutions with a given alkane, the increase of methyl groups in the aromatic ring of the pyridine leads to a decrease of G11 in the following sequences: pyridine > 4-methylpyridine and pyridine > 2-methylpyridine > 2,4-dimethylpyridine > 2,4,6-trimethylpyridine. The same variations are observed for the molar excess enthalpies (HE), and volumes (VE). Systems with benzene or 1-alkanols show lower |G12| values than those with alkanes. This has been ascribed to the existence of interactions between dissimilar molecules, which are of dipolar type. The comparison of G12 for 1-alkanol + pyridine base (or + benzene or + toluene) mixtures clearly reveals that the interactions between dissimilar molecules are much more predominant in amine systems. However, their local mole fractions are scarcely dependent on the intermolecular interactions and the distribution of the molecules in the solution is practically random, even in methanol systems. 1. Introduction To gain insight into the liquid state, thermodynamic properties such as molar excess enthalpy (HE), molar excess volume (VE), or molar excess isobaric heat capacity (CEP) of liquid mixtures can be examined, taking into account differences in molecular size and shape, anisotropy, dispersion, and so forth. From this point of view, amines are a very interesting class of compounds. As a matter of fact, the investigation of mixtures with amines makes it possible to examine the influence of some interesting effects on their thermodynamic properties, as well as to analyze the ability of any theoretical model to predict such properties. For example, linear amines (CH3(CH2)nNH2 or CH3(CH2)nN(CH2)mCH3) allow the study of the size and steric effects produced by alkyl groups attached to the amine group; N,N,Ntrialkylamines allow the effect of a globular shape to be examined, cyclic amines allow one to study the effect of the ring strain, and aromatic amines allow the effect of polarizability to be studied. Pyridine and its alkyl derivatives are useful to investigate the possible steric hindrance effect of the methyl groups. Moreover, the treatment of pyridine systems is a first step for a better understanding of the pyrrole ring, which is especially important to model typical binding sites on proteins.1 Primary and secondary amines are weakly self-associated.1-6 Pyridine bases are examples of tertiary heterocyclic amines. Their Trouton’s constants are rather similar (110.88 J mol-1K-1;7 see Table 1) and exhibit values close to that of nonassociated species7 (92.05 J mol-1 K-1 for 1-alkanols). Nevertheless, the * To whom correspondence should be addressed. Fax: +34-98342-31-35. E-mail address: [email protected].

j ), which is a useful values of their effective dipole moments6,8 (µ magnitude to evaluate the impact of polarity on bulk properties, and of ∆Tb, which represents the difference between the boiling temperatures of a given pyridine base and of its homomorphic hydrocarbon (see Table 1), indicate that interactions between amine molecules are stronger in pyridine than in, e.g., 2,6dimethylpyridine or 2,4,6-trimethylpyridine. It is very interesting to link the thermodynamic properties of liquid mixtures with their microscopic structural description, and particularly with local deviations from the bulk composition. The study of fluctuations in composition in multicomponent mixtures is a standard topic in statistical mechanics.9,10 There are at least two ways of examining the fluctuations in a binary mixture.9-11 We either consider the fluctuations in the number of molecules N1 and N2 (N1 + N2 ) N) of each component and the cross fluctuations 〈∆Ni∆Nj〉 (i,j ) 1, 2) or we study the fluctuations in the number of molecules regardless of the components 〈∆N2〉, the fluctuations in the mole fraction 〈∆x2〉 and the cross fluctuations. In each case, 〈‚〉 represents an ensemble average, in the grand canonical ensemble. The first of these approaches was followed by Kirkwood and Buff.12-14 The second approach was developed by Bhatia and Thornton15 and used in the study of liquid binary alloys,16,17 based on the so-called Bhatia-Thornton partial structure factors. This approach was generalized18,19 to provide a rationale that links the asymptotic behavior of the ordering potential to the interchange energy parameters in the semi-phenomenological theories of thermodynamic properties of liquid mixtures.18-20 Different theories have been applied to characterize mixtures that contain pyridines, or to predict/correlate their thermody-

10.1021/ie071226e CCC: $40.75 © 2008 American Chemical Society Published on Web 01/30/2008

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Ind. Eng. Chem. Res., Vol. 47, No. 5, 2008

Table 1. Physical Constantsa of Pyridine Bases amine

Vi (cm3/mol)

Tb (K)

∆vapH (kJ/mol)

∆vapH/Tb (J mol-1 K-1)

∆Tb (K)

µ (D)

µ j

pyridine 2-methylpyridine 3-methylpyridine 4-methylpyridine 2,4-dimethylpyridine 2,6-dimethylpyridine 3,5-dimethylpyridine 2,4,6-trimethylpyridine

80.86b 99.09b 97.83b 98.01b 115.67d 116.73d 113.11e 132.80d

388.4c 402.6c 417.3c 418.5c 431.5b 417.2b 444.6c 444.2b

35.09c 36.17c 37.35c 37.51c 38.53c 37.46c 39.46c 39.87c

90.3 89.8 89.5 89.6 89.3 89.8 88.7 89.7

35.2 18.8 33.5 34.7 19.2 4.9 32.3 6.3

2.37b 1.97b 2.4b 2.6b 2.3b 1.66b 2.5f 2.05b

1.008 0.757 0.929 1.005 0.819 0.588 0.899 0.680

a V , the molar volume at 298.15 K; T , the boiling point; ∆ H, the standard enthalpy of vaporization at T ; ∆T , the difference between T of a given i b vap b b b pyridine and that of the isomeric aromatic compound (from ref 88); µ, the dipole moment; µ j , the effective dipole moment. b Data taken from ref 74. c Data taken from ref 75. d Data taken from ref 59. e Data taken from ref 63. f Data taken from ref 76.

namic properties. Therefore, systems with alkanes or 1-butanol have been investigated in terms of the ERAS model,21,22 which does not represent the symmetry of the HE curves of mixtures that involve alkanes. The UNIQUAC equation was modified to accurately predict vapor-liquid equilibria (VLE) data over a wide range of temperature.23 In the framework of UNIFAC (the Dortmund version24), interaction parameters for contacts between the pyridine group and other different groups are available.25 In a recent work,26 we have studied pyridine systems in terms of DISQUAC,27 which is a purely physical model based on the rigid lattice theory developed by Guggenheim.28 We have shown that the model describes, rather accurately, an entire set of thermodynamic properties such as VLE, molar excess Gibbs energies (GE), liquid-liquid equilibria (LLE), solid-liquid equilibria (SLE), or HE over a wide range of temperature. An important result is that DISQUAC also predicts the W-shaped CEP of the pyridine + hexadecane mixture.29 This article is concerned with the investigation of mixtures formed by pyridine or one of its alkyl derivatives and alkanes, or aromatic compounds, or 1-alkanols, in terms of the Kirkwood-Buff integrals. To the best of our knowledge, only aqueous solutions of pyridine have been studied using this formalism.30,31 For comparison, some systems that contain 1-alkanol and benzene, or toluene, are also considered.

such as chemical potential, partial molar volumes, and isothermal compressibility factor. The resulting equations are13,32

G11 ) RTκT +

x2V h 22 V x1VD x1

(2)

G22 ) RTκT +

x1V h 12 V x2VD x2

(3)

V h 1V h2 VD

(4)

G12 ) G21 ) RTκT -

where R is the gas constant, xi the mole fraction of component i (for i ) 1, 2), V h i the partial molar volume of component i (for i ) 1, 2), V the molar volume of the solution, and κT, the isothermal compressibility factor of the mixture. Parameter D is defined as

D)1+

theory13,14

describes thermodynamic properties of soluThe tions in an exact manner over the entire concentration range, using the values

Gij )

∫0

(gij - 1)4πr dr 2

(1)

which are called the Kirkwood-Buff integrals. The radial distribution function (gij) denotes the probability of finding a molecule of species i in a volume element at a distance r from the center of a molecule of species j. Therefore, this function provides information about the solution structure on the microscopic level. The product FjGij (where Fj is the number density of molecules of species j) represents the average excess (or deficiency) number of molecules j in the entire space around a molecule i, with respect to the bulk average. The Gij values can be obtained from FjGij using a process of normalization, with respect to concentration, and can be interpreted as follows: Gij > 0 represents the excess of molecules of type i in the space around a given molecule of species j. This means attractive interactions between molecules of i and j. Gij < 0 indicates that interactions of i-i and j-j are preferred over mutual interactions.13,31 The Kirkwood-Buff integrals can be derived from experimental data of thermodynamic properties

(5)

P,T

Using the Gij quantities, it is possible to estimate the so-called linear coefficients of preferential solvation:32

2. Theory

∞

( )

x1x2 ∂2GE RT ∂x 2 1

δ011 ) x1x2(G11 - G12)

(6a)

δ012 ) x1x2(G12 - G22)

(6b)

δ021 ) x1x2(G12 - G11)

(6c)

δ022 ) x1x2(G22 - G12)

(6d)

These are useful quantities to determine the local mole fractions of species i around the molecule central j:32,33

xij ) xi +

δ0ij Vc

(7)

where Vc is the volume for a solvation sphere. This value may be roughly estimated33 as the volume of a sphere of radius Rc ) 3r, where r is the radius of the central molecule. This leads to a value of Vc that can be approximately represented by the expression (33 - 1)V0 ) 26V0, where V0 is the molar volume of the solvated component. 3. Source of Data The VE data required for the calculations were taken from ref 29 and refs 34-42 for systems that contained pyridines, and from refs 43-47 for 1-alkanol + benzene or 1-alkanol + toluene mixtures. Table 2 lists the isothermal compressibilities

Ind. Eng. Chem. Res., Vol. 47, No. 5, 2008 1731 Table 2. Physical Constants at 298.15 K of Pure Compounds Needed for the Application of the Kirkwood-Buff Theory: Molar Volume and Isothermal Compressibility compound

molar volume, Vi (cm3/mol)

isothermal compressibility, κTi (x 10-12 Pa-1)

pyridine 2-methylpyridine 3-methylpyridine 4-methylpyridine 2,4-dimethylpyridine

699.6 753.4 710 691.9 964

2,6-dimethylpyridine

1053

3,5-dimethylpyridine

964

2,4,6-trimethylpyridine heptane decane tetradecane hexadecane benzene toluene methanol ethanol 1-propanol 1-butanol

1059 147.45 195.94 261.32 294.07 89.44 106.78 40.75 58.69 74.78 91.99

of pure compounds (κTi), as well as their molar volumes, Vi (see also Table 1). For the mixtures, their isothermal compressibilities were calculated as κT ) Φ1κT1 + Φ2κT2, where Φi is the volume fraction of component i in the system. That is, when calculating the compressibility of the system, the solution is assumed to be ideal. This assumption does not influence the final calculations of the Kirkwood-Buff integrals.33 D values were obtained from the DISQUAC model, using interaction parameters that we previously determined for the amine/ aliphatic, amine/aromatic, and amine/hydroxyl contacts for the mixtures under study.26,48 The interaction parameters for hydroxyl/aliphatic and hydroxyl/aromatic contacts were taken from the literature.49-51 The method developed in the D calculations has been explained in detail elsewhere.52 The application of group contribution models to evaluate the GE derivatives with the mole fraction is an useful technique, in the absence of the needed experimental data, particularly when a series of mixtures rather than a single system is considered, and then regularities can be observed. Therefore, previous studies show that DISQUAC provides reliable results on Gij for 1-alkanol + amide mixtures,53 whereas UNIFAC has been used in the calculations of the Kirkwood-Buff integrals for some alkylbenzoate systems.54,55 An important advantage of DISQUAC is that the interaction parameters are assumed to be dependent on the molecular structure This is essential for practical purposes, because it leads to improved predictions in the case of systems that involve branched or cyclic molecules, or molecules where proximity effects are present. For the investigated amines, we distinguish between pyridine, 2-methylpyridine, 3- or 4-methylpyridine, 2,4- or 2,6-dimethylpyridine, 3,5-dimethylpyridine and 2,4,6-trimethylpyridine (i.e., each one of these amines are characterized by its own set of interaction parameters). 4. Results and Discussion Results obtained for the Kirkwood-Buff integrals (Gij) and for the linear coefficients of preferential solvation (δ0ij) at 298.15 K and equimolar composition for systems that include pyridine or its alkyl derivatives are listed in Table 3. Table 4 lists the corresponding local mole fractions. Tables 3 and 4 also contain a comparison between the experimental results and the DISQUAC calculations for all these magnitudes. The good

1460.6 1109.6 872 862 966 911.5 1248 1153 1026 942

source of data from ref 59 from ref 59 from ref 77 from ref 77 from adiabatic compressibilities measurements74 using heat capacities from ref 79 from adiabatic compressibilities measurements80 using heat capacities from ref 79 from adiabatic compressibilities measurements74 using heat capacities from ref 79 rom adiabatic compressibilities measurements81 using heat capacities from ref 79 from ref 82 from ref 82 from ref 83 from ref 82 from ref 84 from ref 84 from ref 84 from ref 84 from ref 84 from ref 84

agreement between them is remarkable. Table 5 shows Gij and δ0ij results for some 1-alkanol + benzene, or 1-alkanol + toluene mixtures. Figures 1-9 present graphical depictions of the Gij and δ0ij calculations for some selected systems. Hereafter, we will refer to the thermodynamic properties at equimolar composition and 298.15 K. 4.1. Pyridine Base + Alkane Mixtures. These systems are characterized by positive HE values, which increase as the chain length of the alkane increases.56-58 VE is also positive, except for the shorter alkanes, and behaves similarly.29,34-38 Therefore, the main contribution to these excess functions comes from the disruption of the amine-amine interactions upon mixing. Structural effects are present in solutions with the shorter alkanes, as their S-shaped VE curves would suggest.29,34-38,59 The rather negative G12 values (see Figures 1-4) also indicate that interactions between similar molecules are predominant over those of dissimilar type (types 1-2; see Figure 7). 14N nuclear magnetic resonance (NMR) studies of mixtures of diluted pyridine in heptane suggest the formation of pyridine dimers through hydrogen bonds between the ring nitrogen and the hydrogen in positions γ or β in the other molecule.60 We note that the Gii curves show a maximum at high concentrations of the amine for mixtures that involve pyridine or 4-methylpyridine (see Figures 1 and 2), which is characteristic of solutions where strong interactions exist between similar molecules. In the case of pyridine systems, this leads to miscibility gaps at temperatures close to 298.15 K (e.g., the pyridine + dodecane mixture shows an upper critical solution temperature at 268.7 K61). The same trend is encountered for linear organic carbonate + alkane systems.62 On the other hand, the mentioned maximum increases as the size of the alkane increases and becomes skewed toward higher amine concentrations under these conditions. Similarly, this occurs for the observed minimum of the G12 curve (see Figures 1 and 2). For a given alkane (e.g., heptane), HE decreases in value as follows: 1735 J/mol (pyridine)56 > 1371 J/mol (3-methylpyridine)58 > 1236 J/mol (3,5-dimethylpyridine, at T ) 303.15 K)63 and 1735 J/mol (pyridine)56 > 1346 J/mol (2-methylpyridine)57 > 1100 J/mol (2,4-dimethylpyridine)64 > 944 J/mol (2,4,6-trimethylpyridine).65 This reveals that the amine-amine interactions become weaker in the same sequences. Note that

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Table 3. Kirkwood-Buff Integrals (Gij) and Linear Coefficients of Preferential Solvation (δ0ij) at Equimolar Composition and 298.15 K for Pyridine Base (1) + Organic Solvent (2) Mixturesa Kirkwood-Buff Integrals (cm3/mol) system pyridine + heptane pyridine + decane pyridine + tetradecane pyridine + hexadecane 2-methylpyridine + heptane 2-methylpyridine + decane 4-methylpyridine + heptane 4-methylpyridine + decane 2,4-dimethylpyridine + heptane 2,4-methylpyridine + decane 2,6-methylpyridine + heptane 2,4,6-trimethylpyridine + heptane 2,4,6-trimethylpyridine + decane pyridine + benzene 2-methylpyridine + benzene 2,6-methylpyridine + benzene 3,5-methylpyridine + benzene pyridine + methanol pyridine + ethanol pyridine + 1-propanol pyridine + 1-butanol 2-methylpyridine + methanol 2,6-dimethylpyridine + methanol

Linear Coefficients of Preferential Solvation (cm3/mol)

G11

G22

G12

δ012

δ021

699.9 (687.9)b 684.4 615.8 638.1 208.0 361.7 402.3 639.6 66.8 206.8 66.0 -28.0 78.6 -63.7 -(63.5)c -97.5 -124.5 -149.5 -18.3 -(21.9)d -44.2 -76.3 -100.8 -13.7 (-23.4)d 9.1 (-21.5)d

56.8 (46.3)b -109.5 -248.8 -297.1 -37.8 -124.8 45.1 -58.2 -57.9 -128.9 -57.2 -74.5 -140.2 -82.6 -(82.4)c -77.3 -68.7 -63.1 -92.9 -(94.6)d -87.5 -87.0 -79.9 -115.8 (-117.5)d -134.7 (-137.3)d

-508.7 (-495.8)b -397.1 -296.9 -279.1 -302.4 -330.3 -428.0 -468.7 -254.8 -303.8 -256.0 -222.4 -273.1 -92.1 (-92.3)c -96.3 -101.9 -103.9 -48.4 -(45.8)d -65.1 -69.0 -77.3 -48.3 (-43.0)d -49.6 (-48.3)d

-141.1 (-135.5)b -71.9 -12.0 4.5 -66.2 -51.4 -118.3 -102.6 -49.2 -43.7 -49.7 -36.9 -33.2 -2.4 (-2.5)c -4.8 -8.3 -10.2 11.1 (12.2)d 5.6 4.5 0.6 16.9 (16.4)d 21.3 (23.8)d

-302.2 (-295.9)b -270.4 -228.2 -229.4 -127.6 -173.0 -207.6 -277.1 -80.4 -127.7 -80.5 -48.6 -87.9 -7.1 (-7.2)c 0.3 5.6 11.4 -7.5 -(7.2)d -5.2 1.8 5.9 -8.7 -(6.0)d -12.6 -(5.1)d

a Values given in parentheses are experimental values obtained using VLE and VE data from the literature. b Values obtained using VLE data from ref 84. c Values obtained using VLE data from ref 85. d Values obtained using VLE data from ref 41.

Table 4. Local Mole Fractions (xij) at Equimolar Composition and 298.15 K for Pyridine Base (1) + Organic Solvent (2) Systemsa system pyridine + heptane pyridine + decane pyridine + tetradecane 2-methylpyridine + heptane 2-methylpyridine + decane 4-methylpyridine + heptane 4-methylpyridine + decane 2,4-dimethylpyridine + heptane 2,4-methylpyridine + decane 2,6-methylpyridine + heptane 2,4,6-trimethylpyridine + heptane 2,4,6-trimethylpyridine + decane pyridine + benzene 2-methylpyridine + benzene 2,6-methylpyridine + benzene 3,5-methylpyridine + benzene pyridine + methanol pyridine + ethanol pyridine + 1-propanol pyridine + 1-butanol 2-methylpyridine + methanol 2,6-dimethylpyridine + methanol

x12

x21

0.463 (0.465)b 0.486 0.498 0.483 0.490 0.469 0.479 0.487 0.491 0.487 0.490 0.494 0.499 (0.499)c 0.498 0.496 0.496 0.505 (0.505)d 0.502 0.502 0.500 0.507 (0.507)d 0.506 (0.508)d

0.356 (0.359)b 0.371 0.392 0.451 0.433 0.419 0.391 0.473 0.458 0.473 0.486 0.475 0.497 (0.497)c 0.500 0.502 0.503 0.493 (0.495)d 0.497 0.501 0.503 0.492 (0.495)d 0.488 (0.495)d

Figure 1. Kirkwood-Buff integrals (Gij) at 298.15 K for pyridine (1) + alkane (2) systems: (- - -) mixture with heptane and (s) mixture with decane.

mol (2-methylpyridine)34 > 0.117 cm3/mol (2,4-dimethylpyridine).36 The G11 change for a fixed alkane is given as

pyridine > 4-methylpyridine

a

Values given in parentheses are experimental values obtained using VLE and VE data from the literature. b Values obtained using VLE data from ref 84. c Values obtained using VLE data from ref 85. d Values obtained using VLE data from ref 41.

µ j and ∆Tb usually also decrease as the number of CH3 groups attached to the aromatic ring increase (see Table 1). The weakening of the amine-amine interactions also explains the variation in VE: 0.2657 cm3/mol (pyridine)29 > 0.1977 cm3/

and

pyridine > 2-methylpyridine > 2,4-dimethylpyridine > 2,4,6-trimethylpyridine (see Table 3 and Figure 4). The G12 integral varies in opposite way. The variation of the local mole fractions (x21) reveals that

Ind. Eng. Chem. Res., Vol. 47, No. 5, 2008 1733

Figure 2. Kirkwood-Buff integrals (Gij) at 298.15 K for 4-methylpyridine (1) + alkane (2) systems: (- - -) mixture with heptane and (s) mixture with decane.

Figure 3. Kirkwood-Buff integrals (Gij) at 298.15 K for 2-methylpyridine (1) + alkane (2) systems: (- - -) mixture with heptane and (s) mixture with decane. Table 5. Kirkwood-Buff Integrals (Gij) and Linear Coefficients of Preferential Solvation (δ0ij) at Equimolar Composition and 298.15 K for 1-Alkanol (1) + Benzene (or Toluene) (2) Mixtures Kirkwood-Buff Integrals (cm3/mol) system

G11

G22

G12

methanol + benzene 833.6 71.4 -434.7 ethanol + benzene 337.6 77.9 -339.4 1-propanol + benzene 171.0 71.9 -276.6 1-butanol + benzene 83.3 100.3 -268.7 methanol + toluene 1235.8 62.4 -531.8 ethanol + toluene 511.7 62.7 -406.9 1-propanol + toluene 282.9 48.8 -322.3

Linear Coefficients of Preferential Solvation (cm3/mol) δ012

δ021

-126.5 -104.3 -87.1 -94.4 -148.6 -117.4 -92.8

-317.1 -179.3 -111.9 -77.4 -441.9 -246.7 -151.3

the deficiency of alkane molecules around a central molecule of amine is higher for pyridine systems than for those mixtures with, e.g., 4-methylpyridine or 2,4,6-methylpyridine (see Table 4). This might be interpreted assuming that the number of amine-amine interactions available to be broken when mixed also decreases when the number of methyl groups in the pyridine base is increased, because of the steric effects exerted by such

Figure 4. Kirkwood-Buff integrals (Gij) at 298.15 K for pyridine base (1) + decane (2) systems: (- - -) mixture with 2-methylpyridine, (• • •) mixture with 2,4-dimethylpyridine, and (s) mixture with 2,4,6-trimethylpyridine.

Figure 5. Kirkwood-Buff integrals (Gij) at 298.15 K for methanol (1) + pyridine base (2) systems: (s) mixture with pyridine, (- - -) mixture with 2-methylpyridine, and (• • •) mixture with 2,6-dimethylpyridine.

groups become then more important. The different concentration dependence of the Gii curves of systems that involve pyridine or 4-methylpyridine (see Figures 1 and 2), compared to that of mixtures with 2-methylpyridine, 2,4-dimethylpyridine, or 2,4,6trimethylpyridine (see Figures 2 and 4), indicates that amineamine interactions are stronger in mixtures with the former amines. Previous calculations using the Flory theory also show that orientational effects are weaker in systems with 2,4,6trimethylpyridine, which is consistent with the fact that the x12 and x21 values are close to the bulk values for such mixtures (see Table 4). Now, we will analyze the influence of the relative position of the methyl groups of the aromatic amines studied on the thermodynamic properties of the related systems. In mixtures with heptane, HE changes as follows: 1407 J/mol (4-methylpyridine)58 > 1371 J/mol (3-methylpyridine)58 > 1346 J/mol (2methylpyridine)57 and 1235 J/mol (3,5-dimethylpyridine, T ) 303.15 K)63 > 1047 J/mol (2,4-dimethylpyridine)64 > 1000 J/mol (2,6-dimethylpyridine, T ) 303.15 K),63 which is consistent with the relative variations in µ j and ∆Tb (see Table

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Figure 6. Kirkwood-Buff integrals (Gij) at 298.15 K for the 1-butanol (1) + pyridine (2) system.

Figure 7. Linear coefficients of preferential solvation (δ021) at 298.15 K for pyridine base (1) + heptane (2) systems. Legend: curve 1, pyridine; curve 2, 2-methylpyridine; curve 3, 2,4-dimethylpyridine; and curve 4, 2,4,6trimethylpyridine.

1). However, VE varies in an opposite way: VE (2,4-dimethylpyridine)36 ) 0.117 cm3/mol < VE (2,6-dimethylpyridine)37 ) 0.1847 cm3/mol. The quite different values of the molar volumes of these dimethylpyridines (see Table 1) suggests that such behavior might be due to packing effects. The analysis, in terms of the Kirkwood-Buff integrals, using DISQUAC, is more difficult here, because systems that contain 2,4- or 2,6dimethylpyridine are assumed to be characterized by the same interaction parameters, and no VE data are available for solutions with 3,5-dimethylpyridine. Therefore, we can merely emphasize that G11 increases and that G12 decreases when passing from 4-methylpyridine to 2-methylpyridine (see Table 3). 4.2. Pyridine Base + Aromatic Compound Mixtures. As a trend, there is an increase in G12, with regard to the previous systems (Table 3), which can be ascribed to the existence of interactions between dissimilar molecules. These interactions are assumed to be nonspecific but of dipolar type. Several features support such conclusion: (i) the low HE values of these solutions (HE (pyridine + benzene)66 ) 8 J/mol or HE (3,5dimethylpyridine + benzene)67 ) 33 J/mol); (ii) the solid-liquid phase diagram of the pyridine + benzene mixture, characterized

Figure 8. Linear coefficients of preferential solvation (δ021) at 298.15 K for pyridine base (1) + benzene (2) systems. Legend: curve 1, pyridine; and curve 2, 2-methylpyridine.

by a simple eutectic point;68 (iii) the weak temperature dependence of HE,66 which indicates the great stability of these systems. Finally, it should be remarked that DISQUAC provides an accurate description, for example, of the thermodynamic properties of the pyridine + C6H6 or + C7H8 mixtures, under the assumption that the aromatic/nitrogen contacts are represented by dispersive interaction parameters only.26 In addition, the low absolute values of δ0ij are remarkable (see Table 3 and Figure 8), because they lead to local mole fractions that are close to the bulk values (see Table 4). This may be interpreted assuming that the mixture is approximately random. The same behavior has been observed in amide + 1-alkanol mixtures69 or dialkyl carbonate + C6H6 (or CCl4) mixtures.62 4.3. Alcohol + Pyridine Base Mixtures. The HE and VE values (see below) of systems that contain shorter 1-alkanols (from methanol to 1-butanol) show the existence of interactions between dissimilar molecules, which is characteristic of alkanol + amine mixtures.4,6 As usually, HE and VE each increase as the chain length of the alcohol increases.26 Therefore, for pyridine mixtures, HE(methanol)70 ) -711 J/mol > HE(1butanol)22 ) 182 J/mol and VE(methanol)41 ) -0.483 cm3/mol > VE(ethanol)42 ) -0.372 cm3/mol > VE(1-propanol)42 > -0.287 cm3/mol > VE(1-butanol)(42) ) -0.187 cm3/mol. The HE and VE values of mixtures that contain methanol decrease when the size of the aromatic amine increases in the same order as in systems with a given alkane. In the case of VE,41 -0.483 cm3/mol (pyridine) > -0.958 cm3/mol (2-methylpyridine) > -1.503 cm3/mol (2,6-dimethylpyridine), and, for HE,70 -711 J/mol (pyridine) > -1261 J/mol (2-methylpyridine) > -1635 J/mol (2,6-dimethylpyridine). This variation can be explained by the lower positive contribution to HE from the disruption of the amine-amine interactions when passing from pyridine to 2,6-dimethylpyridine, because the values of µ j and ∆Tb also decrease in the same order (see Table 1). This is supported by the fact that the energies of the OH-N hydrogen bonds are practically independent of the pyridine base considered (approximately -31 kJ/mol).70 The rather low |Gij| values (see Table 3 and Figures 5 and 6) are consistent with the existence of interactions between dissimilar molecules. This is clearly shown by comparing Gij and δ0ij for systems that contain a given 1-alkanol and pyridine, methylpyridine, benzene, or

Ind. Eng. Chem. Res., Vol. 47, No. 5, 2008 1735

5. Conclusions Mixtures that contain a pyridine base and alkane, benzene, or 1-alkanol have been investigated in the framework of the Kirkwood-Buff theory. Systems with alkanes are characterized by interactions between similar molecules (G12 < 0). The Gii curves of mixtures with pyridine, or 4-methylpyridine, show a maximum at high amine concentrations, which suggests that amine-amine interactions here are stronger than in solutions with dimethyl or trimethylpyridines. For solutions with a given alkane, the increase of methyl groups in the aromatic ring of the amine leads to a decrease of G11 in the following sequences: pyridine > 4-methylpyridine and pyridine > 2-methylpyridine > 2,4-dimethylpyridine > 2,4,6-trimethylpyridine. The same variations are observed for HE and VE. Systems with benzene or 1-alkanols show lower |G12| values, because of the existence of interactions between dissimilar molecules. However, their local mole fractions are scarcely dependent on the intermolecular interactions and the distribution of the molecules in the solution is practically random, even in methanol systems. Acknowledgment The authors gratefully acknowledge the financial support received from the Consejerıá de Educacioń y Cultura of Junta de Castilla y Leoń (under Project Nos. VA080A06 and VA075A07) and from the Ministerio de Educacioń y Ciencia (under Project No. FIS2007-61833). Literature Cited

Figure 9. Linear coefficients of preferential solvation (δ021) at 298.15 K for methanol (1) + pyridine base (or benzene or toluene) (2) systems. Legend for panel a: curve 1, pyridine; curve 2, 2-methylpyridine; and curve 3, 2,6-dimethylpyridine. Legend for panel b: curve 1, benzene; and curve 2, toluene.

toluene (see Tables 3 and 5, as well as Figures 9a and 9b). It is important to note that the local mole fractions are scarcely dependent on the intermolecular interactions. The small values of δ021 quantities (see Figure 9a) indicate that the compounds do not form clusters, i.e., aggregates composed by molecules of the same type. If such aggregates were formed, xij would differ strongly from the bulk values. It is possible to conclude that, despite the possible interactions, the distribution of molecules in solutions is practically random, and that the only arrangement in the solution is that which results from orientational effects. As already mentioned, the same behavior has been encountered in amide + 1-alkanol systems.69 In agreement with these findings, 1H NMR spectroscopic data for the 1-butanol + pyridine mixture have been interpreted, assuming a very low equilibrium constant between the two compounds,22 which is also supported by infrared (IR) spectroscopy measurements.71 A similar trend was observed in 2,6-dimethylpyridine + isobutylalcohol.72 In addition, density functional calculations show that interactions between dissimilar molecules in the methanol + pyridine system are more sensitive to the distance than to the angles.73

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ReceiVed for reView September 11, 2007 ReVised manuscript receiVed November 28, 2007 Accepted November 30, 2007 IE071226E

Thermodynamics of Organic Mixtures Containing Amines. VII. Study of

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